2015-2016 Putnam preparation

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2016 Spring

During the Spring semester we plan to meet Fridays 1-3 pm, most likely starting with the second week of classes.

For details, please see the Spring 2016 activities link on the MENTOR site.

BTW, a place you can use anytime you have some time to spend on campus is MUSL, the Mathematics Undergraduate Student Lounge.


2015 Fall

Nov. 20, noon-2pm, AH 10 (underground)
As usual, two sessions, one from noon and one from 1pm.
Discussed the problems on the test and applications of the arithmetic/geometric/harmonic mean inequality (see this Wikipedia page). Among the proofs on that page, there is one by forward-backward induction, due to Cauchy.
For the harmonic mean, see http://www.math.washington.edu/~dumitriu/Inequalities (which also contains the Generalized Means Inequality). The inequality between the geometric and harmonic mean is obtained by applying the inequality between the arithmetic and geometric means to the inverses: for \(x_i \gt 0\) \[ \frac{ \frac{1}{x_1} + \frac{1}{x_2} + \dots +\frac{1}{x_n} }{n} \ge \left( \frac{1}{x_1} \cdot \ldots \cdot \frac{1}{x_n} \right)^{1/n} \] In all these, equality holds if and only if all the variables are equal.
Nov. 13, noon-2pm, AH 10 (underground)
We will have a short practice test (2-3 problems).
The test lasts one hour and will be administered twice, once from noon and once from 1pm. If you cannot make either of these times, please let us know and we will try to find another option.
See the e-mail you received on Monday about more details.
Nov. 6, noon-2pm, AH 10 (underground)
   Undergraduate Colloquium talk & discussion
Krešimir Josić, UH: What can you believe when the truth keeps changing?
Oct. 30, noon-2pm, AH 10 (underground)
As usual, two sessions, one from noon and one from 1pm.
We discussed problems 95 and 96 from the Putnam and Beyond book.
Look at the other problems from section 2.1.2, Inequalities.
Oct. 23, noon-2pm, AH 10 (underground)
We discussed proofs by contradiction. Here are some details:
Oct. 16, noon-2pm, AH 10 (underground)
Oct. 9, noon-2pm, AH 10 (underground)
Oct. 2, noon-1:30pm, AH 10 (underground)
Continued with the Pigeon Hole Principle; see also more detailed proofs.
What was done, and proposed problems from the Putnam and Beyond book, are here.
Sep. 25, noon-2pm, 646 PGH.
Since for now there is not a time good for everyone, this Friday there will be two one-hour sessions, one from noon, the second from 1pm. Come to the one you prefer.
Sep. 18, noon, 646 PGH. Pizza will be provided.
Orientation meeting. We will discuss possible times for the weekly Putnam preparation, and the EURE/REU option for those who participate in both the Putnam preparation/competiion and the Undergraduate Colloquium.

See here more details and a link to the slides from the meeting.
Putnam problems and solutions
UH problem of the week (no new problems since Fall 2014)