Courses

 

Ron Holzman’s office hours:

Monday 11:00-12:00 , Amado 605

 

Combinatorics  (104286),  Spring 2016/17:

  Lecture: Sunday Recitation: Sunday
 Hours:  14:30-16:30 16:30-17:30
 Place:  Amado 234  Amado 234

Syllabus:

1. Elementary enumeration problems.

2. The binomial coefficients and their properties.

3. The inclusion-exclusion principle.

4. Recurrences.

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:

  Monday Thursday
 Hours:  08:30-10:30  13:30-14:30
 Place:  Ullman 603  Ullman 505

Syllabus:

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