Mathematical Reasoning and Logic

          Module 1: Foundations of Mathematical Reasoning

Section 1: The Nature of Mathematical Proofs
- Lesson 1: Understanding the Concept of Proof
  Module 1, Section 1, Lesson 1: Understanding the Concept of Proof
- Lesson 2: Recognizing Proof Structures
  Module 1, Section 1, Lesson 2: Recognizing Proof Structures

Section 2: Elements of Logical Thinking
- Lesson 1: Identifying Premises and Conclusions
  Module 1, Section 2, Lesson 1: Identifying Premises and Conclusions
- Lesson 2: Linking Ideas in Logical Arguments
  Module 1, Section 2, Lesson 2: Linking Ideas in Logical Arguments

Section 3: Foundations of Set Theory
- Lesson 1: Introduction to Sets and Elements
  Module 1, Section 3, Lesson 1: Introduction to Sets and Elements
- Lesson 2: Basic Operations with Sets
  Module 1, Section 3, Lesson 2: Basic Operations with Sets

Section 4: Understanding Mathematical Statements
- Lesson 1: Conditional and Biconditional Statements
  Module 1, Section 4, Lesson 1: Conditional and Biconditional Statements
- Lesson 2: Interpreting Quantifiers
  Module 1, Section 4, Lesson 2: Interpreting Quantifiers

Section 5: Introduction to Number Systems in Logic
- Lesson 1: Logical Properties of Numbers
  Module 1, Section 5, Lesson 1: Logical Properties of Numbers
- Lesson 2: Patterns and Sequences
  Module 1, Section 5, Lesson 2: Patterns and Sequences


Module 2: Basic Logical Reasoning Techniques

Section 1: Building Blocks of Logical Arguments
- Lesson 1: Assigning Truth Values
  Module 2, Section 1, Lesson 1: Assigning Truth Values
- Lesson 2: Understanding Logical Connectives
  Module 2, Section 1, Lesson 2: Understanding Logical Connectives

Section 2: Distinguishing Types of Reasoning
- Lesson 1: Deductive vs. Inductive Reasoning
  Module 2, Section 2, Lesson 1: Deductive vs. Inductive Reasoning
- Lesson 2: Evaluating Argument Validity
  Module 2, Section 2, Lesson 2: Evaluating Argument Validity

Section 3: Introduction to Logical Statements
- Lesson 1: Identifying Simple Logical Statements
  Module 2, Section 3, Lesson 1: Identifying Simple Logical Statements
- Lesson 2: Translating Everyday Language to Logic
  Module 2, Section 3, Lesson 2: Translating Everyday Language to Logic

Section 4: Exploring Logical Fallacies
- Lesson 1: Common Logical Fallacies and Errors
  Module 2, Section 4, Lesson 1: Common Logical Fallacies and Errors
- Lesson 2: How to Avoid Faulty Reasoning
  Module 2, Section 4, Lesson 2: How to Avoid Faulty Reasoning

Section 5: Constructing Valid Arguments
- Lesson 1: Steps in Argument Construction
  Module 2, Section 5, Lesson 1: Steps in Argument Construction
- Lesson 2: Checking Consistency in Reasoning
  Module 2, Section 5, Lesson 2: Checking Consistency in Reasoning


Module 3: Developing Mathematical Proof Techniques

Section 1: Direct Proof Strategies
- Lesson 1: Understanding Direct Proof
  Module 3, Section 1, Lesson 1: Understanding Direct Proof
- Lesson 2: Applying Direct Proof Techniques
  Module 3, Section 1, Lesson 2: Applying Direct Proof Techniques

Section 2: Proof by Contradiction
- Lesson 1: Introduction to Contradiction
  Module 3, Section 2, Lesson 1: Introduction to Contradiction
- Lesson 2: Constructing Proof by Contradiction
  Module 3, Section 2, Lesson 2: Constructing Proof by Contradiction

Section 3: Proof by Contrapositive
- Lesson 1: Concept of Contrapositive
  Module 3, Section 3, Lesson 1: Concept of Contrapositive
- Lesson 2: Using Contrapositive in Proofs
  Module 3, Section 3, Lesson 2: Using Contrapositive in Proofs

Section 4: Proof Techniques with Examples
- Lesson 1: Step-by-Step Direct Proof Example
  Module 3, Section 4, Lesson 1: Step-by-Step Direct Proof Example
- Lesson 2: Analyzing Example Proofs
  Module 3, Section 4, Lesson 2: Analyzing Example Proofs

Section 5: Building Proofs from Definitions
- Lesson 1: Importance of Definitions in Proofs
  Module 3, Section 5, Lesson 1: Importance of Definitions in Proofs
- Lesson 2: Exercises in Proof Construction
  Module 3, Section 5, Lesson 2: Exercises in Proof Construction


Module 4: Exploring Quantifiers and Logical Connectives

Section 1: Understanding Quantifiers
- Lesson 1: Universal Quantifiers: For All
  Module 4, Section 1, Lesson 1: Universal Quantifiers: For All
- Lesson 2: Existential Quantifiers: There Exists
  Module 4, Section 1, Lesson 2: Existential Quantifiers: There Exists

Section 2: Interpreting Complex Statements
- Lesson 1: Nested Quantifiers
  Module 4, Section 2, Lesson 1: Nested Quantifiers
- Lesson 2: Ambiguities in Logical Statements
  Module 4, Section 2, Lesson 2: Ambiguities in Logical Statements

Section 3: Logical Connectives in Depth
- Lesson 1: Conjunction and Disjunction
  Module 4, Section 3, Lesson 1: Conjunction and Disjunction
- Lesson 2: Implication and Equivalence
  Module 4, Section 3, Lesson 2: Implication and Equivalence

Section 4: Translating Mathematical Language
- Lesson 1: From Words to Symbols
  Module 4, Section 4, Lesson 1: From Words to Symbols
- Lesson 2: From Symbols to Words
  Module 4, Section 4, Lesson 2: From Symbols to Words

Section 5: Working with Predicates
- Lesson 1: Understanding Predicate Logic
  Module 4, Section 5, Lesson 1: Understanding Predicate Logic
- Lesson 2: Exercises in Predicate Logic
  Module 4, Section 5, Lesson 2: Exercises in Predicate Logic


Module 5: Application of Mathematical Reasoning and Logic

Section 1: Real-World Applications
- Lesson 1: Logic in Computer Science
  Module 5, Section 1, Lesson 1: Logic in Computer Science
- Lesson 2: Logic in Everyday Decision Making
  Module 5, Section 1, Lesson 2: Logic in Everyday Decision Making

Section 2: Analyzing Mathematical Problems
- Lesson 1: Breaking Down Complex Problems
  Module 5, Section 2, Lesson 1: Breaking Down Complex Problems
- Lesson 2: Logical Strategies for Problem Solving
  Module 5, Section 2, Lesson 2: Logical Strategies for Problem Solving

Section 3: Constructing Rigorous Arguments
- Lesson 1: Developing a Logical Approach
  Module 5, Section 3, Lesson 1: Developing a Logical Approach
- Lesson 2: Peer Review and Feedback Techniques
  Module 5, Section 3, Lesson 2: Peer Review and Feedback Techniques

Section 4: Articulating Complex Ideas
- Lesson 1: Clear Writing in Mathematical Proofs
  Module 5, Section 4, Lesson 1: Clear Writing in Mathematical Proofs
- Lesson 2: Presenting Logical Arguments
  Module 5, Section 4, Lesson 2: Presenting Logical Arguments

Section 5: Review and Consolidation
- Lesson 1: Recapping Key Concepts
  Module 5, Section 5, Lesson 1: Recapping Key Concepts
- Lesson 2: Practice Problem Solving Session
  Module 5, Section 5, Lesson 2: Practice Problem Solving Session