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.
  1. 08/26: set theory, logic, computability, model theory
  2. 08/28: syntax: sentential logic, formulas (1.1)
  3. 08/30: semantics: truth assignments, tautological implication (1.2)
  4. 09/04: tautology and SAT, Boolean functions (1.5)
  5. 09/06: DNF
  6. 09/09: complete set of functions (1.5)
  7. 09/11: Compactness Theorem (1.7)
  8. 09/13: deductions (1.7)
  9. 09/16: algorithms, decidability (1.7)
  10. 09/18 enumerability (1.7)
  11. 09/20: first order language (2.1)
  12. 09/23: fo formulas, free variables, sentences (2.1)
  13. 09/25: L-structures (2.2)
  14. 09/27: models for formulas (2.2)
  15. 09/30: logical implications (2.2)
  16. 10/02: deductions, tautologies (2.4)
  17. 10/04: substitutions (2.4)

Assignments

  1. due 09/04 [pdf] [tex] [solutions]
  2. due 09/11 [pdf]
  3. due 09/18 [pdf]
  4. due 09/25 [pdf] [solutions]
  5. due 10/02 [pdf]
  6. due 10/09 [pdf]

Handouts

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

Reading