Math 496 F1H Home Page

This is the home page for Math 496F1H, "Introduction to Mathematical Research". This class meets for the Spring 2017 semester, MWF 2:00-2:50 in 343 Altgeld.

Class Diary, blogger style

M 3/13 -- No speaker. I talked about my conference, including my talk and realized that the next topic will be the cubic equation.

W 3/1, F 3/3 -- Everybody, please try to come to every class meeting. On W, I talked about this paper, and on F, I talked about various stories from the mathematical life. There is no class for the next week, but we'll make up the time at the end of the semester when you present your projects. Projects. Work on your projects and email me if you have questions. (My turnaround time to reply might be slower, but I will read them.) Starting M 3/13, we need a stronger focus and I'm always happier if you talk more than me.

W 2/22, F 2/24, M 2/27 -- Not full attendance recently and I've been slow to update the website. varieties of discussions. On F, KT presented information on the Stomachion, and I passed out a printed version of the much more colorful website; also a useful guide to LaTex. I talked about O(n) and finite differences and the Bell Numbers. We need more speakers perhaps, but at very least, more attendance. Please let me know if I forgot anything important here, like a speaker on 2/22/

M 2/20 -- No speakers but me, and no handouts. There was an "active learning" segment on Jon Merzel's O(n), and then some discussion of finite differences. More to come on both.

F 2/17 -- MM gave Ivan Niven's proof that pi is irrational. I elaborated a bit and distributed and discussed a list of Oberwolfach speakers for my upcoming trip. We had a brief tour of the wonderful Math library.

W 2/15 -- No speakers. Handouts included a very nice article on Tropical Mathematics and an article on higher Venn diagrams (click the links within to get the picture.) I rambled on about those amazing Chebyshev polynomials.

M 2/13 -- KT talked about dynamical systems and BN introduced tropical algebra to a graph theory algorithm. Handouts included some pages on the Art Gallery problem from our recommended text and a clever blog post comparing unsolved problems with the structure of the Common Core.

F 2/10 -- JB presented some more number theory and theorems about the number of roots of polynomials mod primes. AC talked about the Art Gallery problem. I added a bit here and there. I did a variation on the Goldbach problem, and distributed some matchstick puzzles from a British learning community.

W 2/8 -- Lots of odds and ends. I continued to talk about various topics and told a bunch of stories. I gave Doron Zeilberger's lovely short proof of brilliant tricky proof (handout for Friday) of a problem from Goldbach. Also, some discussion of The On-Line Encyclopedia of Integer Sequences, with some puzzle problems and the entry on the Stern Sequence. I also distributed a couple of pages from a 1986 paper of mine on lattice point simplices.

M 2/6 -- No student speaker, so I filled the full hour. Handouts: Pick's Theorem and the first chapter of the PhD thesis of Wipawee Tangjai. I covered Pick's theorem, barycentric coordinates and several proofs of the centroid theorem.

F 2/3 -- AC talked about Additive Systems and I added some additional things from my own work and that of my student Wipawee Tangjai. Handout: The LAS page honoring David Blackwell in the Gallery of Excellence and his New York Times obituary. Also, I was requested to give class time for a presentation on healthy eating from ARC. I thought it was a worthwhile idea instead to put some links here: Cooking Classes and Nutrition Check up. Eat your vegetables!

W 2/1 -- MM talked about logical models for algebra; their strength and weakness. I distributed my article about writing for the Putnam and on x^y = y^x . I started talking about Pick's Theorem.

M 1/30 -- No handouts (I forgot to give out the one I brought.) AF talked about some combinatorics questions which can be dealt with by generating functions. (And which lead to questions about lattice points in polytopes in R^n.) AM talked about the area of various figures which are variations on the Koch snowflake. (This reminded me of one of my favorite Putnam problems.)

F 1/27 -- PH talked about a strange integral inequality from the 2003 Putnam and BN talked about the Bolzano-Weierstrass Theorem and some generalizations. The handouts were the Mathscinet Search Page and the Subject Classification guide. I talked about the Diophantine equations x^y = y^x and, briefly, a weird solution to x^y = y^(2x). More later.

W 1/25 -- YZ talked about Euclidean domains and multiple acceptable remainders in Z and Z[i] and KT talked about the growth of analytic functions and how bounds can imply polynomials. I distributed the paper by Ram Murty and Scott Kim's What is a puzzle?. I also talked about volunteer activities at the IGL and ICTM. (There are additional links at those places.

M 1/23 -- JB spoke about Wilson's Theorem, Fermat's Theorem and Euler's Theorem in number theory. AC spoke about prime numbers, irreducible polynomials and a proof by Ram Murty. Handout: Two old sets of notes on the Fibonacci numbers, and linear algebra.

F 1/20 -- A few handouts, and our first talk. AG spoke about generalizing an identity for the Fibonacci numbers. Let F(n) be the n-th Fibonacci number. Then F(n+1)F(n-1) - F(n)^2 = (-1)^n. The given proof used matrices and determinants. The handouts were: Prof. Francis Edward Su's guide to writing homework for math classes, Doug Shaw's tips for Making good talks into great ones, Joe Gallian, an expert in undergraduate research, on How to give a good talk, andwo handouts on the Stern sequence. Scheduled to talk on M 1/23: JB and AC. Volunteer and see your google-proof initials here!

W 1/18 -- First day. Several handouts: Course Organization, from George Polya, a problem-solving template , Class questionnaire and "One Introduction to Mathematical Research". This contains the homework assignment for Friday. This should be written up (no more than a page is needed):

  • Present your favorite theorem and proof or problem and solution.
  • Change your favorite in some way, and prove or solve it again.
  • Change your favorite in another way, so that you no longer know how to prove or solve it.

    In advance of the semester, here are three links to lists of REU sites: one run by Prof. Steve Butler of Iowa State, and the others by the NSF and the AMS.

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