| Home | 1st Year Circle | 2nd Year Circle | Archive | About | Math Hour | Math Hour Olympiad |
The Advanced Circle will meet on Thursdays from 5 to 7 PM in Loew Hall room 116.
| Session | Summary | Homework |
|---|---|---|
| Sessions 1...ω (2013-14) | ||
| Session ω+1 (09.25.2014) | Olympiad (TeX / PDF) | Unsolved problems from the Olympiad |
| Session ω+2 (10.02.2014) | Talking about Olympiad problems The dicrete “derivative” of an integer sequence “Guess my polynomial” redux |
|
| Session ω+3 (10.09.2014) | Definion of fields and field extensions Constructible numbers |
Problem Set 1 (TeX / PDF) |
| Session ω+4 (10.16.2014) | Pentagon algebra Constructions with only a compass! |
Problem Set 2 (TeX / PDF) |
| Session ω+5 (10.23.2014) | Counting trees: Two proofs of Cayley's theorem Camille Jordan, “Sur les assemblages des lignes” |
Problem Set 3 (TeX / PDF) |
| Session ω+6 (10.30.2014) | Chromatic polynomials and Tutte relations Stanley's theorem on acyclic orientations |
Problem Set 4 (TeX / PDF) |
| Session ω+7 (11.06.2014) | Predicting possible outcomes of tournaments | Problem Set 5 (TeX / PDF) |
| Session ω+8 (11.13.2014) | Sperner's lemma and some of its continuous comrades Heinrich Tietze, “Einige Bemerkungen über das Problem des Kartenfärbens auf einseitigen Flächen” |
Problem Set 6 (TeX / PDF) |
| Session ω+9 (11.20.2014) | Classification of surfaces by folding polygons Compact surfaces demonstration |
|
| Session ω+10 (12.04.2014) | “Geometric” Math Battle (TeX / PDF) | |
| Session ω+11 (12.01.2014) | Math Auction with First and Second Year Circles (Word / PDF) | |
| Session ω+12 (01.15.2015) | Projective spaces; projective configurations | Problem Set 7 (TeX / PDF) |
| Session ω+13 (01.22.2015) | Matchings in graphs Hall's “Marriage theorem” |
|
| Session ω+14 (01.29.2015) | Means and power means Convexity and Jensen's inequality |
Problem Set 8 (TeX / PDF) |
| Session ω+15 (02.05.2015) | More means | Problem Set 9 (TeX / PDF) |
| Session ω+16 (02.12.2015) | Hunger Games, first round | |
| Session ω+17 (02.19.2015) | Gaussian integers | |
| Session ω+18 (02.26.2015) | BAMO and Fermi problems | Problem Set 10 (TeX / PDF) |
| Session ω+19 (03.05.2015) | Musical scales and tuning fork adventures | |
| Session ω+20 (03.12.2015) | Some optimization problems | |
| Session ω+21 (04.02.2015) | Steiner's porism, stereographic projection, and polar inversion | |
| Session ω+22 (04.16.2015) | Several counting techniques | Problem Set 11 (TeX / PDF) |
| Session ω+23 (04.23.2015) | Closure operators and more counting | Problem Set 12 (TeX / PDF) |
| Session ω+24 (04.30.2015) | Buffon's needle (Buffon's noodle?) Minkowski sums and two proofs of Barbier's theorem |
Problem Set 13 (TeX / PDF) |
| Session ω+25 (05.07.2015) | Cutting squares into triangles: Monsky's theorem Sperner's lemma revisited |
Problem Set 14 (TeX / PDF) |
| Session ω+26 (05.14.2015) | Hunger Games, second round | |
| Session ω+27 (05.21.2015) | Introduction to random graphs, in honour of Queen Victoria's 196th birthday | |
| Session ω+28 (05.28.2015) | Some two-player games John Nash (1928-2015) |
|
| Session ω+28½ (05.31.2015) | Math Hour Olympiad | Olympiad problems with a twist |
| Session 2ω (06.04.2015) | Math Auction with First and Second Year Circles |