MATH 4495 Mathematical Preparation for Graduate Study is designed to give students in the BS in
Mathematics program a coherent overview of undergraduate mathematics as it relates to graduate
study, in a lecture, seminar, mini-research, and oral examination environment. Pre-requisite: senior
standing and approval of the chair of mathematics. 3 credits.
Rationale for Course. Assessment of the major, surveys of recent graduates, and analysis of their initial
year of graduate studies indicate that students lack a coherent overview of undergraduate mathematics,
and not well prepared for the rigors of graduate study, which include participatory seminars, miniresearch, oral examinations, and preparation for prelims. This course puts the undergraduate
mathematical experience into the context of linear algebra, and involves students in learning
environment typical of graduate education.
The course offers a faced paced, interactive overview of the elements of undergraduate mathematics
which figure prominently in graduate school. Topics include
1. Linear Algebra
2. - Real Analysis
3. Calculus of Vector Valued Functions
4. Point Set Topology
5. Classical Stokes’ Theorem
6. Differential Forms and Stokes’ Theorem
7. Curvature for Curves and Surfaces
8. Geometry
9. Complex Analysis
10. Countability and the Axiom of Choice
11. Algebra
12. Lebesgue Integration
13. Fourier Analysis
14. Differential Equations
15. Combinatorics and Probability
16. Algorithms
Learning Objectives. Students will gain a coherent overview of undergraduate mathematics and
become comfortable in a typical graduate mathematics setting which requires participation in seminars,
mini-research, preparation for prelim-examinations, and oral examinations. They will also learn to write
about mathematics in a concise and coherent mathematical style.
Text: Thomas Garrity, All the Math You Missed but Needed to Know for Graduate School. Cambridge
University Press, 2002.
Readings:
Steven G. Krantz, A Mathematician’s Survival Guide: Graduate School and Early Career Development.
American Mathematical Society, 2008.
Timothy Gowers, et al., The Princeton Companion to Mathematics. Princeton University Press, 2008.
Paulo N. de Souza, et al, Berkeley Problem Book in Mathematics. Springer, 2004.
D.J. Newman, A Problem Seminar. Springer, 1982.
Norman Steenrod, et al, How to Write Mathematics. American Mathematical Society, 1973.
Nicholas J. Higham, Handbook of Writing for the Mathematical Sciences. Society for Industrial and
Applied Mathematics, 1998.
George A. Grätzer, More Math into LaTeX. Fourth edition. Springer, 2007.
William J. Strunk, The Elements of Style. Fourth edition. Longman, 1999.
Donald E. Knuth, Mathematical Writing. The Mathematical Association of America, 1996.