SYLLABUS
topics (tentative).
- Introduction to DM- Proofs
- Counting
- Modular arithmetic
- Graphs
- Coloring
- Probability
- More number theory/ algebra
Advanced topic ideas.
- Optional projects. [pdf]Schedule.
[11-Nov-2016] [pdf] Bertrand's postulate. Density bounds.
[10-Nov-2016] [pdf] Prime number estimates.
[07-Nov-2016] [pdf] Super-concentrators via concentrators.
[04-Nov-2016] [pdf] Extremal set family. Super-concentrators.
[03-Nov-2016] [pdf] Discrepancy. Set family.
[31-Oct-2016] [pdf] Probabilistic method examples. Sum-free subset, Ramsey number.
[28-Oct-2016] [pdf] Chernoff inequality. Probabilistic method.
[27-Oct-2016] [pdf] Examples. Chebyshev-Markov, Chernoff inequalities.
[24-Oct-2016] [pdf] Expectation, linearity.
[20-Oct-2016] [pdf] Examples. Random variable.
[17-Oct-2016] [pdf] Examples. Bayes' theorem.
[07-Oct-2016] [pdf] Examples of sigma-field. Conditional probability.
[06-Oct-2016] [pdf] Probability, sigma-field.
[03-Oct-2016] [pdf] Planarity, Euler's formula. Probability.
[30-Sep-2016] [pdf] Hall's theorem. Planarity.
[29-Sep-2016] [pdf] Matching, alternating path.
[26-Sep-2016] [pdf] Coloring, chromatic number.
[23-Sep-2016] [pdf] Independent set, clique, vertex cover.
[22-Sep-2016] [pdf] Max/min eigenvalue of adjacency matrix.
[19-Sep-2016] [pdf] Hamiltonian cycle. Adjacency, incidence matrices.
[09-Sep-2016] [pdf] Tree, Eulerian circuit.
[08-Sep-2016] [pdf] Cycle, connected components.
[05-Sep-2016] [pdf] Graphs, walks, paths, cycles.
[02-Sep-2016] [pdf] Totient function. Möbius inversion.
[01-Sep-2016] [pdf] Modular inverse. FLT.
[29-Aug-2016] [pdf] Fundamental theorem of arithmetic. Modulo.
[20-Aug-2016] [pdf] Extended Euclid's gcd algorithm.
[19-Aug-2016] [pdf] Averaging principle. Basic number theory.
[18-Aug-2016] [pdf] Pigeon-hole principle.
[12-Aug-2016] [pdf] Generating functions.
[11-Aug-2016] [pdf] Fibonacci generating function.
[08-Aug-2016] [pdf] Inclusion-exclusion, recurrence.
[06-Aug-2016] [pdf] Counting techniques.
[05-Aug-2016] [pdf] Countability, induction.
[04-Aug-2016] [pdf] Contrapositive, contradiction.
[01-Aug-2016] [pdf] Proofs.
[28-Jul-2016] [pdf] Introduction.