| Date | Topics | Book sections |
| 01/09 | Course information | -- |
| 01/11 | Propositional logic | 1.1, 1.2 |
| 01/16 | Predicates and quantifiers, sets and set operations | 1.3, 1.4, 1.5 |
| 01/18 | Relations and functions | 6.1, 1.6 |
| 01/23 | Cardinality; countable and uncountable sets | 1.7 (last part) |
| 01/25 | Growth of function: Big O, Omega, and Theta notations | 1.8 |
| 01/30 | Class cancelled | -- |
| 02/01 | Proof methods (direct and indirect proofs, proofs by contradiction), integer arithmetic (primes, fundamental theorem of arithmetic, gcd) | 3.1, 2.3 |
| 02/06 | Gcd characterization, Euclid's gcd algorithm, linear congruences, inverse modulo m | Ex.58 (p.201), 2.4, 2.5 |
| 07/01 | Chinese remainder theorem, Euler's phi-function, Fermat's theorem, the RSA cryptosystem | 2.5 |
| 02/13 | Test #1 | --- |
| 02/15 | Mathematical induction, basic summation formulas | 1.7, 3.2 |
| 02/20 | More induction proofs, second principle of mathematical induction | 3.2 |
| 02/22 | Advanced induction proofs, Euler's formula, arithmetic vs. geometric mean inequality | 7.7, Ex.55 (p.201) |
| 02/27 | More advanced induction proof techniques: ranking players in tournaments | Ex.34 (p.524) |
| 03/01 | Basic counting, the inclusion-exclusion principle (proof by induction) | 4.1, 5.5 |
| 03/13 | Applications of the basic counting rules, the pigeonhole principle | 4.1, 5.6, 4.2 |
| 03/15 | Applications of the Pigeonhole principle | 4.2 |
| 03/20 | Permutations and combinations, binomial coefficients, identities with binomial coefficients, Pascal's triangle, bijective (combinatorial) proofs | 4.3 |
| 03/22 | More identities with binomial coefficients, permutations with repetitions, applications of binomial coefficients to counting | 4.3, 4.6 (examples) |
| 03/27 | Finite probability | 4.4, 4.5 |
| 03/29 | Conditional probability, review for test #2 | 4.5 |
| 04/03 | Test #2 | --- |
| 04/05 | Recurrence relations, Fibonacci numbers, solving linear homogeneous recurrences of fixed degree | 5.1, 5.2 |
| 04/10 | Divide-and-Conquer recurrences, proving asymptotic (Big O) bounds on the solution of a Divide-and-Conquer recurrence | 5.3 (w/ additional material) |
| 04/12 | Undirected graphs: graph terminology, isomorphic graphs, connectivity | 7.1, 7.2, 7.3, 7.4 |
| 04/17 | Review of test #2 results, characterization of bipartite graphs | 7.2 |
| 04/19 | Planar graphs, Euler's formula, Kuratowski's theorem; introduction to trees | 7.7, 8.1 |
| 04/24 | Counting graphs and trees; Lower bound for sorting | 8.4 (Pruffer's code not in book) |
| 04/26 | Review | -- |
| Date | Topics | Book sections |