Math 191
Advanced problem solving
Classes: Tu 3:30-5:00pm, Th 5:00-6:30pm, Room 5 Evans Hall
Office hours: TuTh 10:00-11:00am, Room 821 Evans Hall, and by appt.
Mock Putnam exam took place in class on Monday, October 7th.
Test problems and their solutions are available in PS and
in PDF.
The Putnam test took place
December 6th, 2008 at 8:00am in 102 Wurster Hall.
Here are the
Putnam Test Regulations and
here are the Putnam problems and solutions.
Topics covered
- 08/28: Mathematical induction.
- 09/02: Integers and primes. Congruence.
- 09/04: Rational and irrational numbers.
- 09/09: Discussion of the 1st homework.
- 09/11: Complex numbers. Pigeonhole principle.
- 09/16: Discussion of the 2nd homework.
- 09/18: Generating functions.
- 09/23: Discussion of the 3rd homework.
- 09/25: Invariants and semi-invariants.
- 09/30: Discussion of the 4th homework.
- 10/02: Introductory discrete probability.
- 10/07: Mock Putnam test.
- 10/09: Discussion of the mock Putnam test.
- 10/14: Discussion of the 5th homework.
- 10/16: Polynomials. Gauss-Lucas Theorem.
- 10/21: Discussion of the 6th homework.
- 10/23: Fourier series in one and several variables.
- 10/28: Discussion of the 7th homework.
- 10/30: Binomial identities and generating functions.
- 11/04: Linear algebra. Classical inequalities.
- 11/06: Discussion of the 8th homework.
- 11/13: Determinants. Asymptotics.
- 11/18: Discussion of the 9th homework.
- 11/20: Putnam: format, preparation, recent problems.
- 11/25: Putnam: more recent problems.
- 12/02: Discussion of the 10th homework.
- 12/04: Evaluating the zeta function.
- 12/09: Discussion of the Putnam test problems.
- Books.
- Gleason, A. M.; Greenwood, R. E.; Kelly, L. M.; The William Lowell Putnam Mathematical Competition. Problems and solutions: 1938--1964. Mathematical Association of America, Washington, D.C., 1980. ISBN 0-88385-428-7
- The William Lowell Putnam mathematical competition. Problems and solutions: 1965--1984. Edited by Gerald L. Alexanderson, Leonard F. Klosinski and Loren C. Larson. Mathematical Association of America, Washington, DC, 1985. ISBN 0-88385-441-4
-
Kedlaya, Kiran S.; Poonen, Bjorn; Vakil, Ravi; The William Lowell Putnam Mathematical Competition, 1985--2000. Problems, solutions, and commentary. MAA Problem Books Series. ISBN 0-88385-807-X
-
Contests in higher mathematics. Miklos Schweitzer Competitions 1962--1991. Edited by Gabor J. Szekely. Problem Books in Mathematics. Springer-Verlag, New York, 1996. ISBN 0-387-94588-1
-
Honsberger, Ross; Mathematical morsels. The Dolciani mathematical expositions,
no.3. The Mathematical Association of America, 1978. ISBN 0-88385-303-5
- Shklarsky D. O.; Chentzov N. N.; Yaglom I. M.; The USSR Olympiad problem
book. W. H. Freeman and Company, San Francisco and London, 1962.
- Journals.
- Web links.
- William Kahan, who has been teaching a similar class H90, has put together a large
collection of notes and problems with solutions at his Math H90 website.
- International Mathematics Olympiads official website and an unofficial one
with additional info and references.
- William Lowell Putnam Mathematics Competition
Archive.
The instructor welcomes cooperation among students and the use of books.
However, handing in homework that makes use of other people's work (be
it from a fellow student, a book or paper, or whatever) without explicit
acknowledgement is considered academic misconduct. Make sure to include
proper acknowledgement when quoting anything directly or paraphrasing.
Homework is due at the beginning of class on the day specified. No late homework.
If you cannot make it to class, find a way to submit your work before the deadline.
- Homework #1 due September 9th, in
PS and in
PDF.
- Homework #2 due September 16th, in
PS and in PDF.
- Homework #3 due September 23rd, in
PS and in PDF.
- Homework #4 due September 30th, in
PS and in PDF.
- Homework #5 due October 9th, in
PS and in PDF.
- Homework #6 due October 21st, in
PS and in PDF.
- Homework #7 due October 28th, in
PS and in PDF.
- Homework #8 due November 6th, in
PS and in PDF.
- Homework #9 due November 17th, in
PS and in PDF.
- Homework #10 due December 2nd, in
PS and in PDF.
- Solutions to homework assignment #1, in
PS and in
PDF.
- Solutions to homework assignment #2, in
PS and in PDF.
- Solutions to homework assignment #3, in
PS and in PDF.
- Solutions to homework assignment #4, in
PS and in PDF.
- Solutions to homework assignment #5, in
PS and in PDF.
- Solutions to homework assignment #6, in
PS and in PDF.
- Solutions to homework assignment #9, in
PS and in PDF.
- Solutions to homework asignment #10, in
PS and in PDF.
Mathematical induction, in PS and in
PDF.
Integers and primes, in PS and in
PDF.
Congruence, in PS and in PDF.
Rational and irrational numbers, in PS and in
PDF.
Complex numbers, in PS and in PDF.
Progressions and sums, in PS and in
PDF.
Diophantine equations, in PS and
in PDF.
Quadratic reciprocity, in PS and
in PDF.
Polynomials, in PS and in
PDF.
Rolle's theorem and Descartes' rule of signs, in PS and in PDF.
Polynomial equations and symmetric functions, in
PS and in PDF.
Classical inequalities, in PS
and in PDF.
Complex analysis in a nutshell, in PS
and in PDF.
Linear algebra in a nutshell, in PS and in
PDF.
Inclusion-exclusion principle, in PS
and in PDF.
Pigeonhole principle, in PS and in
PDF.
Generating functions, in PS and in PDF.
Last modified: Dec 5, 2008