Combinatorics (Math 4707 and Math 4990), Fall 2017

Darij Grinberg (203B Vincent Hall)

Main resources:

Syllabus.

List of references and notations.

David Galvin's notes "Basic discrete mathematics". This is a rather nice set of notes that will have a lot of overlap with this class. Please mail darijgrinberg@gmail.com for questions and comments (I am maintaining these notes currently).

Quick book references: Loehr (errata); Graham/Knuth/Patashnik (errata); Bogart; Bóna.

Basics on equivalence relations and equivalence classes: class materials by Melissa Lynn and by Jonathan Rogness (part 1 and part 2).

Extra notes: Why log and exp are inverse; Sandpiles with proofs (HW5 from 5707S17).

See Math 5707 from Spring 2017 for some graph theory, and my notes on graph theory for more.

Blackboard writing from 4990 (only from the second half of the semester):

• October 10 (source code).
• October 17 (source code).
• October 24 (source code).
• October 31 (source code).
• November 7 (source code).
• November 14 (source code).
• November 21 (bonus material).
• November 28 (see my notes on graph theory for a detailed treatment).
• December 5 (see my notes on graph theory for a detailed treatment).

Homework and other problems:

A LaTeX template for those who want to write their solutions in LaTeX. (Compiled PDF.)

Math 4707:

• Homework set 1 (TeX source). Solutions (TeX source). Alternative solutions by Mark Richard.
• Homework set 2 (TeX source). Solutions (TeX source).
• Midterm 1 (TeX source). Solutions (TeX source). Note: The solutions include some extra questions.
• Homework set 3 (TeX source). Solutions (TeX source).
• Homework set 4 (TeX source). Provisional solutions (TeX source).
• Midterm 2 (TeX source). Provisional solutions to Exercises 1-5, 7 (TeX source).
• Homework set 5 (TeX source). Solutions (TeX source).
• Homework set 6 (TeX source). Solutions to Exercises 2, 3, 4, 7 by Angela Chen. Provisional solution sketches to Exercises 1, 3-6 (TeX source).
• Midterm 3 (TeX source). Solutions to Exercises 1, 3 by Angela Chen. For a solution to Exercise 2, see Exercise 5.27 in [detnotes] (version of 10 January 2019). For a solution to Exercise 9, see my Notes on network flows.

Math 4990:

• Homework set 1 (TeX source). Solutions (TeX source). Alternative solutions by Mark Richard.
• Homework set 2 (TeX source). Solutions (TeX source).
• Homework set 3 (TeX source). Solutions (TeX source).
• Homework set 4 (TeX source). Solutions (TeX source).
• Homework set 5 (TeX source). Provisional solutions (TeX source).
• Homework set 6 (TeX source). Provisional solutions to Exercises 1-5, 7 (TeX source).
• Homework set 7 (TeX source). Solutions (TeX source).
• Homework set 8 (TeX source). Solutions to Exercises 2, 3, 4, 7 by Angela Chen. Provisional solution sketches to Exercises 1, 3-6 (TeX source).
• Homework set 9 (TeX source). Solutions to Exercises 1, 3 by Angela Chen. For a solution to Exercise 2, see Exercise 5.27 in [detnotes] (version of 10 January 2019).