COURSE DESCRIPTION: We'll
develop and explore topics and concepts from real analysis, with special
emphasis on subjects and techniques useful for graduate study and
applications in industry. Topics include Benford's law, random matrix theory &
Fourier analysis. This will be an intense, fast paced class. Students will
assist in writing both reviews for MathSciNet and referee reports for papers for
journals, write programs to investigate and conjecture, and read classic and
current research papers, and possibly apply these and related methods to real
world problems.
CONTACTING ME: You can reach me in Bascom 106D (413 597 3293; if I'm there it's office hours), email sjm1@williams.edu, or anonymously through ephsmath@gmail.com (password 1793williams).
GRADING / HW: Homework 15%, Class Participation 5%, Midterms 40%, Final 40%. Can do a project and adjust percentages. Exams are black tie optional. Homework is to be handed in on time, stapled and legible. Late, messy or unstapled homework will not be graded. I encourage you to work in small groups, but everyone must submit their own homework assignment. Extra credit problems should not be included in the general homework, but handed in separately. Very little partial credit is given on these problems.
OBJECTIVES: There are two main goals to this course: to explore advanced concepts in analysis, and to learn problem solving skills and see how material is used. We will constantly emphasize the techniques we use to solve problems, as these techniques are applicable to a wide range of problems in the sciences. For a fuller statement as to the objectives of this course, please click here. This includes some fascinating videos with some thought provoking comments about what you should get out of your education.
TEXTBOOK: An Invitation to Modern Number Theory: http://press.princeton.edu/titles/8220.html
COURSE DISCLAIMER: I may occasionally say things such as `Probability is one of the most useful courses you can take' or 'If you know probability, stats and a programming language then you'll always be able to find employment'. I really should write `you should always be able to find employment', as nothing is certain. Thus, please consider yourself warned and while you may savor the thought of suing me and/or Williams College, be advised against this! I'm saying this because of the recent lawsuit of a graduate who was upset that she didn't have a job, and sued her school!