University Of Chicago Math Program

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University Of Chicago Math Program

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Mathematics has fascinated humans since our earliest intellectual endeavors. Ancient peoples were intrigued by the mathematical relationships between the sun, moon, and stars. This fascination began one of the most fundamental human intellectual endeavors. While mathematicians, philosophers, and scientists debate whether mathematics is a human description of nature or the fundamental structure of reality, there is no question that mathematics has driven most of humanity’s technological and intellectual advancement.

The mathematicians of today examine everything from the complex mathematical relationships found in living organisms to the bizarre, non-Euclidean geometries of extra-dimensional spaces. The schools on this list, many with faculty who have earned Fields Medals (the mathematics equivalent of a Nobel Prize), lead way in the ever-evolving field of mathematics.

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Methodology

From the QS World University Rankings, we identified the 50 best programs in the latest 2019 University Rankings for Mathematics.

Taking the QS ranking as our point of departure, we set their ranking against the ranking for mathematics programs produced by AcademicInfluence.com. Using machine learning and search algorithms to characterize academic influence on the web, AcademicInfluence.com avoids the human bias that infects most academic rankings.

The rankings uncovered by AcademicInfluence.com are based on the influential faculty and alum publications, citations, and references associated with a school, degree programs, departments, or discipline. This ranking by influence approach elevates a school or degree program based on which members of its academic community are objectively influential in a given discipline.

By weighing both the QS Programmatic World Rankings and Academic Influence’s rankings, we not only created a unique ranking of the top 50 mathematics programs, but we reveal why each university mathematics program appears where it does.

The 50 Best Mathematics Programs in the World

1. Massachusetts Institute of Technology (MIT)

Cambridge, Massachusetts

MIT enjoys a reputation as a world-renowned, specialized research institution that focuses on the intersection of science and technology. As such, the study of mathematics plays a key role for most students throughout all the school’s programs. The 60 faculty members, including two MacArthur fellows, are distinguished scholars with a dedication to research and the education of their students. MIT has produced two Fields Medals and numerous Nobel Prize winners.

Divided into pure and applied mathematics, the Mathematics Department at MIT is home to approximately 330 undergraduate students and 115 graduate students. Undergraduate students can choose concentration options that include:

Applied Mathematics
General Mathematics
Mathematics With Computer Science
Theoretical Mathematics

Graduate studies and research areas are divided into the following areas:

Algebra
Computational Biology
Geometry
Representation theory
Theoretical Computer Science

Students can find all the academic support they need, from tutoring to scheduling, through MIT’s Math Academic Services team.

2. Harvard University

Cambridge, Massachusetts

Harvard University’s Benjamin Peirce, father of Charles Sanders Peirce, was the first American to make original, major contributions to the field of mathematics. In his wake, the department made progress in the areas of topology, algebraic geometry, complex analysis, and number theory.

Comprehensive in nature, Harvard’s Department of Mathematics offers a variety of some of the best mathematics and research programs that include bachelor’s degrees, master’s programs, and Ph.D.s. Current faculty members exhibit strong interest in:

Differential Equations
Diophantine Geometry
Lie Groups
Mathematical Physics
Modular forms
Number theory

Most programs require a capstone project or senior thesis before graduation. Seminars, tutoring centers, and peer-led clubs offer additional opportunities for networking and classwork assistance.

Harvard’s math department runs multiple regular conferences such as the Current Developments Conference and the Conference on Geometry and Topology. Harvard, near Boston, also sits at the center of America’s university capital. With schools like MIT, Boston College, Boston University, and Tufts within miles, Harvard provides its faculty and students with a massive network of additional resources.

3. Stanford University

Stanford, California

Celebrating 125 years of thriving success and global impact at the heart of California’s Silicon Valley, Stanford University has produced a proud academic tradition and many research achievements. Boasting 16 postdocs/research assistants, six visiting professors, and 59 professors and lecturers, the school’s Department of Mathematics offers a diverse range of courses and resources to its students.

Stanford serves as a hub where leaders in mathematics gather to push the field forward. Professors possess specialized expertise in a broad array of subjects, including financial math, number theory, representation theory, and symplectic geometry. Twenty-nine famous competitors in the International Mathematical Olympiad can claim affiliations with Stanford.

In addition to numerous courses and excellent degree programs, the department also supports and manages the Mathematics Research Center (MRC). Though research is the primary goal, MRC also provides seminars, conferences, and outreach activities to the community and high school students in particular. The Mathematics and Statistics Library and the Stanford University Mathematical Organization function as excellent resources run by the department.

4. University of Oxford

Oxford, United Kingdom

One of the oldest universities in the world, Oxford had plenty of time to develop an outstanding reputation in many fields. Along with the university’s science department, Oxford Mathematics has been home to historic alumni such as Edwin Hubble, Robert Hooke, and Stephen Hawking.

The natural connection between math and science lends itself towards departmental collaboration through the Mathematical Institute at Oxford. Research is conducted by physicists, medical professionals, engineers, social scientists, and others who contribute to the success of the school’s math department. Students in both the pure and applied mathematics programs attend classes in the same building, which further encourages partnerships and collaboration among students in one of the best mathematics programs in the world.

Approximately 1,200 undergraduate and graduate students participate in the various programs taught by 170 expert faculty members. A total of 16 focus groups and centers on campus conduct most the research, including the Geometry Group, the History of Mathematics Group, and the Oxford Centre for Nonlinear Partial Differential Equations. The department also networks with the Oxford Solid Mechanics initiative and the Clay Mathematical Institute.

5. (tie) University of Cambridge

Cambridge, England

Home to Isaac Newton and many other great scientists and mathematicians from history, Cambridge is one of the oldest centers of learning in the world. Today, Cambridge serves students as a large research university that consists of 31 colleges and 150 departments and faculties.

Cambridge separates its Faculty of Mathematics into two departments: (1) applied mathematics and theoretical physics, and (2) pure mathematics and mathematical statistics. The applied mathematics department employs 50 academic faculty members who monitor 110 research students. The pure mathematics department hosts 42 academic faculty members who also help manage the faculty’s Statistical Laboratory.

Undergraduate studies in mathematics at Cambridge are known as the “Mathematical Tripos.” Students may complete the program in three or four years and are then eligible for further study at the graduate level.

In addition to providing a broad range of quality degree programs, the math department also manages more than nine centers of research excellence and numerous outreach programs. Maintaining business and industrial partnerships both locally and nationally has served as both a highlight of the department’s success and a key to future endeavors.

5. (tie) Princeton University

Princeton, New Jersey

Princeton University has come a long way from its humble beginnings as the College of New Jersey. Under the combined leadership of mathematician Henry Burchard Fine and Woodrow Wilson, Princeton University at large — and its mathematics and physics departments in particular — flourished. The school provided the momentum that propelled American education from obscurity to comparability with European standards in the early 20th century.

Today, Princeton’s historic Department of Mathematics carries on this grand tradition with 64 faculty members and 17 researchers who continue to push the boundaries of the field. As is the case with the best mathematics programs, Princeton’s students enjoy engaging and supportive classroom settings that provide the opportunity to develop their own contributions to the field through tutoring options.

At the graduate level, students typically spend two years expanding their background in mathematics before focusing on independent research under professor mentorship. Students are expected to attend several informal seminars to hear peers, professors, and experts present papers on current research topics. The department also rubs shoulders with the renowned Institute for Advanced Study, where such luminaries as Albert Einstein, John von Neumann, and Kurt Gödel conducted research.

7. University of California – Berkeley

Berkeley, California

Located in Evans Hall on the scenic University of California – Berkeley campus, the school’s Mathematics Department includes 55 faculty members and nearly 1,000 graduate and undergraduate students. UCB’s math department provides students access to an extensive collection of research and scholarship resources in the Mathematics Statistics Library and works closely with the school’s Mathematical Sciences Research Institute to offer workshops, seminars, and colloquia.

Undergraduate students studying math at UCB can pursue any of three tracks: teaching, applied mathematics, or pure mathematics. The teaching concentration provides learners with coursework on math fundamentals and builds their skills in curriculum development. The applied mathematics track offers core coursework in theory and analysis, plus three cluster classes specific to a field of application. Pure mathematics students focus on math fundamentals and complete elective coursework in geometry, logic, or computing.

The graduate program at UCB includes two doctoral degrees: one in mathematics and one in applied mathematics. Students complete preliminary coursework along with oral and written exams, a seminar, and a dissertation.

Student organizations in the math department include Women in Mathematics at Berkeley, Math Undergraduate Student Association, Mathematics Graduate Student Association. Learners may also join the Noetherian Ring, an organization of women graduate students, postdocs, and professors in UC Berkeley’s mathematics department. This department performs outreach to community groups, schools, and local prisons.

8. University of California – Los Angeles

Los Angeles, California

Offering some of the best mathematics programs available today — including bachelor’s degrees, master’s programs, and doctorates — the Department of Mathematics at UCLA offers a dynamic and engaging educational approach. Presented with the 2007 Award for an Exemplary Program or Achievement Award from the American Mathematical Society, UCLA’s math department has received high praise for its academic and research successes.

UCLA faculty and students benefit from the school’s Institute for Pure and Applied Mathematics. In addition to hosting numerous world-class mathematicians for public lectures and running various programs and seminars for students, the institute also manages extended, three-month programs with visiting scholars. During these programs, a collection of highly respected thinkers gather for a week of tutorials followed by several workshops that conclude with work at the UCLA Lake Arrowhead Conference Center.

The math-related undergraduate majors available through UCLA’s math department cover a wide range of subjects, including:

Applied Mathematics
Financial Actuarial Mathematics
General Mathematics
Mathematics for Teaching
Mathematics of Computation
Mathematics/Economics

UCLA also emphasizes community outreach via programs aimed at stimulating interest in mathematics in children at a young age. To this end, the school has established both the Philip C. Curtis Jr. Center for Mathematics and Teaching and the Los Angeles Math Circle.

9. California Institute of Technology

Pasadena, California

Caltech plays a unique role; it is a very small college with just over 2,000 students, yet it is populated by many of the best scientists and mathematicians in the world. This gives the Division of Physics, Mathematics, and Astronomy at Caltech an innovative approach to education.

Enjoying an impressive 3-to-1 student/faculty ratio, students at Caltech might feel like they’re in mentor relationships. At the same time, each student enjoys access to world-class resources like seminars, topics classes, and even a few light-hearted things like a pizza course. The 17 faculty members of the math department serve as excellent resources of knowledge and field-based experience for the 67 undergraduates and 34 graduates participating in some of the best mathematics programs in existence today. Undergraduate students interested in the mathematics major participate in a four-year track ending in a bachelor of science.

After completing required liberal arts classes, junior and senior students should take a minimum of 18 credits per semester for the mathematics major. Caltech encourages senior students to complete a bachelor’s thesis. Throughout the graduate program, master’s and doctoral students are expected to regularly attend seminars and colloquia. The application process requires students to complete a qualifying exam.

10. New York University

New York, New York

Sitting at the heart of the economic and business hub of the United States, students at NYU’s Courant Institute of Mathematical Sciences enjoy a distinct advantage. With extraordinary networking opportunities and the dedication of 70 faculty members, students can excel in all the school’s degree programs.

NYU’s math department divides its numerous undergraduate math programs into pure and applied mathematics. Undergraduates should declare their intentions for the mathematics major no later than the beginning of their junior year. At the graduate level, students can choose between an MS in mathematics, an MS in scientific computing, and an MS in mathematics in finance. Math students at NYU can also choose to pursue doctoral studies.

The research centers and groups on NYU’s campus have made efforts to combine pure and applied mathematics in order to observe the interaction between the two. Areas of major research include:

Algebraic Geometry
Analysis and Partial Differential Equations
Dynamical Systems and Ergodic theory
Probability theory
Scientific Computing

11. Columbia University

New York, New York

The Department of Mathematics at Columbia University is part of a preeminent Ivy League institution located in upper Manhattan. With an abundance of resources, the department lists course offerings through three separate administrative entities: Columbia College, the School of General Studies, and the Graduate School of Arts and Sciences.

The graduate-level studies are intensive. In addition to a complete mastery of the traditional mathematics subjects, the Ph.D. requires reading knowledge of a second language. Columbia divides doctoral work in math into a standard program and an applied program. Allied doctoral programs include statistics and computer science. The 56 full-time faculty members provide daily tea and refreshments for the graduate students as a networking opportunity.

Participants in math programs at Columbia conduct research in several areas, including:

Algebraic Geometry
Geometric Analysis
Mathematical Physics
Number theory
Probability and Financial Mathematics
Topology

Students and faculty gather at least once a week for regular seminars in each of these fields. These regular gatherings are in addition to the host of special seminars and lectures available, such as those sponsored by the Minerva Research Foundation.

12. University of Chicago

Chicago, Illinois

Receiving its start-up capital from the wealthy John D. Rockefeller in 1890, the University of Chicago quickly established its Department of Mathematics soon after the school’s founding. Now well-established and offering some of the best mathematics programs out there, the department offers a wide range of degree tracks and engaging classes taught by expert faculty members.

There are four bachelor’s programs available:

A BA in Mathematics
A BS in Applied Mathematics
A BS in Mathematics with Specialization in Economics
A BS in Mathematics

Classes range from basic number theory to honors combinatorics. Required total units for graduation vary from 1,400 to 1,800.

The graduate program enrolls approximately 80 Ph.D. candidates each year. Students are expected to participate in both research and peer-run seminars, in addition to presenting an oral topic dissertation and written report. Research interest groups include:

Algebra
Algebraic Geometry
Analysis
Applied Mathematics
Logic
Probability Theory
Theoretical Computer Science
Topology and Dynamics

13. ETH Zürich

Zürich, Switzerland

Since 1855, the Swiss Federal Institute of Technology (commonly known by its German initials, ETH) has specialized in the research of technology and the natural sciences. Today, ETH receives acclaim as an international leader in these fields. The school’s technical background has endowed its faculty with a thorough understanding of how essential a role mathematics plays in today’s modern society.

Providing an ideal environment for study and research, the Department of Mathematics at ETH boasts an extensive history of excellence and can claim Albert Einstein as a former student. Currently, 50 full-time professors administer to more than 700 students through a variety of degree programs. In addition to traditional undergraduate and graduate studies, ETH offers teacher training and continuing education opportunities.

The math department at ETH manages several seminars and exceptional research centers. In addition, networking relationships have been established with the ETH Institute for Theoretical Studies and National Centers of Competence in Research.

14. Imperial College London

London, England, UK

The Department of Mathematics at the Imperial College of London offers undergraduate and graduate students access to academic programs, industry partnerships, and research opportunities at its South Kensington Campus in London. Undergraduate degrees include nine honors undergraduate programs. Learners can also enroll in a joint mathematics and computer science program. In the Imperial College of London’s undergraduate programs, learners study math fundamentals before advancing to specialized subsets of the field.

Master’s and doctoral programs in mathematics include programs in:

Applied Mathematics
Mathematics and Finance
Pure Mathematics
Statistics

Full-time learners can complete a master’s degree in one year, while part-time learners might need two years to finish their master’s. Doctoral students can also specialize in applied and pure math, statistics, or finance. Doctoral degrees are typically earned in three to four years of full-time study. Part-time doctoral students can complete the program in five to six years.

The math department provides its faculty, staff, students, and the mathematics community with seminars and publications. These come from collaborations with the school’s Centre for Complexity Science, Centre for Plasmonics and Metamaterials, and EPSRC Centre for Mathematics of Precision Healthcare. In addition to student organizations, undergraduate and graduate students have access to prizes and awards through the department. The department also hosts colloquia several times each year, during which mathematics experts and leaders speak and interact with students and faculty.

15. Yale University

New Haven, Connecticut

As the third-oldest university in the United States and a private Ivy League institution, Yale University has had the time and financial means to greatly expand its academic influence. The Department of Mathematics is no exception; it offers an impressive array of educational degrees, research areas, and supplemental programs.

For a BA in mathematics, students are required to complete 10 term courses numbered 222 or higher. The BS in mathematics has the same requirements; however, students must complete an additional two courses in the physical sciences. Core areas of algebra, real analysis, and complex analysis are covered in each program. Senior students must complete a research essay and oral report before commencement.

At the Yale Graduate School of Arts and Sciences, some of the best mathematics programs at the graduate level are offered. Most students in the graduate school will complete a master’s degree on their way to a doctorate. Doctoral students typically complete their studies in a four-year period.

16. University of Michigan

Ann Arbor, Michigan

When the University of Michigan was founded at the flagship Ann Arbor campus in 1817, one of the first four subjects taught was mathematics. As the school grew, so did the Department of Mathematics; the department currently claims 145 academic faculty members. Serving hundreds of students each year, the department offers a diverse array of programs, research areas, and outreach opportunities.

Undergraduate students have four main tracks to choose from:

Applied Mathematical Sciences
Actuarial Mathematics
Mathematics of Finance and Risk Management
Pure Mathematical Sciences
Teaching Mathematics

The master’s program offers three main degrees with multiple subdivisions within each:

Applied and Interdisciplinary Mathematics
Quantitative Finance and Risk Management
General Mathematics Master’s Degree

Doctoral studies at U-M first take two semester courses in algebra, analysis, applied analysis, and geometry/topology. After establishing a strong foundation in these areas, students then begin developing their own contributions to the field as they pursue more specialized work and dissertation writing. Students benefit from 15 areas of research, as well as a long-term grant program for elite students interested in pursuing groundbreaking topics. These academic and research areas include:

Combinatorics
Differential Equations and Geometry
Logic and Foundations
Number and Probability Theory

17. University of Toronto

Toronto, Ontario

The University of Toronto opened its first mathematics program in 1877, and the school soon established itself as one of the leading math research institutes in Canada. Today, U of T’s Department of Mathematics is spread out across three of the school’s campuses in Scarborough (UTSC), Mississauga (UTM), and St. George (UTSG).

Undergraduate students at U of T can complete an honors BS degree in mathematics at both its UTSG and UTSC campuses. The Scarborough campus offers program streams for its students, including a comprehensive stream, a statistics stream, and a teaching stream. Graduate students can choose from an MS or Ph.D. in mathematics. A master of mathematical finance (MMF) program is available as well.

The school hosts weekly events and seminars through its partnership with the Fields Institute for Research in Mathematical Sciences, where leading academic and industry experts cover topics such as machine learning, geometry, topology, and Hamiltonian systems.

18. Carnegie Mellon University

Pittsburgh, Pennsylvania

Carnegie Mellon University was founded as a technical school in 1900 under the patronage of entrepreneur and industrialist Andrew Carnegie. The institution now offers undergraduate and graduate programs through seven individual colleges, and features a mathematics department dedicated to academic and research excellence.

The Mathematical Sciences Department within Carnegie Mellon’s Mellon College of Science offers undergraduate degrees in mathematics with concentrations available in:

Applied Mathematics
Discrete Mathematics and Logic
Mathematical Sciences
Operations Research
Statistics

The department also works closely with Carnegie Mellon’s departments of arts and sciences, computer science, and economics to provide access to interdisciplinary programs combining math with other areas of study. Carnegie Mellon supports undergraduate research through its summer undergraduate research fellowship and undergraduate research apprenticeship programs.

Graduate students studying mathematics at Carnegie Mellon can earn a doctor of arts or a doctor of science in the subject. Learners can also specialize in pure and applied logic or algorithms, combinatorics, and optimization — both interdisciplinary degrees offered in conjunction with the departments of computer science and philosophy and the Tepper School of Business. Doctoral students can concentrate their research in applied analysis and scientific computing, discrete mathematics and operations, or probability and mathematical finance.

19. The University of Tokyo

Tokyo, Japan

Undergraduate studies at the University of Tokyo are organized into 10 faculties, including the Faculty of Science. This Faculty is further organized into 10 departments, one of which is the Mathematics Department. With a general introduction at the undergraduate level, over 90% of the department’s students continue studying at the graduate level.

The Graduate School of Mathematical Sciences is arguably the most prestigious department at UTokyo. A total of 53 master’s students and 32 doctoral candidates gain acceptance each year, which makes admission to the school highly competitive.

Entrance to the master’s programs requires students to pass two written examinations and an oral examination. Knowledge of the Japanese language is not required for admission, but a lack thereof limits student participation throughout the program. Typical program time requirements include two years of study for the master’s degree and three for the doctoral program.

20. University of Pennsylvania

Philadelphia, Pennsylvania

Located in David Rittenhouse Laboratory alongside the Department of Physics and Astronomy, the Department of Mathematics at the University of Pennsylvania hosts experts in partial differential equations, functional analysis, mathematical physics, algebraic geometry, and algebraic number theory. The DRL houses an extensive physics library in addition to computer labs, seminar rooms, and lecture rooms on the east end of Penn’s Philadelphia campus.

Penn’s undergraduate program in mathematics prepares students to understand theories, methods, and practices in mathematics and apply them to real-world experiences. Learners also gain the skills to teach math or continue onto graduate coursework in the field. Math majors can also apply to the submatriculation program, and enter graduate coursework while still in the bachelor’s program. Penn’s interdisciplinary biological mathematics specialization is also available to math majors, in which students focus on computational and discrete mathematical practices applicable to scientific research.

Graduate curricula in mathematics at Penn include:

Applied Mathematics Degrees
Computational Science Degrees
A Terminal Master’s Degree
A Masters’s Degree Bridge to Doctoral Study
A Doctorate

Learners can earn dual master’s degrees in mathematics and computer science or mathematics and statistics. Penn Math’s funded research projects provide graduate students with several areas of study to choose from. They can pursue their chosen subject with faculty in the math department or as part of an interdisciplinary study.

21. University of Warwick

Coventry, England, UK

With little more than 50 years of academic history, the University of Warwick finds innovative ways to expand its services and leave a mark on the world of higher education. Founded in 1965, the school’s Mathematics Institute has played an integral role since its inception. Originally focused on just three areas of research — analysis, algebra, and topology — the department has since expanded into number theory, discrete mathematics, and applied mathematics.

Contrary to other schools and research departments, Warwick combines pure and applied mathematical research to create a unique academic atmosphere and increased productivity in offering some of the best mathematics programs available. Centers and programs for research opportunities include:

The Centre for Complexity Science
The Centre for Discrete Mathematics and Its Application
The Hyperbolic Geometry Program

Without compromising quality, the department features one of the largest undergraduate student acceptance rates in the UK. Joint degrees are available at the undergraduate level through the departments of economics, philosophy, and business, while graduate students are encouraged to pursue cross-disciplinary studies through seven top doctoral training centers.

22. Cornell University

Ithaca, New York

The resume of Cornell University is impressive: a private endowment, a federal land-grant, membership in the Ivy League, and a partnership with the State University of New York system. Part of the College of Arts and Sciences, the university’s Department of Mathematics shares a 150-year history with the great achievements of Cornell as a whole.

The undergraduate track offers a wide selection of courses through several mathematics majors and minor programs considered among the best mathematics programs in the world. Introductory courses are taught with the understanding that not all students are mathematically inclined. At the graduate level, students take an average of 5-6 years to complete their studies. All 43 tenured and tenure-track faculty members are experienced and hold unique interests in research areas. From algebra and applied mathematics to logic and topology, most mathematical fields are represented.

Through 150 years of history, the department has several achievements worth celebrating. These include its support of women in mathematics since 1917 and prominent role at the quadrennial International Congress of Mathematicians since 1893.

23. (tie) The University of Texas at Austin

Austin, Texas

Within an already large and impressive institution, the Department of Mathematics at the UT Austin campus boasts its own striking history and list of achievements. The current 55 full-time faculty members include two members of the National Academy of Science, two MacArthur fellows, and five Guggenheim fellows. All the professors help create a stimulating academic environment for the department’s 138 graduate students and 900 undergraduate students.

The math department at UT Austin offers degree tracks in the form of bachelor of arts, bachelor of science, master of arts, and doctor of philosophy programs. Study and research areas include:

Analysis
Combinatorics
Computational Biology
Dynamical Systems
Geometry
Scientific Computation

Regular colloquia and seminars are held with presentations from leaders in the field.

Community outreach groups associated with UT Austin’s math department include the Saturday Morning Math Group, which targets junior and senior high school students, and the Math Teacher’s Circle of Austin.

23. (tie) University of California – San Diego

La Jolla, California

The Department of Mathematics at the University of California – San Diego offers several excellent undergraduate degrees in math-related fields, including applied mathematics, applied science, computer science, economics, general mathematics, probability and statistics, scientific computation, and secondary education.

Three master’s programs are offered in pure or applied mathematics or statistics. At the doctoral level, candidates can study general mathematics or choose specialized courses in computational science or statistics.

In addition to providing these many opportunities to connect mathematics to cutting-edge technology, UCSD places an uncommon emphasis on the social aspects of this objective field. The department’s curriculum covers the historic development of the field as well as its connection to the humanities.

Representing nearly all areas of mathematics, approximately 20 research interest groups have been established through UCSD’s math department, including:

Bioinformatics
Complex Variables
Logic and Computational Complexity
Mathematics Education
Representation Theory

The mathematics department utilizes over 60 faculty to teach roughly 100 Ph.D. candidates and 35 master’s students.

25. Peking University

Beijing, China

Located in China’s capital, Peking University established itself as one of the first modern research institutions committed to progressive thought. Consisting of 30 colleges and 12 departments, Peking offers a full range of courses at all academic levels. There are 93 undergraduate fields of specialization, 199 master’s programs, and 173 doctoral degrees. The study of mathematics is found at each level.

The School of Mathematical Sciences is dedicated to educating its students while maintaining a level of research excellence. Of the 12 National Key Laboratories run by the university, the Department of Mathematics manages the Key Laboratory of Mathematics and Applied Mathematics. Graduate students and professors can publish research findings in the monthly journal, Acta Physico-Chimica Sinica.

International students are welcomed at the Department of Mathematics. The graduate school maintains global relations with 128 institutions of higher education in more than 40 countries.

26. National University of Singapore

Singapore

The Department of Mathematics at the National University of Singapore includes more than 60 faculty and teaching staff in one of the institution’s largest departments. Undergraduate math students at NUS can major in pure mathematics, applied mathematics, data science and analytics, or quantitative finance. Learners can also enroll in the special program in mathematics, which includes an advanced curriculum for passionate math scholars. Dual majors are also available.

Mathematics master’s programs at NUS allow students to focus on either research or coursework, depending on their educational backgrounds and future goals. The research track best serves undergraduate math majors who want to continue to doctoral study. NUS’s master’s degree in qualitative finance comprises 40 credit hours of coursework, which students can complete either at the Singapore campus or part-time at Shanghai Jiao Tong University.

Students enrolled in the graduate program by research at NUS can also earn a doctoral degree in mathematics. Learners study coursework in topics including:

Imaging and Vision Science
Mathematical Economics
Mathematical Finance
Mathematical Logic
Theoretical Computer Science

They must also complete comprehensive exams, write a thesis, and defend their work in an oral presentation.

NUS’s mathematics department offers conferences, workshops, colloquia, and seminars to math students and scholars from around the world. It also provides outreach activities and puts on the annual Oppenheim Lecture Series.

27. University of Bonn

Bonn, Germany

A leading institution of higher education in Germany, the University of Bonn has dedicated itself to cutting-edge research and global outreach. The school’s Department of Mathematics has taken the university’s goals to heart and has created a student-centered program for furthering education. There are four institutes established by the department:

The Institute for Applied Mathematics
The Institute for Numerical Simulation
The Mathematical Institute
The Research Institute for Discrete Mathematics

Each of these institutes provides unique networking and study opportunities. The Department of Mathematics’ distinguished faculty members include two Fields Medal recipients.

Other national relationships include partnerships with the Max Planck Institute for Mathematics and the Hausdorff Center for Mathematics. The department also manages the Bonn Mathematical Society, which furthers the study of mathematics and the sciences through the support of monetary grants and prizes for young students and researchers.

28. University of British Columbia

Vancouver, British Columbia

The University of British Columbia houses 16 faculties, 18 schools, and two colleges. The Mathematics Department at UBC includes 60 faculty members and more than 130 graduate and postgraduate students, with undergraduate learners pursuing degrees such as mathematical education, mathematics and music, and mathematics and economics.

Undergraduate learners can major or minor in mathematics at UBC. Mathematics majors complete either a bachelor of arts or a bachelor of science; the latter offers learners the opportunity to double-major in education. The bachelor of arts degree includes a cooperative education option and a computing coursework requirement. Both bachelor’s degrees also include honors options for students.

Graduate programs in mathematics at UBC offer learners two-year master’s degrees. Doctorate students may complete their degrees in three to four years. Graduate students can work closely with UCB’s expert faculty members to specialize in areas such as:

Applied Mathematics
Harmonic Analysis
Number Theory
Probability

Master’s and doctoral students can also participate in weekly seminars and lectures, or research opportunities with the school’s Institute of Applied Mathematics, affiliate organization Pacific Institute for the Mathematical Sciences, or the Banff International Research Station for Mathematical Innovation and Discovery.

The math department also performs outreach with Vancouver schools through learning exercises, competitions, and teacher trainings.

29. Australian National University

Canberra, Australia

With more than 25,000 students, Australian National University provides educational programs through eight academic units.

The Mathematical Sciences Institute in the ANU College of Science offers an undergraduate degree in mathematical sciences with an additional honors program option. The bachelor’s degree in mathematical sciences emphasizes quantitative modelling and research-oriented practice; these disciplines are applicable to careers in government and industry or continued graduate study. The honors program comprises 10 months of coursework, a thesis, and seminars to enhance subject knowledge.

Learners can pursue a master of science or doctor of philosophy in mathematics at ANU. The master of philosophy in mathematical sciences curriculum emphasizes theoretical mathematics, while the master of science in mathematics focuses on building quantitative and computational skills. ANU’s doctorate of philosophy in mathematics includes coursework and a mentored research project, and students can typically complete the program in three years.

The Mathematical Sciences Institute offers research groups for students in fields such as algebra, geometry, statistical science, and mathematical physics. Through research programs and projects, students can work with faculty members who specialize in their specific interest areas, and gain valuable expertise applicable to their degrees and career goals.

ANU’s Mathematical Sciences Institute also hosts visitors from around the world and offers events for alumni and the community. Outreach programs include ANU Maths Day, coursework through the Secondary College, and the Canberra Mathematics Enrichment program.

30. Kyoto University

Kyoto, Japan

Of the higher education institutions in Japan, Kyoto University is the second-oldest and one of the most recognized in the nation. In the school’s Department of Mathematics, the 17 full-time professors are well-established in their field and include two Fields Medal recipients. The department is responsible for the general mathematics education for all undergraduate students. Basic education in calculus, algebra, geometry, and analysis is emphasized. At the graduate level, 24 Ph.D. candidates are involved with intensive research and study.

The numerous research groups associated with some of the best mathematics programs cover:

Algebraic Geometry
Applied Mathematics
Differential and Algebraic Topology
Discrete Geometric Analysis
Harmonic Analysis
Number Theory
Partial Differential Equations
Probability Theory

Yoshida-jyuku and Yoshida-jyuku Senior are mathematics camps managed by the department where students can learn about advanced mathematics through lectures and seminars. Those enrolled in Yoshida-jyuku Senior usually continue to graduate studies.

31. The University of Hong Kong

Hong Kong

As the oldest post-secondary institution in Hong Kong, the University of Hong Kong advances innovations in educational programming and research initiatives through undergraduate and graduate degrees that build student competencies and foster intellectual collaboration.

The Department of Mathematics at HKU carries out this mission with bachelor’s degrees in mathematics that concentrate on:

Computational Mathematics and Operational Research
Mathematics, Economics, and Finance
Pure Mathematics

Students can also pursue a bachelor’s degree in mathematics and physics or a minor in the mathematics. Undergraduate students can participate in one of the department’s research fellowships, international exchange programs, or internships to expand their skills and knowledge.

HKU’s graduate programs in mathematics include a master’s degree and a doctorate, both of which combine the theories and principles of pure and applied mathematics. Students work with faculty in one of four research groups, including:

Computational and Financial Mathematics
Geometry
Number Theory
Optimization and Operations Research

Research conferences, seminars, and workshops offer additional learning opportunities for students and bring together leaders and experts in the field.

Outreach programs through HKU include:

Community Engagement
Enrichment Courses
Public Lectures
Summer Programs

The Mathematical Garden provides games and information on mathematical method information to learners of all ages.

32. University of Wisconsin – Madison

Madison, Wisconsin

The University of Wisconsin – Madison, the flagship institution of the University of Wisconsin system, houses its Department of Mathematics in Van Vleck Hall. Undergraduate students studying mathematics at UW-Madison can pursue a general mathematics bachelor’s degree, focus on a specialized area, or double-major in a related area such as engineering or physics. UW-Madison also offers an interdisciplinary applied mathematics, engineering, and physics undergraduate program. Master’s and doctoral degrees in mathematics at UW-Madison, including the master’s program foundations of advanced studies degree, provide students with advanced research skills.

The Department of Mathematics at UW-Madison houses the Kleene Mathematics Library, named for noted mathematics scholar Stephen Cole Kleene. The department features a math circle program for middle and high school students interested in mathematics, a math club for undergraduate students, and Girls Night Out!, a 12-week mentorship program for gender minority high school students who aim to pursue careers in mathematics and the sciences. Female graduate students can also join the Women in Mathematics at Wisconsin group. Each school year, the department also conducts a talent search, posing five math questions to high school and middle school students from around the world to scout talented mathematicians and foster their skills.

33. Brown University

Providence, Rhode Island

Brown University in Providence, Rhode Island offers mathematics courses and programs for students who are interested in math and want to dedicate themselves to the field. Brown’s Department of Mathematics offers undergraduate courses that help learners gain competency in algebra and calculus as well as honors degrees that prepare students for graduate study.

In addition to bachelor’s degrees in honors mathematics, Brown offers undergraduate degrees that combine mathematics with physics, economics, and computer science. Undergraduate students can take graduate coursework as they work toward a master’s or doctoral degree. Brown’s mathematics department does not offer a terminal master’s degree.

Brown’s department of mathematics provides student resources including library materials and the informative Horizon Seminar, offered in conjunction with the Institute for Computational and Experimental Research in Mathematics. Students can join several mathematics clubs. The Math Departmental Undergraduate Group is an undergraduate community of math learners. The Mentoring Women in Mathematics network id dedicated to making connections within the larger math community. The Math Resource Center provides tutoring to students at all skill levels.

34. Georgia Institute of Technology

Atlanta, Georgia

When it opened in 1885, Georgia Tech initially offered only a degree in mechanical engineering. Though the school still functions as a specialized institution focusing on science and technology, the degree programs have expanded to include architecture, business administration, computing, and liberal arts.

The School of Mathematics is heavily involved with most student curricula and offers a wide variety of classes. For the undergraduate mathematics major, there are two options: a BS in applied mathematics or a BS in discrete mathematics. There are approximately 20 master’s students and 80 doctoral candidates participating in some of the best mathematics programs available at Georgia Tech.

Faculty interests in research range from algebra and differential equations to mathematical biology and physics. With access to various conferences, seminars, and colloquia, students sit at the forefront of the newest ideas and research in the mathematics community.

35. École polytechnique fédérale de Lausanne

Lausanne, Switzerland

The École polytechnique fédérale de Lausanne emphasizes education, research, and innovation in engineering and the sciences. As one of Switzerland’s Federal Institutes of Technology, EPFL engages with technology industries and partners in cutting-edge academic programs.

Earning a bachelor’s degree in mathematics from EPFL entails three years of coursework. Students complete 180 credit hours, where they focus their first year on preparatory theories and methods. During their second and third years of study, learners take classes on advanced mathematical fields and principles. The undergraduate program prepares students to continue to graduate study.

EPFL offers master’s degrees in four areas of mathematics. Learners can pursue a master’s in pure mathematics, through which they study analysis, algebra, geometry, topology, and number theory. The master’s in mathematics comprises 90 credit hours, and students can complete it in 1.5 years.

EPFL’s master’s in applied mathematics includes similar content, and also builds problem-solving and critical thinking skills applicable to computer science, financial, and governmental contexts. The master’s degree in computational sciences and engineering provides interdisciplinary coursework to build competencies in high-performance computing, numerical mathematics, and multiscale and multi-physics modeling. EPFL’s teaching mathematics curriculum provides information on building curricula, communication, and instruction. The applied mathematics and computational sciences degrees each entail 120 credit hours, which students typically complete in two years.

EPFL offers a doctoral program in mathematics, through which degree candidates study advanced theory and methods while completing qualifying exams, a dissertation, and a public defense. Learners can hone their research to one of nine fields of research expertise hosted at EPFL.

36. University of Waterloo

Waterloo, Ontario

The mathematics faculty at the University of Waterloo traces its origins to 1967, although the school offered outstanding mathematics instruction through the Faculty of Arts for almost a decade prior. Currently, the Faculty of Mathematics at the University of Waterloo provides entrepreneurship opportunities, research options, and funding through the Mathematics Endowment Fund for undergraduate and graduate students alike.

The University of Waterloo features five departments in its mathematics faculty. Learners can specialize their degree and research in:

Applied Mathematics
Combinatorics and Optimization
Computer Science
Pure Mathematics
Statistics and Actuarial Science

Master’s and doctoral programs at the University of Waterloo correspond with these areas of study, offering coursework and faculty based on students’ research interest and academic expertise.

Within the faculty of mathematics, students can enroll in one of 14 undergraduate math majors, including mathematics optimization, mathematical physics, and statistics. Learners also have a mathematics teaching and co-op option for students who want to earn education degrees and gain valuable classroom experience. Students can pursue dual and interdisciplinary mathematics degrees as well in computer science, business and accounting, or English.

The University of Waterloo mathematics faculty also hosts the Center for Education in Mathematics and Computing, Canada’s largest outreach center for activities and instruction in mathematics and computer science.

37. Tsinghua University

Beijing, China

Tsinghua University, established in Beijing in 1911, offers undergraduate and graduate programs to more than 47,000 students around the world. Tsinghua University’s 20 colleges and 58 departments offer degrees to English and Chinese speakers alike.

Tsinghua University stays true to its motto of self-discipline and social commitment by offering extensive mathematics programming through its Department of Mathematical Sciences. The mathematics department, founded in 1927, includes 87 faculty members organized into research groups. Students can study with scholars in one of four research groups:

Applied Mathematics and Probability Statistics
Computational Mathematics and Operations Research
Mathematics Education
Pure Math

Undergraduate degrees in mathematics at Tsinghua University include two specializations: one in pure mathematics and one in applied mathematics. Graduate programs offer advanced coursework in mathematical research, theory, and practice. This coursework is applicable to commercial industries, academic settings, and governmental work.

At Tsinghua University’s Yau Mathematical Sciences Center, students train to become leaders in the mathematics field as they conduct specialized research with mathematics experts. The Yau Mathematical Sciences Center offers lectures, workshops, and awards to mathematicians at all levels of study. The center also engages young learners with mathematics competitions and forums.

38. The Chinese University of Hong Kong

Hong Kong

At the Chinese University of Hong Kong, mathematics serves as an essential discipline for all graduating students. Undergraduates pursuing programs through the university’s Department of Mathematics can choose from two tracks: a bachelor of science in mathematics and a bachelor of science in mathematics and information engineering. The mathematics and education degree is managed by the Faculty of Education.

Courses throughout undergraduate studies in math cover information like a general introduction to mathematics through Fourier analysis and game theory. Recently, a new standard has been put in place for students who wish to double-major in mathematics; this standard gives double-majors an additional year to complete their classes. Graduate students have numerous fields of specialization to select from, including:

Algebra and Number Theory
Analysis
Computational Mathematics
Geometry and Topology
Partial Differential Equations

Counted among the best mathematics programs in the world, these programs run for 2-3 years, depending on full- or part-time enrollment. A specialized computing laboratory has been established for research and the teaching of undergraduate courses in mathematics. Only mathematics students and professors may use the laboratory.

39. École polytechnique

Paris, France

The École polytechnique in Paris, France offers two mathematics departments. The Department of Pure Mathematics trains learners in the fundamentals of mathematics by providing a theoretical framework for continued study and interdisciplinary collaboration. École polytechnique’s Department of Applied Mathematics features programs that engage with the technological and industrial aspects of mathematics, along with trends in the field and innovative research.

The undergraduate pure mathematics program at École polytechnique includes coursework on algebra, analysis, calculus, and mathematical theory, while master’s degrees offer learners access to advanced research techniques and simulation development. Students complete coursework, a thesis, or an internship based on area of emphasis.

The applied mathematics bachelor’s degree includes four years of engineering training. The first two years build general knowledge while the last two years deepen specialized competencies. A master’s degree in applied mathematics at École polytechnique offers learners the option to specialize in areas such as:

Data Science
Mathematics in Finance
Numerical Analysis
Probability and Statistics

Doctoral students studying mathematics can earn a degree through the Hadamard Doctoral School of Mathematics (EDMH). The EDMH brings together pure and applied mathematics fundamentals with fields such as economics, computer science, mechanics, physics, engineering sciences, and life sciences in degree interfaces to expand potential within all disciplines.

40. École normale supérieure

Paris, France

Conceived and initiated during the French Revolution, ENS has continued in the progressive spirit and critical thinking of the Enlightenment. Paris has one of the largest concentrations of mathematicians in the world. Much of the mathematical success of the nation can be traced back to ENS.

With 10 out of 53 Fields Medal recipients coming from ENS, the school has gained a reputation for mathematical genius. Adrien Douady and his son, Raphael, are just two of the recent and well-respected mathematicians from ENS.

Approximately 200 students are enrolled in the Department of Mathematics and Their Applications at ENS. Most students partake in a three-year program that culminates in a master’s degree in pure or applied mathematics. Most students continue to obtain a Ph.D. as well. Every year, the school opens its doors to 30 of the most promising international students for enrollment in this prestigious program.

41. University of Melbourne

Melbourne, Australia

Founded in 1863 with just four professors and 16 students, the University of Melbourne now houses more than 8,000 faculty and staff who educate over 48,000 students worldwide. The School of Mathematics and Statistics reflects this growth with extensive educational and research opportunities for both undergraduate and graduate students.

In addition to a one-year diploma in mathematical sciences, the University of Melbourne offers three undergraduate degrees in mathematics. Students can complete degrees in computational biology, mathematical statistics, or mathematical physics. These programs teach foundational coursework in mathematics, and integrate scientific knowledge into their curricula to hone students’ critical thinking, analytical, and application skills. Undergraduate students studying math at the University of Melbourne have access to educational support and resources through the department’s Mathematics and Statistics Learning Centre.

The University of Melbourne offers a master’s degree in mathematics and statistics that incorporates advanced coursework in pure and applied mathematics. Learners also study discrete mathematics and operational research during the two-year degree. The School of Mathematics and Statistics also offers master’s degrees in:

Mathematics and Computer Science
Statistics with Scientific Content.

Students complete master’s programs through coursework or a research-based thesis.

42. Lomonosov Moscow State University

Moscow, Russia

Moscow State University is famous for possessing the tallest educational building in the world and the largest library system in Russia; however, the school is known for more than just its sweeping architecture — its academic programs and research initiatives are some of the best in the nation.

The school has established two divisions dedicated to the advancement of mathematics: the Faculty of Mechanics and Mathematics, and the Faculty of Computational Mathematics and Cybernetics.

The Faculty of Mechanics and Mathematics is organized into 25 departments and 15 research laboratories. There are 350 professors for approximately 2,000 undergraduates and 450 graduates. Research areas include:

Complex Function Theory
Mechanized Wing Theory and the Theory of Screws
The Calculus of Variations
The Theory of Gyroscopes

The Faculty of Computational Mathematics and Cybernetics contains 19 departments and 16 research laboratories. Popular study and research areas consist of:

Game Theory and Operations Research
Mathematical Logic
Mathematical Modeling
Systems Analysis

43. University of Sydney

Sydney, Australia

The University of Sydney holds to its foundations as a modern and progressive institution with academic programming that builds individual and community excellence. The School of Mathematics at the University of Sydney was founded in 1991 by merging the applied mathematics, pure mathematics, and mathematical statistics departments.

The mathematics programs at the University of Sydney offers coursework for bridge learners who need to build their math skills before declaring a major. There are also master’s and doctoral degree programs in mathematics. Undergraduate students studying mathematics at the University of Sydney can focus on financial mathematics through interdisciplinary coursework or earn a degree in advanced mathematics through the school’s talented students program. Students can also attend summer and winter classes.

Master’s and doctoral students in the mathematics school at the University of Sydney can apply for financial aid from the research training program stipend and the university postgraduate award program. Students also have access to MAGMA, a software package for computations in algebra, number theory, algebraic geometry, and algebraic combinatorics. The department also hosts an annual joint colloquium for mathematics researchers and educators from the schools of mathematics and statistics at the University of Sydney and the University of New South Wales.

44. Hong Kong University of Science and Technology

Hong Kong

The Hong Kong University of Science and Technology enrolls almost 15,000 students in its undergraduate and graduate programs. Formed in 1986, HKUST was the third university built in Hong Kong and remains dedicated to the city’s social and commercial growth and development.

University Of Chicago Math Curriculum

HKUST’s Department of Mathematics offers undergraduate degrees in mathematics with concentrations in:

Applied Mathematics
General Mathematics
Pure Mathematics
Statistics and Finance

Learners can also enroll in mathematics programs that integrate computer science, physics, economics, and data science, or they may complete advanced honors degrees. Graduate programs in mathematics at HKUST include three master’s degrees and one doctoral offering. Students can complete master of science programs in financial mathematics or mathematics education, or earn a master of philosophy in mathematics. The doctorate in mathematics includes three specializations: applied mathematics, probability and statistics, and pure mathematics.

Programs for mathematics students at HKUST offer opportunities for advanced learning both inside and outside of the classroom. Undergraduate students can participate in the department’s S.S. Chern Class (named in honor of the famous mathematician). The class includes advanced coursework, personal mentoring, and funding opportunities. Learners can also partake in one of the department’s undergraduate exchanges, or compete in the annual undergraduate mathematics competition. Graduate students can attend seminars and lectures, or apply for one of the departments many research funding opportunities.

45. Nanyang Technological University

Singapore

University Of Chicago Mathematics

Nanyang Technical University, located on a garden campus in the southwestern part of Singapore, provides colloquia, seminars, and public lectures in addition to undergraduate and graduate programs in mathematics.

The Division of Mathematical Sciences within the School of Physical Science and Mathematics at NTU includes more than 50 full- and part-time faculty members who specialize in subjects ranging from data streams to coding theory. Research among the seven cryptography and coding experts at NTU continue to advance these areas of study and build upon practical and theoretical applications in the field.

Undergraduate students can enroll in the one of the division’s honors bachelor’s programs, which include offerings in pure mathematics, data science and artificial intelligence as well as mathematics with a minor in finance. Students can also double-major in mathematics and economics or mathematics and computer science. As part of the undergraduate program, learners can complete a professional internship or practical work experience in an industrial, educational, or research location. These programs, which last either 12 or 22 weeks, provide students with valuable insights into potential mathematics careers.

The master of science degree at NTU includes coursework and a thesis requirement, which learners can complete in one to three years. Students complete the doctoral degree in mathematical sciences in four years of extensive coursework, research, and mentorship. Doctoral learners can work with researchers in fields such as computational mathematics and coding as they complete a thesis and accompanying defense.

46. University of New South Wales

Kensington, Australia

The School of Mathematics at the University of New South Wales employs more than 90 faculty members. The university participates in outreach programs to local high schools, offering mathematics competitions, mentorship and clubs for young women, teacher workshops, and fellowship opportunities. Industrial partnerships bring together researchers in mathematics and learning opportunities for students through scholarship and co-op options.

Research areas emphasized in the school include pure mathematics subsets, such as number theory and combinatorics, areas of applied mathematics including optimization and nonlinear phenomena, and aspects of statistics like Stochastic analysis and Bayesian methods.

UNSW, Sydney offers undergraduate degrees in mathematics that incorporate content applicable to careers in law, economics, engineering, humanities, and computer science. Students complete three years of coursework before undertaking an optional honors year. The honors year includes advanced coursework and a thesis option.

Graduate programs at UNSW, Sydney include master’s degrees in statistics, finance, and pure mathematics. Learners complete a postgraduate coursework project worth 12 credit hours, during which they apply theoretical knowledge to practical problem-solving scenarios. Students also complete a thesis to prepare for careers in their respective fields or for additional study.

47. City University of Hong Kong

Hong Kong

Formed in 1991, the current Department of Mathematics at the City University of Hong Kong came from the division of the Department of Applied Mathematics. This department was then split into two separate areas: mathematics and applied statistics/operational research. The mathematics department is managed by 24 outstanding faculty members who each have a commitment to both research and education.

The mathematics department created its bachelor of science in computing mathematics in 1994 and its master of science in applied mathematics in 1997. Offering some of the best mathematics programs available today, the department is rapidly becoming a comprehensive global leader in research and academics.

Research areas are broad in scope and open to progressive ideas and new theories. Faculty members have achieved international recognition. They study areas such as:

Approximation Theory
Fluid Machines
Mathematical Finance
Nonlinear Elasticity
Partial Differential Equations
Wave Propagation

The Liu Bie Ju Center for Mathematical Sciences has played a large role in the organization and dissemination of research achievements.

48. University of Auckland

Auckland, New Zealand

The University of Auckland, New Zealand’s largest university, offers learners academic and community involvement programs to promote educational excellence and global engagement.

The Department of Mathematics at the University of Auckland features diverse faculty, research emphases, and curricula. Students study pure mathematics, applied mathematics, and mathematics education as undergraduates, where they complete three stages of coursework to build foundational knowledge. The department also offers pre-degree coursework to students who require additional assistance developing mathematics competencies.

Postgraduate learners can pursue master’s degrees in professional studies in mathematics education to advance their skills as mathematics instructors. They may also pursue a research-based master’s degree in preparation for doctoral study. Full-time students in the University of Auckland’s doctoral program in mathematics can complete the degree in three to five years. Part-time learners complete the program in six to eight years.

The Centre for Mathematical Social Science at the University of Auckland brings together mathematics professionals and researchers with social scientists to actively extend the application of mathematics and computational modelling to social choice and economics. The department also offers community-building opportunities to students, including the Community for Undergraduate Learning in the Mathematical Sciences and the Women in Mathematics program.

49. Technische Universität Berlin

Berlin, Germany

The Institute of Mathematics at Technische Universität Berlin (TU Berlin) brings together mathematics, engineering, and natural science disciplines to advance students’ theoretical, structural, and technological knowledge. Through research groups, industrial partnerships, and academic coursework, the Institute of Mathematics prepares students to work in business settings, become educators, and pursue advanced research opportunities. Undergraduate students studying mathematics at TU Berlin can pursue bachelor’s degrees in mathematics education, technomathematics, or business mathematics. TU Berlin also offers master’s degrees in these fields, plus a scientific computing degree.

Four research groups at the Institute of Mathematics offer application-based opportunities for faculty, visitors, and students. These groups are as follows:

The Institute of Mathematics partners with ECMath – Einstein Center for Mathematics Berlin and affiliate organizations, such as Matheon and the Berlin Mathematical School, to provide access to research initiatives and practical projects throughout Berlin. Matheon is housed at TU Berlin, bringing together experts from three Berlin universities (Freie Universität Berlin, Humboldt University Berlin, and Technische Universität Berlin) and two research institutes (Weierstrass Institute for Applied Analysis and Stochastics and Zuse Institute Berlin). Students at TU Berlin can gain knowledge applicable to their degrees and career aspirations.

50. National Taiwan University

Taipei, Taiwan

National Taiwan University was founded in 1929 as the Taihoku (Taipei) Imperial University. Renamed when the Chinese regained control of Taiwan in 1946, NTU’s Department of Mathematics originated that same year. NTU began offering master’s and doctoral programs in mathematics in 1960 and 1976, respectively.

Through the Institute of Applied Mathematical Sciences (iAMS) at NTU, applied mathematicians and mathematical statisticians come together with researchers from other sciences to train learners for careers in the industry. The iAMS offers 24-credit hour master’s programs that students complete in one to four years. Graduate students studying mathematics at NTU can work with faculty members who specialize in fields including partial differentiation equations, differential geometry, and ring theory. Students can also participate in the Student Geometric Analysis Seminar and the NTU mathematics and NTU applied mathematics colloquia.

Mathematicians at NTU work with the National Center for Theoretical Sciences (NCTS) and the Taida Institute for Mathematical Sciences (TIMS). NCTS, established by the National Science Council in 2001, is housed in the mathematics division of NTU, where it promotes interdisciplinary research among theoretical scientists. TIMS, directed by NTU professor Jing Yu, fosters international and interdisciplinary research and innovation among scholars in mathematics.

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Admission and Degree Requirements

Mathematics
Mathematical Computer Science
Mathematics Teaching
Statistics

Mathematics Courses

MATH 410. Advanced Calculus I. 3 or 4 hours.

Functions of several variables, differentials, theorems of partial differentiation. Calculus of vector fields, line and surface integrals, conservative fields, Stokes's and divergence theorems. Cartesian tensors. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 210.

MATH 411. Advanced Calculus II. 3 or 4 hours.

Implicit and inverse function theorems, transformations, Jacobians. Point-set theory. Sequences, infinite series, convergence tests, uniform convergence. Improper integrals, gamma and beta functions, Laplace transform. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 410.

MATH 414. Analysis II. 3 or 4 hours.

Riemann-Stieltjes integration. Topology of metric spaces with emphasis on R^n. (Uniform) Continuity of functions on metric spaces. Multi-dimensional differentiation theory. Implicit and Inverse Function Theorem and applications. Introduction to Lebes. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade C or better in MATH 313 and MATH 310, or MATH 320.

MATH 417. Complex Analysis with Applications. 3 or 4 hours.

Complex numbers, analytic functions, complex integration, Taylor and Laurent series, residue calculus, branch cuts, conformal mapping, argument principle, Rouche's theorem, Poisson integral formula, analytic continuation. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade C or better in MATH 210.

MATH 419. Models in Applied Mathematics. 3 or 4 hours.

Introduction to mathematical modeling; scaling, graphical methods, optimization, computer simulation, stability, differential equation models, elementary numerical methods, applications in biology, chemistry, engineering and physics. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 220 and grade of C or better in MCS 260.

MATH 425. Linear Algebra II. 3 or 4 hours.

Canonical forms of a linear transformation, inner product spaces, spectral theorem, principal axis theorem, quadratic forms, special topics such as linear programming. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 320.

MATH 430. Formal Logic I. 3 or 4 hours.

First order logic, syntax and semantics, completeness-incompleteness. Course Information: 3 undergraduate hours. 4 graduate hours. Credit is not given for MATH 430 if the student has credit for PHIL 416. Prerequisite(s): Grade of C or better in CS 202 or grade of C or better in MCS 261 or grade of C or better in MATH 215.

MATH 431. Abstract Algebra II. 3 or 4 hours.

Further topics in abstract algebra: Sylow Theorems, Galois Theory, finitely generated modules over a principal ideal domain. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 320 and grade of C or better in MATH 330.

MATH 435. Foundations of Number Theory. 3 or 4 hours.

Primes, divisibility, congruences, Chinese remainder theorem, primitive roots, quadratic residues, quadratic reciprocity, and Jacobi symbols. The Euclidean algorithm and strategies of computer programming. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 215.

MATH 436. Number Theory for Applications. 3 or 4 hours.

Primality testing methods of Lehmer, Rumely, Cohen-Lenstra, Atkin. Factorization methods of Gauss, Pollard, Shanks, Lenstra, and quadratic sieve. Computer algorithms involving libraries and nested subroutines. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 435.

MATH 442. Differential Geometry of Curves and Surfaces. 3 or 4 hours.

Frenet formulas, isoperimetric inequality, local theory of surfaces, Gaussian and mean curvature, geodesics, parallelism, and the Guass-Bonnet theorem. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 320.

MATH 445. Introduction to Topology I. 3 or 4 hours.

Elements of metric spaces and topological spaces including product and quotient spaces, compactness, connectedness, and completeness. Examples from Euclidean space and function spaces. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 313.

MATH 446. Introduction to Topology II. 3 or 4 hours.

Topics in topology chosen from the following: advanced point set topology, piecewise linear topology, fundamental group and knots, differential topology, applications to physics and biology. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 445.

University Of Chicago Mathematics

MATH 480. Applied Differential Equations. 3 or 4 hours.

Linear first-order systems. Numerical methods. Nonlinear differential equations and stability. Introduction to partial differential equations. Sturm-Liouville theory. Boundary value problems and Green's functions. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 220.

MATH 481. Applied Partial Differential Equations. 3 or 4 hours.

Initial value and boundary value problems for second order linear equations. Eiqenfunction expansions and Sturm-Liouville theory. Green's functions. Fourier transform. Characteristics. Laplace transform. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 220.

MATH 494. Special Topics in Mathematics. 3 or 4 hours.

Course content is announced prior to each term in which it is given. Course Information: 3 undergraduate hours. 4 graduate hours. May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department.

MATH 496. Independent Study. 1-4 hours.

Reading course supervised by a faculty member. Course Information: May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the instructor and the department. Class Schedule Information: This course counts toward the limited number of independent study hours accepted toward the degree and the major.

MATH 502. Mathematical Logic. 4 hours.

First order logic, completeness and incompleteness theorems, introduction to model theory and computability theory. Course Information: Same as PHIL 562. Prerequisite(s): MATH 430 or consent of the instructor.

MATH 504. Set Theory. 4 hours.

Naive and axiomatic set theory. Independence of the continuum hypothesis and the axiom of choice. Course Information: Same as PHIL 565. Prerequisite(s): MATH 430 or MATH 502 or PHIL 562.

MATH 506. Model Theory I. 4 hours.

Elementary embeddings, quantifier elimination, types, saturated and prime models, indiscernibles, Morley's Categoricity Theorem. Course Information: Same as PHIL 567. Prerequisite(s): MATH 502 or PHIL 562.

MATH 507. Model Theory II. 4 hours.

Stability theory: forking and indpendence, stable groups, geometric stability. Course Information: Same as PHIL 568. Prerequisite(s): MATH 506 or PHIL 567.

MATH 511. Descriptive Set Theory. 4 hours.

Polish spaces and Baire category; Borel, analytic and coanalytic sets; infinite games and determinacy; coanalytic ranks and scales; dichotomy theorems. Course Information: Recommended background: MATH 445 or MATH 504 or MATH 533 or MATH 539.

MATH 512. Advanced Topics in Logic. 4 hours.

Advanced topics in modern logic; e.g. large cardinals, infinitary logic, model theory of fields, o-minimality, Borel equivalence relations. Course Information: Same as PHIL 569. May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department.

MATH 514. Number Theory I. 4 hours.

Introduction to classical, algebraic, and analytic, number theory. Euclid's algorithm, unique factorization, quadratic reciprocity, and Gauss sums, quadratic forms, real approximations, arithmetic functions, Diophantine equations.

MATH 515. Number Theory II. 4 hours.

Introduction to classical, algebraic, and analytic number theory. Algebraic number fields, units, ideals, and P-adic theory. Riemann Zeta-function, Dirichlet's theorem, prime number theorem. Course Information: Prerequisite(s): MATH 514.

MATH 516. Second Course in Abstract Algebra I. 4 hours.

Structure of groups, Sylow theorems, solvable groups; structure of rings, polynomial rings, projective and injective modules, finitely generated modules over a PID. Course Information: Prerequisite(s): MATH 330 and MATH 425.

$University of chicago statistics$

MATH 517. Second Course in Abstract Algebra II. 4 hours.

Rings and algebras, polynomials in several variables, power series rings, tensor products, field extensions, Galois theory, Wedderburn theorems. Course Information: Prerequisite(s): MATH 516.

MATH 518. Representation Theory. 4 hours.

Major areas of representation theory, including structure of group algebras, Wedderburn theorems, characters and orthogonality relations, idempotents and blocks. Course Information: Prerequisite(s): MATH 517.

MATH 520. Commutative and Homological Algebra. 4 hours.

Commutative rings; primary decomposition; integral closure; valuations; dimension theory; regular sequences; projective and injective dimension; chain complexes and homology; Ext and Tor; Koszul complex; homological study of regular rings. Course Information: Prerequisite(s): MATH 516 and MATH 517; or consent of the instructor.

MATH 525. Advanced Topics in Number Theory. 4 hours.

Introduction to topics at the forefront of research in number theory. Topics will vary and may include elliptic curves, automorphic forms, diophantine geometry or sieve methods. Course Information: May be repeated. Prerequisite(s): MATH 515; or consent of the instructor.

MATH 531. Advanced Topics in Algebra. 4 hours.

Researchlevel topics such as groups and geometries, equivalencies of module categories, representations of Lie-type groups. Course Information: May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department.

MATH 533. Real Analysis I. 4 hours.

Introduction to real analysis. Lebesgue measure and integration, differ entiation, L-p classes, abstract integration. Course Information: Prerequisite(s): MATH 411 or MATH 414 or the equivalent.

MATH 534. Real Analysis II. 4 hours.

Continuation of MATH 533. Course Information: Prerequisite(s): MATH 417.

MATH 535. Complex Analysis I. 4 hours.

Analytic functions as mappings. Cauchy theory. Power Series. Partial fractions. Infinite products. Course Information: Prerequisite(s): MATH 411.

MATH 536. Complex Analysis II. 4 hours.

Normal families, Riemann mapping theorem. Analytic continuation, Harmonic and subharmonic functions, Picard theorem, selected topics. Course Information: Prerequisite(s): MATH 535.

MATH 537. Introduction to Harmonic Analysis I. 4 hours.

Fourier transform on L(p) spaces, Wiener's Tauberian theorem, Hilbert transform, Paley Wiener theory. Course Information: Prerequisite(s): MATH 533; and MATH 417 or MATH 535.

MATH 539. Functional Analysis I. 4 hours.

Topological vector spaces, Hilbert spaces, Hahn-Banach theorem, open mapping, uniform boundedness principle, linear operators in a Banach space, compact operators. Course Information: Prerequisite(s): MATH 533.

MATH 546. Advanced Topics in Analysis. 4 hours.

Subject may vary from semester to semester. Topics include partial differential equations, several complex variables, harmonic analysis and ergodic theory. Course Information: May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department.

MATH 547. Algebraic Topology I. 4 hours.

The fundamental group and its applications, covering spaces, classification of compact surfaces, introduction to homology, development of singular homology theory, applications of homology. Course Information: Prerequisite(s): MATH 330 and MATH 445.

MATH 548. Algebraic Topology II. 4 hours.

Cohomology theory, universal coefficient theorems, cohomology products and their applications, orientation and duality for manifolds, homotopy groups and fibrations, the Hurewicz theorem, selected topics. Course Information: Prerequisite(s): MATH 547.

MATH 549. Differentiable Manifolds I. 4 hours.

Smooth manifolds and maps, tangent and normal bundles, Sard's theorem and transversality, embedding, differential forms, Stokes's theorem, degree theory, vector fields. Course Information: Prerequisite(s): MATH 445; and MATH 310 or MATH 320 or the equivalent.

MATH 550. Differentiable Manifolds II. 4 hours.

Vector bundles and classifying spaces, lie groups and lie algbras, tensors, Hodge theory, Poincare duality. Topics from elliptic operators, Morse theory, cobordism theory, deRahm theory, characteristic classes. Course Information: Prerequisite(s): MATH 549.

MATH 551. Riemannian Geometry. 4 hours.

Riemannian metrics and Levi-Civita connections, geodesics and completeness, curvature, first and second variation of arc length, comparison theorems. Course Information: Prerequisite(s): MATH 442 and MATH 549.

MATH 552. Algebraic Geometry I. 4 hours.

Basic commutative algebra, affine and projective varieties, regular and rational maps, function fields, dimension and smoothness, projective curves, schemes, sheaves, and cohomology, posiive characteristic.

MATH 553. Algebraic Geometry II. 4 hours.

Divisors and linear systems, differentials, Riemann-Roch theorem for curves, elliptic curves, geometry of curves and surfaces. Course Information: Prerequisite(s): MATH 552.

MATH 554. Complex Manifolds I. 4 hours.

Holomorphic functions in several variables, Riemann surfaces, Sheaf theory, vector bundles, Stein manifolds, Cartan theorem A and B, Grauert direct image theorem. Course Information: Prerequisite(s): MATH 517 and MATH 535.

MATH 555. Complex Manifolds II. 4 hours.

Dolbeault Cohomology, Serre duality, Hodge theory, Kadaira vanishing and embedding theorem, Lefschitz theorem, Complex Tori, Kahler manifolds. Course Information: Prerequisite(s): MATH 517 and MATH 535.

MATH 568. Topics in Algebraic Topology. 4 hours.

Homotopy groups and fibrations. The Serre spectral sequence and its applications. Classifying spaces of classical groups. Characteristic classes of vector bundles. Course Information: May be repeated. Students may register in more than one section per term. Prerequisite(s): MATH 548 or consent of the instructor.

MATH 569. Advanced Topics in Geometric and Differential Topology. 4 hours.

Topics from areas such as index theory, Lefschetz theory, cyclic theory, KK theory, non-commutative geometry, 3-manifold topology, hyperbolic manifolds, geometric group theory, and knot theory. Course Information: Prerequisite(s): Approval of the department.

MATH 570. Advanced Topics in Differential Geometry. 4 hours.

Subject may vary from semester to semester. Topics may include eigenvalues in Riemannian geometry, curvature and homology, partial differential relations, harmonic mappings between Riemannian manifolds hyperbolic geometry, arrangement of hyperplanes. Course Information: May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department.

MATH 571. Advanced Topics in Algebraic Geometry. 4 hours.

Various topics such as algebraic curves, surfaces, higher dimensional geometry, singularities theory, moduli problems, vector bundles, intersection theory, arithematical algebraic geometry, and topologies of algebraic varieties. Course Information: May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department.

MATH 576. Classical Methods of Partial Differential Equations. 4 hours.

First and second order equations, method of characteristics, weak solutions, distributions, wave, Laplace, Poisson, heat equations, energy methods, regularity problems, Green functions, maximum principles, Sobolev spaces, imbedding theorems. Course Information: Prerequisite(s): MATH 410 and MATH 481 and MATH 533; or consent of instructor.

MATH 577. Advanced Partial Differential Equations. 4 hours.

Linear elliptic theory, maximum principles, fixed point methods, semigroups and nonlinear dynamics, systems of conservation laws, shocks and waves, parabolic equations, bifurcation, nonlinear elliptic theory. Course Information: Prerequisite(s): MATH 533 and MATH 576 or consent of the instructor.

MATH 578. Asymptotic Methods. 4 hours.

Asymptotic series, Laplace's method, stationary phase, steepest descent method, Stokes phenomena, uniform expansions, multi-dimensional Laplace integrals, Euler-MacLaurin formula, irregular singular points, WKBJ method. Course Information: Prerequisite(s): MATH 417 and MATH 481; or consent of instructor.

MATH 580. Mathematics of Fluid Mechanics. 4 hours.

Development of concepts and techniques used in mathematical models of fluid motions. Euler and Navier Stokes equations. Vorticity and vortex motion. Waves and instabilities. Viscous fluids and boundary layers. Asymptotic methods. Course Information: Prerequisite(s): Grade of C or better in MATH 410 and grade of C or better in MATH 417 and grade of C or better in MATH 481.

MATH 581. Special Topics in Fluid Mechanics. 4 hours.

Geophysical fluids with applications to oceanography and meteorology, astrophysical fluids, magnetohydrodynamics and plasmas. Course Information: Prerequisite(s): Grade of C or better in MATH 580.

MATH 582. Linear and Nonlinear Waves. 4 hours.

Analysis of partial differential equations describing (non-) linear wave phenomena. In particular, dispersive and hyperbolic equations. Analytical techniques include Fourier transformation and fixed point theorems. Course Information: Prerequisite(s): Graduate standing and MATH 533 and MATH 576 OR MATH 539 or consent of the instructor.

MATH 584. Applied Stochastic Models. 4 hours.

Applications of stochastic models in chemistry, physics, biology, queueing, filtering, and stochastic control, diffusion approximations, Brownian motion, stochastic calculus, stochastically perturbed dynamical systems, first passage times. Course Information: Prerequisite(s): MATH 417 and MATH 481 and STAT 401, or consent of the instructor.

MATH 585. Ordinary Differential Equations. 4 hours.

Introduction to ordinary differential equations, existence, uniqueness of solutions, dependence on parameters, autonomous and non-autonomous systems, linear systems, nonlinear systems, periodic solutions, bifurcations, conservative systems. Course Information: Prerequisite(s): MATH 313 or MATH 480 or approval of the department.

MATH 586. Computational Finance. 4 hours.

Introduction to the mathematics of financial derivatives; options, asset price random walks, Black-Scholes model; partial differential techniques for option valuation, binomial models, numerical methods; exotic options, interest-rate derivatives. Course Information: Prerequisite(s): Grade of C or better in MATH 220 and grade of C or better in STAT 381; or consent of the instructor.

MATH 589. Teaching and Presentation of Mathematics. 2 hours.

Strategies and techniques for effective teaching in college and for mathematical consulting. Observation and evaluation, classroom management, presenting mathematics in multidisciplinary research teams. Required for teaching assistants in MSCS. Course Information: No graduation credit awarded for students enrolled in the Master of Science in the Teaching of Mathematics degree program.

MATH 590. Advanced Topics in Applied Mathematics. 4 hours.

Topics from areas such as: elastic scattering, nonlinear problems in chemistry and physics, mathematical biology, stochastic optimal control, geophysical fluid dynamics, stability theory, queueing theory. Course Information: Prerequisite(s): Approval of the department.

MATH 591. Seminar on Mathematics Curricula. 4 hours.

Examination of research and reports on mathematics curricula. Analysis of research in teaching and learning mathematics. Developments in using technology in mathematics teaching. Course Information: Prerequisite(s): Enrollment in the Doctor of Arts program in mathematics or consent of the instructor.

MATH 592. Seminar on Mathematics: Philosophy and Methodology. 4 hours.

Problems related to teaching and learning mathematics. Analysis of work of Piaget, Gagne, Bruner, Ausabel, Freudenthal, and others and their relation to mathematics teaching. Course Information: Prerequisite(s): Enrollment in the Doctor of Arts program in mathematics or consent of instructor.

MATH 593. Graduate Student Seminar. 1 hour.

For graduate students who wish to receive credit for participating in a learning seminar whose weekly time commitment is not sufficient for a reading course. This seminar must be sponsored by a faculty member. Course Information: Satisfactory/Unsatisfactory grading only. May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department.

MATH 594. Internship in Mathematics. 0-8 hours.

Under the direction of a faculty adviser, students work in government or industry on problems related to their major field of interest. At the end of internship, the student must present a seminar on the internship experiences. Course Information: Satisfactory/Unsatisfactory grading only. May be repeated to a maximum of 8 hours. Only 4 credit hours count toward the 32 credit hours required for the M.S. in MISI degree. Does not count toward the 12 credit hours of 500-level courses requirement. Prerequisite(s): Completion of the core courses in the degree program in which the student is enrolled and approval of the internship program by the graduate adviser and the graduate studies committee.

MATH 595. Research Seminar. 1 hour.

Current developments in research with presentations by faculty, students, and visitors. Course Information: Satisfactory/Unsatisfactory grading only. May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department.

MATH 596. Independent Study. 1-4 hours.

MATH 598. Master's Thesis. 0-16 hours.

Research work under the supervision of a faculty member leading to the completion of a master's thesis. Course Information: Satisfactory/Unsatisfactory grading only. Prerequisite(s): Approval of the department.

MATH 599. Thesis Research. 0-16 hours.

Research work under the supervision of a faculty member. Course Information: Satisfactory/Unsatisfactory grading only. May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department.

Mathematical Computer Science Courses

MCS 401. Computer Algorithms I. 3 or 4 hours.

Design and analysis of computer algorithms. Divide-and-conquer, dynamic programming, greedy method, backtracking. Algorithms for sorting, searching, graph computations, pattern matching, NP-complete problems. Course Information: Same as CS 401. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MCS 360; or Grade of C or better in CS 202.

MCS 411. Compiler Design. 3 or 4 hours.

Language translation: lexical analysis, parsing schemes, symbol table management, syntax and semantic error detection, and code generation. Development of fully-functional compiler. Course Information: Same as CS 473. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in CS 301 or Grade of C or better in MCS 441; and Grade of C or better in CS 251 or Grade of C or better in MCS 360; and Grade of C or better in CS 261.

MCS 415. Programming Language Design. 3 or 4 hours.

Definition, design, and implementation of programming languages. Syntactic and semantic description; variable bindings, control and data structures, parsing, code generation, optimization; exception handling; data abstraction. Course Information: Same as CS 476. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): MCS 360; or CS 341.

MCS 421. Combinatorics. 3 or 4 hours.

The pigeonhole principle, permutations and combinations, binomial coefficients, inclusionexclusion principle, recurrence relations and generating functions, special counting sequences, Polya theory of counting. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 215; and Grade of C or better in MATH 310 or Grade of C or better in MATH 320; or consent of the instructor.

MCS 423. Graph Theory. 3 or 4 hours.

Basic concepts of graph theory including Eulerian and hamiltonian cycles, trees, colorings, connectivity, shortest paths, minimum spanning trees, network flows, bipartite matching, planar graphs. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 215; and Grade of C or better in MATH 310 or Grade of C or better in MATH 320; or consent of the instructor.

MCS 425. Codes and Cryptography. 3 or 4 hours.

Mathematics of communications theory, basic information theory necessary to understand both coding theory and cryptography, basic ideas and highlights for both coding theory and cryptography, including public-key cryptosystems. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 215; and Grade of C or better in MATH 310 or Grade of C or better in MATH 320; or consent of the instructor.

MCS 441. Theory of Computation I. 3 or 4 hours.

Introduction to formal languages; relations between grammars and automata; elements of the theory of computable functions. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): MATH 215.

MCS 451. Object-Oriented Programming in C++. 3 or 4 hours.

C++ as an object-oriented language, classes and member functions, access control, class scope, constructors, destructors, overloading, conversions, streams, derived classes, polymorphism through virtual functions, templates, class libraries. Course Information: 3 undergraduate hours. 4 graduate hours. Credit is not given for MCS 451 if the student has credit for CS 474. Extensive computer use required. Prerequisite(s): Grade of C or better in MCS 360 or the equivalent or consent of the instructor.

MCS 471. Numerical Analysis. 3 or 4 hours.

Introduction to numerical analysis; floating point arithmetic, computational linear algebra, iterative solution to nonlinear equations, interpolation, numerical integration, numerical solution of ODEs, computer subroutine packages. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MCS 275 or grade of C or better in CS 102 or grade of C or better in CS 108; or consent of instructor.

MCS 472. Introduction to Industrial Math and Computation. 3 or 4 hours.

Technical writing and oral presentations in preparation for industrial projects. Topics include quality control, operations research, cost-benefit analysis, differential equations, using scientific software. Course Information: Extensive computer use required. Prerequisite(s): Grade of C or better in MCS 471 or consent of the instructor. Recommended background: Designed for students with a desire to explore mathematics via practical field work.

MCS 481. Computational Geometry. 3 or 4 hours.

Algorithmic problems on sets of points, rectangles, intervals, arcs, chords, polygons. Counting, reporting, location, intersection, pairing; static and dynamic data structures. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MCS 401 or consent of the instructor.

MCS 494. Special Topics in Computer Science. 3 or 4 hours.

Topics in mathematical computer science, such as symbolic compution, automated reasoning, cryptography or geometric algorithms. Course Information: 3 undergraduate hours. 4 graduate hours. May be repeated to a maximum of 12 hours. Students may register in more than one section per term. Prerequisite(s): Approval of the department.

MCS 496. Independent Study. 1-4 hours.

Reading course supervised by a faculty member. Course Information: May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the instructor and the department. Class Schedule Information: This course counts toward the limted number of independent study hours accepted toward the degree and the major.

MCS 501. Computer Algorithms II. 4 hours.

Continuation of MCS 401 (same as CS 401). Advanced topics in algorithms. Lower bounds. Union-find problems. Fast Fourier transform. Complexity of arithmetic, polynomial, and matrix calculations. Approximation algorithms. Parallel algorithms. Course Information: Same as CS 501. Prerequisite(s): MCS 401 or CS 401.

MCS 507. Mathematical, Statistical and Scientific Software. 4 hours.

The design, analysis, and use of mathematical, statistical, and scientific software. Course Information: Prerequisite(s): Grade of B or better in MCS 360 or the equivalent or consent of instructor.

MCS 521. Combinatorial Optimization. 4 hours.

Combinatorial optimization: network flows, bipartite matching, Edmonds algorithm for non-bipartite matching, the matching polytope, matroids, greedy algorithm, matroid union and intersection algorithms, matroid polyhedra, polymatroids. Course Information: Prerequisite(s): MCS 423 and STAT 471.

MCS 541. Computational Complexity. 4 hours.

Time and space complexity of computations, classification of mathproblems according to their computational complexity, P not equal NP problem. Course Information: Prerequisite(s): Consent of the instructor.

MCS 548. Mathematical Theory of Artificial Intelligence. 4 hours.

Valiant's learning model, positive and negative results in learnability, automation inference, perceptrons, Rosenblatt's theorem, convergence theorem, threshold circuits, inductive inference of programs, grammars and automata. Course Information: Prerequisite(s): MCS 541.

MCS 549. Mathematical Foundations of Data Science. 4 hours.

Topics will include random graphs, small world phenomena, random walks, Markov chains, streaming algorithms, clustering, graphical models, singular value decomposition, and random projections. Course Information: Prerequisite(s): MCS 401 and MCS 441; or consent of the instructor.

MCS 563. Analytic Symbolic Computation. 4 hours.

Analytic computation, including integration algorithms, differential equations, perturbation theory, mixed symbolic-numeric algorithms, and other related topics. Course Information: Prerequisite(s): Grade of C or better in MCS 460 or the equivalent, and MATH 480 or consent of the instructor.

MCS 565. Mathematical Theory of Databases. 4 hours.

Abstract systems for databases, sysntax and semantics of operational languages, dependencies and normal forms, axiomizations, queries and query optimization, null values, algebraic interpretations.

MCS 571. Numerical Analysis of Partial Differential Equations. 4 hours.

Numerical analysis of Finite Difference methods for PDE of mathematical physics: Wave, heat, and Laplace equations. Introduction to numerical analysis of the Finite Element method. Course Information: Prerequisite(s): MATH 481 and MCS 471 or consent of the instructor.

MCS 572. Introduction to Supercomputing. 4 hours.

Introduction to supercomputing on vector and parallel processors; architectural comparisons, parallel algorithms, vectorization techniques, parallelization techniques, actual implementation on real machines. Course Information: Prerequisite(s): MCS 471 or MCS 571 or consent of the instructor.

MCS 573. Topics in Numerical Analysis of Partial Differential Equations. 4 hours.

Topics in numerical analysis of partial differential equations which may include: High-order Finite Element methods, Discontinuous Glerkin methods, Spectral methods, or Integral Equation methods. Course Information: May be repeated if topics vary. Prerequisite(s): MATH 481 and MCS 471; and consent of the instructor.

MCS 582. The Probabilistic Method. 4 hours.

Introduction to the probabilistic method, which includes a range of applications to address various problems that arise in combinatorics. Prerequisite(s): MCS 421 and 423, or consent of the instructor.

MCS 583. Extremal Combinatorics. 4 hours.

Extremal combinatorics, including extremal graph and set theory, Ramsey theory, the linear algebra method, and applications to computer science. Prerequisite(s): MCS 421 and MCS 423, or consent of the instructor.

MCS 584. Enumerative Combinatorics. 4 hours.

Enumerative methods in combinatorics, including inclusion/exclusion, recursion, partitions, Latin squares and other combinatorial structures. Prerequisite(s): MCS 421 and MCS 423, or consent of the instructor.

MCS 590. Advanced Topics in Computer Science. 4 hours.

Topics in areas such as: mathematical aspects of artificial intelligence, symbolic methods in mathematics, mathematical cryptography, automated reasoning. Topics may vary from term to term. Course Information: May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department.

MCS 591. Advanced Topics in Combinatorial Theory. 4 hours.

Some of the following topics: combinatorial enumeration, designs, graph theory, matroid theory, combinatorial matrix theory, Ramsey theory. Contents vary from year to year. Course Information: May be repeated. Prerequisite(s): MCS 423.

MCS 593. Graduate Student Seminar. 1 hour.

MCS 595. Graduate Seminar. 1 hour.

MCS 596. Independent Study. 1-4 hours.

University Of Chicago Math Summer Program

MCS 598. Master's Thesis. 0-16 hours.

MCS 599. Thesis Research. 0-16 hours.

Research work under the supervision of a faculty member leading to the completion of a doctoral thesis. Course Information: Satisfactory/Unsatisfactory grading only. May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department.

Mathematics Teaching Courses

MTHT 400. Methods of Teaching Secondary Mathematics I. 3 or 4 hours.

Philosophies, issues, techniques, and styles of teaching high school mathematics. Implications of psychological models. Mathematics in the evolving curriculum. Preparation of lessons. Course Information: 3 undergraduate hours. 4 graduate hours. To be taken in the year prior to student teaching. Prerequisite(s): Grade of C or better in MTHT 410, enrollment in B.S. or M.S. in the Teaching of Mathematics program in Secondary Mathematics Education, and a 2.50 grade point average in mathematics courses at the level of calculus or above.

MTHT 401. Methods of Teaching Secondary Mathematics II. 3 or 4 hours.

Philosophies, issues, techniques and styles of teaching high school mathematics. Preparation of diverse lessons. Supervised teaching experience. Course Information: 3 undergraduate hours. 4 graduate hours. To be taken in year prior to student teaching. Prerequisite(s): Grade of C or better in MATH 210 and enrollment in the B.S. or M.S. in the Teaching of Mathematics program in Secondary Mathematics Education; and a 2.50 grade point average in mathematics courses at the level of calculus or above.

MTHT 411. Advanced Euclidean Geometry. 3 or 4 hours.

Axioms for Euclidean geometry are developed based upon reflections. Further concepts in Euclidean geometry which arise from these axioms are explored. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 215.

MTHT 420. Computers in Secondary School Mathematics. 3 or 4 hours.

An overview of techniques, topics and tools for teaching secondary level mathematics using computers. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 210.

MTHT 430. Mathematical Analysis for Teachers I. 3 or 4 hours.

Basic properties of numbers, functions, graphs, limits, differentiation, continuity, completeness of the system of real numbers. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 210 and Grade of C or better in MATH 215.

MTHT 435. Abstract Algebra. 3 or 4 hours.

Sets, properties of integers, groups, rings, fields. Focus on concepts applicable to high school teaching. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): MATH 210 and MATH 215.

MTHT 438. Educational Practice with Seminar I. 6 hours.

The first half of a two-segment sequence of practice teaching, including seminar, to meet certification requirements for teaching in grades six through twelve. Course Information: Graduate credit only with approval of the department. Prerequisite(s): 2.50 grade point average in mathematics courses at the level of calculus or above, successful completion of 100 clock hours of pre-student-teaching field experiences, and approval of the department. Class Schedule Information: To be properly registered, students must enroll in one Lecture-Discussion and one Practice.

MTHT 439. Educational Practice with Seminar II. 6 hours.

The second half of a two-segment sequence of practice teaching, including seminar, to meet certification requirements for teaching in grades six through twelve. Course Information: Graduate credit only with approval of the department. Prerequisite(s): Credit or concurrent registration in MTHT 438; and approval of the department and a 2.50 grade point average in mathematics courses at the level of calculus or above and successful completion of 100 clock hours of pre-student teaching field experiences. Class Schedule Information: To be properly registered, students must enroll in one Conference and one Practice.

MTHT 450. Concepts and Methods in Elementary and Middle School Mathematics I. 3 or 4 hours.

Advanced analysis of concept development and teaching methods. Sorting, classifying, counting, number tracks, addition, subtraction, group, place value, length, area and alternative teaching strategies. Course Information: 3 undergraduate hours. 4 graduate hours. For elementary school teachers. Prerequisite(s): Graduate standing and admission to the M.S. in the Teaching of Mathematics program (Option for Elementary School Teachers) or consent of the instructor.

MTHT 465. Teaching Algebra for Understanding. 3 or 4 hours.

Manipulatives and other representations of mathematical concepts used for teaching algebra to middle grade students. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Admission to the M.S. in the Teaching of Mathematics program (Option for Elementary School Teachers) or consent of the instructor.

MTHT 466. Introduction to Calculus and the Graphing Calculator. 4 hours.

Problem solving using derivatives, differentials, and their applications followed by integrals and their applications. Maximumminimum problems solved directly by graphing, then by derivatives. Course Information: Prerequisite(s): Admission to the Mathematics Education Concentrators Program or consent of the instructor.

MTHT 467. Introduction to Number Theory with Application. 4 hours.

Classical topics of elementary number theory and how they pertain to teaching the upper grades. Primes, GCF, LCM, divisibility, floor and ceiling functions, Gaussian Residue, lattices. Course Information: Prerequisite(s): Admission to the Mathematics Education Concentrators Program or consent of the instructor.

MTHT 468. Geometry with Applications for Middle Grade Teachers. 4 hours.

Plane and solid figures and their properties. Polygons and polyhedra. Euler's formula. Volume versus surface area. Spacial visualization; two dimensional representations of three dimensional figures. Course Information: Prerequisite(s): Admission to the Mathematics Education Concentrators Program or consent of the instructor.

MTHT 470. Teaching Mathematics with Science: An Activity Approach I. 3 or 4 hours.

Introduction to basic variables (length, area, volume, mass, time) and the Scientific Method (picture, table, graph, questions). Extensive use of TIMS project curriculum. Course Information: 3 undergraduate hours. 4 graduate hours. For elementary school teachers. Prerequisite(s): Admission to the M.S. in the Teaching of Mathematics program (Option for Elementary School Teachers) or consent of the instructor.

MTHT 490. Topics in Teaching Secondary Mathematics. 1-5 hours.

Course content is announced prior to each term in which it is given. Course Information: May be repeated. Students may register in more than one section per term. Prerequisite(s): Prerequisites may vary according to topic.

MTHT 491. Topics in Teaching Elementary/Junior High School Mathematics. 1-5 hours.

MTHT 496. Independent Study. 1-4 hours.

MTHT 510. Introduction to Higher Geometry. 4 hours.

Projective geometry, as an extension of Euclidean geometry, treated synthetically and/or algebraically. Desargues' and Pappus' theorems, subgeometries, conics and the underlying skew field. Course Information: For graduate students in mathematics teacher education programs. Other students enroll in MATH 440. Prerequisite(s): Grade of C or better in MATH 330.

MTHT 530. Mathematical Analysis for Teachers II. 4 hours.

Derivatives, inverse functions, Riemann integral, trigonometric functions, logarithmic and exponential functions. Course Information: Prerequisite(s): Grade of C or better in MTHT 430 or consent of the instructor.

MTHT 550. Concepts and Methods in Elementary and Middle School Mathematics II. 4 hours.

Methods of teaching middle school mathematics: concept development; focus on classroom materials to promote learning. Area, volume, rational numbers, decimals, function machines. Course Information: Prerequisite(s): MTHT 450 or consent of the instructor.

MTHT 560. Introduction to Analytic Geometry and Calculus. 4 hours.

Programmable calculators used to investigate ideas and applications of analytic geometry, differential and integral calculus. Examples and ideas relevant to elementary mathematics and science curicula. Course Information: For elementary school teachers. Do not purchase a calculator until after the first day of class. Prerequisite(s): MTHT 460 or consent of the instructor.

MTHT 565. Teaching Geometry: An Activity Approach. 4 hours.

Informal geometry using manipulatives, elementary topological concepts, polygons, polyhedra, metric geometry, motion geometry, geometric constructions, spherical geometry, introduction to research on the learning of geometry. Course Information: For elementary school teachers. Prerequisite(s): Enrollment in the M.S. in the Teaching of Mathematics program (Option for Elementary School Teachers) or consent of the instructor.

MTHT 575. Principles of Probability and Statistics. 4 hours.

Probability, descriptive and inferential statistics, implications for teaching. Emphasis on collection and analysis of data, classroom activities and software. Course Information: For elementary school teachers. Prerequisite(s): Admission to the M.S. in the Teaching of Mathematics program (Option for Elementary School Teachers) or approval of the department.

MTHT 589. Practicum in Teaching Elementary School Mathematics. 4 hours.

Culminating experience for students in the M.S. in the Teaching of Mathematics (Option for Elementary School Teachers). Major project is required. Supervised weekly seminars. Course Information: Prerequisite(s): Admission to the M.S. in the Teaching of Mathematics program (Option for Elementary School Teachers) and consent of the instructor.

MTHT 590. Topics in Teaching Secondary Mathematics. 1-5 hours.

MTHT 591. Topics in Teaching Elementary/Junior High School Mathematics. 1-5 hours.

MTHT 592. Topics in Advanced Mathematics for Teachers. 1-5 hours.

Course content is announced prior to each term in which it is given. Course Information: May be repeated. Students may register in more than one section per term. For students in the M.S. in the Teaching of Mathematics program. Prerequisite(s): Prerequisite may vary according to topic.

MTHT 596. Independent Study. 1-4 hours.

Statistics Courses

STAT 401. Introduction to Probability. 3 or 4 hours.

Probability spaces, random variables and their distributions, conditional distribution and stochastic independence, special distributions, sampling distributions, limit theorems. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 210; or approval of the department.

STAT 411. Statistical Theory. 3 or 4 hours.

Estimation, tests of statistical hypotheses, best tests, sufficient statistics, Rao-Cramer inequality, sequential probability ratio tests, the multivariate normal distribution, nonparametric methods. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in STAT 401.

STAT 416. Nonparametric Statistical Methods. 3 or 4 hours.

Distribution free tests for location and dispersion problems, one-way and two-way layouts, the independence problem, regression problems involving slopes, detecting broad alternatives, resampling methods. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in STAT 381 or STAT 411.

STAT 431. Introduction to Survey Sampling. 3 or 4 hours.

Simple random sampling; sampling proportions; estimation of sample size; stratified random sampling; ratio estimators; regression estimators; systematic and cluster sampling. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in STAT 411 or STAT 481.

STAT 451. Computational Statistics. 3 or 4 hours.

Modern computationally-intensive statistical methods including Monte Carlo integration and simulation, optimization and maximum likelihood estimation, EM algorithm, MCMC, sampling and resampling methods, non-parametric density estimation. Course Information: 3 undergraduate hours. 4 graduate hours. Extensive computer use required. Prerequisite(s): STAT 411.

STAT 461. Applied Probability Models I. 3 or 4 hours.

Computing probabilities and expectations by conditioning, Markov chains, Chapman-Kolmogorov equations, branching processes, Poisson processes and exponential distribution, continuous-time Markov chains, reversibility, uniformization. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in STAT 401.

STAT 471. Linear and Non-Linear Programming. 3 or 4 hours.

Linear programming, simplex algorithm, degeneracy, duality theorem sensitivity analysis, convexity, network simplex methods, assignment problems. Constrained and unconstrained minima. Quasi-Newton methods. Ellipsoidal methods of Kachian. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 310.

STAT 473. Game Theory. 3 or 4 hours.

Introduction to the basic ideas of game theory. Static and dynamic games; mixed strategies, imperfect information; economic, political and biological applications. Course Information: Same as ECON 473. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): STAT 381; or ECON 270; or equivalents.

STAT 475. Mathematics and Statistics for Actuarial Sciences I. 3 or 4 hours.

Financial mathematics as it pertains to the valuation of deterministic cash flows. Basic concepts and techniques regarding the theory of interest. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): MATH 210.

STAT 481. Applied Statistical Methods II. 3 or 4 hours.

Linear regression, introduction to model building, analysis of variance, analysis of enumerative data, nonparametric statistics, product and system reliability, quality control. SAS and SPSSX applications. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in STAT 381.

STAT 486. Statistical Consulting. 3 or 4 hours.

Introduction to statistical consulting methods and techniques. Handling and transformation of raw data sets in CMS. Statistical analysis of data sets with SAS and SPSSX. Course Information: 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in STAT 411 or STAT 481.

STAT 494. Special Topics in Statistics, Probability and Operations Research. 3 or 4 hours.

Course content announced prior to each semester in which it is given. Topics drawn from areas such as distribution theory; Bayesian inference; discrete optimization; applied probability models; resampling techniques; biostatistics; environmental sampling. Course Information: 3 undergraduate hours. 4 graduate hours. May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department.

STAT 496. Independent Study. 1-4 hours.

STAT 501. Probability Theory I. 4 hours.

Abstract measure theory, probability measures, Kolmogorov extension theorem, sums of independent random variables, the strong and weak laws of large numbers, the central limit theorem, characteristic functions, law of iterated logarithm, infinitely divisible laws. Course Information: Prerequisite(s): MATH 534 or consent of the instructor.

STAT 502. Probability Theory II. 4 hours.

Radon-Nikodym theorem, conditional expectations, martingales, stationary processes, ergodic theorem, stationary Gaussian processes, Markov chains, introduction to stochastic processes, Brownian motions. Course Information: Prerequisite(s): STAT 501.

STAT 511. Advanced Statistical Theory I. 4 hours.

Statistical models, criteria of optimum estimation, large sample theory, optimum tests and confidence intervals, best unbiased tests in exponential families, invariance principle, likelihood ratio tests. Course Information: Prerequisite(s): STAT 411.

STAT 512. Advanced Statistical Theory II. 4 hours.

Basic concepts in decision theory, prior and posterior distributions, Bayesian decision theory, hierarchical models, robustness, minimax analysis, invariance principle, sequential analysis, completeness. Course Information: Prerequisite(s): STAT 511.

STAT 521. Linear Statistical Inference. 4 hours.

Estimation and testing in linear models, generalized inverses of matrices, n-dimensional normal distribution, quadratic forms, likelihood ratio tests, best invariant tests, analysis of variance. Course Information: Prerequisite(s): STAT 411.

STAT 522. Multivariate Statistical Analysis. 4 hours.

Multivariate normal distribution, estimation of mean vector and covariance matrix, T-square statistic, discriminant analysis, general linear hypothesis, principal components, canonical correlations, factor analysis. Course Information: Prerequisite(s): STAT 521.

STAT 531. Sampling Theory I. 4 hours.

Foundations of survey design and inference for finite populations;the Horvitz-Thompson estimator;simple random, cluster,systematic survey designs;auxiliary size measures in design and inference. Course Information: Prerequisite(s): STAT 411.

STAT 532. Sampling Theory II. 4 hours.

Uses of auxiliary size measures in survey sampling; cluster sampling; systematic sampling; stratified sampling; superpopulation methods; randomized response methods; resampling; nonresponse; small area estimations. Course Information: Prerequisite(s): STAT 531.

STAT 535. Optimal Design Theory I. 4 hours.

Gauss-Markov theorem,optimality criteria, optimal designs for 1-way, 2-way elimination of heterogeneity models,repeated measurements, treatment-control ; Equivalence theorem,approximate designs for polynomial regression. Course Information: Prerequisite(s): STAT 521.

STAT 536. Optimal Design Theory II. 4 hours.

Construction of optimal designs: BIB , Latin square and generalized Youden , repeated measurements , treatment-control studies; construction of factorial designs including orthogonal arrays Course Information: Prerequisite(s): STAT 535 or consent of the instructor.

STAT 591. Advanced Topics in Statistics, Probability and Operations Research. 4 hours.

Special topics. Topics drawn from areas such as: Data analysis; Bayesion inference; Nonlinear models; Time series; Computer aided design; reliability models; game theory. Course Information: May be repeated. Prerequisite(s): Approval of the department.

STAT 593. Graduate Student Seminar. 1 hour.

STAT 595. Research Seminar. 1 hour.

Current developments in research with presentations by faculty, students, and visitors. Researchers and practitioners from academia, industry and government will present talks on topics of current interest. Course Information: Satisfactory/Unsatisfactory grading only. May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department.

STAT 596. Independent Study. 1-4 hours.

STAT 598. Master's Thesis. 0-16 hours.

STAT 599. Doctoral Thesis Research. 0-16 hours.

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