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The Advanced Circle will meet on Thursdays from 5 to 8 PM in Loew Hall 114.

Session | Summary | Homework | (Sketches of) Solutions |
---|---|---|---|

Session 1 (09.26.2013) | Olympiad | Homework 1: Unsolved problems from the Olympiad | Olympiad solutions |

Session 2 (10.03.2013) | Extreme values, semi-invariants and continuity | Homework 2: Problem Set 1 | Problem Set 1 solutions |

Session 3 (10.10.2013) | Metric Topology I (definitions) | Homework 3: Problem Set 2 | Problem Set 2 solutions |

Session 4 (10.17.2013) | Metric Topology II (convexity) | Homework 4: Problem Set 3 | Problem Set 3 solutions |

Session 5 (10.24.2013) | Functional equations | Homework 5: Problem Set 4 | Problem Set 4 solutions |

Session 6 (10.31.2013) | Math Auction with First and Second Year circles | No homework! | |

Session 7 (11.07.2013) | Metric Topology III (compactness and convergence) “Guess my polynomial” game |
Homework 6: Problem Set 5 | Problem Set 5 solutions |

Session 8 (11.14.2013) | Operations with rational knots | Homework 7: Problem Set 6 | Problem Set 6 solutions |

Session 9 (11.21.2013) | Symmetries of plane figures and solids “Vector speedway” game |
No homework! | |

Session 10 (12.05.2013) | What is (un)known about prime numbers Proof of Bertrand's postulate / Chebyshëv's theorem |
Homework 8: Problem Set 7 | Problem Set 7 solutions |

Session 11 (12.12.2013) | Zometool Contest with First and Second Year circles | No homework! | |

Session 12 (01.09.2014) | Guest talk by Matt Campagna, “A lesson in classical cryptography” | No homework! | |

Session 13 (01.16.2014) | “Labyrinth” game | Homework 9: Problem Set 8 | Problem Set 8 solutions |

Session 14 (01.23.2014) | Group Theory I (definitions) | Homework 10: Problem Set 9 | Problem Set 9 solutions |

Session 15 (01.30.2014) | Group Theory II (subgroups and cyclic subgroups) | Homework 11: Problem Set 10 | Problem Set 10 solutions |

Session 16 (02.06.2014) | Group Theory III (permutations) | Homework 12: Problem Set 11 | Problem Set 11 solutions |

Session 17 (02.13.2014) | Exploring the 2×2×2 and 3×3×3 Rubik's Cubes | No homework! | |

Session 18 (02.20.2014) | Lecture by Austin on elliptic curves A Relatively Easy to Understand Primer on ECC from Ars Technica |
(Optional) Homework 13: Problem Set 12 | |

Session 18½ (02.25.2014) | Bay Area Mathematical Olympiad from 4 to 8:30 PM in Miller Hall room 302B | ||

Session 19 (03.06.2014) | Group Theory IV (Lagrange's theorem) Quotients Homophones des Groupes Libres / Homophonic Quotients of Free Groups |
Homework 14: Problem Set 13 | |

Session 20 (03.20.2014) | Cayley graphs and domino tilings Domino tiling animation and Conway's Tiling Groups |
Homework 15: Problem Set 14 | |

Session 21 (03.27.2014) | The geometric series and random walks on graphs | Homework 16: Problem Set 15 | |

Session 22 (04.03.2014) | Favourite rational numbers Some of the many things counted by the Catalan numbers |
Homework 17: Problem Set 16 | |

Session 23 (04.10.2014) | Banach-Tarski Paradox I (construction of a Vitali set) | No homework! | |

Session 24 (04.24.2014) | Banach-Tarski Paradox II (free groups) The Robinson-Schensted correspondence and “civilized pictures” a.k.a. standard Young tableauxParking functions |
Homework 18: Problem Set 17 | |

Session 25 (05.01.2014) | More RSK and Schützenberger's jeu de taquinMore parking functions |
Homework 19: Problem Set 18 | |

Session 26 (05.08.2014) | Recursive counting Dungeon game |
No new homework! | |

Session 27 (05.15.2014) | The “extreme principle” in geometry Incidence geometry: points, lines, coloured points, coloured lines Coloured lines game |
Homework 20: Problem Set 19 | |

Session 28 (05.22.2014) | Forbidden minors for graphs (Kuratowski, Wagner, Robertson-Seymour theorems) Geometry with mass points |
Homework 21: Problem Set 20 | |

Session 29 (05.29.2014) | Some very↑↑↑very big numbers The joys of cutting polygons into triangles (Fáry's, Pick's, Bolyai-Gerwien theorems) |
No homework! | |

Session 29½ (06.01.2014) | Math Hour Olympiad from 9 AM to 3 PM in Savery Hall | ||

Session ω (06.05.2014) | Math Auction with First and Second Year circles |

All TeX, DVI, and PDF files can be found in this directory. Some sources of problems and materials.