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About the Book
Active Learning
Problem-based Learning
Python Programming Language
Acknowledgments
Mathematical Thinking in Computer Science
Proofs: Convincing Arguments
Warm Up
Existence Proofs
Finding an Example
How to Find an Example
Optimality
Computer Search
Recursion and Induction
Recursion
Induction
Logic
Examples and Counterexamples
Logic
Reductio ad Absurdum
Invariants
Double Counting
Searching for Invariants
Termination
Even and Odd Numbers
Project: -Puzzle
The Puzzle
Permutations and Transpositions
Why -puzzle Has No Solution
When -puzzle Has a Solution
Implementation
Appendix
Cutting a Figure
Using SAT-solvers
Using ILP-solvers
Visualizing Football Fans
Combinatorics and Probability
Basic Counting
Starting to Count
Recursive Counting
Tuples and Permutations
Binomial Coefficients
Number of Games in a Tournament
Combinations
Binomial Theorem
Practice Counting
Advanced Counting
Review
Combinations with Repetitions
Practice Counting
Probability
What is Probability?
Probability: Do's and Don'ts
Conditional Probability
Monty Hall Paradox
Random Variables
Random Variables and Their Expectations
Linearity of Expectation
Expectation is Not All
Markov's Inequality
Dice Games
Dice Game Problem
Optimal Strategy