Last updated 2 December 2010.
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 sections of this course. Section A should be accessible to any interested student (including freshmen). Section B will be better suited for students who already have prior experience with the variety of mathematics which appears in these competitions.
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.
Therefore, the homework sets mentioned above will not be graded. They are meant to supply deeper problems which require more time to think about (and therefore cannot be done together in lecture). Nevertheless, students are encouraged to work on them either individually or in groups. They will be briefly discussed at the beginning of each lecture.
Week 1
(Aug 24 / 26) |
No class.
Instead, try this problem for fun, and tell us next week how much money you can manage to earn. Note: in the context of the problem, when you press button A (or B), you also choose the number i it is applied with (the number i is not random). |
Week 2
(Aug 31 / Sep 2) |
Proof by contradiction
Handout |
Week 3
(Sep 7 / 9) |
Mathematical induction
Handout |
Week 4
(Sep 14 / 16) |
The pigeonhole principle
Handout |
Week 5
(Sep 21 / 23) |
Polynomials
Handout Bonus class: Fri Sep 24, 4:30-5:30 in Wean 8220. |
Week 6
(Sep 28 / 30) |
Calculus
Handout Bonus class: Wed Sep 29, 4:30-5:30 in Wean 5302. |
Week 7
(Oct 5 / 7) |
Number theory
Handout Bonus class: Wed Oct 6, 4:30-5:30 in Wean 5302. |
Week 8
(Oct 12 / 14) |
Inequalities
Handout Bonus class: Wed Oct 13, 4:30-5:30 in Wean 5302. |
Week 9
(Oct 19 / 21) |
Games
Handout Bonus class: Wed Oct 20, 4:30-5:30 in Wean 5302. |
Week 10
(Oct 26 / 28) |
Recursions
Handout Bonus class: Wed Oct 27, 4:30-5:30 in Wean 5302. |
VTRMC
(Sat Oct 30) |
Competition from 9:00am - 11:30am, in Scaife 125 |
Week 11
(Nov 2 / 4) |
Functional equations
Handout No bonus class. |
Week 12
(Nov 9 / 11) |
Geometry
Handout Bonus class: Mon Nov 8, 4:30-5:30 in Wean 5302. |
Week 13
(Nov 16 / 18) |
Combinatorics
Handout Bonus class: Mon Nov 15, 4:30-5:30 in Wean 5302. |
Week 14
(Nov 23) |
Elementary methods.
No advanced class (Thu 25th)
Handout Bonus class: Mon Nov 22, 4:30-5:30 in Wean 5302. |
Week 15
(Nov 30 / Dec 2) |
General strategy and wrap-up
Handout A; Handout B Bonus class: Fri Dec 3, 4:30-5:30 in Wean 8220. |
Putnam
(Sat Dec 4) |
Competition from 10:00am - 1:00pm and 3:00pm - 6:00pm, in Scaife 125 |
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