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Math Circle at the University of Washington

Advanced Circle 2014-2015 (Archive)

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