Discrete Mathematics for Computer Science

Lecture Topic
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Pancakes with a problem
Deterministic Finite Automata
Solving problems and writing proofs
Inductive Reasoning
Ancient Wisdom: Unary and Binary
Counting I: Correspondences and Choice Trees
Counting II: Recurring Problems and Correspondences
Counting III
The Mathematics of 1950's Dating
Probability Theory: Counting in Terms of Proportions
Probability Theory: Great Expectations
Random Walks
Ancient Wisdom: On Raising A Number to a Power
Euclid's Algorithm and Continued Fractions
Fibonacci Numbers, Polynomial Coefficients, Vector Programs
Randomness and Computation
Modular Arithmetic and the RSA Cryptosystem
Group Theory
Graphs II
The Big Oh
Grade School Revisited: How to Multiply Two Numbers
Cantor's Legacy: Infinity and Diagonalization
Turing's Legacy: The Limits of Computation
Godel's Legacy: What is a Proof?
Complexity Theory: Reductions Between Computational Problems
Complexity Theory: The P vs. NP Question

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