Instructor: Marcia Groszek
Course on Canvas: https://canvas.dartmouth.edu/courses/46263 ⇗
Syllabus
1. March 29-April 2
(a) Monday: Introduction to set theory. Chapter 1, section (a), pages 1-7.
(b) Tuesday (x-hour): Proof-writing workshop: proof by cases; uniqueness.
(c) Wednesday: Overview of axiomatic set theory. Chapter 1, sections (b)-(f), pages 7-16.
(d) Friday: The first axioms. Chapter 2, sections (a)-(b), pages 17-26.
2. April 5-9
(a) Monday: Algebra of sets Chapter 2, sections (c)-(e), pages 27-34.
(b) Tuesday (x-hour): Proof-writing workshop: mathematical induction.
(c) Wednesday: Ordered pairs and relations. Chapter 3, sections (a)-(c), pages 35-42.
(d) Friday: Functions. Chapter 3, sections (d)-(e), pages 42-55.
3. April 12-16
(a) Monday: Equivalence relations. Chapter 3, section (f), pages 55-62.
(b) Tuesday (x-hour): Proof-writing workshop: well-defined functions and relations on equivalence classes, part 1.
1(c) Wednesday: Ordering relations. Chapter 3, sections (g)-(h), pages 62-66.
(d) Friday: Natural numbers. Chapter 4, sections (a)-(b), pages 67-73.
4. April 19-23
Exam this week on material covered in weeks 1-3.
(a) Monday: Recursion on ω. Chapter 4, section (c), pages 73-78.
(b) Tuesday (x-hour): No x-hour this week.
(c) Wednesday: Arithmetic. Chapter 4, section (d), pages 79-82.
(d) Friday: Ordering the natural numbers. Chapter 4, sections (e)-(f), pages 83-89.
5. April 26-30
(a) Monday: Integers. Chapter 5, section (a), pages 90-101.
(b) Tuesday (x-hour): Proof-writing workshop: contradiction and contraposition.
(c) Wednesday: Representing mathematical objects as sets. Chapter 5, section (e), pages 123-127.
(d) Friday: Sizes of sets. Chapter 6, section (a), pages 128-133.
6. May 3-7
(a) Monday: Finite sets. Chapter 6, Section (b), pages 133-138.
(b) Tuesday (x-hour): Proof-writing workshop: well-defined functions and relations on equivalence classes, part 2.
2(c) Wednesday: Cardinal arithmetic. Chapter 6, section (c), pages 138-145.
(d) Friday: Ordering cardinal numbers. Chapter 6, section (d), pages 145-151.
7. May 10-14 Exam this week on material in weeks 1-6 (mostly weeks 4-6).
(a) Monday: The axiom of choice. Chapter 6, section (e), pages 151-159.
(b) Tuesday (x-hour): No x-hour today.
(c) Wednesday: Infinite cardinals. Chapter 6 sections (f)-(h), pages 159-166.
(d) Friday: Partial orderings. Chapter 7, section (a), pages 167-172.
8. May 17-21
(a) Monday: Well orderings. Chapter 7, section (b), pages 172-179.
(b) Tuesday (x-hour): Proof-writing workshop: transfinite induction.
(c) Wednesday: Replacement axioms. Chapter 7, section (c), pages 179-18
(d) Friday: Epsilon images and isomorphisms. Chapter 7, sections (d)-(e), pages 182-187.
9. May 24-28
(a) Monday: Ordinal numbers. Chapter 7, section (f), pages 187-195.
(b) Tuesday (x-hour): Proof-writing workshop: wrap-up.
(c) Wednesday: Cardinal numbers. Chapter 7, section (g), pages 195-200.
3(d) Friday: Rank. Chapter 7, section (h), pages 200-208.
10. May 31-June 4
(a) Monday: No class; Memorial Day.
(b) Tuesday (x-hour): No x-hour today.
(c) Wednesday: Conclusion. Last day of class.
11. Exam during finals period, cumulative, concentrating on material in weeks 7-9.