Homepage of MTH 3002
MTH 3002, Winter 2024
Course Handout: See Moodle.
Books that were used in the past
A Transition to Advanced Mathematics by Douglas Smith, Maurice Eggen and Richard St. Andre
Mathematical Thinking: Problem-Solving and Proofs by John P. D'Angelo and Douglas B. West
Lectures (Updated January 9, 2024) (This will be updated as some topics may change depending on the interests of the students.)
January 4: abridged version of Chapter 2.
January 9: abridged version of Chapter 2, Chapter 3-Chapter 5.
January 11: Technology Evaluation, Chapter 1, Chapter 3-Chapter 5.
January 16: Chapter 3-Chapter 5.
January 18: Chapter 3-Chapter 5.
January 23: Chapter 3-Chapter 5.
January 25: Chapter 6.
January 30: Equivalency of WOP, PMI and PMI(SF).
February 1: Equivalency of WOP, PMI and PMI(SF), Chapter 7, Chapter 8.
February 6: Chapter 7, Chapter 8.
February 8: Chapter 7, Chapter 8.
February 13: Chapter 9.
February 15: Catch-up.
February 20: Chapter 9, construction of integers and construction of rational numbers.
February 22: Q&A, Chapter 9, construction of integers and construction of rational numbers.
February 24: Winter break, no class.
February 27: Winter break, no class.
March 5: Test 1.
March 7: Discussion of Test 1, Chapter 9, construction of integers and construction of rational numbers.
March 12: Chapter 9, Chapter 10.
March 14: Chapter 9, Chapter 10.
March 19: Chapter 10
March 21: Chapter 10, Cancellation laws for function compositions.
March 26: Chapter 11.
March 28: Chapter 11.
April 2: Q&A, Chapter 11.
April 4: Test 2.
April 9: Discussion of Test 2, Chapter 11, additional topics.
April 11: Addition topics.
April 16: Q&A, addition topics on video: More Axiom of Choice, Zorn's Lemma, every vector space has a basis.
Relevant Exercises
For the exercises in the book, you may use either a direct proof or indirect proof even if the question asks for a specific one. After reviewing the exercise sets, I concluded that all the questions from Chapter 1 to Chapter 11 are appropriate.