Math 220: Introduction to Proofs
TTh 1:05-:2:20pm
Jessica Sidman, jsidman at amherst dot edu
Office hours
Gradescope
Course notes

Tuesday Thursday
9/2 9/4
  • Read: Sections 1.5-1.7.
  • Video lecture: Operations on sets
  • Self-check problems:
    • Section 1.5: 1abc, 3ad
    • Section 1.6: 1acd, 5
  • Quiz: Self-check problems from Sections 1.1 and 1.2.
  • Journal check-in: due Friday on Gradescope. If you want to use LaTex, you can use this starter code
9/9
  • Read: Sections 2.1-2.3.
  • Video: Introduction to logic
  • Self-check problems:
    • Section 2.2:1, 3, 5, 7, 9, 11
    • Section 2.3: 1, 3, 5, 7, 9, 11
  • Homework 1 due.
  • 9/11
  • Read: 2.7-2.10.
  • Video: Quantifiers and negation
  • Self-check problems:
    • Section 2.7: 1
    • Section 2.9: 3, 5, 7
    • Section 2.10: 1, 3
  • Quiz: Sections 1.5-1.7.
  • Journal check-in: due Friday on Gradescope.
  • 9/16
  • Read: Page 115, Pages 118-120, Section 5.3.
  • Video: Introduction to direct proof: even and odd integers
  • Self-check problems:
    • Chapter 4:1, 3, 5
  • Homework 2 due.
  • 9/18
  • Read: Page 121 - first proposition on Page 122, Sections 8.1-8.3..
  • Video: Examples of direct proof: divisibility and sets
  • Self-check problems:
    • Chapter 4: 7, 11
    • Chapter 8: 1, 7
  • Quiz: Quantifiers and negations: problems like the self-check problems from Sections 2.7, 2.9, 2.10.
  • Journal check-in: due Friday on Gradescope.
  • 9/23
  • Read: Sections 5.1, 6.1, and 6.2.
  • Video: Proof by contrapositive and contradiction compared
  • Video: The square root of 2 is irrational
  • Self-check problems:
    • Chapter 6: 1, 11
  • Homework 3 due.
  • 9/25
  • Read:Section 5.2 for more on congruence and page 31 for another proof of (part of) the division algorithm.
  • Video: Division algorithm: examples
  • Video: Division algorithm: proof
  • Self-check problems:
  • Quiz: One direct proof like the self-check problems from Chapter 4 or 8.
  • Journal check-in: due Friday on Gradescope.
  • 9/30
  • Read: Section 10.4 in Hammack's Discrete Mathematics.
  • Video: Euclidean algorithm: Examples
  • Video: Euclidean algorithm: proof
  • Self-check problems:
  • Homework 4 due.
  • 10/2
  • Read: Section 10.1.
  • Video: Induction divisibility example
  • Self-check problems:
    • Chapter 10: 1, 9, 17. (All of the odd-numbered problems 1-21 are great practice.)
  • Quiz: One proof like a problem from Homework 4.
  • Journal check-in: due Friday on Gradescope.
  • 10/7
  • Self-check problems:
    • Chapter 10: 3, 5, 19
  • Homework 5 due.
  • 10/9 Exam I
    10/14 Break! 10/16
  • Read: Sections 11.1-11.4.
  • Video: Introduction to relations
  • Self-check problems:
    • Chapter 11.2: 1, 3.
    • Chapter 11.3: 1, 3.
  • Optional induction assignment (2 engagement credits): due Friday on Gradescope.
  • 10/21
  • Read: Sections 12.1 and 12.2.
  • Self-check problems:
    • Chapter 12.1: 1, 3, 7, 9.
    • Chapter 12.2: 3, 5, 7
  • Homework 6 due.
  • 10/23
  • Read: Section 12.4.
  • Self-check problems:
    • Chapter 12.4: 1, 9.
  • Miro board for proof puzzle
  • Journal check-in: due Friday on Gradescope.
  • Quiz: Problems like the self-check problems from Sections 11.2, 11.3, 12.1 or 12.2.
  • 10/28
  • Read: Section 12.5.
  • Self-check problems:
    • Chapter 12.5: 5, 7.
  • Homework 7 due.
  • 10/30
  • Read: Section 12.6.
  • Self-check problems:
    • Chapter 12.6: 1, 9.
    • Journal check-in: due Friday on Gradescope.
    • Quiz: Problems like in Homework 7.
  • 11/4
  • Read: Section 12.3.
  • Self-check problems:
    • Chapter 12.3: 1.
    • Homework 8 due.
  • 11/6 Exam II
    11/11
  • Read: 14.1
  • Self-check problems:
    • Chapter 14.1: 1, 3, 7.
    • Mini homework 9 due
  • 11/13
  • Read: 14.2
  • Self-check problems:
    • Chapter 14.2:TBA
    • Quiz: Problems like the self-check problems from Section 14.1.
  • 11/18
  • Read: Section 2.2 in Abbott (Download from the library here.)
  • Self-check problems:
  • 11/20
  • Read: Section 2.3 in Abbott (through the proof of Theorem 2.3.3 (ii))
  • Self-check problems:
  • Journal check-in: due Friday on Gradescope.
  • Quiz: Problems like in homework 10
  • 12/2
  • Read: Secion 2.3 in Abbott
  • Self-check problems:
  • Homework 11 due.
  • 12/4
  • Journal check-in: due Friday on Gradescope.
  • Quiz: Problems like in Homework 11.
  • 12/9
  • Homework 12 due.