Celebrating a Century of Advancing Mathematics Designing a Major in the Mathematical Sciences 2015 CUPM Curriculum Guide to Majors in the Mathematical Sciences

Designing a Major in the Mathematical Sciences A successful major offers a program of courses that gradually and intentionally leads students from basic to advanced levels of critical and analytical thinking, while encouraging creativity and excitement about mathematics.

Designing a Major in the Mathematical Sciences Major programs in the mathematical sciences should ensure that all students come to see mathematics as an engaging field, rich in beauty, with powerful applications to other subjects and to contemporary open questions. Each department should create and maintain a community that welcomes and supports all students, including those from groups that have been traditionally underrepresented in mathematics.

General Recommendations A healthy mathematical sciences program should incorporate intentional evolution and continual improvement. Every mathematical sciences department should have and follow a strategic plan that acknowledges local conditions and resources, but is also informed by recommendations from the larger mathematical community.

General Recommendations Planning and renewal should be guided by consultation both within the department and with outside stakeholders. Departments should assess their progress in meeting cognitive and content goals through systematic collection and evaluation of evidence.

Cognitive Recommendations 1.Students should develop effective thinking and communication skills. 2.Students should learn to link applications and theory. 3.Students should learn to use technological tools. 4.Students should develop mathematical independence and experience open-ended inquiry.

Content Recommendations 1.Calculus and linear algebra 2.Proofs 3.Data analysis, computing, and mathematical modeling 4.The breadth of mathematics

Content Recommendations 5.Mathematics from the perspective of another discipline 6.Contrasting but complementary points of view Continuous and discrete Algebraic and geometric Deterministic and stochastic Exact and approximate

Content Recommendations 7.Depth in a mathematical area 8.“High impact” experiences 9.Orientation to careers in mathematics

The 2015 CUPM Curriculum Guide to Majors in the Mathematical Sciences

The 2015 CUPM Curriculum Guide

Course Area Study Group Reports Abstract Algebra Linear Algebra Calculus Transitions to Proof Ordinary Differential Equations Partial Differential Equations Probability and Stochastic Processes Statistics Real Analysis Complex Analysis Numerical Analysis Number Theory Geometry Topology Modeling Discrete Mathematics History of Mathematics

Program Area Study Group Reports Biomathematics Actuarial Mathematics Financial Mathematics and Mathematical Economics Statistics Teacher Education Middle School Secondary School Applied Mathematics Chemistry Physics Engineering Computing and Computational Science Environmental Science Social and Behavioral Sciences

Preparing Students for Graduate Study Ph.D. programs in Mathematics Professional Science Master’s degrees Advice in particular program areas

Beyond the Curriculum Departmental Responsibilities Mathematics as a Liberal Art Recruitment and Retention Articulation and Placement Assessment Technology Undergraduate Research

What’s Next? Trifold brochure (available at JMM and at section meetings) Hard copy, printed short report distributed early in 2015 Presentations at section meetings Regularly scheduled revisions and updates to the 2015 report Online community input to course and program area reports Additional course and program area study group reports CRAFTY working with CUPM on parts of the TPSE-Math Initiative

Steering Committee for the Guide David Bressoud (Macalester College) Jenna Carpenter (Louisiana Tech University) Harriet Pollatsek (Mt. Holyoke College) Carol Schumacher (Kenyon College) co-chair Martha Siegel (Towson University) co-chair Michael Starbird (University of Texas Austin) Alan Tucker (Stony Brook University) Elizabeth Yanik (Emporia State University)

Thanks also Editors: Paul Zorn (St. Olaf College) Harriet Pollatsek (Mt. Holyoke College) COMET and chair: Beth Burroughs (Montana State University) MAD and chairs: Joe Malkevitch (York University of the City of NY) Jason Douma (University of Sioux Falls) MAA Staff: Michael Pearson, Linda Braddy, and Carol Baxter Educational Advancement Foundation and Harry Lucas National Science Foundation (DUE )