Ron Holzman’s office hours:
Monday 11:00-12:00 , Amado 605
Combinatorics (104286), Spring 2016/17:
|Lecture: Sunday||Recitation: Sunday|
|Place:||Amado 234||Amado 234|
1. Elementary enumeration problems.
2. The binomial coefficients and their properties.
3. The inclusion-exclusion principle.
5. The pigeonhole principle.
6. Graphs: basic notions.
7. Eulerian graphs.
8. The marriage theorem.
9. Ramsey’s theorem.
10. Coloring and planarity.
Mathematical Logic (106156), Spring 2016/17:
|Place:||Ullman 603||Ullman 505|
1. The propositional calculus: Atomic and composite propositions, logical connectives, truth tables, tautologies. Axioms and rules of inference. The deduction theorem. The completeness theorem. The strong completeness theorem. The compactness theorem and its applications.
2. The predicate calculus: Quantifiers, variables, constants, functions and predicates, terms, formulas, substitutions. Structures and assignments, the satisfaction of a formula. Axioms and rules of inference. The completeness theorem. First order theories and their models. The Skolem-Lowenheim theorem. The compactness theorem. Categorical, complete, and decidable theories.
3. Godel’s incompleteness theorem: Formal number theory, the incompleteness theorem and a sketch of its proof