Unless otherwise specified, all readings are in RosenBook. Click on each date for detailed notes (if available). As always, the future is uncertain, so you should take parts of the schedule that haven't happened yet with a grain of salt.

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Readings: RosenBook Section 1.1.

Readings: RosenBook Section 1.2.

Readings: RosenBook Sections 1.3 and 1.4.

Note: The "unique successor" axiom from the nested quantifiers example given in lecture isn't one of the PeanoAxioms; instead one uses a "unique predecessor" axiom that says for all x, x', y, and y' that if x'=y' and Sxx' and Syy', then x=y. Together with the other axioms, this gives something that looks much more like the natural numbers.

Readings: RosenBook Section 1.5.

Readings: Section 1.5.

Readings: Sections 1.6 and 1.7.

  • More SetTheory. Ordered pairs, intersections, set difference. Proving equality and subset relations between sets. Constructing the universe.

Readings: Section 1.8.

Readings: RosenBook Section 3.3. (Note: some of the examples will depend on topics that appear earlier in RosenBook that we haven't covered yet; you should feel free to ignore these, or to read the appropriate earlier sections.)

  • More InductionProofs: strong induction. Sequences.

  • We also talked about the diagonal Ramsey numbers as an example of a sequence for which we have a definition but we don't know (and probably will never be able to find) all of its values. The sequence starts 1, 2, 6, 18, but subsequent numbers in the sequence are unknown. You don't need to know about Ramsey numbers for the course, but if you want to find out more about them a good starting point is here.

Readings: RosenBook Section 3.2.

Readings: RosenBook Section 3.2.

Readings: RosenBook Section 3.4.

Readings: RosenBook Sections 4.1 and 4.2.

Readings: RosenBook sections 4.4 and 4.5.

Readings: RosenBook section 6.4.

Readings: RosenBook Sections 6.1 and 6.2.

Readings: RosenBook sections 5.1 and 5.2.

Readings: Section 5.3.

  • Last of ProbabilityTheory (for now): Variance and applications. Chebyshev's inequality.

  • Relations, digraphs, and matrices. Properties of relations.

Readings: RosenBook 7.1 and 7.3.

  • More Relations: equivalence relations and partial orders.

Readings: RosenBook sections 7.5 and 7.6.

  • GraphTheory basics. Directed vs undirected graphs. Multigraphs, hypergraphs, bipartite graphs. Some standard graphs.

Readings: RosenBook Section 8.1 and 8.2.

  • More GraphTheory: Operations on graphs: homormorphisms, isomorphisms, automorphisms; subgraphs; unions, intersections, and products.

Readings: RosenBook Section 8.3.

Readings: RosenBook Sections 7.4 and 8.4.

  • GraphTheory: Cycles in graphs. Eulerian and Hamiltonian graphs.

Readings: RosenBook Section 8.5.

  • More AlgebraicStructures: subalgebras, homomorphisms, free algebras, product algebras, quotient algebras.

  • More GroupTheory. Subgroups and quotient groups. Generators and relations.

  • NumberTheory: divisibility and primality. The extended GCD algorithm.

Readings: RosenBook Section 2.4.

  • More NumberTheory. The Fundamental Theorem of Arithmetic. The multiplicative group Z*m.

  • Some theorems in NumberTheory: Fermat's Little Theorem, Euler's Theorem, the Chinese Remainder Theorem.

CS202/2004/Schedule (last edited 2007-12-25 23:42:28 by localhost)