MATH 181

Course info

Time: MWF 2:00-2:50
Place: 343 Altgeld Hall
Study session: Thu 5:00-5:50, 141 Altgeld Hall

Instructor: Anton Bernshteyn
Office: 129 Altgeld Hall
Office hours: by appointment
Email: bernsht2 _at_ illinois _dot_ edu

Emergency info.

Important dates

Labor Day: Sept 4 (no class)
Midterm I: Sept 29 (in class)
Project proposal due: Oct 20
Deadline to drop without W: Oct 20
Midterm II: Oct 27 (in class)
Fall break: Nov 20, 22, 24 (no classes)
Midterm III: Dec 1 (in class)
Project due: Dec 8
Last class: Dec 13
Final exam: Dec 15, 8-11am, 343 Altgeld Hall

Homework

Homework 1 (due September 8).
Homework 2 (due September 25).
Homework 3 (due October 23).
Homework 4 (due December 8).

Project

Project guidelines (project proposals are due October 20).

For Exam 1: Practice Exam 1. The topics may include:
• basic graph theory definitions;
• isomorphic graphs;
• P vs. NP question;
• Euler circuits;
• Hamiltonian cycles;
• TSP;
• spanning trees;
• graph coloring;
• planar graphs.
For Exam 2: Practice Exam 2. The topics may include:
• exponential growth and decay;
• logarithms and logarithmic scales;
• continued fractions and rational approximations;
• basic cryptography;
• binary codes;
• data compression;
• error correction.
For Exam 3: Practice Exam 3. The topics may include:
• modular arithmetic;
• positional notation;
• prime numbers;
• RSA;
• voting systems.
For the Final: Review the worksheets, the quizzes, the midterms, and the homework. Make sure you remember and understand everything!

8/28: 10th ed: Chapter 1, Skills Check 1, 2, 4, 10, 14, 18; Ex. 1, 2, 5, 6. 9th ed: Chapter 1, Skills Check 1, 2, 4, 10, 14, 18; Ex. 4, 5, 10.
8/30: 10th ed: Chapter 1, Skills Check 5, 6, 7, 8, 9, 12, 13, 16; Ex. 4. 9th ed: Chapter 1, Skills Check 5, 6, 7, 8, 9, 12, 13, 16; Ex. 2.
9/6: Do the worksheet. 10th ed: Chapter 1, Skills Check 15, 17, 19, 20; Ex. 20. 9th ed: Chapter 1, Skills Check 15, 17, 19, 21; Ex. 18.
9/11: 10th ed: Chapter 2, Skills Check 2, 3, 5, 6, 9, 10, 12; Ex. 1, 3, 5, 6, 19. 9th ed: Chapter 2, Skills Check 2, 3, 5, 6, 9, 10; Ex. 1, 3, 4, 15, 17.
9/13: 10th ed: Chapter 2, Skills Check 22, 24, 25, 26; Ex. 56, 57, 58, 59, 60. 9th ed: Chapter 2, Skills Check 22, 24, 25, 26; Ex. 54, 55, 56, 57, 58.
9/15: Take the route that you found!
9/18: 10th ed: Chapter 3, Skills Check 25, 27, 29, 30; Ex. 75, 77, 78, 82. 9th ed: Chapter 3, Skills Check 25, 26, 29, 30; Ex. 71, 72, 76.
10/4: Finish the worksheet. 10th ed: Chapter 21, Skills Check 6, 8, 10, 13, 15; Ex. 10, 12, 14. 9th ed.: Chapter 21, Skills Check 6, 8, 10, 13, 15; Ex. 6, 17(b).
10/9: Finish the worksheet.
10/13: Finish the worksheet.
10/16: 10th ed: Chapter 17, Skills Check 15; Ex. 35 (use shift 3), 36, 37. 9th ed: Chapter 17, Skills Check 13; Ex: 31 (use shift 3), 33.
10/18: 10th ed: Chapter 17, Ex. 20, 21, 22, 23, 24, 25, 29, 31, 32. 9th ed: Chapter 17, Ex. 16, 17, 18, 19, 20, 21, 25, 27, 28, 29.
10/20: 10th ed: Chapter 16, Ex. 23, 24, 25, 26, 27, 28, 29. 9th ed: Chapter 16, Ex. 21, 22, 23, 24, 25, 26, 27.
10/30: 10th ed: Chapter 17, Skills Check 13; Ex. 33, 34. 9th ed: Chapter 17, Skills Check 12; Ex. 30.
11/13 10th ed: Chapter 9, Ex. 5, 6, 7, 8, 9, 10. 9th ed: Chapter 9, Ex. 6, 7, 8, 9, 10, 11.

Exams

Exam 1 [Solutions]
Exam 2 [Solutions]
Exam 3 [Solutions]
Final Exam [Solutions]

Quizzes

Quiz 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]
Quiz 10 [Solutions]
Quiz 11 [Solutions]

Class log

8/28: Intro to Graph Theory (Chapter 1.1). Basic definitions. [Summary] [Worksheet]
8/30: Isomorphisms. [Summary] [Worksheet]
9/1: Euler circuits (Chapter 1.1). Definitions. [Summary] [Worksheet]
9/4: Labor Day (no class).
9/6: Euler's theorem (Chapter 1.1). [Summary] [Worksheet]
9/8: Activity: Graeco-Latin squares. [Worksheet]
9/11: Hamiltonian cycles and the TSP (Chapters 2.1, 2.2, 2.3) [Summary] [Worksheet]
9/13: Spanning trees (Chapter 2.4). [Summary] [Worksheet]
9/15: Activity: TSP in Altgeld Hall. [Worksheet]
9/18: Graph coloring (Chapter 3.5). Definitions. [Summary] [Worksheet]
9/20: Four Color Theorem. [Summary] [Worksheet]
9/22: Planar graphs. [Summary] [Worksheet] [Project guidelines]
9/25: Euler's formula. [Summary] [Worksheet]
9/27: Platonic solids. [Summary] [Worksheet]
9/29: Midterm I.
10/2: Musical intervals. [Summary]
10/4: Exponential growth (Chapter 21.2). [Summary] [Worksheet]
10/6: Musical intervals II. [Summary]
10/9: Logarithms and logarithmic scales. [Summary] [Worksheet]
10/11: Musical intervals III: rational approximations. [Summary]
10/13: Continued fractions. [Summary] [Worksheet]
10/16: Intro to Cryptography (Chapter 17.4). [Summary] [Worksheet] [Challenge problem]
10/18: Data compression (Chapter 17.3). [Summary] [Worksheet]
10/20: Checksums. [Summary] [Worksheet]
10/23: Error correction (Chapters 17.1 and 17.2). [Summary]
10/25: Hamming codes. [Worksheet]
10/27: Midterm II.
10/30: Modular arithmetic (Chapter 17.4). [Summary] [Worksheet]
11/1: RSA. [Summary]
11/6: RSA II. [Summary] [Worksheet]
11/8: Positional notation. [Worksheet]
11/10: Prime numbers and the RSA. [Summary] [Worksheet] [Prime Number Contest]
11/13: Voting systems (Chapters 9.1, 9.2, 9.3). [Worksheet]
11/15: Voting systems II (Chapters 9.1, 9.2, 9.3). [Summary]
11/17: Impossibility theorems in voting theory. [Summary] [Optional problem]
11/27: Testing divisibility by 9. [Summary] [Worksheet]
11/29: Ultrafilters. [Summary]
12/1: Midterm III.
12/4: Combinatorial games. [Summary] [Worksheet]
12/6: Game of Life. [Summary 1] [Summary 2] [Worksheet]
12/8: Review (thanks to Kanea Hughes!). [Link to the game]
12/11: Project presentations (thanks to Jose Fernandez and Anthony Kim!). [Jose's Worksheet] [Anthony's Slides]
12/13: Review. [Worksheet]

Department of Mathematics     University of Illinois at Urbana-Champaign     College of Liberal Arts & Sciences