Last updated 9 December 2011.
Yet although competitions are the title of this course, the syllabus will actually be constructed around general problem-solving techniques in mathematics. The instructor's aim is to use the competition problems to teach some mathematics which is not usually seen in ordinary classes, but is also beneficial to learn.
There is no official reference for this course, as much of the material will come from the instructor's experience in coaching the United States Math Olympiad team. Nevertheless, it should be mentioned that there will be some correlation with the book Putnam and Beyond, by Razvan Gelca and Titu Andreescu. Students are not required to purchase the book!
There are two official sections of this course, and two optional sections.
Learning goals: By the end of the course, students should develop fundamental problem solving skills, and become accustomed to concentrating on a problem for an extended period of time. Students should also be able to recognize when proofs are written with sufficient rigor, and should gather a greater appreciation for mathematics as a broad field.
Learning goals: to increase ability to solve Putnam problems, and to communicate solutions effectively.
Learning goals: to master questions at the Putnam 1-3 level.
Learning goals: to master questions at the Putnam 4-6 level.
Score = (number of classes attended) + (3 for the VTRMC) + (6 for the Putnam).
Ratio = Score / MaximumPossible.
MaximumPossible is 23 for Section A and 22 for Section B (due to Thanksgiving).
Grades are then based on the Ratio, using the standard scale A = 90%+, B = 80%+, etc.
Week 1
(Aug 30 / Sep 1) C: Wed Aug 31 |
Proof by contradiction
Handouts: A/B, C |
Week 2
(Sep 6 / 8) C: Mon Sep 5 |
Mathematical induction
Handouts: A/B, C, D |
Week 3
(Sep 13 / 15) C: Wed Sep 14 |
The pigeonhole principle
Handouts: A/B, C, D |
Week 4
(Sep 20 / 22) C: Mon Sep 19 |
Polynomials
Handouts: A/B, C, D |
Week 5
(Sep 27 / 29) C: Wed Sep 28 |
Calculus
Handouts: A/B, C |
Week 6
(Oct 4 / 6) C: Mon Oct 3 |
Number theory
Handouts: A/B, C, D |
Week 7
(Oct 11 / 13) C: Wed Oct 12 |
Inequalities
Handouts: A/B, C, D |
Week 8
(Oct 18 / 20) C: Mon Oct 17 |
Convergence
Handouts: A/B, C, D |
Week 9
(Oct 25 / 27) C: Wed Oct 26 |
Recursions
Handouts: A/B, C, D |
VTRMC
(Sat Oct 29) |
Competition from 9:00am - 11:30am, in Gates 4307 |
Week 10
(Nov 1 / 3) C: Mon Oct 31 |
Linear Algebra
Advanced class (Thu Nov 3) meets in Wean 5302.
Handouts by Misha Lavrov: A, B, C |
Week 11
(Nov 8 / 11) C: Wed Nov 9 |
Geometry
Advanced class meets on Fri Nov 11, not Thu Nov 10.
Handouts: A/B, C, D |
Week 12
(Nov 15 / 17) C: Wed Nov 16 |
Functional equations
Handouts: A/B, C, D |
Week 13
(Nov 22) C: Mon Nov 21 |
Elementary methods.
Handouts: A/B, C, D No advanced class (Thu Nov 24) |
Week 14
(Nov 29 / Dec 1) C: Wed Nov 30 |
General strategy and wrap-up
Handouts: A/B, C, D |
Putnam
(Sat Dec 3) |
Competition from 10:00am - 1:00pm and 3:00pm - 6:00pm, in Scaife 125 |
Week 15
(Dec 6 / 8) |
No class; Putnam solutions will be discussed between 1-3pm and after 6pm on Sat Dec 3. |
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