Math H90
Seminar on mathematical problem solving
MF 16:10-18:00, 71 Evans Hall
Mock Putnam exam (5 problems, 2 hours) took place in class
on Monday, October 4th. Test problems in PS
and in PDF and their solutions
in PS and in PDF
are available.
Results of the Putnam exam on 12/04/04 can be found
here.
The UC-Berkeley team (Boris Bukh, Carol Xia Hua and
Vedran Sohinger) received an honorable mention. Jeremy Tauzer
received an honorable mention as an individual. Congratulations.
- 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.
The first 4 books are on reserve at the Moffitt Library reserve collection.
- Journals.
- Web links.
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 #1 due September 10th, in
PS and in
PDF.
Hints for homework #1, in PS and
in PDF.
- Homework #2 due September 17th, in
PS and in PDF.
Hints for homework assignment #2, in
PS and
in PDF.
-
Homework #3 due September 24th, in
PS and
in PDF.
Hints for homework assignment #3, in
PS and in PDF.
- Homework #4 due October 8th, in
PS and in PDF.
Hints for homework assignment #4, in
PS and in PDF.
- Homework #5 due October 18th, in
PS and
in PDF.
Hints for homework assignment #5, in
PS
and in PDF.
- Homework #6 due October 29th, in
PS and
in PDF.
Hints re homework #6, in PS and in
PDF.
- Homework #7 due November 8th, in
PS and in
PDF.
Hints re #7 were given in class.
- Homework #8 due November 19th, in
PS
and in PDF.
Hints re #8, in PS
and in PDF.
- Homework #9 due November 29th, in
PS
and in PDF.
Homework is due at 4:15p.m. on the day specified. No late homework.
If you cannot make it to class, find a way to submit your work
before the deadline.
- Solutions to homework assignment #1, in
PS
and in PDF.
For extensive commentary on problems ## 5,10,11, see pp. 148-151, 155-156,
159-160 of the most recent Putnam collection by Kedlaya et al.
- 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 #7, in
PS and in PDF.
- Solutions to homework assignment #8, in
PS and in PDF.
- Solutions to homework assignment #9, 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.
If you find a misstatement/omission/typo in a problem/solution/handout,
please let me know as soon as you can. Thanks to Boris Bukh, Tanya Gordeeva,
and Brock Mendel for corrections made so far.
Thanks to Ioana Dumitriu for her help with the course.
Last modified: Mar 15, 2005