CS202: Sequences and Recursion | Saylor Academy

This video relates numeric sequences to recursion. There is also a discussion on notation.

Source: University of Minnesota, https://www.youtube.com/watch?v=ob4hmqdqBPk
This work is licensed under a Creative Commons Attribution 3.0 License.

Last modified: Friday, 26 January 2024, 12:31 PM

Course Introduction

Course Syllabus

Unit 1: Sets, Set Relations, and Set Functions

1.1: Set Notation and Relations

Set Notation and Relations

Notation

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1.2: Basic Set Operations

Basic Set Operations

Types of Sets

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1.3: Cartesian Products and Power Sets

Cartesian Products and Power Sets

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1.4: Summation Notation and Generalizations

Summation Notation and Generalizations

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Unit 1 Assessment

Unit 1 Assessment

Unit 2: Counting Theory

2.1: Rule of Products

Introduction to the Rule of Products

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2.2: Permutations

Ordering Elements of a Set

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2.3: Partitions of Sets and the Law of Addition

Partitions and Addition Laws

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2.4: Combinations and the Binomial Theorem

Combinations and the Binomial Theorem

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Unit 2 Assessment

Unit 2 Assessment

Unit 3: Mathematical Logic

3.1: Propositions and Logical Operators

Propositional Logic

Propositions and Logical Operators

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3.2: Truth Tables and Propositions Generated by a Set

Summary of Logic Notation

Truth Tables and Propositions Generated by a Set

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3.3: Equivalence and Implication

Equivalence and Implication

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3.4: The Laws of Logic

The Laws of Logic

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Unit 3 Assessment

Unit 3 Assessment

Unit 4: Mathematical Induction and Proofs

4.1: Mathematical Systems

Mathematical Systems

4.2: Direct Proof

Direct Proof

4.3: Indirect Proof

Indirect Proof

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4.4: Propositions over a Universe

Propositions and Truth Sets

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4.5: Mathematical Induction

Discussion and Examples

4.6: Strong Induction

Strong Mathematical Induction

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Unit 4 Assessment

Unit 4 Assessment

Unit 5: Probability

5.1: Introduction

Introduction to Discrete Probability

5.2: Sample Spaces, Events, and Their Probabilities

Sample Spaces, Events, and Their Probabilities

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5.3: Complements, Intersections, and Unions

Complements, Intersections, and Unions

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5.4: Conditional Probability and Independent Events

Conditional Probability