CIT5920 Module Linkups

CIT5920 Modules mapped to useful book and video resources (Linkups)

NOTE: Due to github markdown wikilink incompatibility, it's best to view this on a markdown editor (like Obsidian) that supports wikilinks.

Also, please ignore the numbering of each resource (ie "0109.000 - Discrete Math ...") and the aliases after the resource title (ie "MATHB_DMA"). The numbering and aliases just pertain to my note-taking system for easier navigation.

Module Linkups

All Resources

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• Title: Discrete Mathematics and its Applications
• Author: Kenneth H. Rosen
• Edition: 7th (10th edition isn’t too different)
• Solutions: Yes, 7th edition only - in-book and separate pdf (for all problems)

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• Title: Discrete Mathematics with Applications
• Author: Susanna S. Epp
• Edition: 5th (better for reading), 3rd (found solutions)
• Solutions: Yes, 3rd edition only - in-book and separate pdf (for almost all problems)

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• Title: Mathematics - A Discrete Introduction
• Author: Edward R. Scheinerman
• Edition: 3rd
• Solutions: Yes, Provided in book (for all problems)

[[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT

• Playlist 1: Discrete Math 1 - TrevTutor (YouTube)
• Playlist 2: Discrete Math 2 - TrevTutor (YouTube)
  • Referred to as “II-#”
• Author: TrevTutor

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• Title: Discrete Mathematics
• Author: Gary Chartrand & Ping Zhang
• Edition: 1st
• Solutions: Yes, Provided in book (for odd numbered problems only)

[[0109.006 - Problems on Discrete Mathematics (Parts I-II)]] - MATHB_PoDMP

• Title: Problems on Discrete Mathematics (Parts I-II)
• Author: Chung Chih-Li & Kishan Mehrotra
• Edition: 1
• Solutions: Yes, Provided in book (for all problems)
• Comments: Hit or miss. A lot of problems with solutions, but may be beyond our level.

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• Title: Discrete Mathematics for Computer Science
• Author: David Liben-Nowell
• Edition: 1st
• Solutions: None

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• Title: Discrete Mathematics
• Author: Seymour Lipschutz & Marc Lars Lipson
• Edition: 3rd
• Solutions: Yes, but not the best. Provided in book (for all problems)

[[0110.000 - How to Prove It]] - MATHB_H2PI

• Title: How to Prove It
• Author: Daniel J. Velleman
• Edition: 3rd
• Solutions: For few select problems
• best read in order, no linkups provided yet

[[0113.000 - Probability and Random Variables]]

• Title: Probability and Random Variables (MITOCW)
• Author: Prof. Scott Sheffield
• Course Number: 18.600
• Link: Probability and Random Variables | Mathematics | MIT OpenCourseWare
• Solutions: For exams only. Assignment problems come from [[0113.001 - A First Course on Probability]]

[[0113.001 - A First Course on Probability]]

• Title: A First Course on Probability
• Author: Sheldon Ross
• Edition: 8th
• Solutions: For 7th edition (but 8th edition is mostly same)
• Best used in conjunction with [[0113.000 - Probability and Random Variables]] which uses the 8th edition of this book.

[[0113.002 - Statistical Inference]]

• Title: Statistical Inference
• Authors: George Casella & Roger L. Berger
• Edition: 2nd
• Solutions: For all odds (and most evens)

[[0113.003 - Introduction to Probability (Lecture Series)]]

• Title: Introduction to Probability (MITOCW)
• Authors: John Tsitsiklis
• Course Number: RES.6-012
• Link: Introduction to Probability | Supplemental Resources | MIT OpenCourseWare
• Lecture videos and notes only

Personal Tier List (so far)

• S Tier
  • [[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA
    • Pros:
      • Great explanations.
      • Self-test questions help reinforce material as you’re reading.
      • Many practice problems of varying difficulty
    • Cons:
      • Doesn’t cover everything
      • Most solutions available (with solution manual), but not all
  • [[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ
    • Pros:
      • Covers quite a bit
      • Great explanations with plenty of examples to go with them
    • Cons:
      • Solutions manual difficult to find. Answers/hints to odd-numbered exercises provided but not always to great detail.
  • [[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT
    • Pros:
      • Amazing explanations
      • Often in line with course content
    • Cons:
      • Does not cover everything
• A Tier
  • [[0109.000 - Discrete Mathematics and its Applications]]- MATHB_DMA
  • [[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI
  • [[0110.000 - How to Prove It]] - MATHB_H2PI
• B Tier
  • [[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN
  • [[0109.006 - Problems on Discrete Mathematics (Parts I-II)]] - MATHB_PoDMP
  • [[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

Table of Contents

• [[#Linkups - Module 1]]
• [[#Linkups - Module 2]]
• [[#Linkups - Module 3]]
• [[#Linkups - Module 4]]
• [[#Linkups - Module 5]]
• [[#Linkups - Module 6]]
• [[#Linkups - Module 7]]
• [[#Linkups - Module 8]]
• [[#Linkups - Module 9]]
• [[#Linkups - Module 10]]

---

Linkups - Module 1

1.1 - Addition and Multiplication Rules

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• 4.2 - Integer Representations and Algorithms

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• 5th edition:
  • 9.2 - Possibility Trees and the Multiplication Rule
  • 9.3 - Counting Elements of Disjoint Sets: The Addition Rule
• 3rd edition
  • 6.2 - Possibility Trees and the Multiplication Rule
  • 6.3 - Counting Elements of Disjoint Sets: The Addition Rule

[[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT

• 28. Rule of Sum and Rule of Product
• 29. Rule of Sum and Rule of Product Examples

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• 8.1 - The Multiplication and Addition Principles
• Optionally:
  • Chapter 0 - What is Discrete Mathematics?

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• Optionally:
  • Chapter 1 - On the Point of this Book

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• 5.1 - Introduction
• 5.2 - Basic Counting Principles

1.2 - Odd and Even

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• same as [[#1 1 - Addition and Multiplication Rules]]

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• 5th edition:
  • 4.1 - Direct Proof and Counterexample I: Introduction
  • 4.2 - Direct Proof and Counterexample II: Writing Advice
• 3rd edition:
  • 3.1 - Direct Proof and Counterexample I: Introduction

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• Chapter 1 - Fundamentals (entire chapter)

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• 3.2 - Direct Proof
• Optionally:
  • 3.1 - Quantified Statements

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• 2.1 - Why You Might Care
• 2.2 - Booleans, Numbers, and Arithmetic

1.3 - Divisibility and Primes

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• 4.1 - Divisibility and Modular Arithmetic
• 4.3 - Primes and Greatest Common Divisors

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• 5th edition:
  • 4.4 - Direct Proof and Counterexample IV: Divisibility
• 3rd edition:
  • 3.2 - Direct Proof and Counterexample II: Rational Numbers
  • 3.3 - Direct Proof and Counterexample III: Divisibility

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• Chapter 7 - Number Theory (entire chapter)

[[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT

• 61. Divisibility
• 62. Divisibility Examples
• 66. Primes and GCD

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• 7.1 - Divisibility Properties
• 7.2 - Primes
• Optionally:
  • 7.3 - The Division Algorithm

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• 7.1 - Why You Might care
• 7.2 - Modular Arithmetic
• 7.3 - Primality and Relative Primality

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• 11.1 - Introduction
• 11.2 - Order and Inequalities, Absolute Value
• 11.4 - Division Algorithm
• 11.5 - Divisibility, Primes
• 11.7 - Fundamental Theorem of Arithmetic

1.4 - Two Proofs and Primes

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• same as [[#1 3 - Divisibility and Primes]]

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• For both 5th/3rd editions:
  • same as [[#1 3 - Divisibility and Primes]]
• Also for 3rd edition:
  • 3.4 - Direct Proof and Counterexample IV: Division into Cases and the Quotient-Remainder Theorem

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• same as [[#1 2 - Odd and Even]]
• Optionally:
  • 2.8 - Lists
  • 2.9 - Factorials

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• same as [[#1 3 - Divisibility and Primes]]

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• Chapter 4 - 4.1-4.6

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• same as [[#1 3 - Divisibility and Primes]]

1.5 - Subsets and Set-builder Notation

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• 2.1 - Sets

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• 5th edition:
  • 1.1 - Variables
  • 1.2 - The Language of Sets
• 3rd edition:
  • 5.1 - Basic Definitions of Set Theory

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• 2.10 - Sets I: Introduction to Subsets

[[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT

• 1. Introduction to Set Theory
• 3. Subsets and Power Sets
• 4. Subsets and Power Sets Examples
• 5. Three Exercises in Sets and Subsets

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• 2.1 - Sets and Subsets

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• 1.1 - Introduction
• 1.2 - Sets and Elements, Subsets
• 1.3 - Venn Diagrams

1.6 - Set Operations and Cardinality

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• 2.2 - Set Operations
• 2.6 - Cardinality of Sets

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• 5th edition:
  • 6.1 - Set Theory
  • 6.2 - Properties of Sets
• 3rd Edition:
  • 5.2 - Properties of Sets

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• 2.12 - Sets II: Operations

[[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT

• 6. Set Operations
• 7. Set Operations Examples # 2
• 8. How to do Proof in Set Theory

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• 2.2 - Set Operations and Their Properties
• 2.3 - Cartesian Products of Sets

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• 2.3 - Sets: Unordered Collections

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• 1.4 - Set Operations
• 1.5 - Algebra of Sets, Duality

1.7 - Powerset and Cartesian Product

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• same as [[#1 5 - Subsets and Set-builder Notation]] and [[#1 6 - Set Operations and Cardinality]]

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• 5th edition:
  • 6.3 - Disproofs and Algebraic Proofs
  • 6.4 - Boolean Algebras, Russell’s Paradox, and the Halting Problem
• 3rd edition:
  • 5.3 - Disproofs, Algebraic Proofs, and Boolean Algebras
  • Optionally:
    • 5.4 - Russell’s Paradox and the Halting Problem

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• same as [[#1 5 - Subsets and Set-builder Notation]]

[[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT

• 2. Cartesian Products and Ordered Pairs
• 9. How to do a Proof with Cartesian Products

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• same as [[#1 6 - Set Operations and Cardinality]]

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• 2.4 - Sequences, Vectors, and Matrices: Ordered Collections

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• 1.7 - Classes of Sets, Power Sets, Partitions

For all sections

[[0109.006 - Problems on Discrete Mathematics (Parts I-II)]] - MATHB_PoDMP

• Chapter 1 - Sets (most of chapter)
• 6.2 - Divisibility
• 7.2 - Principles and Typical Problems for Counting
• Not ready to do any problems yet

[[0110.000 - How to Prove It]] - MATHB_H2PI

• 1.3 - Variables and Sets
• 1.4 - Operations and Sets
• 2.3 - More Operations on Sets
• 7.1 - Greatest Common Divisors
• 7.2 - Prime Factorization

---

Linkups - Module 2

2.1 - Counting Subsets

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• 2.5 - Cardinality of Sets
• 6.1 - The Basics of Counting

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• same as [[#1 1 - Addition and Multiplication Rules]]

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• same as [[#1 6 - Set Operations and Cardinality]]

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• same as [[#1 6 - Set Operations and Cardinality]]

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• 9.1 - Why You Might care
• 9.2 - Counting Unions and Sequences

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• 1.6 - Finite Sets, Counting Principle

2.2 - Counting Words and Strings

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• 6.1 - The Basics of Counting

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• same as [[#1 6 - Set Operations and Cardinality]]

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• 2.8 - Lists
• 2.9 - Factorials

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• same as [[#2 1 - Counting Subsets]]

2.3 - Permutations

• Includes Counting Words with Restrictions

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• 6.3 - Permutations and Combinations

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• same as [[#1 1 - Addition and Multiplication Rules]]
• Optionally:
  • 5th edition:
    • 9.1 - Introduction to Probability
  • 3rd edition:
    • 6.1 - Introduction

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• 5.27 - Permutations

[[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT

• 30. Factorials and Permutations
• 31. Permutations Practice

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• 8.4 - Permutations and Combinations
• 8.5 - Applications of Permutations and Combinations

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• 9.4 - Combinations and Permutations

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• 5.4 - Permutations

2.4 - Logical Structure of Statements

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• Chapter 1 (entire chapter)

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• 5th edition:
  • 2.1 - Logical Form and Logical Equivalence
  • 2.2 - Conditional Statements
    • Optionally:
      • 2.3 - Valid and Invalid Arguments
      • 2.4 - Application: Digital Logic Circuits
      • 2.5 - Application: Number Systems and Circuits for Addition
• 3rd edition:
  • 1.1 - Logical Form and Logical Equivalence
  • 1.2 - Conditional Statements
  • Optionally:
    • 1.3 - Valid and Invalid Arguments
    • 1.4 - Application: Digital Logic Circuits
    • 1.5 - Application: Number Systems and Circuits for Addition

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• 2.11 - Quantifiers

[[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT

• 12. Introduction to Propositional Logic
• 13. Statement Identification and Translation

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• Chapter 1 (entire chapter)

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• 3.1 - Why You Might care
• 3.2 - An Introduction to Propositional Logic

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• 4.1 - Introduction
• 4.2 - Propositions and Compound Statements

2.5 - Two Basic Proof Patterns

• Includes Proofs about Sets

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• same as [[#2 4 - Logical Structure of Statements]]

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• same as [[#1 4 - Two Proofs and Primes]]

[[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• 3.2 - Direct Proof

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• same as [[#1 4 - Two Proofs and Primes]]

2.6 - Combinations

• Includes Counting Grid Shortest Paths

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• same as [[#2 3 - Permutations]]

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• 5th edition:
  • 9.5 - Counting Subsets of a Set: Combinations
• 3rd Edition:
  • 6.4 - Counting Subsets of a Set: Combinations

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• 2.17 - Binomial Coefficients

[[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT

• 32. Combinations
• 33. Permutations and Combinations Examples
• 34. Permutations and Combinations Examples 2

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• same as [[#2 3 - Permutations]]

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• same as [[#2 3 - Permutations]]

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• 5.5 - Combinations

2.7 - Predicates and Quantifiers

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• same as [[#2 4 - Logical Structure of Statements]]

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• 5th edition:
  • 3.1 - Predicates and Quantied Statements I
• 3rd edition:
  • 2.1 - Introduction to Predicates and Quantified Statements I

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• same as [[#2 4 - Logical Structure of Statements]]

[[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT

• 25. Predicate Logic and Quantifier Negation

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• 3.1 - Quantified Statements

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• 3.3 - Propositional Logic: Some Extensions
• 3.4 - An Introduction to Predicate Logic

For all sections

[[0109.006 - Problems on Discrete Mathematics (Parts I-II)]] - MATHB_PoDMP

• Chapter 1 - Sets (entire chapter)
  • Ready to do problems now
• 2.1 - Definitions (Logic)
• 7.2 - Principles and Typical Problems for Counting

[[0110.000 - How to Prove It]] - MATHB_H2PI

• Chapter 1 - Sentential Logic (entire chapter)
• 2.1 - Quantifiers
• 3.1 - Proof Strategies

---

Linkups - Module 3

3.1 - Stars and Bars

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• 6.5 - Generalized Permutations and Combinations
• Optionally:
  • 6.6 - Generating Permutations and Combinations

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• 5th edition:
  • 9.6 - r-Combinations with Repetition Allowed
• 3rd edition:
  • 6.5 - r-Combinations with Repetition Allowed

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• 3.18 - Counting Multisets

[[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT

• 36. Combinations with Repetition
• 37. Combinations with Repetition Examples

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• 9.2 - Permutations and Combinations with Repetition

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• 9.4 - Combinations and Permutations

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• 5.4 - Permutations with Repetitions
• 5.5 - Combinations

3.2 - Negating Statements

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• Chapter 1 (entire chapter)

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• 5th edition:
  • 3.2 - Predicates and Quantified Statements II
  • 3.3 - Statements with Multiple Quantifiers
  • Optionally:
    • 3.4 - Arguments with Quantified Statements
• 3rd edition:
  • 2.2 - Introduction to Predicates and Quantified Statements II
  • 2.3 - Statements Containning Multiple Quantifiers
  • Optionally:
    • 2.4 - Arguments with Quantified Statements

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• 2.11 - Quantifiers

[[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT

• 22. Conditionals
• 23. Conditional Examples
• 26. Negating Quantifiers and Translation Examples
• Optionally:
  • 27. Unique Quantifier

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• 1.2 - Negation, Conjunction, and Disjunction
• 3.1 - Quantified Statements
• 3.2 - Direct Proof

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• 3.4 - An Introduction to Predicate Logic
• 3.5 - Predicate Logic: Nested Quantifiers

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• 4.3 - Basic Logical Operations
• 4.10 - Propositional Functions, Quantifiers
• 4.11 - Negation of Quantified Statements

3.3 - Converse and Contrapositive

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• same as [[#3 2 - Negating Statements]]

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• 5th edition:
  • 4.7 - Indirect argument: Contradiction and Contraposition
  • 4.8 - Indirect Argument: Two Famous Theorems
• 3rd edition:
  • 3.6 - Indirect Argument: Contradiction and Contraposition
  • 3.7 - Two Classical Theorems

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• 4.20 - Contradiction

[[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT

• 40. Direct Proofs
• 41. Direct Proof Examples
• 43. Proof by Case
• 44. Proof by Case Examples
• 45. Proof by Contraposition

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• 3.3 - Proof by Contrapositive
• 3.4 - Proof by Cases

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• 4.3 - Proofs and Proof Techniques
• 4.4 - Some Examples of Proofs
• 4.5 - Common Errors in Proofs

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• 4.6 - Logical Equivalence
• 4.7 - Algebra of Propositions
• 4.8 - Conditional and Biconditional Statements
• 4.9 - Arguments

3.4 - Truth Tables

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• same as [[#3 2 - Negating Statements]]

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• same as [[#2 4 - Logical Structure of Statements]]

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• 1.7 - Boolean Algebra

[[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT

• 14. Truth Tables
• 15. Proofs with Truth Tables
• 16. Truth Table Examples
• 19. Logic Laws
• 20. Logic Laws Examples
• 21. Logic Laws Examples 2

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• 1.3 - Implications
• 1.4 - Biconditionals
• 1.5 - Tautologies and Contradictions
• 1.6 - Some Applications of Logic
• 11.3 - Boolean Algebras

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• 3.2 - An Introduction to Propositional Logic
• 3.3 - Propositional Logic: Some Extensions

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• 4.4 - Propositions and Truth Tables
• 4.5 - Tautologies and Contradictions

3.5 - Proofs by Contradiction

• Also includes There are Infinitely Many Primes

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• same as [[#3 2 - Negating Statements]]

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• same as [[#3 3 - Converse and Contrapositive]]

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• same as [[#3 3 - Converse and Contrapositive]]
• 4.21 - Smallest Counterexample

[[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT

• 46. Proof by Contradiction
• Optionally:
  • 42. Cartesian Product Proofs

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• 3.7 - Proof by Contradiction
• Optionally:
  • 3.5 - Counterexamples
  • 3.6 - Existence Proofs

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• same as [[#3 3 - Converse and Contrapositive]]

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• same as [[#3 3 - Converse and Contrapositive]]

3.6 - Counting Anagrams (Multisets)

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• same as [[#3 1 - Stars and Bars]]

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• same as [[#3 1 - Stars and Bars]]

[[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT

• 38. Counting Practice

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• same as [[#3 1 - Stars and Bars]]

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• same as [[#3 1 - Stars and Bars]]

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• same as [[#3 1 - Stars and Bars]]

For all sections

[[0109.006 - Problems on Discrete Mathematics (Parts I-II)]] - MATHB_PoDMP

• Chapter 2 - Logic (entire chapter)
  • Ready to do problems now
• 7.2 - Principles and Typical Problems for Counting

[[0110.000 - How to Prove It]] - MATHB_H2PI

• Chapter 2 - Quantificational Logic (entire chapter)
• Chapter 3 - Proofs (entire chapter)

---

Linkups - Module 4

4.1 - Pascal’s Triangle

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• 6.4 - Binomial Coefficients and Identities

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• 5th edition:
  • 9.7 - Pascal’s Formula and the Binomial Theorem
• 3rd edition:
  • 6.7 - The Binomial Theorem

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• 3.17 - Binomial Coefficients

[[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT

• 35. Binomial Theorem and Pascal’s Triangle

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• 9.1 - The Pascal Triangle and the Binomial Theorem

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• 9.4 - Combinations and Permutations

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• 5.3 - Mathematical Functions

4.2 - Combinatorial Proofs

• Includes:
  • Algebraic Verification of Pascal’s Identity
  • Counting Two Gender Committees

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• Chapter 6 (sprinkled throughout chapter)

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• same as [[#4 1 - Pascal’s Triangle]]
• 6.6 - The Algebra of Combinations

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• 2.12 - Sets II: Operations
• 2.13 - Combinatorial Proof: Two Examples
• 3.17 - Binomial Coefficients
• 3.18 - Counting Multisets

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• same as [[#4 1 - Pascal’s Triangle]]

4.3 - Functions

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• 2.3 - Functions
• 2.4 - Sequences and Summations
• 2.5 - Cardinality of Sets

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• Both 5th and 3rd editions:
  • 7.1 - Functions Defined on General Sets

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• 5.24 - Functions

[[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT

• 53. Functions

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• 5.3 - Functions

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• 2.5 - Functions

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• 3.1 - Introduction
• 3.2 - Functions

4.4 - Integer Intervals

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• 2.1 - Sets

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• 5th edition:
  • 5.5 - Cardinalities of Sets
• 3rd edition:
  • 7.5 - Cardinality with Applications to Computability

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• 2.1 - Why You Might Care
• 2.2 - Booleans, Numbers, and Arithmetic

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• 11.1 - Introduction
• 11.2 - Order, Inequalities, Absolute Value

4.5 - Surjections and Injections

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• same as [[#4 3 - Functions]]

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• Both 5th and 3rd editions:
  • 7.2 - One-to-One, Onto, and Inverse Functions

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• same as [[#4 3 - Functions]]

[[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT

• 54. Injective, Surjective, and Bijective Functions
• 55. Functions Examples
• 56. Surjective Functions Examples

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• same as [[#4 3 - Functions]]

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• same as [[#4 3 - Functions]]

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• 3.3 - One-to-One, Onto, and Invertible Functions
• 3.4 - Mathematical Functions, Exponential and Logarithmic Functions

For all sections

[[0109.006 - Problems on Discrete Mathematics (Parts I-II)]] - MATHB_PoDMP

• 5.1 (Functions) - Definitions, Theorems, and Comments
• Chapter 7 - Binomial Theorem and Counting (entire chapter)
  • Ready to do problems now

[[0110.000 - How to Prove It]] - MATHB_H2PI

• 5.1 - Functions
• 5.2 - One-to-one and Onto

---

Linkups - Module 5

5.1 - Bijections & Inverse Functions / 5.2 - Counting Injections

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• 2.3 - Functions

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• 5th edition:
  • 7.2 - One-to-one, Onto, and Inverse Functions
  • 7.3 - Composition of functions
• 3rd edition:
  • 7.2 - One-to-one, Onto, and Inverse Functions
  • 7.4 - Composition of functions

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• 5.24 - Functions
• 5.26 - Compositions

[[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT

• 57. Inverse Function Examples
• 58. Inverses Examples 2

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• 5.4 - Bijective Functions
• 5.5 - Cardinalities of Sets

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• 2.5 - Functions

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• 3.1 - Introduction
• 3.2 - Functions
• 3.3 - One-to-One, Onto, and Invertible Functions
• 3.4 - Mathematical Functions, Exponential and Logarithmic Functions

5.3 - Principle of Inclusion-Exclusion (PIE), Floor and Ceiling, and Derangements

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• 2.3 - Functions
• 6.1 - The Basics of Counting
• 8.5 - Inclusion-Exclusion
• 8.6 - Applications of Inclusion-Exclusion

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• 5th edition:
  • 9.3 - Counting elements of Disjoint Sets: The Addition rule
  • 4.6 - Direct Proof and Counterexample VI: Floor and Ceiling
• 3rd edition:
  • 6.3 - Counting elements of Disjoint Sets: The Addition rule
  • 3.5 - Direct Proof and Counterexample V: Floor and Ceiling

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• 3.19 - Inclusion-Exclusion

[[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT

• 63. Floor and Ceiling Examples
• II-6. Inclusion-Exclusion Principle
• II-7. Inclusion Exclusion Problems
• II-8. Inclusion-Exclusion: At Least & Exactly
• II-9. Derangements

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• 8.2 - The Principle of Inclusion-Exclusion

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• 9.2 - Counting Unions and Sequences
  • Didn’t understand bitstring example (Example 9.3) 💫
  • Computer Science Connections - come back to when there is time 🔍
• 9.3 - Using Functions to Count

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• 1.6 - Finite Sets, Counting Principle
• 5.7 - Inclusion/Exclusion Principle
• 6.4 - Inclusion/Exclusion Principle Revisited　💫

5.4 - The Pigeonhole Principle

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• 6.2 - The Pigeonhole Principle

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• 5th edition:
  • 9.4 - The Pigeonhole Principle
• 3rd edition:
  • 7.3 - Application: The Pigeonhole Principle

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• 5.25 - The Pigeonhole Principle

[[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT

• 59. Pigeonhole Principle
• 60. Pigeonhole Principle Examples

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• 8.3 - The Pigeonhole Principle

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• 9.3 - Using Functions to Count 🌟
  • Computer Science Connections - come back to when there is time 🔍

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• 5.6 - The Pigeonhole Principle
• 6.5 - The Pigeonhole Principle Revisited

5.5 - Friends and Strangers Theorem

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• 6.2 - The Pigeonhole Principle

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• 5.25 - The Pigeonhole Principle (near the end of chapter, 5.25.3)

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• not much but on page 438, there’s some stuff on Erdős

For all sections

[[0109.006 - Problems on Discrete Mathematics (Parts I-II)]] - MATHB_PoDMP

• Chapter 5 - Functions (entire chapter)
  • Ready to do problems now
• Chapter 6 - Integers (entire chapter)
  • Ready to do problems now

[[0110.000 - How to Prove It]] - MATHB_H2PI

• 5.3 - Inverses of Functions

---

Linkups - Module 6

6.1 - Ordinary Induction

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• 5.1 - Mathematical Induction

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• 5th edition:
  • 5.1 - Sequences
  • 5.2 - Mathematical Induction I: proving Formulas
• 3rd Edition:
  • 4.1 - Sequences
  • 4.2 - Mathematical Induction I

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• 4.22 - Induction

[[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT

• 47. Mathematical Induction

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• 4.1 - The Principle of Mathematical Induction

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• 5.1 - Why You Might Care
• 5.2 - Proofs by Mathematical Induction

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• 11.3 - Mathematical Induction

6.2 - Induction Examples

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• same as [[#6 1 - Ordinary Induction]]

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• 5th edition:
  • 5.3 - Mathematical Induction II: Applications
• 3rd edition:
  • 4.3 - Mathematical Induction II

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• 4.22 - Induction

[[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT

• 48. Mathematical Induction Examples
• Optionally:
  • 49. Mathematical Induction with Derivatives and Matrices

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• 4.2 - Additional Examples of Induction Proofs

6.3 - Strong Induction

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• 5.3 - Recursive Definitions and Structural Induction

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• 5th edition:
  • 5.4 - Strong Mathematical Induction and the Well-Ordering principle for the Integers
  • Optionally:
    • 5.5 - Application: Correctness of Algorithms
• 3rd edition:
  • 4.4 - Strong Mathematical Induction and the Well-Ordering principle
  • Optionally:
    • 4.5 - Application: Correctness of Algorithms

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• same as [[#6 2 - Induction Examples]]

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• 4.3 - Sequences
• 4.4 - The Strong Principle of Mathematical Induction

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• 5.3 - Strong Induction

6.4 - Pizza Cutting Recurrence

• Includes Counting Pizza Pieces with Cross-points

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• 2.4 - Sequences and Summations
• 8.1 - Applications of Recurrence Relations

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• 5th edition:
  • 5.6 - Defining Sequences Recursively
  • 5.7 - Solving Recurrence Relations by Iteration
• 3rd Edition:
  • 8.1 - Recursively Defined Sequences
  • 8.2 - Solving Recurrence Relations by ITeration

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• 4.23 - Recurrence Relations

[[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT

• 50. Relations
• 51. Relations Examples
  • Last example (part ii) was confusing
• II-17. Homogeneous Recurrence Relations
• II-18. Homogeneous Recurrence Relations Examples
• II-19. Homogeneous Recurrence Relations Examples 2

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• same as [[#6 1 - Ordinary Induction]]

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• 5.4 - Recursively Defined Structures and Structural Induction

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• 6.6 - Recurrence Relations
• 6.7 - Linear Recurrence Relations with Constant Coefficients

6.5 - Fibonacci Numbers

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• 2.4 - Sequences and Summations
• 5.3 - Recursive Definitions and Structural Induction
• 8.2 - Solving Linear Recurrence Relations
• Optionally:
  • 5.4 - Recursive Algorithms
  • 5.5 - Program Correctness

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• 5th edition:
  • 5.8 - Second-Order Linear Homogeneous Recurrence Relations with Constant Coefficients
  • 5.9 - General Recursive Definitions and Structural Induction
• 3rd edition:
  • 8.3 - Second-Order Linear Homogeneous Recurrence Relations with Constant Coefficients
  • 8.4 - General Recursive Definitions

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• 4.22 - Induction
• 4.23 - Recurrence Relations

[[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT

• II-20. Non-Homogeneous Recurrence Relations
• II-21. Non-Homogeneous Recurrence Relation Examples

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• same as [[#6 3 - Strong Induction]]

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• same as [[#6 3 - Strong Induction]]

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• 6.8 - Solving Second-Order Homogeneous Linear Recurrence Relations
• 6.9 - Solving General Homogeneous Linear Recurrence Relations

For all sections

[[0109.006 - Problems on Discrete Mathematics (Parts I-II)]] - MATHB_PoDMP

• Chapter 3 - Mathematical Induction (entire chapter)
  • Ready to do problems now

[[0110.000 - How to Prove It]] - MATHB_H2PI

• Chapter 6 - Mathematical Induction (entire chapter)

---

Linkups - Module 7

• resources given for entire module, not just each module section (as this module doesn’t jump around like the other modules)

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• 7.1 - An Introduction to Discrete Probability
• 7.2 - Probability Theory

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• 5th edition:
  • 9.1 - Introduction to Probability
  • 9.8 - Probability Axioms and Expected Values
• 3rd edition:
  • 6.1 - Introduction to Probability
  • 6.8 - Probability Axioms and Expected Values

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• 6.30 - Sample Space
• 6.31 - Events

[[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT

• II-3 - Discrete Probability
• II-4 - Axioms of Probability

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• 10.1 - The Probability of an Event

[[0109.006 - Problems on Discrete Mathematics (Parts I-II)]] - MATHB_PoDMP

• Chapter 9 - Discrete Probability (most of chapter)
• Comment: Haven’t learned enough to do the problems yet

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• 10.1 - Why You Might Care
• 10.2 - Probability, Outcomes, and Events

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• 7.1 - Introduction
• 7.2 - Sample Space and Events
• 7.3 - Finite Probability Spaces

[[0113.000 - Probability and Random Variables]]

• Sessions 1-5

[[0113.001 - A First Course on Probability]]

• 1 - Combinatorial Analysis (entire chapter)
• 2 - Axioms of Probability (entire chapter)

[[0113.002 - Statistical Inference]]

• 1.1 - Set Theory
• 1.2 - Basics of Probability Theory

[[0113.003 - Introduction to Probability (Lecture Series)]]

• L01.1 Lecture Overview - YouTube
• L01.2 Sample Space - YouTube
• L01.3 Sample Space Examples - YouTube
• L01.4 Probability Axioms - YouTube
• L01.5 Simple Properties of Probabilities - YouTube
• L01.6 More Properties of Probabilities - YouTube
• L01.7 A Discrete Example - YouTube
• L01.8 A Continuous Example - YouTube
• L01.9 Countable Additivity - YouTube
• L01.10 Interpretations & Uses of Probabilities - YouTube
• S01.0 Mathematical Background Overview - YouTube
• S01.1 Sets - YouTube
• S01.2 De Morgan's Laws - YouTube
• S01.3 Sequences and their Limits - YouTube
• S01.4 When Does a Sequence Converge - YouTube
• S01.5 Infinite Series - YouTube
• S01.6 The Geometric Series - YouTube
• S01.7 About the Order of Summation in Series with Multiple Indices - YouTube
• S01.8 Countable and Uncountable Sets - YouTube
• S01.9 Proof That a Set of Real Numbers is Uncountable - YouTube
• S01.10 Bonferroni's Inequality - YouTube

---

Linkups - Module 8

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• 7.2 - Probability Theory
• 7.3 - Bayes’ Theorem

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• 5th edition:
  • 9.9 - Conditional Probability, Bayes’ Formula, and independent events
• 3rd Edition:
  • 6.9 - Conditional Probability, Bayes’ Formula, and independent events

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• 6.32 - Conditional Probability and Independence

[[0109.003 - Discrete Mathematics - TrevTutor]] - YTM_DMTT

• II-5. Conditional Probability

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• 10.2 - Conditional Probability and Independent Events

[[0109.006 - Problems on Discrete Mathematics (Parts I-II)]] - MATHB_PoDMP

• 9.2 - Theorems of Probability

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• 10.3 - Independence and Conditional Probability

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• 7.4 - Conditional Probability
• 7.5 - Independent Events

[[0113.000 - Probability and Random Variables]]

• Sessions 6-7

[[0113.001 - A First Course on Probability]]

• 3 - Conditional Probability and Independence (entire chapter)

[[0113.002 - Statistical Inference]]

• 1.3 - Conditional Probability and Independence

[[0113.003 - Introduction to Probability (Lecture Series)]]

• L02.1 Lecture Overview - YouTube
• L02.2 Conditional Probabilities - YouTube
• L02.3 A Die Roll Example - YouTube
• L02.4 Conditional Probabilities Obey the Same Axioms - YouTube
• L02.5 A Radar Example and Three Basic Tools - YouTube
• L02.6 The Multiplication Rule - YouTube
• L02.7 Total Probability Theorem - YouTube
• L02.8 Bayes' Rule - YouTube
• L03.1 Lecture Overview - YouTube
• L03.2 A Coin Tossing Example - YouTube
• L03.3 Independence of Two Events - YouTube
• L03.4 Independence of Event Complements - YouTube
• L03.5 Conditional Independence - YouTube
• L03.6 Independence Versus Conditional Independence - YouTube
• L03.7 Independence of a Collection of Events - YouTube
• L03.8 Independence Versus Pairwise Independence - YouTube
• L03.9 Reliability - YouTube
• L03.10 The King's Sibling - YouTube
• L04.1 Lecture Overview - YouTube
• L04.2 The Counting Principle - YouTube
• L04.3 Die Roll Example - YouTube
• L04.4 Combinations - YouTube
• L04.5 Binomial Probabilities - YouTube
• L04.6 A Coin Tossing Example - YouTube
• L04.7 Partitions - YouTube
• L04.8 Each Person Gets An Ace - YouTube
• L04.9 Multinomial Probabilities - YouTube

---

Linkups - Module 9

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• 7.4 - Expected Value and Variance

[[0109.001 - Discrete Mathematics with Applications]] - MATHB_DMwA

• 5th edition:
  • 9.8 - Probability Axioms and Expected Value
• 3rd edition:
  • 6.8 - Probability Axioms and Expected Value

[[0109.002 - Mathematics - A Discrete Introduction]] - MATHB_MADI

• 6.33 - Random Variables
• 6.34 - Expectation

[[0109.004 - Discrete Mathematics (Chartrand and Zhang)]] - MATHB_DMCZ

• 10.3 - Random Variables and Expected Values

[[0109.006 - Problems on Discrete Mathematics (Parts I-II)]] - MATHB_PoDMP

• Chapter 9 - Discrete Probability (entire chapter)

[[0109.103 - Discrete Mathematics for Computer Science]] - MATHB_DM4CSDLN

• 10.4 - Random Variables and Expectation
• 10.5 - Chapter at a Glance

[[0109.104 - Schaum’s Outline of Discrete Mathematics]] - MATHB_SOofDM

• 7.7 - Random Variables

[[0113.000 - Probability and Random Variables]]

• Sessions 8-9

[[0113.001 - A First Course on Probability]]

• 4.1 - Random Variables
• 4.2 - Discrete Random Variables
• 4.3 - Expected Value
• 4.4 - Expectation of a Function of a Random Variable

[[0113.002 - Statistical Inference]]

• 1.4 - Random Variables

[[0113.003 - Introduction to Probability (Lecture Series)]]

• L05.1 Lecture Overview - YouTube
• L05.2 Definition of Random Variables - YouTube
• L05.3 Probability Mass Functions - YouTube
• L05.4 Bernoulli & Indicator Random Variables - YouTube
• L05.5 Uniform Random Variables - YouTube
• L05.6 Binomial Random Variables - YouTube
• L05.7 Geometric Random Variables - YouTube
• L05.8 Expectation - YouTube
• L05.9 Elementary Properties of Expectation - YouTube
• L05.10 The Expected Value Rule - YouTube
• L05.11 Linearity of Expectations - YouTube
• S05.1 Supplement: Functions - YouTube

---

Linkups - Module 10

[[0109.000 - Discrete Mathematics and its Applications]] - MATHB_DMA

• 7.4 - Expected Value and Variance

[[0113.000 - Probability and Random Variables]]

• Sessions 10-11

[[0113.001 - A First Course on Probability]]

• 4.5 - Variance
• 4.6 - The Bernoulli and Binomial Random Variables

[[0113.002 - Statistical Inference]]

• 1.5 - Distribution Functions
• 2.1 - Distributions of Functions of a Random Variable
• 2.2 - Expected Values
• 2.3 - Moments and Moment Generating Functions
• Optionally:
  • 1.6 - Density and Mass Functions
  • 2.4 - Differentiating Under an Integral Sign

[[0113.003 - Introduction to Probability (Lecture Series)]]

• L06.1 Lecture Overview - YouTube
• L06.2 Variance - YouTube
• L06.3 The Variance of the Bernoulli & The Uniform - YouTube
• L06.4 Conditional PMFs & Expectations Given an Event - YouTube
• L06.5 Total Expectation Theorem - YouTube
• L06.6 Geometric PMF Memorylessness & Expectation - YouTube
• L06.7 Joint PMFs and the Expected Value Rule - YouTube
• L06.8 Linearity of Expectations & The Mean of the Binomial - YouTube
• L07.1 Lecture Overview - YouTube
• L07.2 Conditional PMFs - YouTube
• L07.3 Conditional Expectation & the Total Expectation Theorem - YouTube
• L07.4 Independence of Random Variables - YouTube
• L07.5 Example - YouTube
• L07.6 Independence & Expectations - YouTube
• L07.7 Independence, Variances & the Binomial Variance - YouTube
• L07.8 The Hat Problem - YouTube
• S07.1 The Inclusion-Exclusion Formula - YouTube
• S07.2 The Variance of the Geometric - YouTube
• S07.3 Independence of Random Variables Versus Independence of Events - YouTube