Math 4000 Fall 24
## MATH 4000/5000: Foundations of Mathematics (Fall 2024)

Syllabus
### Office hours

M 11:15 - 12:15 pm, W 12 - 1 pm, 3 pm - 3:30 pm at Math 310
### Schedule

Numbers are for orientation and refer to sections with related material in
the book by Enderton.
- 08/26: set theory, logic, computability, model theory
- 08/28: syntax: sentential logic, formulas (1.1)
- 08/30: semantics: truth assignments, tautological implication (1.2)
- 09/04: tautology and SAT, Boolean functions (1.5)
- 09/06: DNF
- 09/09: complete set of functions (1.5)
- 09/11: Compactness Theorem (1.7)
- 09/13: deductions (1.7)
- 09/16: algorithms, decidability (1.7)
- 09/18 enumerability (1.7)
- 09/20: first order language (2.1)
- 09/23: fo formulas, free variables, sentences (2.1)
- 09/25: L-structures (2.2)
- 09/27: models for formulas (2.2)
- 09/30: logical implications (2.2)
- 10/02: deductions, tautologies (2.4)
- 10/04: substitutions (2.4)

### Assignments

- due 09/04 [pdf] [tex] [solutions]
- due 09/11 [pdf]
- due 09/18 [pdf]
- due 09/25 [pdf] [solutions]
- due 10/02 [pdf]
- due 10/09 [pdf]

### Handouts

- quantifying over variables in some set using unary predicates [pdf]

### Reading

- Herbert B. Enderton. A mathematical introduction to logic (2nd edition, available electronically via the CU library)