Discrete Mathematics for Computer Science

0 About the Book
	0.1 Active Learning
	0.2 Problem-based Learning
	0.3 Python Programming Language
	0.4 Acknowledgments
Part I — Mathematical Thinking in Computer Science
	1 Proofs: Convincing Arguments
		1.1 Warm Up
		1.2 Existence Proofs
	2 Finding an Example
		2.1 How to Find an Example
		2.2 Optimality
		2.3 Computer Search
	3 Recursion and Induction
		3.1 Recursion
		3.2 Induction
	4 Logic
		4.1 Examples and Counterexamples
		4.2 Logic
		4.3 Reductio ad Absurdum
	5 Invariants
		5.1 Double Counting
		5.2 Searching for Invariants
		5.3 Termination
		5.4 Even and Odd Numbers
	6 Project: 15-Puzzle
		6.1 The Puzzle
		6.2 Permutations and Transpositions
		6.3 Why 15-puzzle Has No Solution
		6.4 When 15-puzzle Has a Solution
		6.5 Implementation
	7 Appendix
		7.1 Cutting a Figure
		7.2 Using SAT-solvers
		7.3 Using ILP-solvers
		7.4 Visualizing Football Fans
Part II — Combinatorics and Probability
	8 Basic Counting
		8.1 Starting to Count
		8.2 Recursive Counting
		8.3 Tuples and Permutations
	9 Binomial Coefficients
		9.1 Number of Games in a Tournament
		9.2 Combinations
		9.3 Binomial Theorem
		9.4 Practice Counting
	10 Advanced Counting
		10.1 Review
		10.2 Combinations with Repetitions
		10.3 Practice Counting
	11 Probability
		11.1 What is Probability?
		11.2 Probability: Do's and Don'ts
		11.3 Conditional Probability
		11.4 Monty Hall Paradox
	12 Random Variables
		12.1 Random Variables and Their Expectations
		12.2 Linearity of Expectation
		12.3 Expectation is Not All
		12.4 Markov's Inequality
	13 Dice Games
		13.1 Dice Game Problem
		13.2 Optimal Strategy