Course information

• Math 23b: Introduction to Proofs
  • Syllabus
  • Text: D'Angelo and West ``Mathematical thinking, problem solving and proofs''.
• Instructor: Kiyoshi Igusa
  • Location: Goldsmith 305
  • Hours: TBA
  • Phone 63062.
  • email: igusa(at)brandeis(dot)edu
• Information about the Math 23b Exemption Exam.

Homework (extracted from lecture notes)

• Homework 1 (page 10 in notes). Due Thursday, Jan 28.
• HW 2 is on page 22 of the notes. Due Thursday, Feb 4.
• HW 4 is on page 45
• HW 5 is on pages 52-53
• Homework 6 (misprint on problem 7 corrected)

Worksheets/ Quizzes/ Review

• Worksheet 1.1. On inequalities. Other worksheets are in the notes.
• answers to Quiz 0
• Worksheet for Quiz 1 with answers
• Review A for Quiz 2

Lecture notes

• Chap 1, combined Notes (pp 0-22, corrected)
• Notes on quantifiers (Monday) (pp 23-25 including Quiz 0 on p25)
• symbolic logic (Wednesday) (pp 26-29 including Worksheet on p.29 with some answers)
• negation and proof (Thursday) (pp 30-34 including HW 3 on p.34)
• review, tautologies, simple induction (pp 35-38)
• strong induction (pp 39-41)
• well-ordered property of N (pp 42-45, including HW 4 on p. 45)
• Bijections and Cardinality 1 (pp 50-53, including HW 5 on pp 52-53)
• Bijections and Cardinality 2 (pp 54-56)
• Composition of functions (pp 57-58)
• short notes on countable sets (p 59)
• Graphs: basic definitions (p 63-67)
• more graphs (p 68-70, including HW7 on page 70)
• even more graphs (p 71-72)
• Recurrence relations