Math 3012 Applied Combinatorics

M - W - F 8:00 - 8:50 amKlaus 1456

Spring 2018

- Office: Skiles 108 D
- Office Hours: Thursday 8:00 - 8:55 and 13:30 - 14:20.
- Office Hours: Friday 9:05 - 9:55.
- Email: trotter at math dot gatech dot edu

- Applied Combinatorics: Keller and Trotter

- Although geared primarily for Distance Learning Students, the videos prepared in 2015 and available at Math 3012 Open Resources Web Site should also be of value to students taking the course on-campus. Pdf slides were also prepared in 2015 which correlate with these videos. However, during the fall 2017 semester, these slides were updated and I expect that the new versions will be a better match for our spring 2018 course. These new versions are listed immediately below. In any case, course content always varies somewhat from semester to semester, reflecting both my efforts to improve the course while highlighting current and unfolding developments in combinatorics. As the semester progresses, I expect to upload new materials, especially when topics being discussed are not covered in the text.
- 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

- Test 1 - 2017 Test 1 - 2017 - Solutions
- Test 2 - 2017 Test 2 - 2017 - Solution
- Test 3 - 2017 Test 3 - 2017 - Solutions
- Final Exam - 2017 Final Exam - 2017 - Solutions

- Test 1 - 2015 Test 1 - 2015 - Solutions
- Test 2 - 2015 Test 2 - 2015 - Solutions
- Test 3 - 2015 Test 3 - 2015 - Solutions
- Final Exam - 2015 Final Exam - 2015 - Solutions

- Test 1 - 2014 Test 1 - 2014 - Solutions
- Test 2 - 2014 Test 2 - 2014 - Solutions
- Test 3 - 2014 Test 3 - 2014 - Solutions
- Final Exam - 2014 Solutions not available.

- Test 1 - 2013 Test 1 - 2013 - Solutions
- Test 2 - 2013 Test 2 - 2013 - Solutions
- Test 3 - 2013 Test 3 - 2013 - Solutions
- Final Exam - 2013 Final Exam - 2013 - Solutions

- Test 1 - 2011 Test 1 - 2011 - Solutions
- Test 2 - 2011 Test 2 - 2011 - Solutions
- Test 3 - 2011 Test 3 - 2011 - Solutions
- Final Exam - 2011 Final Exam - 2011 - Solutions

- Test 1 - 2010 - Solutions
- Test 2 - 2010 - Solutions
- Test 3 - 2010 - Solutions
- Final Exam - 2010 Final Exam - 2010 - Solutions

- Test 1 - 2009 - Solutions
- Test 2 - 2009 - Solutions
- Test 3 - 2009 - Solutions
- Final Exam - 2009 - 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