## MATH 181: A Mathematical World## Course infoTime: MWF 2:00 - 2:50 pmPlace: 141 Altgeld Hall *new*Syllabus: link
Instructor: Ruth LuoOffice: Coble Hall B2Office hours: Thursdays 2:00 - 4:00 pm or by appointmentEmail: ruthluo2(at)illinois.edu
Login to check your grades Emergency info ## Important Dates9/28 - Midterm 1Topics include:Eulerian walks and circuits Hamiltonian cycles Traveling Salesman Problem Graph coloring Isomorphisms Planar graphs Stable Marriage Problem Matchings Practice exam Midterm 1 [Solutions] 10/26 - Midterm 2Topics include:Voting systems for 2 candidates May's Theorem (no proof) Voting systems for 3 candidates Arrow's Impossibility Theorem Examples of how to manipulate elections Fair Division (cake cutting procedures) Proportional vs. envy-free procedures Gerrymandering Probability (introduction) Practice exam Midterm 2 [Solutions] 11/30 - Midterm 3Topics include:Conditional probability Expected value Game Theory Prisoner's Dilemma Stag Hunt Nash equilibria Modular arithmetic Practice exam Midterm 3 [Solutions] 12/14 - Final ExamTopics include:All previous topics Caesar cipher Decimation cipher Basic idea of RSA Additional questions [Solutions] ## Group ProjectGuidelines10/29 - Group proposals due12/7 - Group projects due (if presenting, have presentations ready)
## HomeworkHomework 1 - Now complete! - Due 9/24Homework 2 - Now complete! - Due 10/29 Homework 3 - Now complete! - Due 12/03 Homework 4 ## QuizzesQuiz 1 [Solutions]Quiz 2 [Solutions] Quiz 3 [Solutions] Quiz 4 [Solutions] Quiz 5 [Solutions] Quiz 6 [Solutions] Quiz 7 [Solutions] Quiz 8 [Solutions] Quiz 9 [Solutions] ## Class Log8/27 - Seven Bridges of Konigsberg, into to Graph Theory, Eulerian walks and circuits; Introduction slides8/29 - Eulerian walks and circuits (cont.), complete graphs, cycles, paths, connected graphs, Euler's Theorem; WS 1 Solutions8/31 - Finding Eulerian walks and circuits, Hamiltonian cycles, TSP9/5 - Hamiltonian cycles, TSP (cont.); WS 2 Solutions9/7 - P vs. NP, graph coloring, chromatic number; Slides9/10 - Graph coloring (cont.), isomorphisms, planar graphs9/12 - Planar graphs (cont.), Euler's formula; WS 3 solutions9/14 - Planar graphs (cont.)9/17 - Kuratowski's Theorem, Four Color Theorem, stable marriage problem; WS 4 solutions9/19 - Stable matchings, Gale-Shapley algorithm; WS 5 solutions9/21 - Matchings (maximal, maximum, perfect matchings, augmenting paths, Berge's Theorem)9/24 - Practice exam 19/26 - Exam 1 review9/28 - Exam 110/1 - Voting systems10/3 - Voting systems (cont.)10/5 - Voting systems (cont.), proof of May's Theorem; Proof writeup, WS 6 solutions10/8 - Cake-division, divide-and-choose10/10 - Cake-division (cont.), lone-divider10/12 - Cake-division (cont.); WS 7 solutions10/15 - Last-Diminisher method, Selfridge-Conway method10/17 - Gerrymandering, Last-Diminisher WS; WS 8 solutions; WS 9 solutions10/19 - Introduction to probability10/22 - Introduction to probability (cont.), conditional probability10/24 - Exam 2 review10/26 - Exam 210/29 - Conditional probability, expected value10/31 - Expected value (cont.); WS 10 solutions11/2 - WS 10 cont., Introduction to Game Theory11/5 - Prisoner's Dilemma, Stag Hunt, Nash Equilibria (pure vs. mixed)11/7 - Calculating mixed Nash equilibria; WS 11 solutions
11/9 - Hawk/Dove game; WS 12 solutions 11/12 - Introduction to Number Theory11/14 - Modular arithmetic WS 13 solutions11/26 - Modular arithmetic (cont.)11/28 - Exam 3 review11/30 - Exam 312/3 - Cryptology, Prime number contest (details to be sent)12/5 - Cryptology (cont.); WS 14 solutions 12/7 - Group project presentations12/10 - RSA
## Helpful ResourcesGlossary of graph theory termsGraph Creator - draw graphs, drag around vertices (useful for showing two graphs are isomorphic) Random map generator/coloring demo |