**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.