Discrete Mathematics and Combinatorics Ranking

The U.S. News & World Report 2007 rankings of Discrete Mathematics and Combinations Programs in the United States provide valuable insights into the leading institutions in the field of discrete mathematics, a branch of mathematics that focuses on structures that are fundamentally discrete rather than continuous. The rankings showcase a selection of elite institutions renowned for their outstanding research, faculty, and contributions to mathematical sciences, specifically in areas like combinatorics, graph theory, coding theory, and other areas related to discrete structures. The 2007 rankings list Massachusetts Institute of Technology (MIT), Princeton University, Rutgers University-New Brunswick, University of California, San Diego (UCSD), and University of Michigan, Ann Arbor as the top five universities for discrete mathematics programs in the country. These universities have long been at the forefront of research and innovation in the field of discrete mathematics, contributing to both the theoretical and applied aspects of mathematics.

Massachusetts Institute of Technology (MIT) - Rank 1

MIT, ranked number one for Discrete Mathematics and Combinations in the 2007 U.S. News rankings, has a long history of excellence in mathematics, particularly in the field of discrete mathematics. MIT's Department of Mathematics is widely recognized for its cutting-edge research and is home to a number of distinguished faculty members who are leaders in the field of combinatorics, graph theory, and coding theory. Faculty members such as László Lovász, David Karger, and Michel Goemans have made groundbreaking contributions to the study of discrete structures and algorithms, elevating MIT’s reputation as a leader in the field.

MIT’s research strengths in discrete mathematics include areas like randomized algorithms, network theory, and complexity theory. The department has a collaborative and interdisciplinary environment, where students are encouraged to work across different domains, such as computer science, electrical engineering, and operations research. MIT’s focus on theoretical computer science, mathematical modeling, and algorithmic design intersects perfectly with the study of discrete mathematics, making the university an ideal environment for students interested in combining theoretical mathematical research with practical applications. MIT's graduate program in discrete mathematics offers students the opportunity to work on influential research projects, supported by the university’s substantial research funding and access to state-of-the-art facilities.

Princeton University - Rank 2

Princeton University, also ranked second in the 2007 U.S. News rankings, is another powerhouse in the field of discrete mathematics. Princeton's Department of Mathematics has a rich tradition of contributing to the development of mathematical theory, including substantial work in combinatorics, number theory, and algebraic geometry. The university has produced numerous leading mathematicians in discrete mathematics and related fields, further solidifying its position as a top-tier institution for mathematical research.

The faculty in Princeton’s mathematics department are known for their groundbreaking work in both the theoretical and applied aspects of discrete mathematics. Researchers like Donald Knuth, a pioneering figure in algorithmic combinatorics, and Robert Wilson, who has made significant contributions to combinatorial designs, have helped elevate Princeton’s discrete mathematics program. Princeton’s program emphasizes deep theoretical understanding while encouraging students to explore practical applications in fields such as cryptography, computer science, and data analysis. Princeton's collaborative approach, which includes strong ties to computer science, engineering, and other scientific fields, provides students with ample opportunities to engage with interdisciplinary research.

Princeton’s graduate students benefit from close mentorship by faculty members and a rigorous curriculum that challenges them to engage with both the mathematical theory and its real-world applications. The university’s reputation for excellence in pure mathematics and its commitment to fostering a dynamic research environment make it one of the top destinations for students interested in discrete mathematics.

Rutgers University-New Brunswick - Rank 2

Rutgers University-New Brunswick, also tied for second place in the 2007 U.S. News rankings, is another leading institution in the study of discrete mathematics. Rutgers has a strong mathematics department with a particular focus on combinatorics, graph theory, and discrete optimization. The university’s program in discrete mathematics is known for its emphasis on research, particularly in the areas of extremal combinatorics, random structures, and graph algorithms.

Rutgers has a number of distinguished faculty members who have made significant contributions to the field, including Miklós Simonovits and László Lovász, who have been influential in the study of random graphs and combinatorial optimization. The university is also known for its collaborative environment, where students often work on interdisciplinary projects that bridge discrete mathematics with computer science, operations research, and theoretical physics.

The graduate program at Rutgers provides a strong foundation in both the theoretical and applied aspects of discrete mathematics. Students have the opportunity to work on cutting-edge research projects in a supportive and intellectually stimulating environment. With its commitment to producing high-quality research, strong faculty mentorship, and ample opportunities for interdisciplinary collaboration, Rutgers is a highly regarded institution for students pursuing advanced degrees in discrete mathematics.

University of California, San Diego (UCSD) - Rank 2

The University of California, San Diego (UCSD), also tied for second in the 2007 rankings, has a mathematics department renowned for its work in combinatorics, discrete geometry, and theoretical computer science. UCSD's Department of Mathematics is particularly recognized for its strengths in areas such as discrete geometry, graph theory, and algorithmic combinatorics. The department has a number of leading researchers in discrete mathematics, including faculty members like Benjamin Sudakov and Sanjeev Arora, whose work in algorithmic design and discrete optimization has gained international acclaim.

UCSD’s graduate program in mathematics emphasizes both theoretical foundations and practical applications, with students encouraged to engage in interdisciplinary research across computer science, engineering, and data science. The university’s proximity to Silicon Valley and the tech industry also provides unique opportunities for students to apply their research in the context of real-world problems, including network theory, cryptography, and data analytics.

The collaborative and vibrant research environment at UCSD, combined with the opportunity to work with some of the leading mathematicians in the world, makes the university an ideal place for students pursuing advanced studies in discrete mathematics. UCSD’s program is distinguished by its strong emphasis on research, its focus on innovation in mathematical theory, and its commitment to producing high-caliber graduates.

University of Michigan, Ann Arbor - Rank 5

The University of Michigan, Ann Arbor, ranked fifth in the 2007 U.S. News rankings, is another institution known for its excellence in discrete mathematics. Michigan's Department of Mathematics is renowned for its research in combinatorics, graph theory, and algebraic combinatorics. The university’s program is distinguished by its focus on both pure mathematical theory and applied mathematical techniques, allowing students to explore a wide range of topics within the field of discrete mathematics.

The faculty at Michigan includes several prominent mathematicians who have made significant contributions to the study of combinatorial optimization, graph theory, and extremal combinatorics. Faculty members like László Babai and János Komlós have helped shape the university’s reputation as a leader in discrete mathematics research. The graduate program at Michigan is designed to provide students with a solid foundation in mathematical theory, while also offering opportunities for research in cutting-edge areas such as random structures, combinatorial designs, and algorithmic analysis.

Michigan's program is characterized by its supportive environment, where students can work closely with faculty on research projects that have both theoretical and practical applications. The university’s strong connections with industries and research institutes also provide students with ample opportunities to apply their research in real-world settings, making it an attractive destination for those interested in the applications of discrete mathematics.

Rankings of US Discrete Mathematics and Combinations Programs 2007:

Rank, University

1 Massachusetts Institute of Technology
2 Princeton University
2 Rutgers University New Brunswick
2 University of California San Diego
5 University of Michigan Ann Arbor
6 University of California Berkeley
7 Georgia Institute of Technology
7 The Ohio State University,Columbus
9 University of Illinois Urbana Champaign
10 California Institute of Technology
11 Harvard University
11 Stanford University
11 University of Minnesota Twin Cities
14 Emory University
14 University of California Los Angeles
14 University of Memphis

Source: US News and World Report 2007