Class Schedule
All textbook sections come from the official course textbook, Introduction to Set Theory by Karel Hrbacek and Thomas Jech. Your homework sets also use many problems from that textbook. For more details, consult the syllabus.
Expect this calendar to update weekly. At the end of each week, we will usually have an extra handout which can either show you more examples or can go through a detailed example more thoroughly. Make sure to check this calendar at least on Mondays and Fridays.
UNIT 1
Week 1 and first day of class
Day

Book Sections

Topics / Due Dates

Friday Jan 6

1.3 (skim 1.1 and 1.2) 
Russell's Paradox, axioms of ZFC (part 1) 
Monday Jan 9

1.3

Axioms (part 2), Existence of union and intersection

Wednesday Jan 11

1.4

Several operations, proving set identities

Friday Jan 13

2.1, 2.2

HW 1 due
Ordered pairs, def of relation

Extra handout of the week: Practice with the membership relation and Cartesian products
HW 1 is due on Friday, January 13.
Week 2
Day

Book Sections

Topics / Due Dates

Monday Jan 16


Martin Luther King Jr Day
no class

Wednesday Jan 18

2.2, 2.3

Domain and range, inverse and composite, images and preimages

Friday Jan 20

2.3

Notation for functions and sequences, onetoone functions

Extra handout of the week: Indexed collections, characteristic functions
HW 2 is due on Monday, January 23.
Week 3
Day

Book Sections

Topics / Due Dates

Monday Jan 23

2.5, 3.1
(You may want to skim 2.4.)

HW 2 due
Partial orders, inductive sets
(Skip the parts in 2.5 about isomorphisms for now.)

Wednesday Jan 25

3.2

Proof that < is linear on N, and wellordering

Friday Jan 27

3.2, 3.3

Strong induction, the Recursion Theorem

Extra handout of the week: Minimal vs. least members, a "partial recursion" theorem that can end early
HW 3 is due on Monday, January 30.
Week 4
Day

Book Sections

Topics / Due Dates

Monday Jan 30

3.3, 3.4

HW 3 due
Enumerating subsets of N, recursive definitions of plus and times

Wednesday Feb 1

3.4

Multiplication, Exponentiation, some more recursion practice

Friday Feb 3

4.1

Comparing cardinality A = B and A <= B, CantorBernstein Theorem

Extra handout of the week: Strong induction practice, and basic properties of A <= B
HW 4 is due on Monday, February 6.
Test 1 is next Friday, February 10. (It lasts 55 minutes, not 50!)
 You'll find review material uploaded in next week's schedule. This includes a topic list and a practice set of questions!
 Solutions to those practice questions will be made available as well.
 Inclass review for the test is Wednesday, February 8.
UNIT 2
Week 5
Day

Book Sections

Topics / Due Dates

Monday Feb 6

5.1 
HW 4 due
Basic cardinal arithmetic

Wednesday Feb 8


Test 1 Review

Friday Feb 10


TEST 1 (55 minutes)

Test 1 Review Information:
UNIT 2
Week 6
Day

Book Sections

Topics / Due Dates

Monday Feb 13

4.2, part of 4.6 
Finite cardinality, showing P(S) = 2^S 
Wednesday Feb 15

4.3

Countable sets

Friday Feb 17

4.4

Isomorphic orderings, and a uniqueness property of Q

Extra handout of the week: The famous diagonalization argument, and N^N
HW 5 is due on Monday, February 20.
Week 7
Day

Book Sections

Topics / Due Dates

Monday Feb 20

6.1 
HW 5 due
Properties of wellorderings, existence of sups (completeness), initial segments W[a]

Wednesday Feb 22

6.2

Definition of transitive set and ordinal, showing alpha in beta iff alpha is a subset of beta

Friday Feb 24

6.2, beginning of 6.4

Main ordinal properties, principles of Transfinite Induction

Extra handout of the week: More isomorphism practice, and exploration of limit ordinals
HW 6 is due on Monday, February 27.
 This was edited on Thursday February 23 to fix #4.
Week 8
Day

Book Sections

Topics / Due Dates

Monday Feb 27

6.4, though briefly look at Theorem 6.3.6

HW 6 due
Proper classes and operations, Replacement Scheme, Transfinite Recursion Theorem

Wednesday Mar 1

6.4, 6.3

Versions of recursion, enumerating any wellorder, Mostowski collapse

Friday Mar 3

Not really in the book, but related to Sections 6.4 and start of 6.6

More examples, increasing continuous operations (leading up to Sections 6.5 and 6.6)

Extra handout of the week: Wellordered recursion, and a proof by transfinite induction
HW 7 is due on Monday, March 13, after Spring Break.
 However, it is a shorter assignment, and it's only based on class material up through Wednesday. You could try to finish it by Friday this week!
Week 9
Day

Book Sections

Topics / Due Dates

Monday Mar 13

6.5 
HW 7 due
Definition of ordinal sum, isomorphism to W_1 + W_2

Wednesday Mar 15

6.5, 6.6

Ordinal product, simplifying some calculations with ordinals, quotients and remainders

Friday Mar 17

6.5, 6.6

Isomorphism to W_2 x W_1, ordinal exponentiation, omeganormal form

Extra handout of the week: Sups and infs, and designing subsets of Q with certain order types
HW 8 is due on Monday, March 20.
Test 2 is next Friday, March 24. (It lasts 55 minutes, not 50!)
 You'll find review material uploaded in next week's schedule. This includes a topic list and a practice set of questions!
 Solutions to those practice questions will be made available as well.
 Inclass review for the test is Wednesday, March 22.
Week 10
Day

Book Sections

Topics / Due Dates

Monday Mar 20

6.6 
HW 8 due
Addition and multiplication in base omega form, Goodstein sequences

Wednesday Mar 22


Test 2 Review

Friday Mar 24


TEST 2 (55 minutes)

If you're curious about more information on Goodstein sequences, check out this blog posting and this applet to compute Goodstein sequences!
 The applet is a little clumsy when I tried it out, so the initial number you try might not work quite like you want, but you should still be able to click "Calculate" repeatedly in that applet and see some cool behavior. You may also have to reload the page to try a new number.
Test 2 Review Information:
UNIT 3
Week 11
Day

Book Sections

Topics / Due Dates

Monday Mar 27

7.1 
Initial ordinals / cardinals, the Hartog's number and the aleph hierarchy

Wednesday Mar 29

7.1, 7.2

The main theorem about sum and product of two infinite cardinals

Friday Mar 31

7.2, 8.1

Some more cardinal simplification, discussion of wellordering and choice functions

Extra handout of the week: Wellorderable sets, cardinality operations with sets of real numbers
HW 9 is due on Monday, April 3.
Week 12
Day

Book Sections

Topics / Due Dates

Monday Apr 3

8.1 
HW 9 due
Axiom of Choice, Zorn's Lemma

Wednesday Apr 5

8.1, 8.2

Equivalent versions of Zorn's Lemma, some misc applications of AC / Zorn (not tested)

Friday Mar 31

9.1, 9.2

Sum and product of a collection of cardinals, introduction to cofinality of limit ordinals

Extra handout of the week: Tukey's Lemma about finite character, and building a nonmeasurable set of reals
Also, watch this for more information on the BanachTarski Paradox. (Thank you to a student who shared this!)
HW 10 is due on Monday, April 10.
Week 13
Day

Book Sections

Topics / Due Dates

Monday Apr 10

9.1, 9.2

HW 10 due
Regular and singular cardinals, cofinality results, Konig's Theorem

Wednesday Apr 12

9.2, 9.3, 14.1

A couple results about kappa^lambda and cofinality, wellfounded relations

Friday Apr 14

14.1

WellFounded Induction and Recursion, revisit the Mostowski Collapse

Extra handout of the week: Continuous operations and cofinality, wellfounded classes and "setlike" relations
HW 11 is due on Monday, April 17.
 This is the final HW set of the course!
 On Monday April 17, we have one more class to finish Section 14.2. This is not going to be on Test 3.
 After Test 3, we'll just have one last class with new material (not testable on the final), and then one day of final exam review!
Test 3 is next Friday, April 21. (It lasts 55 minutes, not 50!)
 You'll find review material uploaded in next week's schedule. This includes a topic list and a practice set of questions!
 Solutions to those practice questions will be made available as well.
 Inclass review for the test is Wednesday, April 19.
Weeks 14 and 15
Day

Book Sections

Topics / Due Dates

Monday Apr 17

14.2 
HW 11 due
The V_{alpha} sets, wellfounded sets, Axiom of Foundation

Wednesday Apr 19


Test 3 Review

Friday Apr 21


TEST 3 (55 minutes)

Monday Apr 24

Parts of 10.1, 4.5

Conclusion: where do numbers come from? Dedekind cuts

Wednesday Apr 26


Final Review

Test 3 Review Information:
Final exam information
Date and time:
 Monday 5/1 from 8am to 11am in Boyd 322 (our usual classroom)
Office hours for finals:
 Wednesday April 26: 2:00pm to 4:30pm
 Thursday April 27: all day (8am to 5pm), but try to email in advance
 Friday April 28: 3:30pm to 5:30pm
 Sunday office hours may be possible if several people request them by email.
Expectations for questions on the final exam:
 The final should be about twice the length of an inclass test, so expect about 1012 questions for 200 points in total.
 There will be one or two extracredit challenge questions at the end.
 One question will cover definitions. There will also be a question asking for short examples with no proofs required!
 For example, for "a nonlinear partial ordering", possible answers include "P(omega) ordered by subset" or "N ordered by divisibility ".
 Most questions should be similar in difficulty and scope to previous test problems: expect about 23 problems per unit of class material.
 However, some questions may incorporate material from several units.
 Study your old tests!
 Any topics that were offlimits from earlier tests are still offlimits on this final exam.
Last updated: 4/25/17