CalcCheck Notebooks for COMPSCI&SFWRENG 2DM3, Fall 2017

This page contains the kept-alive CalcCheck notebooks from the course “Discrete Mathematics I, COMPSCI&SFWRENG 2DM3” as held Fall 207 at McMaster University.

This page and the notebooks linked here will disappear some time in August 2018.

For some basic introduction to the CalcCheckWeb web-app interface, see Getting Started with CalcCheckWeb, and for some help with what to write into the boxes, see Getting Started with the CalcCheck Language.

Week 1

• Example 1.1: Portia's Suitor's Dilemma
• Exercise 1.1 on CalcCheckWeb: Calculations in the Equational Theory of Integers
• Reference 1.1: Equational Axioms for the Integers
• Reference 1.2: Operator Precedences in the Spirit of LADM
• Example 1.2: The Answer
• Exercise 1.3: Solving Systems of Integer Equations in a Very Constrained Way
• Exercise 1.4: Equational Theory of Integers ─ without automatic associativity and symmetry
• Exercise 1.5: Equational Theory of Integers ─ with rigid matching
• Assignment 1.1: Calculations in the Equational Theory of Integers
• Assignment 1.2: Proving in the Equational Theory of Integers
• Assignment 1.3: Proving Integer Theorems without Automatic Associativity and Symmetry
• Assignment 1.4: Proving Integer Theorems with Rigid Matching

Week 2

• Exercise 2.1: Substitution
• Exercise 2.2: Simple Induction over the Natural Numbers
• Assignment 2.1: Substitution
• Assignment 2.2: Natural Induction — Maximum and Minimum

Week 3

• Exercise 3.1: Order on the Natural Numbers
• Exercise 3.2: Integer Proofs Using Cancellation of Addition
• Exercise 3.3: Variations of Reasoning with Implications
• Assignment 3.1: More About Maximum and Minimum
• Assignment 3.2: Monotony of Maximum

Week 4

• Exercise 4.1: Equivalence, Negation, Inequivalence
• Exercise 4.2: Disjunction
• Exercise 4.3: Conjunction
• Exercise 4.4: Knights and Knaves
• Exercise 4.4: Knights and Knaves — with solutions for Scenarios A-E
• Assignment 4.1: Disjunction and Conjunction: Absorption
• Assignment 4.2: Conjunction
• Assignment 4.3: Knights and Knaves

Week 5

• Exercise 5.1: Implication
• Exercise 5.2: Inequality
• Exercise 5.3: Distinguishing Natural Numbers
• Exercise 5.4: Permutations and Combinations
• Exercise 5.5: Conditional
• Assignment 5.1: Implication
• Assignment 5.2: Permutations
• Assignment 5.3: Conditionals

Week 6

• Exercise 6.1: Leibniz's Rule as an Axiom, Substitution Theorems
• Exercise 6.2: Distinguishing Natural Numbers — Now With “Substitution” Theorems Available
• Exercise 6.3: More Properties of Conditional
• Exercise 6.4: Assuming the Antecedent (Demo)
• Exercise 6.5: Monotonicity with Respect to Implication
• Exercise 6.6: Integer Ordering
• Exercise 6.7: More order properties on ℕ
• Exercise 6.8: Sum Quantification in ℕ
• Exercise 6.9: Product Quantification in ℕ
• Assignment 6.1: Conditional
• Assignment 6.2: Even More Order Properties on ℕ
• Assignment 6.3: Sum Quantification in ℕ
• Assignment 6.4: Product Quantification in ℕ

Week 7

• Exercise 7.1: “Sum shift”: Simple Induction with ∀ Quantification
• Exercise 7.2: More about Maximum and Minimum: Proving ∀ Quantifications using Induction
• Exercise 7.3: Universal Quantification
• Exercise 7.4: Existential Quantification
• Exercise 7.5: Quantification Practice
• Assignment 7.1: Sum Quantification in ℕ
• Assignment 7.2: Equivalence Chains

Week 8

• Exercise 8.1: Maximum and Minimum on Integers
• Exercise 8.2: Practice with Universal and Existential Quantification in ℕ
• Assignment 8.1: Maximum and Minimum on Integers
• Assignment 8.2: Practice with Universal and Existential Quantification in ℤ
• Assignment 8.3: Fake Gold

Week 9

• Exercise 9.1: Sets
• Exercise 9.2: Sequences
• Assignment 9.1: Sets
• Assignment 9.2: Sequences
• Bonus Assignment 9.3: Snoc Decomposition

Week 10

• Exercise 10.1: Practice with Sets
• Exercise 10.2: Pseudocomplements of Sets
• Assignment 9.4: More Practice with Sets
• Assignment 9.5: More About Sequences
• Bonus Assignment 9.6: Even More About Sequences

Week 11

• Exercise 11.1: Relationship Reasoning
• Exercise 11.2: Relation Algebra: Starting from Inclusion, Composition, and Converse
• Exercise 11.3: Relation Algebra: Continuing with Intersection and Dedekind Rule
• Assignment 10.1: Relationship Reasoning
• Assignment 10.2: Relation Algebra: Continuing with Union
• Bonus Assignment 10.3: Relationship Reasoning

Week 12

• Exercise 12.1: Relation Algebra: Heterogeneous Relation Properties
• Exercise 12.2: Sequences