Week 1 Friday: Quantifiers and Negation
Jan 24: Sample Tests
Jan 31: Writing Proofs (here is a shorter version and examples from Chapter 1)
Feb 6: Test 1 and answers, and how (not) to prove that a function is onto (test 1 Ex 4).
Feb 8: Hotel Infinity
Feb 13: Organizing Proofs (see March 1 handout below).
Feb 16: ZFC Axioms of Set Theory (list of all statements that mathematicians accept without a proof)
Feb 22: overview Section 2.1 and overview Chapter 2 (List of Facts) (LoF).
Feb 23: Here is an excellent youtube video about Cardinal numbers and Ordinal numbers. It is solid mathematically, and a joy to watch. (The book covers Cardinal numbers in Chapter 2, and Ordinal numbers in Chapter 3, but we will skip most of Chapter 3 to spend more time on Chapters 4 and 5.)
March 1: Organizing Proofs (added two more items to the Feb 13 handout). Whenever you write a proof, make sure you look at the handouts "Organizing Proofs" and "Writing Proofs".
March 6: Test 2 and answers
March 7: I wrote a text to explain why circular definitions are not allowed in math. It also explains the motivation for the ZFC Axioms of Set Theory and concludes with a short definition of cardinal numbers.
March 27: Answers to Ex 1-6 in Section 4.2.
April 15: Test 3.
April 17: Updated version (now includes section 4.4) of: List of Facts for Chapter 4.
April 26: shortened version of List of Facts (for use with final test).