# The 50 Best Mathematics Programs in the World Today

Mathematics is, in the view of many, the most basic science. Accordingly, all other scientific disciplines attempt to reconfigure their empirical observations and theoretical insights in terms of mathematics.

In the view of others, math is the universal language of science. Thus, rather than being a science itself, mathematics is the means by which science expresses itself, and consequently that which makes science possible.

Either way, all agree that math is essential to the advance of science. But the impact of mathematics does not end there. Indeed, any area calling for measurement and rigor employs math. This is why math is essential to such diverse fields as finance, engineering, and psychological testing.

Not surprisingly, this makes math one of the most powerful and applicable fields available in the current university curriculum. Mathematics can shed light on problems in almost any area. Thus, students looking to make their mark in an ever-evolving job market need to consider mathematics. Likewise, students wanting to contribute research in any field must have the requisite math background.

But where to study math? A math department needs many things to be successful. Most importantly, it requires a talented scholarly community where innovative professors guide bright students. Many of the programs on this list have produced winners of the Fields Medal (the "Nobel Prize" of mathematics) as well as numerous other honors signifying mathematical achievement.

In addition, a world-class math department needs to develop and maintain strong connections with other well-established mathematics research centers as well as to possess the resources to bring in a steady stream of top-flight visiting scholars, colloquium speakers, and conference participants.

And finally, mathematics particularly benefits from cross-disciplinary collaboration with other departments. The universities on this list are well known for expertise in many fields, and regularly integrate their research in math with various other research endeavors.

For this ranking, we looked to the Center for World-Class Universities operated by Shanghai Jiao Tong University (right). This center specializes in ranking universities as well as their individual programs of study. International in scope and focused on academic performance, these are known as the "Shanghai Rankings."

From the Shanghai Rankings, we therefore identified the 50 best programs in the latest 2015 Academic Ranking of World Universities in Mathematics. Taking this Shanghai Ranking as our point of departure, we researched the most important characteristics of each of the top 50 mathematics programs on the list in order to reveal *why* each university mathematics program appears where it does.

Editor's Note: The 2015 Shanghai Ranking for mathematics is based on two sorts of criteria, namely, awards for achievement in mathematics (such as the Fields Medal) and strength of research (such as measured by publications in high profile journals). While we think that this list gives a generally accurate global representation of the top programs for mathematics, we also find it a bit idiosyncratic.For instance, the University of Chicago, which in past years the Shanghai Ranking has placed in the top ten math programs in the world has now fallen to #34 (note that, year after year, USNews places it in the top ten). At the same time, two Saudi Arabian universities have come out of nowhere and now are highly ranked on this list (see the #6 and #23 positions).

An article in

Sciencesuggests an answer to this meteoric rise in Saudi Arabian mathematics: these Saudi Arabian universities offer lucrative part-time professorships to top mathematicians and scientists, where they need to spend just a few weeks every year but also list the university as a secondary affiliation. These affiliations seem to be boosting the ranking of these schools even though the research that is ultimately responsible for the boost is conducted outside Saudi Arabia.Simply put, some of the programs are on the Shanghai list because their universities are "gaming" the rankings. This phenomenon is not confined to the Shanghai Rankings but seems to infect all highly influential and prestigious rankings (even the revered USNews Rankings). Nonetheless, even if these rankings need to be taken with a grain of salt, we still think they provide value and insight.

## The 50 Best Math Schools

### 1Princeton University

*(Princeton, NJ)*

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. Princeton provided the momentum that pushed American education from obscurity to comparability with European standards in the early 20th century.

Now, Princeton's historic math department carries on the grand tradition. Its impressive 64 faculty members and 17 visitors/researchers push the boundaries of the field. Classroom settings are engaging and supportive, and provide every student with the opportunity to develop their own contributions to the field through tutoring options.

At the graduate level, students spend two years expanding their background in mathematics before focusing on independent research under heavy professor mentorship. Students are expected to attend a number of 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 (a 15-minute walk away), where such luminaries as Albert Einstein, John von Neumann, and Kurt Gödel once did research. Thus, there is never a shortage of world-class thinkers presenting their ideas in Princeton.

- See Princeton's ranking among "The 100 Best Universities in the World."
- See Princeton's ranking among "The 50 Best Physics Schools in the World Today."
- See Princeton's ranking among "The 100 Best Computer Science Programs in the World."

### 2Stanford University

*(Stanford, CA)*

Celebrating 125 years of thriving success and global impact from the heart of California's Silicon Valley, Stanford University has produced a proud academic tradition and astute research achievements. A department of such size (it currently boasts 16 post docs/research assistants, six visiting professors, and 59 professors and lecturers) and resources is able to offer a diverse range of courses.

But more importantly, Stanford is a hub where the leaders in the field gather to push mathematics forward. Professors have specializations in a broad array of subjects, including Financial Math, Number Theory, Representation Theory, and Symplectic Geometry. Twenty-nine famous competitors in the internationally renowned Mathematical Olympiad have affiliations with Stanford.

In addition to the 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 specifically high school students. The Mathematics and Statistics Library is another excellent resource run by the department, as well as SUMO (Stanford University Mathematical Organization).

- See Stanford's ranking among "The 100 Best Universities in the World."
- See Stanford's ranking among "The 100 Best Computer Science Programs in the World."
- See Stanford's ranking among "The 50 Best Physics Schools in the World Today."

### 3Harvard University

*(Cambridge, MA)*

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

Being comprehensive in nature, the Mathematics Department offers a variety of programs and research areas, from Bachelor's to PhD levels. Current faculty members have strong interest in Number Theory, Diophantine Geometry, Modular Forms, Differential Equations, Lie Groups, and Mathematical Physics. The majority of programs require a Capstone project or Senior Thesis before graduation. Seminars, tutoring centers, and peer-led clubs offer additional opportunities for networking and class work assistance.

The Harvard department runs multiple regular conferences such as the Current Developments Conference and the Conference on Geometry and Topology. Harvard, being near Boston, is also at the center of America's university capital. With schools like MIT, Boston College, Boston University, and Tufts within miles, Harvard affords its faculty and students a massive network of additional resources and people to work with.

- See Harvard's ranking among "The 100 Best Universities in the World."
- See Harvard's ranking among "The 100 Best Computer Science Programs in the World."
- See Harvard's ranking among "The 50 Best Physics Schools in the World Today."

### 4University of California, Berkeley

*(Berkeley, CA)*

Overlooking the idyllic San Francisco Bay, the Mathematics Department at Berkeley has been recognized for its outstanding faculty members and cutting-edge research. The 55 full-time professors represent most major fields of study and have research experience in Algebra, Mathematical Analysis, Applied Mathematics, Geometry/Topology, Mathematical Logic, and Probability. They are assisted by 25--30 post-doctoral candidates.

The 180 graduate students and 500 undergraduate students can expect a personalized educational experience with support from the dedicated admissions staff, stellar tutoring centers, experienced professors, and knowledgeable peers. Depending on the chosen degree program, students may be asked to complete the Calculus Placement Exam and/or the Advance Placement Exam.

The comprehensive Mathematical Library and the Mathematical Sciences Research Institute are both sponsored by the department. The latter attracts about 1,700 mathematicians from around the world annually. Other affiliated research centers include the Mathematics Department at Lawrence Berkeley National Laboratory and the Adolf C. and Mary Sprague Miller Institute for Basic Research in Science. Berkeley's Math department has two National Science Foundation founded research training groups.

- See UC Berkeley's ranking among "The 100 Best Universities in the World."
- See UC-Berkeley's ranking among "The 50 Best Physics Schools in the World Today."
- See UC Berkeley's ranking among "The 100 Best Computer Science Programs in the World."

### 5Pierre and Marie Curie University (Paris VI)

*(Paris, France)*

Labeled as one of the most research active institutions in France, the Pierre and Marie Curie University carries on the same heritage of excellence in science and medicine as its namesake patrons did. Offering a full range of academic degrees in both pure and applied mathematics, the department of Mathematics is a cornerstone of the school and one of the largest in the area.

With over 290 teachers and researchers on staff and 50 researches who oversee more than 250 postgraduates, Paris VI boasts one of the largest mathematics centers in the world. Thus, students can find researchers interested in almost any area of the field. Many of these scholars study at one of the department's five research laboratories, four of which are associated with the highly respected French Center for Scientific Research. The department admits over 5,000 students each year who can take advantage of the many opportunities available.

The majority of courses are also offered via online distance education. Tutoring in English is available upon request. Numerous conferences and seminars, summer school, and the Mathematical Library are also available to students.

- See Pierre and Marie Curie's ranking among "The 100 Best Universities in the World."
- See Pierre and Marie Curie's ranking among "The 50 Best Physics Schools in the World Today."

### 6King Abdulaziz University

*(Jeddah, Saudi Arabia)*

King Faisal bin Abdulaziz of Saudi Arabia approved the building of a University bearing his name in 1967. Opening in 1968 with just under 100 students, the University has made great strides to spread higher education to the surrounding area and made tremendous progress as a public research institution.

Established in conjunction with the Faculty of Science in 1973, the Mathematics Department of King Abdulaziz University is the leading academic and research program in the Middle East. The school has made considerable efforts to attract first-class, international talent, who join the department as visiting faculty. This attempt to integrate the school into the larger arena of academic scholarship has rapidly propelled it from obscurity to a reputable worldwide presence.

Students have a variety of degree tracks and research areas from which to choose. Areas of specialization include Analysis, Differential Equations, Algebra, Topology, Differential Geometry, Numerical Analysis, and Applied Mathematics. The typical undergraduate degree will require 128 credit hours for completion. Master's and Doctoral level studies are also available.

### 7University of Oxford

*(Oxford, United Kingdom)*

As one of the oldest universities in the world, Oxford has had plenty of time to develop an outstanding reputation in many fields. The Mathematics and Science Departments at Oxford were home to historic alumni such as Edwin Hubble, Robert Hooke, and Stephen Hawking.

This naturally lends itself towards departmental collaboration through the Mathematical Institute at Oxford. Research is performed together with physicists, medical professionals, engineers, social scientists, and others who contribute to the success of the department. Both the Pure and Applied Mathematics programs are held in the same building, further encouraging student partnerships.

Approximately 1,200 undergraduate and graduate students are enrolled in the various programs taught by 170 expert faculty members. A total of 16 focus groups and centers on campus conduct the majority of the research. Areas include the Geometry Group, History of Mathematics Group, and the Oxford Center for Nonlinear PDE. The department also networks with the Oxford Solid Mechanics group and the Clay Mathematical Institute.

- See Oxford's ranking among "The 100 Best Universities in the World."
- See Oxford's ranking among "The 50 Best Physics Schools in the World Today."

### 8University of California Los Angeles (UCLA)

*(Los Angeles, CA)*

Offering a variety of degree programs from Bachelor's to Doctoral level, the department of Mathematics at UCLA is dynamic and engaging in its educational approach. Presented with the Exemplary Program or Achievement Award from the American Mathematical Society in 2007, the department has been given high praise for its academic and research success.

UCLA faculty and students benefit from the Institute for Pure and Applied Mathematics. Besides from bringing in numerous world class mathematicians for public lectures and running various programs and seminars for students, the institute also runs extended three-month programs with visiting scholars. Here, a collection of highly respected thinkers gather for a week of tutorials followed by several workshops that conclude with work completed at the Arrowhead Conference Center.

The math-related undergraduate majors cover a wide range of fields, including degrees in Mathematics, Applied Mathematics, Mathematics of Computation, Mathematics for Teaching, Mathematics/Economics, and Financial Actuarial Mathematics. 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 the Curtis Center and Los Angeles Math Circle.

- See UCLA's ranking among "The 100 Best Universities in the World."
- See UCLA's ranking among "The 100 Best Computer Science Programs in the World."
- See UCLA's ranking among "The 50 Best Physics Schools in the World Today."

### 9University of Cambridge

*(Cambridge, United Kingdom)*

Home to Isaac Newton and many other great scientists and mathematicians down the ages, Cambridge is one of the oldest centers of learning in the world. Today, it is also a large research university with 31 colleges and 150 departments/faculties.

The Faculty of Mathematics is broken down into two departments: Applied Mathematics and Theoretical Physics, and Pure Mathematics and Mathematical Statistics. The department of Applied Mathematics employs 50 academic faculty members who monitor 110 research students. The department of Pure Mathematics has 42 academic faculty members who also help manage the Statistical Laboratory. The undergraduate studies in Mathematics are known as the "Mathematical Tripos." Students may complete the program in three or four years and will be eligible for further study at the graduate levels.

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

- See Cambridge's ranking among "The 100 Best Universities in the World."
- See Cambridge's ranking among "The 100 Best Computer Science Programs in the World."
- See Cambridge's ranking among "The 50 Best Physics Schools in the World Today."

### 10University of Paris-Sud (Paris XI)

*(Orsay, France)*

Well known in France for its research in Mathematics and Science, the University of Paris-Sud, also known as Paris XI, offers a broad range of disciplines for students from around the world. Founded in 1971, the school has already grown to a student body of 30,000 pupils and 1,800 faculty.

Despite its youth the school has been awarded the Fields Medal on five occasions, making Paris XI tied for third among universities receiving the subject's most sought-after accolade. Paris XI has also produced two Nobel Prize--winners in physics.

The school maintains partnerships with over 100 international laboratories, 11 of which have been deemed Laboratories of Excellence and receive funding from the French government. The school is especially noted for its physics laboratories, which commonly collaborate with its mathematics resources.

- See Paris Sud's ranking among "The 100 Best Universities in the World."
- See Paris Sud's ranking among "The 50 Best Physics Schools in the World Today."

### 11University of Minnesota

*(Minneapolis/St. Paul, MN)*

The University of Minnesota has established five campuses which offer a full range of degree programs. Going above and beyond the academic expectations is the College of Science and Engineering's School of Mathematics, located at its flagship Twin Cities campus.

A full panoply of undergraduate majors, Master's programs, and PhD studies makes the School of Mathematics comprehensive in nature and research intensive. The department has 19 particularly strong areas of research excellence, including Applied Mathematics, Combinatorics, Lie Theory, Number Theory, Probability and Stochastic Processes, and Real, Harmonic, and Functional Analysis. Degree programs specializing in education and finance are also available.

Students will also find a number of events, programs and centers, seminars, and even clubs dedicated to math. The School is also proud to host the Student Chapter of the Association for Women in Mathematics.

### 12Massachusetts Institute of Technology (MIT)

*(Cambridge, MA)*

MIT has the reputation of being 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 the majority of students throughout all programs in the school. 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 Prizes.

Divided into Pure versus Applied Mathematics, the department is home to approximately 330 undergraduate students and 115 graduate students. Undergraduate students have the concentration options of Applied Mathematics, Theoretical Mathematics, General Mathematics, and Mathematics with Computer Science.

The graduate studies and research areas, also divided into Pure and Applied Mathematics, include Algebra, Geometry, Representation Theory, Computational Biology, and Theoretical Computer Science. Students can find all the academic support they need, from tutoring to scheduling, through the adept Math Academic Services team.

- See MIT's ranking among "The 100 Best Computer Science Programs in the World."
- See MIT's ranking among "The 50 Best Physics Schools in the World Today."
- See MIT's ranking among "The 100 Best Universities in the World."

### 13University of Warwick

*(Warwick, UK)*

With little more than 50 years of academic history, the University of Warwick is finding innovative ways to expand its services and leave a mark on history. Founded in 1965, the Mathematics Department has been integral to the school since its inception. Originally focusing on just three areas of research, Analysis, Algebra, and Topology, the department expanded into Number Theory, Discrete Mathematics, and Applied Mathematics.

Contrary to other schools and research departments, Warwick combines Pure and Applied Mathematical research for a unique academic atmosphere and increased productivity. Centers and programs for research opportunities include the Center for Discrete Mathematics and its Application, the Hyperbolic Geometry program, and the Complexity Complex.

Without compromising quality, the department has one of the largest undergraduate student acceptance rates in the UK. Joint degrees are available at the undergraduate level with Economics, Philosophy, and Business, while graduate students are encouraged to be cross-disciplinary through seven top Doctoral Training Centers.

### 14Swiss Federal Institute of Technology (ETH)

*(Zurich, 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 and today is recognized as an international leader in these fields. The technical background of the school has given it a thorough understanding of how essential Mathematics is in today's modern society.

Providing an ideal environment for study and research, the Mathematics Department has an extensive history of excellence (Einstein once studied here). There are currently 50 full-time professors for over 700 students through all the degree programs. In addition to the traditional undergraduate and graduate studies, Swiss Federal also offers Teacher training and Continuing Education opportunities.

A number of seminars and exceptional research centers are managed by the department. Networking relationships have been established with the ETH Institute for Theoretical Studies and the National Center of Competence in Research.

- See ETH's ranking among "The 100 Best Universities in the World."
- See ETH's ranking among "The 100 Best Computer Science Programs in the World."
- See ETH's ranking among "The 50 Best Physics Schools in the World Today."

### 15Texas A&M University

*(College Station, TX)*

Engaged in research and education in all areas of Mathematics, the Department of Mathematics at Texas A&M strives to provide quality results with global impact. Collaboration between departments is strongly encouraged and already established with the faculty of Computer Science, Physics, Life Sciences, and Engineering. Mutual cooperation and respect has made research areas plentiful and productive.

The outreach of the department extends beyond the 25,000 students enrolled yearly and out to the surrounding community. Middle school and high school programs are actively sparking students' interest in mathematics at an early age, while better equipping their teachers. The university campus, too, is replete with similar opportunities. The Society for Industrial and Applied Mathematics (SIAM) just approved A&M's chapter.

Undergraduate studies are flexible and comprehensive. Students will graduate with one of three degrees, BA in Mathematics, BS in Mathematics, or BS in Applied Mathematics. The Master's tracks include the traditional program, the teaching program, or the applied program with concentrations in Computational, Industrial, or Biological Mathematics. PhD training is also available in a wide variety of sub-disciplines.

### 16University of Michigan

*(Ann Arbor, MI)*

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, to the current total of 145 academic faculty members. Serving hundreds of students each year, the department offers a diverse number of programs, research areas, and outreach opportunities.

Undergraduate students have four main tracks to choose from: Teaching Mathematics, Actuarial Mathematics, Mathematics of Finance and Risk Management, and Mathematical Sciences, which is subdivided into Pure and Applied Mathematics. The Master's program offers three main degrees with multiple subdivisions within each: Quantitative Finance and Risk Management, Applied and Interdisciplinary Mathematics, and the general Mathematics Master's Degree.

Doctoral studies at Michigan are based on two semester courses in algebra, analysis, applied analysis, and geometry/topology. After establishing a strong foundation in these areas students will then begin developing their own, unique 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, and Number and Probability Theory.

- See Michigan's ranking among "The 100 Best Universities in the World."
- See Michigan's ranking among "The 100 Best Computer Science Programs in the World."
- See Michigan's ranking among "The 50 Best Physics Schools in the World Today."

### 17Columbia University

*(New York, NY)*

The Mathematics Department of Columbia University is part of a preeminent Ivy League institution located in upper Manhattan. With an abundance of resources at its disposal, the department's course offerings are listed with 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 Mathematic subjects, the PhD also requires reading knowledge of a second language. Columbia divides its doctoral work in math into a standard 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.

Columbia divides its research in several areas, including algebraic geometry, geometric analysis, mathematical physics, number theory, probability and financial mathematics, and 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 such as those sponsored by the Minerva Research Foundation.

- See Columbia's ranking among "The 50 Best Physics Schools in the World Today."
- See Columbia's ranking among "The 100 Best Universities in the World."

### 18University of Washington

*(Seattle, WA)*

Mathematics is understood as both a science and an art at the University of Washington. The 60 faculty members see it as a privilege to educate the 100 graduate students and over 800 undergraduate students.

The undergraduate students have five main degree programs to choose from: two Bachelor of Science tracks and three Bachelor of Arts tracks. Each program will work towards a senior thesis with the possibility of departmental honors. At the graduate level there are five central Master's programs and Doctoral studies. Students will be prepared to complete both oral and written competency exams.

The school also partners with Microsoft to run summer research internships. Students interested in Washington's program can also earn a Master's in Applied Mathematics online over the course of three years.

### 19University of Wisconsin

*(Madison, WI)*

As the first public university established in the state, the University of Wisconsin's flagship campus at Madison has had a significant impact on the surrounding community and the world at large. The Mathematics Department, in particular, has an impressive history of academic success and outreach. Currently over 43 faculty members contribute their time and expertise to the benefit of the students.

A full range of degrees, from certificate to PhD, is offered to students both in class and online. Additional resources include the Mathlab, a free tutorial program for those who require assistance with classwork or projects. The department also offers Non-Math Major Placement advising for those with a Mathematics requirement to fill. The department engages in community outreach through the Talent Search, Math Circle, Wisconsin Mentorship Program for Women in Mathematics and Science, and the Math Club.

Wisconsin also runs two separate research training groups which cover topics such as algebraic geometry, applied algebra, number theory, and analysis and applications. These research training groups are funded by the National Science Foundation.

- See Wisconsin's ranking among "The 50 Best Physics Schools in the World Today."
- See Wisconsin's ranking among "The 100 Best Universities in the World."

### 20Duke University

*(Durham, NC)*

Ranked as the seventh-wealthiest private university in America, Duke University has impressive funds at its disposal. The Mathematics Department has seen its share of the financial resources, enough to establish 13 separate groups and centers dedicated to high-quality research, including the Mathematical Biology group, the Center for Theoretical and Mathematical Sciences, and the Differential Geometry group.

There are currently 30 tenured and tenure-track faculty members for approximately 98 undergraduate majors and 53 graduate students. Covering a broad range of disciplines, from Analysis and Geometry to Abstract Algebra and Topology, the professors are able to bring a wealth of knowledge and personal experience to each classroom.

Approximately one third of the Mathematics majors are women. Duke University has established a mentoring program for women and run by women, titled the "Noetherian Ring," to encourage further participation in Mathematics and the Sciences.

### 21University of Texas

*(Austin, TX)*

Within an already large and impressive institution, the Mathematics Department at the University of Texas's flagship Austin campus has 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, among other award recipients. All of the professors help create a stimulating academic environment for the 138 graduate students and 900 undergraduate students.

The department 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, Geometry, Combinatorics, Computational Biology, Dynamical Systems, and Scientific Computation. Regular Colloquium and Seminars are held with presentations from leaders in the field.

Community outreach groups include the Saturday Morning Math group targeting junior and senior high students and the Math Teacher's Circle of Austin.

- See UT Austin's ranking among "The 100 Best Computer Science Programs in the World."
- See UT Austin's ranking among "The 100 Best Universities in the World."
- See UT-Austin's ranking among "The 50 Best Physics Schools in the World Today."

### 22City University of Hong Kong

*(Kowloon Tong, Hong Kong SAR)*

Formed in 1991, the current Mathematics Department 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 with a commitment to both research and education.

Of its many achievements, the Mathematics Department opened its Bachelors of Science in Computing Mathematics in 1994 and its Master's of Science in Applied Mathematics in 1997. With numerous other programs to choose from, 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, studying areas such as Approximation Theory, Fluid Machines, Mathematical Finance, Nonlinear Elasticity, Partial Differential Equations, and Wave Propagation. The Liu Bie Ju Center for Mathematical Sciences has played a large role in the organization and dissemination of research achievements.

### 23New York University

*(New York, NY)*

Being at the heart of the economic and business hub of the United States, students in the Mathematics Department at New York University have a distinct advantage. With extraordinary networking opportunities and the dedication of 70 notable faculty members, students can excel through all degree programs.

Numerous undergraduate programs are offered which are divided 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 the MS in Mathematics, MS in Scientific Computing, or the MS in Mathematics in Finance. Doctoral studies are available.

The research centers and groups on 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 PDE, Dynamical Systems and Ergodic Theory, Probability Theory, and Scientific Computing.

### 24King Fahd University of Petroleum and Minerals

*(Dhahran, Saudi Arabia)*

Known as one of the most selective schools in Saudi Arabia, the King Fahd University of Petroleum and Minerals is a specialized institution focusing on the Sciences and Engineering. Taking advantage of the vast petroleum and mineral resources in the area, the school has dedicated itself to educating dynamic leaders for the industry.

Six main colleges provide the bulk of the undergraduate and graduate programs: College of Engineering Science/Applied Engineering, College of Sciences, College of Environmental Design, College of Industrial Management, College of Computer Science and Engineering, and the College of Petroleum Engineering and Geosciences. Approximately 5,000 undergraduate students are currently enrolled throughout the colleges.

Being so heavily involved in the sciences, Mathematics is an integral part of the majority of classes and programs. The department of Mathematics and Statistics does manage its own Bachelor programs, as well as two research groups: the Commutative Algebra Research Group and the Fixed Point Theory Applications Research Group.

### 25Aix-Marseille University

*(Marseille, France)*

Located in the great Mediterranean port city of Marseille, France's second-largest city, Aix-Marseille University is technically the youngest institution for higher education in the nation. Created from a merger of three province universities, the current structure of the school has been in place only since 2012. The Mathematics Department is one of eight sections comprising the Faculty of Science.

Academic training as an undergraduate provides students with the foundations necessary for further education at the graduate levels. Professional Licenses, Master's Degrees, Doctoral studies, and Continuing Education classes are also available. The Mathematics License offers basic training in Analysis, Algebra, Probability, and Statistics.

With a total of 130 research structures throughout the school, academic advancement is integral to all departments. Within the Mathematics Department over 20 areas of research are in progress including Coding Theory, Complex Geometries, Risk Modeling, Wave Propagation Phenomena, and Mathematics Applied to Health Sciences.

### 26École Normale Supérieure

*(Paris, France)*

Conceived and initiated during the French Revolution, École Normale Supérieure (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 Medalists coming from ENS, the school has gained a reputation for mathematical genius. Adrien and his son Raphael Douady are just two of the recent and well-respected Mathematicians from ENS.

Approximately 200 students are enrolled in the Mathematics Department. The majority are partaking in a three-year program culminating in a Master's degree in Pure or Applied Mathematics. Most students will continue on to obtain their PhD, as well. Every year the school opens its doors to 30 of the most promising international students for enrollment in this prestigious program.

- See École Normale Supérieure's ranking among "The 50 Best Physics Schools in the World Today."
- See École Normale Supérieure's ranking among "The 100 Best Universities in the World."

### 27Kyoto 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 Mathematics Department, 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 PhD candidates are involved with intensive research and study.

The numerous research groups cover Algebraic Geometry, Number Theory, Differential and Algebraic Topology, Probability Theory, Partial Differential Equations, Harmonic Analysis, Applied Mathematics, and Discrete Geometric Analysis.

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 will usually continue on for graduate studies.

- See Kyoto University's ranking among "The 50 Best Physics Schools in the World Today."
- See Kyoto University's ranking among "The 100 Best Universities in the World."

### 28Paris Dauphine University (Paris IX)

*(Paris, France)*

The Paris Dauphine University (Paris IX) embraces international students and study-abroad opportunities with a welcoming spirit. The global-mindedness of the school has spread throughout its departments, allowing for increased collaborative research and scheduling flexibility.

The Mathematics Department embraces this eclectic approach to education by offering multidisciplinary classes. This internationality allows for easy transfer to degrees in Engineering, Business, Economics, or other math intensive fields. Overall, Paris Dauphine offers 26 double Bachelor's and Master's degrees and maintains 300 international relationships with other universities.

The majority of undergraduate and graduate programs in the Mathematics Department are three-year tracks. A broad range of topics are covered at Paris IX, but the main focus of the academic and research areas is either in Mathematics or sister fields like Computer Science and Economics. The expert faculty members dedicated to teaching students include 10 Fields Medalists.

### 29University of Bonn

*(Bonn, Germany)*

A leading institution in Germany for higher education, the University of Bonn has dedicated itself to superior education, cutting-edge research, and global outreach. The Mathematics Department 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, each committed to different aspects and research area of Mathematics.

The Mathematical Institute, the Institute for Applied Mathematics, the Institute for Numerical Simulation, and the Research Institute for Discrete Mathematics all provide unique networking and study opportunities. The distinguished faculty members include two Fields Medalists.

Other national relationships include partnerships with the Max Planck Institute for Mathematics and the Cluster of Excellence 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 the Mathematical Library and monetary grants and prizes for young students and researchers.

### 30University of California San Diego

*(La Jolla, CA)*

The Mathematics Department at the University of California San Diego offers a number of excellent undergraduate degrees in math-related fields, including General Mathematics, Applied Mathematics, and Mathematics in conjunction with Scientific Computation, Secondary Education, Applied Science, Computer Science, Economics, and Probability and Statistics. 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 Computation Science or Statistics.

Yet, despite these many opportunities to connect mathematics to cutting-edge technology, San Diego also places an uncommon emphasis on the social aspects of this objective subject. The curriculum here also covers the historic development of the field, as well as its connection to the humanities.

Approximately 20 research interest groups have been established representing nearly all areas of Mathematics, including Bioinformatics, Complex Variables, Logic and Computational Complexity, Mathematics Education, and Representation Theory. The Mathematics Department utilizes over 60 faculty to teach roughly 100 PhD candidates and 35 Master's Students.

- See UC San Diego's ranking among "The 100 Best Computer Science Programs in the World."
- See UC San Diego's ranking among "The 100 Best Universities in the World."

### 31Moscow 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---the academic programs and research initiatives are some of the best in the nation.

The school has established two institutions 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, the Calculus of Variations, Mechanized Wing Theory and the Theory of Screws, and 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 Mathematical Modeling, Systems Analysis, Game Theory and Operations Research, and Mathematical Logic.

### 32Paris Diderot University (Paris VII)

*(Paris, France)*

Though it is a comprehensive university with studies in the Humanities, Sciences, and Medicine, Paris Diderot University is most well known for its education and research successes in the field of Mathematics. Working in conjunction with Pierre and Marie Curie University (Paris VI), Paris VII's Mathematics Department has discovered many fundamental theories of Probability in its Laboratory of Probability and Random Models.

The first two years of obtaining any degree at Paris Diderot are spent studying foundational and multidisciplinary courses. The third year of a Mathematics degree is organized into three sections: Fundamental Mathematics, Applied Mathematics, and Mathematics in Education. Students can also study Mathematics together with the related disciplines of Physics and Information Technology.

Faculty members in the department not only offer quality education, but also personal experience and individualized assistance. Of the past and present educators associated with the school, two have been awarded Nobel Prizes, and one has received the Fields Medal.

### 33Hebrew University of Jerusalem

*(Jerusalem, Israel)*

As an institution that had Albert Einstein and Sigmund Freud on its first Board of Governors, the Hebrew University of Jerusalem has set high standards of excellence for all departments, including the department of Mathematics. In total, the Faculty of Science, which houses the Mathematics Department, has 240 expert faculty members, 2,000 undergraduates, and 1,400 Master's and Doctoral candidates.

The Bachelor degrees provide students with general introductory knowledge of a broad range of Mathematics disciplines. Students are encouraged to pursue graduate-level course work through Master's or PhD programs. The Master's programs require an overall 80 average in order to be considered a viable candidate.

The Faculty of Science manages a total of six high-ranking research laboratories, all of which---especially the Einstein Institute---draw from the school's mathematicians. Popular areas of study include Algebra and Group Theory, Representation Theory, Ergodic Theory, Probability, Combinatorics, and Game Theory.

### 34University of Chicago

*(Chicago, IL)*

Receiving its start-up capital from the wealthy John D. Rockefeller in 1890, the University of Chicago quickly established its Mathematics Department from the onset. Now a well-established program, the department offers a wide range of degree tracks and engaging classes taught by expert faculty members.

There are four Bachelor programs available: the BA in Mathematics, the BS in Mathematics, the BS in Applied Mathematics, and the BS in Mathematics with specialization in Economics. 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 PhD candidates yearly. Students are expected to participate in both research and peer-run seminars, in addition to presenting an oral topic dissertation and written report. Research interests groups include Algebra, Algebraic Geometry, Applied Mathematics, Analysis, Probability Theory, Topology and Dynamics, Logic, and Theoretical Computer Science.

- See University of Chicago's ranking among "The 50 Best Physics Schools in the World Today."
- See University of Chicago's ranking among "The 100 Best Universities in the World."

### 35Pennsylvania State University

*(University Park, PA)*

One of the largest Universities in the United States, Penn State has the resources necessary for a world-class, comprehensive Mathematics Department. There are 53 tenured and tenure-track faculty members with international recognition for ground-breaking research. Awards and accolades include members of the National Academy of Sciences, the American Academy of Arts and Sciences, and the Royal Society.

The undergraduate program confers Bachelor of Science and Bachelor of Arts degrees in six areas: Systems Analysis, Actuarial Mathematics, Computational Mathematics, General Mathematics, Applied and Industrial Mathematics, and Graduate Studies. For the Graduate program, students can choose between a thesis or non-thesis Master's degree and Doctoral studies. All students are welcomed to join the departmental coffee and tea hour for conversation and networking.

Aside from the academic opportunities which include various research groups, running seminars, and workshops, the department is also very supportive of women in Mathematics.

- See Penn State's ranking among "The 50 Best Physics Schools in the World Today."
- See Penn State's ranking among "The 100 Best Universities in the World."

### 36University of Maryland

*(College Park, MD)*

Located just nine miles from the U.S. capital, the University of Maryland's flagship College Park campus provides students with an educational experience worthy of the many accolades it has achieved. Its 65 distinguished faculty members teach at Maryland's highly respected Math Department. These faculty also share their building space with the Engineering and Physical Sciences Library, which allows for easy access to the latest academic materials and resources from sister fields.

For the undergraduate student, there are four major tracks to select from: the Traditional degree program, the Secondary Education program, the Statistics program, and the Applied Mathematics program.

Graduate students have the support of the Brin Postdoctoral program. This allows graduate students the opportunity for a one-to-three year teaching appointment with a minimum requirement of one course per semester. Graduate studies are divided between the standard math program and the statistics program.

- See Maryland's ranking among "The 100 Best Universities in the World."
- See Maryland's ranking among "The 100 Best Computer Science Programs in the World."
- See Maryland's ranking among "The 50 Best Physics Schools in the World Today."

### 37Lanzhou University

*(Lanzhou, Gansu Province, China)*

Known as the best institution in the northwestern region of China, Lanzhou University has a well-established history of excellence in Chemistry, Biology, Physics, Mathematics, and Geology. With a total of 84 Bachelor's programs, 187 Master's programs, and 56 Doctoral programs, students are able to make a complete study of Mathematics at any level.

The School of Mathematics and Statistics is just one of 25 areas covering 11 disciplines. Other faculties which integrate Mathematics throughout the curriculum include the School of Information Science and Engineering, the School of Physical Science and Technology, and the School of Chemistry and Chemical Engineering.

All of the schools throughout the University place a heavy emphasis on peer-reviewed research. On average, faculty produce over 1,000 publications each year. To supplement the global perspective of the research groups, Lanzhou University has maintained partnerships with over 100 universities worldwide in over 80 countries.

### 38Georgia Institute of Technology

*(Atlanta, GA)*

When it opened in 1885, Georgia Tech initially offered only a degree in Mechanical Engineering. Though it is still a specialized institution focusing on Science and Technology, the degree programs have expanded to include Architecture, Business Administration, Computing, and Liberal Arts.

The Mathematics Department is heavily involved with the majority of student curricula, and so 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 enrolled in the Math Department, who often work alongside of the other 25 Master's and Doctoral programs available.

Faculty interests in research range from Algebra and Differential Equations to Mathematical Biology and Physics. With various conferences, seminars, and colloquia, students sit at the forefront of the newest ideas and research in the Mathematics community.

- See Georgia Tech's ranking among "The 100 Best Computer Science Programs in the World."
- See Georgia Tech's ranking among "The 100 Best Universities in the World."

### 39California Institute of Technology (Caltech)

*(Pasadena, CA)*

Caltech is unique in that it is both a very small college with just over 2,000 students, and yet is populated by many of the best scientists and mathematicians in the world. This gives the Mathematics Department at CalTech a unique and innovative approach to education.

Attending Caltech feels like being in an intimate mentor relationship with an impressive 3-to-1 student/faculty ratio. But at the same time, each student has access to world-class resources. The latter include seminars, topics classes, and even a few light-hearted things like a pizza course. The 17 faculty members of the math department are excellent resources of knowledge and field based experience for the 67 undergraduates and 34 graduates. Undergraduate students interested in the Mathematics major will participate in a four-year track ending in a Bachelor's of Science.

After the required Liberal Arts classes have been completed, students in their junior and senior years should take a minimum of 18 credits per semester towards the Mathematics major. Senior students are encouraged to complete a Bachelor's thesis. Throughout the graduate program, whether Master's or Doctoral, regular attendance at seminars and colloquia is encouraged. The application process requires students to complete a qualifying exam.

- See Caltech's ranking among "The 100 Best Universities in the World."
- See Caltech's ranking among "The 100 Best Computer Science Programs in the World."
- See Caltech's ranking among "The 50 Best Physics Schools in the World Today."

### 40Chinese University of Hong Kong

*(Shatin, NT, Hong Kong SAR)*

At the Chinese University of Hong Kong, Mathematics is an essential discipline for all graduating students. For those declaring Mathematics as a major there are two tracks: the Bachelors of Science in Mathematics and the Bachelors of Science in Mathematics and Information Engineering. The Mathematics and Education degree is managed by the Faculty of Education.

Courses throughout the undergraduate studies cover information from General Mathematics Introduction through Fourier Analysis, Game Theory, and Research Seminars. Recently, a new standard has been put in place for students wishing to double-major in Mathematics, allowing for an additional year to complete classes. Graduate students have numerous fields of specialization to select from, including Algebra and Number Theory, Analysis, Computational Mathematics, Geometry and Topology, and Partial Differential Equations.

The programs run for two to three 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.

### 41University of Geneva

*(Geneva, Switzerland)*

Originally established as a theological seminary by John Calvin, the University of Geneva has grown to the second-largest university in Switzerland by number of students. Now offering a wide range of subjects as a secular school, Mathematics is among the many disciplines.

Students obtaining a Bachelor's of Science in Mathematics will typically finish the 180 required credit hours in six semesters. Course content includes the traditional elementary Math classes of Algebra and Geometry all the way to higher-level Mathematics courses in Tilings and Symmetries, Hopf Algebra, and Riemann surfaces.

The Master's of Science in Mathematics requires an additional 90 credit hours over approximately three semesters. Offering more advanced training in Mathematics, there are several areas of specialization from which students can select. Areas of study and research include Algebra and Geometry, Analysis and Mathematical Physics, Probability and Statistics, and Numerical Analysis. Doctoral studies are also available.

### 42Shanghai Jiao Tong University

*(Shanghai, China)*

Originally established by an imperial edict in 1896, Shanghai Jiao Tong University is one of the oldest and most prestigious institutes of higher learning in China. Course offerings include a wide variety of educational opportunities through 63 undergraduate programs, 250 Master's programs, and 203 Doctoral programs. Admission to the school is highly competitive.

The School of Sciences covers the Mathematics and Physics degrees. The Mathematics courses include a broad range of topics, including Mathematical Experiment, Analysis, Algebra, Engineering Mathematics, Differential Equations, and Probability Theory. Graduate training started in 1996 and offers more detailed and intensive courses. A total of 116 faculty members are involved in the Mathematics Department, with 96 percent of the professors holding Doctorates.

Two research facilities are managed by the department: the Institute of Mathematical Sciences and the Institute of Complex Systems. There are also a number of affiliated programs, including the Institute of Aerospace Science and Technology and the Institute of Energy.

### 43Peking University

*(Beijing, China)*

Located in China's capital (which was formerly known as "Peking"), Peking University has 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 fields, and 173 Doctoral fields. The study of Mathematics can be found at each level.

The School of Mathematical Sciences is dedicated to the complete education of its students, while also maintaining a level of research excellence. Of the 12 National Key Laboratories run by the University, the Mathematics Department manages the Key Laboratory of Mathematics and Applied Mathematics. Graduate students and professors have the opportunity to publish research findings in the monthly journal, *Acta Physico-Chemica Sinica*.

International students are welcomed with open arms to the Department of Mathematics. The Graduate School alone has maintained global relations with 128 institutions of higher education in over 40 countries.

### 44Rutgers University

*(New Brunswick, NJ)*

Rutgers University, which is the state of New Jersey's public university system (and also possesses one of its most well-respected academic programs), maintains an academic rigor comparable to its Ivy League neighbors. Serving all students from Liberal Arts majors to Accounting, Pharmaceuticals, and the Mathematical Sciences, the Mathematics Department has ensured an appropriate class for everyone. With the aid of the Mathematics Placement exam, students can find the course that is right for their individual needs.

Individuals majoring directly in Mathematics have the option to extend their studies out one additional year to complete a five-year combined BA/MA program. The MS program has two options: traditional studies or the Mathematical Finance option. Approximately 85 Doctoral candidates are mentored each year.

As a supplement to the 50 graduate courses, weekly seminars, Friday colloquia, and special lecture series are offered. Five research centers provide the resources necessary for significant research.

- See Rutgers' ranking among "The 50 Best Physics Schools in the World Today."
- See Rutgers' ranking among "The 100 Best Universities in the World."

### 45Imperial College of Science, Technology, and Medicine

*(London, UK)*

As the product of mergers between three technical schools and four medical institutes, Imperial College is looked upon as a leading expert in the areas of Science, Engineering, Medicine, and Business. The Mathematics Department is one of the largest in the UK. Approximately 750 undergraduates, 150 Master's students, and 150 doctoral candidates are enrolled in the department.

At the undergraduate level, three- and four-year Mathematics programs are available, as well as three joint degrees in Mathematics with other disciplines. In an effort to meet the growing industrial demand for better mathematicians, the department is offering four one-year MSc programs. Subjects covered include Applied Mathematics, Pure Mathematics, Mathematical Finance, and Statistics.

Though the department works as an integrated unit, individual research sections have been formed for organizational purposes. Pure Mathematics, Applied Mathematics, Mathematical Physics, Numerical Analysis, Statistics, and Mathematical Finance are the most active research areas.

- See Imperial College's ranking among "The 50 Best Physics Schools in the World Today."
- See Imperial College's ranking among "The 100 Best Universities in the World."

### 46University of Colorado

*(Boulder, CO)*

As the flagship of the University of Colorado system, the Boulder campus is looked to by all Coloradoans for academic leadership and research excellence. The Mathematics Department has taken upon itself the goal of preparing students for technical roles in government, industry, and education.

To encourage diversity, the department offers a range of research and study interests, including Algebraic and Differential Geometry, Combinatorics, Logic and Foundations, Mathematical Physics, Number Theory, Noncommutative Geometry, Operator Algebras, Probability, and Topology. Over 500 undergraduate majors and minors and over 50 graduate students are currently enrolled throughout the department.

The 25 tenured and tenure-track faculty members have a high level of expertise to bring to the classroom. Academic support through tutoring, seminars, and peer-run groups is strongly encouraged.

### 47Yale University

*(New Haven, CT)*

As the third-oldest university in the United States and a private Ivy League institution, Yale University in general has had the time and financial means to greatly expand its academic influence. The Mathematics Department is no exception, with 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, with 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, an equally impressive diversity of programs is offered. The majority of students in the Graduate School will complete a Master's degree in route to the Doctorate. Doctoral students typically complete their studies in a timely four-year period.

- See Yale's ranking among "The 50 Best Physics Schools in the World Today."
- See Yale's ranking among "The 100 Best Universities in the World."

### 48Cornell University

*(Ithaca, NY)*

The résumé of Cornell University is impressive: a private endowment, a federal land-grant institution, a member of the Ivy League, and a partner with the State University of New York system. Part of the College of Arts and Sciences, the Mathematics Department 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. Introductory courses are taught with the understanding that not all students are mathematically inclined. At the graduate level, students take on average five to six years to complete their studies. All 43 tenured and tenure-track faculty members are well experienced and hold unique interests in research areas. From Algebra and Applied Mathematics to Logic and Topology, the majority of Mathematical fields are represented.

Through 150 years of history the department has a number of achievements worth celebrating, including its support of women in Mathematics since 1917 and its maintaining a prominent role at the quadrennial International Congress of Mathematicians since 1893.

- See Cornell's ranking among "The 100 Best Computer Science Programs in the World."
- See Cornell's ranking among "The 100 Best Universities in the World."
- See Cornell's ranking among "The 50 Best Physics Schools in the World Today."

### 49University of Tokyo

*(Tokyo, Japan)*

Undergraduate studies at the University of Tokyo are organized into 10 Faculties, one of which is the Faculty of Science. This area if further organized into 10 departments, one of which is wholly dedicated to the study of Mathematics. With a general introduction at the undergraduate level, over 90 percent of the students continue studying at a graduate level.

The Graduate School of Mathematical Sciences is arguably the most prestigious department at the university. A total of 53 Master's students and 32 Doctoral candidates are accepted each year, making admission to the school highly competitive.

Entrance to the Master's programs requires students to pass two written examinations and a third oral examination. Knowledge of the Japanese language is not required for admission, but will limit student participation throughout the program if it is not obtained. Typical time requirements include two years of study for the Master's degree and three for the Doctoral.

### 50Harbin Institute of Technology

*(Harbin, Heilongjiang, China)*

A research-intensive school with specific focus on Science and Technology, Harbin Institute of Technology is a specialized institution with campus locations throughout China. Its dedication to Science has been bolstered by the support of covert government research projects in Space Science and Self Defense Technologies. With such highly sensitive research topics, admission to the school is extremely selective. Only the very brightest students with trustworthy backgrounds are allowed access to such projects.

Fourteen out of 20 schools within HIT rely heavily on Mathematics, including the Schools of Astronautics, Energy Science and Engineering, and Computer Science and Technology. A number of subdivisions within Engineering are themselves key areas of study and research, making Mathematics all the more integral to the school.

After obtaining a strong foundation in scientific theory and acquiring many opportunities to work on sensitive projects, students will feel confident in applying their skills in government research or the work force.