Schedule

A week-by-week breakdown of the material.

Week 1

Monday

• Introduction
• Writing Mathematics
• Sets, set notation
• Subsets
• Set Operations
• Quiz 0 (Due Monday night together with Quiz 1)
• Homework 1 due Tuesday
• Prepare for class presentation:
  • Exercises 1.9, 1.19, 1.34

Tuesday

• Indexed Collections of sets
• Set Partitions
• Cartesian Products
• Quiz 1 (Due Monday night together with Quiz 2)
• Homework 2 due Wednesday
• Prepare for class presentation:
  • Exercises 1.41, 1.54

Wednesday

• Statements
• Negations
• Disjunction and Conjunction
• Implications
• Quiz 2 (Due Tuesday night)
• Homework 3 due Thursday
• Prepare for class presentation:
  • Exercises 2.18, 2.29, 2.32

Thursday

• Biconditional
• Tautologies, Contradictions
• Logical Equivalence
• Fundamental properties of logical equivalence
• Quiz 3 (Due Wednesday night)
• Homework 4 due Friday
• Prepare for class presentation:
  • Exercises 2.39, 2.50, 2.53

Friday

• Exam 1

Week 2

Monday

• Quantified Statements
• Characterization
• Quiz 4 (Due Sunday night)
• Homework 5 due Tuesday

Tuesday

• Trivial and Vacuous Proofs
• Direct Proofs
• Proof by Contrapositive
• Prepare for class presentation:
  • Exercises 3.10, 3.18
• Quiz 5 (Due Monday night)
• Homework 6 due Wednesday

Wednesday

• Proof by cases
• Direct and Contrapositive proofs for divisibility
• Direct and Contrapositive proofs for congruence
• Prepare for class presentation:
  • Exercises 3.28, 4.16
• Quiz 6 (Due Tuesday night)
• Homework 7 due Thursday

Thursday

• Direct and Contrapositive proofs for real numbers
• Proofs involving sets
• Properties of set operations, cartesian products
• Prepare for class presentation:
  • Exercises 4.34, 4.38, 4.44, 4.58, 4.62, 4.64
• Quiz 7 (Due Wednesday night)
• Homework 8 due Friday

Friday

• Catching up
• Exam 2

Week 3

Monday

• Proofs by counterexample
• Proofs by contradiction
• Existence proofs
• Prepare for class presentation:
  • Exercises 5.6, 5.18
• Quiz 8 (Due Sunday night)
• Homework 9 due Tuesday

Tuesday

• Principle of Mathematical Induction
• General Principle of Mathematical Induction
• Proofs by Minimum Counterexample
• Prepare for class presentation:
  • Exercises 6.8, 6.18
• Quiz 9 (Due Monday night)
• Homework 10 due Wednesday

Wednesday

• Strong Principle of Mathematical Induction
• Testing Statements
• Introduction to Relations
• Prepare for class presentation:
  • Exercises 6.44, 7.33, 7.50, 7.68, 8.4
• Quiz 10 (Due Tuesday night)
• Homework 11 due Thursday

Thursday

• Review/Catchup

Friday

• Catchup
• Exam 3

Week 4

Monday

• Sick day

Tuesday

• Properties of Relations
• Equivalence Relations
• Prepare for class presentation:
  • Exercises 8.14, 8.18, 8.28, 8.29
• Quiz 11 (Due Sunday night)
• Homework 12 due Wednesday

Wednesday

• Equivalence Classes
• Congruences as an equivalence
• Optional reading: Arithmetic on Integers modulo n, section 8.6
• Prepare for class presentation:
  • Exercises 8.36, 8.41, 8.42, 8.46
• Quiz 12 (Due Tuesday night)
• Homework 13 due Thursday

Thursday

• Definition of functions
• Optional reading, highly recommended for anyone with interest in higher mathematics: 9.3-9.5
• Prepare for class presentation:
  • Exercises 9.8, 9.12
• Quiz 13 (Due Tuesday night)
• Homework 14 due Friday

Friday

• Wrap-up
• Exam 4