Math 3012 Applied Combinatorics

T-Th 8:00 - 9:15 amSkiles 249

Fall 2017

- Office: Skiles 108 D
- Office Hours: 9:30 - 10:20 am, Tuesday.
- Office Hours: 9:05 - 9:55 am, Wednesday.
- Email: trotter at math dot gatech dot edu

- Applied Combinatorics: Keller and Trotter

- Although geared primarily for Distance Learning Students, the videos available at Math 3012 Open Resources Web Site should also be of value to students taking the course on-campus. In support of these videos, a set of powerpoint slides were prepared and these are listed in pdf format below. As the semester progresses, I will be editing and updating these slides so the new versions will be listed first. This list will expand with time. Please note that the list of topics for the videos and the slides from 2015 may not match exactly with our course this year, so these materials should be considered as course supplements. The updated versions should be a better match.
- 1 - Introduction to Combinatorics
- 2 - Strings and Binomial Coefficients
- 3 - Induction and Recursion
- 4 - Pigeon Hole Principle and Complexity
- 5 - Graph Theory Basics
- 6 - Euler Circuits and Hamiltonian Cycles
- 7 - Graph Coloring
- 8 - Planar Graphs
- 9 - Graph Theory Advanced Topics
- 10 - Posets Basic Concepts
- 11 - Chain and Antichain Partitions
- 12 - Cover Graphs and Comparability Graphs
- 13 - Interval Orders and Interval Graphs
- 14 - Subset Lattices
- 15 - Inclusion-Exclusion
- 16 - Generating Functions
- 17 - Advancement Operator Equations
- 18 - Spanning Tree Algorithms
- 19 - Shortest Paths Algorithms
- 20 - Network Flows
- 21 - Flows with Unit Capacities
- 22 - Solving the Dilworth Problem
- 23 - Applications of Probability to Combinatorics
- Lecture 1 - August 18, 2015
- Lecture 2 - August 20, 2015
- Lecture 3 - August 25, 2015
- Lecture 4 - August 27, 2015
- Lecture 5 - September 1, 2015
- Lecture 6 - September 3, 2015
- Lecture 7 - September 8, 2015
- Lecture 8 - September 10, 2015
- Lecture 9 - September 15, 2015
- Lecture 10 - September 22, 2015
- Lecture 11 - September 24, 2015
- Lecture 12 - September 29, 2015
- Lecture 13 - October 1, 2015
- Lecture 14 - October 6, 2015
- Lecture 15 - October 8, 2015
- Lecture 16 - October 15, 2015
- Lecture 17 - October 20, 2015
- Lecture 18 - October 27, 2015
- Lecture 19 - October 29, 2015
- Lecture 20 - November 3, 2015
- Lecture 21 - November 5, 2015
- Lecture 22 - November 10, 2015
- Lecture 23 - November 12, 2015
- Lecture 24 - November 17, 2015
- Lecture 25 - November 19, 2015
- Lecture 26 - December 1, 2015
- Lecture 27 - December 3, 2015

- One of the down-sides to a freely available text is that professionally prepared solutions are not typically available. Here is the partial list of solutions that we have to date.
- Chapter 2 Solutions
- Chapter 3 Solutions
- Chapter 5 Solutions
- Chapter 6 Solutions
- Chapter 7 Solutions
- Chapter 8 Solutions
- Chapter 9 Solutions

- Graphs - Basic Concepts
- Partially Ordered Sets - Basic Concepts
- Euler Circuits in Graphs
- Dijkstra's Algorithm
- Spanning Tree Algorithms

- sum_recursive.c
- sum_loop.c
- collatz_sequence.c
- gcd_lcm.c
- combinatorics.h
- mergesort.c random_ints.txt
- big_integer_addition.c
- two_big_integers.txt