Lajos Soukup

SET2020SPRING Course

Budapest Semester in Mathematics


Instructor: Dr Lajos Soukup

E-mail: lsoukup@gmail.com

Text: The course is based on printed handouts distributed in class

Link to the Handout

Learning Outcomes
we learn how to use set theory as a powerful tool in algebra, analysis, combinatorics, and even in geometry; we study how to build up a rich mathematical theory from simple axioms; we get an insight how set theory can serve as the foundation of mathematics
Course outline
Introduction. Logic in nutshell
Set theory as the study of infinity.
Countable sets and their combinatorics.
Cardinalities. Cardinal arithmetic.
Axiom of Choice. Ordered and well-ordered sets. Zorn lemma and its applications.
Well-ordering Theorem. Transfinite induction and recursion.
Applications in algebra, analysis, combinatorics and geometry
Ordinals, ordinals arithmetic and its applications.
Cardinalities revisited. Cofinalities.
Infinite combinatorics. Continuum hypothesis.
Axiomatic Set Theory


Homeworks:
Link to file Availability Deadline
HW1 available since Feb. 4, 2020, 10 a.m. Feb. 11, 2020, 8:15 a.m.
HW2 available since Feb. 11, 2020, 10 a.m. Feb. 25, 2020, 8:15 a.m.
HW3 available since Feb. 25, 2020, 10 a.m. March 3, 2020, 8:15 a.m.
HW4 available since March 3, 2020, 10 a.m. March 10, 2020, 8:15 a.m.
2020s-HW5 available since March 10, 2020, 10 a.m. March 17, 2020, 8:15 a.m.


Grading
  • Homework assignments: 40%, midterm exam: 20%, final exam: 40%
  • 12 homework assigments, the best 10 count
  • Extra hw problems for extra credits
  • A: 80-100%, B: 60-79%, C: 50-59%, D: 40-49% take-home midterm, in class, open book, comprehensive final.