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Mathematical Sciences Introductory Courses

Scores from advanced placement exams (AP, IB and Cambridge), combined with scores from the online placement test, are used to place incoming students into one of the following three calculus courses:

  • 21-120 Differential and Integral Calculus (Similar to AP/AB, but more sophisticated.)
  • 21-122 Integration, Differential Equations and Approximation (Similar to AP/BC, but more sophisticated.)
  • 21-259 Calculus in Three Dimensions (Calculus of 2 and 3 variables.)

Students who are interested in majoring in mathematics and who have been placed into 21-259 and have a combined Math SAT I & II score of 1550 or greater might consider taking 21-242 Matrix Theory and 21-127 Concepts of Math in the Fall instead of 21-259. Matrix Theory is an Honors course that will emphasize proofs and mathematical reasoning.

After taking Matrix Theory in the Fall, students would have the option of taking Honors Multivariable Calculus in the Spring. The Honors Multivariable class will study the calculus of functions from n-dimensional space to m-dimensional space in great generality.

Students interested in majoring in Mathematics should take 21-127, Concepts of Mathematics, in the fall or spring of their first year. Concepts of Mathematics is an introduction to proofs and abstract mathematics that will lay the foundation for your future studies.

In the second year of study, talented and motivated students will have the opportunity to take Honors courses in abstract algebra and real analysis. The typical enrollment in these classes is 12 to 15 students.

These courses are quite rigorous and demanding, so permission from the Department of Mathematical Sciences is required to enroll in them.

Our Honors Program

This program offers exceptionally talented and ambitious students the opportunity to complete a masters degree in Mathematical Sciences at the same time as their undergraduate degree. It requires taking five graduate mathematics courses and writing a thesis. Nearly all such students have completed Honors courses in Mathematics.

Teaching Opportunity

Some of our most capable undergraduates are offered the opportunity to be teaching assistants for basic courses. This is an excellent opportunity - it not only looks good to graduate schools but teaching others often helps your own learning.

Putnam Team

The William Lowell Putnam Competition, run by the Mathematical Association of America, is the premier mathematics contest for undergraduate students. It is the university-level analogue of the International Mathematical Olympiad. Our take on the Putnam seminar uses the competition as the context for a free-wheeling tour of topics throughout mathematics. Taught by Po-Shen Loh, the Deputy Leader of the USA International Mathematical Olympiad team, 21-295 identifies problems which are mathematically beautiful, and which inspire discussions about concepts in higher mathematics. Indeed, we see math contests as opportunities to spark your imagination, to tease your creativity and ingenuity, and as an excuse to get together at the end of a day of classes, to enjoy the camaraderie of other like-minded people.

In Fall 2012, our Putnam seminar enrolled over 120 students — about 2% of the entire undergraduate student body — hailing from departments ranging from Chemical Engineering to Architecture. The CMU Putnam team achieved two consecutive top-5 rankings in 2011 (#2, cmu.edu front page) and 2012 (#5, press release). In 2012, 30 CMU students individually placed among the top 500 contestants — the 2nd-most among all universities.

Secondary Certification

Certification to teach mathematics at the secondary level is available through Chatham, a neighboring college.