Instructor: Foster Tom

Course on canvas.dartmouth.edu ⇗

Syllabus

Date Topic Homework/Exams Other notes
M Mar 30 Introductions, introduction to set theory
W Apr 1 Introduction to logic, proof writing (Part 1)
F Apr 3 Logic, proof writing (Part 2)

 
M Apr 6 Algebra of sets

Homework 1:

Math19HW1.pdfDownload Math19HW1.pdf

Math19HW1.texDownload Math19HW1.tex
W Apr 8

Ordered pairs
F Apr 10 Functions, injective/surjective, left/right inverses
M Apr 13 Axiom of choice, infinite Cartesian products

Homework 2:

Math19HW2.pdfDownload Math19HW2.pdf

Math19HW2.texDownload Math19HW2.tex
W Apr 15 Equivalence relations, set partitions
F Apr 17 Equivalence classes, well-definedness
M Apr 20

Midterm 1

Homework 3:

Math19HW3.pdfDownload Math19HW3.pdf

Math19HW3.texDownload Math19HW3.tex
W Apr 22 Natural numbers, inductive sets
F Apr 24 Cardinality, countable sets
M Apr 27 Countable union of countable sets, Cantor-Schroder-Bernstein theorem

Homework 4:

Math19HW4.pdfDownload Math19HW4.pdf

Math19HW4.texDownload Math19HW4.tex
W Apr 29 Non-measurable sets
F May 1 Cardinal arithmetic
M May 4 Ordering cardinal numbers

Homework 5: 

Math19HW5.pdfDownload Math19HW5.pdf

Math19HW5.texDownload Math19HW5.tex
W May 6 Zorn's lemma
F May 8 Zorn's lemma (part 2)
M May 11

Midterm 2

Homework 6:

Math19HW6.pdfDownload Math19HW6.pdf

Math19HW6.texDownload Math19HW6.tex
W May 13 Well-orderings 
F May 15 Transfinite recursion
M May 18 Isomorphsisms of well-ordered structures

Homework 7:

Math19HW7.pdfDownload Math19HW7.pdf

Math19HW7.texDownload Math19HW7.tex

 
W May 20 Ordinal arithmetic
F May 22 Goodstein's theorem
M May 25

Homework 8:

Math19HW8.pdfDownload Math19HW8.pdf

Math19HW8.texDownload Math19HW8.tex

 No class
W May 27 Construction of the Real Numbers
F May 29
M June 1

Practice Final Exam:

Math19PracticeFinal.pdfDownload Math19PracticeFinal.pdf

Math19PracticeFinal.texDownload Math19PracticeFinal.tex

 Last day of classes
Su June 7 Final exam at 8am