Last updated 1 December 2012.
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!
This year, we will offer 4 levels of the Putnam seminar, so that students can personalize their experience by selecting the one(s) that they benefit the most from. No prior math competition experience is required, and beginners are welcome. Indeed, this seminar seeks to complement the standard math curriculum by concentrating on the raw creative problem-solving skills which are essential for original work in almost every field. The levels are roughly divided as follows.
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 weekly points) + (3 for the VTRMC) + (6 for the Putnam).
Ratio = Score / MaximumPossible.
MaximumPossible is 23 for Tue, 22 for Mon (due to Labor Day), and 22 for Thu/Fri (due to Thanksgiving).
Grades are then based on the Ratio, using the standard scale A = 90%+, B = 80%+, etc.
Week 1 | Proof by contradiction
Lecture / Wed |
Week 2 | Number theory
Sun / Lecture / Wed |
Week 3 | Polynomials
Sun / Lecture / Wed |
Week 4 | Calculus
Sun / Lecture / Wed |
Week 5 | Continuous functional equations
Sun / Lecture / Wed |
Week 6 | Inequalities
Sun / Lecture / Wed |
Week 7 | Convergence
Sun / Lecture / Wed |
Week 8 | Recursions
Sun / Lecture / Wed |
Week 9 | Linear algebra
Sun / Lecture / Wed |
VTRMC
(Sat Oct 27) |
Competition from 9:00am - 11:30am, in Scaife 125. |
Week 10 | Combinatorics
Lecture / Wed |
Week 11 | Geometry
Sun / Lecture / Wed |
Week 12 | Integer polynomials
Sun / Lecture / Wed |
Week 13 | Basic arguments
Sun / Lecture / Wed Wed/Sun meetings will still run, with optional attendance, for students who stay at CMU for Thanksgiving. |
Week 14 | Higher math
Sun / Lecture / Wed |
Putnam
(Sat Dec 1) |
Competition from 10:00am - 1:00pm and 3:00pm - 6:00pm, in Scaife 125. |
Week 15 | Beyond Putnam (optional, and Monday only) |
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