Discrete Math Fall 2013
Course Syllabus:
Final Exam: 10:30am-1:15pm Thursday Dec 12 in Kleist 102
Office hours:
M 6:15-7:15 pm
T 2:00-4:00 pm
W 6:15-7:15 pm (or by appointment -- einsko@fgcu.edu)
MAD 3107 is an introduction to concepts of discrete mathematics, as used by computer scientists.
Topics include: symbolic logic and Boolean algebra, prepositional and predicate calculus, sets,
functions, and relations, enumeration and counting principles, introduction to graphs, trees,
spanning trees, shortest path and matching algorithms, finite state automata, and Turing machines.
Prerequisities:
MAC 2312 with a minimum grade of C.
Course text:
Discrete Mathematics, 5th edition, by Dossey, Otto, Spence, and Vanden Eynden, Addison-Wesley.
Class Resources:
Lecture 2 - Algorithms and their efficiency
Lecture 4 - Sets, operations, and relations
Lecture 5 - Partial Orderings and Functions
Lecture 9 - Multigraphs and Euler Circuits
Lecture 10 - Distance in Graphs and Shortest Paths
Lecture 11 - Directed Graphs and Multigraphs
Lecture 12 - Properties of Trees
Lecture 13 - Depth-First Search
Lecture 14 - Binary trees and traversals
Lecture 14 - Optimal binary trees
Lecture 15 - Pascal's Triangle and the Binomial Theorem
Lecture 15 -Three Fundamental Principles
Lecture 16- Permutations and Combinations
Lecture 16 - Arrangements and Selections with Repetition
Lecture 18 - Inclusion-Exclusion
Lecture 18 - Recurrence Relations
Lecture 19 - The Method of Iteration
Lecture 20 -- Linear Difference Equations with Constant Coefficients
Lecture 21 -- Counting with Generating Functions
Lecture 22 -- The Algebra of Generating Functions
Lecture 23 -- Boolean Algebra and Logical Gates
Lecture 23 -- Creating Combinatorial Circuits
Lecture 23 -- Supplementary Material
Homework Sets:
- Assignment 1C
- Assignment 2C
- Assignment 3C
- Assignment 4C Assignment 4C Assignment 4C
- Assignment 5C Assignment 5C Assignment 5C
- Assignment 13C
- Assignment 14C
- Assignment 15C
- Assignment 16C Assignment 16C
- Assignment 20C Assignment 20C
- Assignment 21C Assignment 21C Assignment 21C
- Assignment 22C
- Induction Examples
- A website discussing the combinatorics of relations
- Wikipedia page on combinatorial proofs
Review Assignments:
Some interesting research papers in related subjects:
- Roman Domination of Grids and Toroidal Grids
- Weighted Domination of Grids
- Broadcasting Domination in Graphs
- Capturing a Drunk Robber on a Graph
- The Robber Strikes Back!
- Braess' Paradox in Wireless Networking
A tech article on Braess' Paradox in social networking:
Here are some fun computer projects that you can complete by logging onto Sagenb.org.
Sage is free open source mathematical software based in the python language. In the process, you will learn some basics about programming in python.
Fun Computer Projects:
Here is an interesting blog post on what it is like for mathematicians to learn math