I have uploaded videos to YouTube for exercises in Basic Discrete Mathematics. Each section has a link that goes to a particular playlist with all the exercises that I have recorded.

Chapter One

• 1.4 — Constructing truth tables for a compound proposition
  • 1.4.1
  • 1.4.2 (a), (b), (c), (d), (e), (f), (g)
  • 1.4.3 (a), (b), (c), (d), (e), (f), (g), (h), (i), (j), (k), (l), (m), (n)
• 1.6 — Tautologies and Contradictions
  • 1.6.2 (a), (b), (c)
  • 1.6.3 (a), (b), (c), (d)
  • 1.6.4 (a), (b), (c), (d)
• 1.7 — Logical Equivalence and Derived Logical Implications
  • 1.7.1
  • 1.7.2 (a), (b), (c), (d), (e), (f), (g)
  • 1.7.3
  • 1.7.4 (a), (b), (c)
  • 1.7.5 (a), (b), (c), (d), (e), (f)
  • 1.7.9 (a), (b), (c)

Chapter Two

• 2.2 — Rules of Inference
  • 2.2.3 (a), (b), (c)
  • 2.2.5
  • 2.2.6
  • 2.2.7
  • 2.2.8
  • 2.2.9
  • 2.2.14
  • 2.2.15
  • 2.2.17
  • 2.2.19

MAE 106 — Discrete Mathematics with Probability (Fall 2021)

This is a course that I give to students who specialize in the arts (including business administration and economics). In-person lectures were suspended due to the 2020 global pandemic, and so these videos were livestreamed over YouTube.

• Lecture 1 – Introduction
• Lecture 2 – Introduction to Logic
• Lecture 3 – Logical Connectives
• Lecture 4 – Constructing a Truth Table
• Lecture 5 – Logical Equivalence and Derived Logical Implications
• Lecture 6 – Rules of Inference
• Lecture 7 – Using the Rules of Inference
• Lecture 8 – More Examples using the Rules of Inference
• Lecture 9 – Arguments
• Lecture 10 – Fallacies
• Lecture 11 – More Arguments
• Lecture 12 – Sets
• Lecture 13 – Venn Diagrams and the Principle of Inclusion Exclusion
• Lecture 14 – Example using the Principle of Inclusion Exclusion
• Lecture 15 – Set Operations Revisited
• Lecture 16 – Pigeonhole, Multiplication, and Sum Principles
• Lecture 17 – Permutations
• Lecture 18 – Permutation Examples and Combinations
• Lecture 19 – Combination Examples and Pascal’s Triangle
• Lecture 20 – Permutations with Repetition of Indistinguishable Objects
• Lecture 21 – An Approach to Solving Counting Problems
• Lecture 22 – An Introduction to Probability
• Lecture 23 – Probability in a Uniform Sample Space
• Lecture 24 – Using Counting Techniques to Calculate Probability
• Lecture 25 – Conditional Probability
• Lecture 26 – Independence
• Lecture 27 – Bayes’ Theorem
• Lecture 28 – More on Bayes’ Theorem
• Lecture 29 – Random Variables, Probability Distributions, and Expected Value
• Lecture 30 – Variance
• Lecture 31 – Worked Examples of Probability Distribution Questions
• Lecture 32 – The Binomial Distribution
• Lecture 33 – Examples of the Binomial Distribution
• Lecture 34 – Review and Summary