 Computer Science
CSC3492
Discrete Structures

This course has been designed to provide you with a clear, accessible introduction to discrete mathematics. Discrete mathematics describes processes that consist of a sequence of individual steps (as compared to calculus, which describes processes that change in a continuous manner). The principal topics presented in this course are logic and proof, induction and recursion, discrete probability, and finite state machines. As you progress through the units of this course, you will develop the mathematical foundations necessary for more specialized subjects in computer science, including data structures, algorithms, and compiler design. Upon completion of this course, you will have the mathematical know-how required for an in-depth study of the science and technology of the computer age.

8 Units

### Unit 1: The Logic of Comp...

This is Unit 1 from Saylor.org's Discrete Structures course.

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Logic

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Translating from English to Logic Symbols

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Validity and Arguments

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Rules of Inference Instructions

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List of Rules of Inference, Table: Rules of Infere...

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Proofs

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Modus Ponens and Other Types of Reasoning

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Logic of Compound Statements "Problem Set 1"

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Logic of Compound Statements Solutions Guide for "...

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Arithmetic, Logic and Numbers: Unit BF: Boolean Fu...

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Translating from English to Symbols-“Arithmetic, L...

### Unit 2: The Logic of Quan...

This is Unit 2 from Saylor.org's Discrete Structures course.

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The Definition of a Limit

### Unit 3: Introduction to N...

This is Unit 3 from Saylor.org's Discrete Structures course.

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Proving Properties of Rational Numbers

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Number Theory I

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Induction I

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General Theorem: Divisibility of Algebraic Express...

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Arithmetic, Logic and Numbers: Unit SF: Sets and F...

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Arithmetic, Logic and Numbers: Unit NT: Number The...

### Unit 4: Mathematical Indu...

This is Unit 4 from Saylor.org's Discrete Structures course.

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Sums and Approximations

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Properties of Summation

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Sums, Approximations, and Asymptotics II

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Counting II

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Counting III

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]Mathematical Induction: “Induction III”

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Loop Invariants

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Arithmetic, Logic and Numbers: Unit IS: Induction,...

### Unit 6: Introduction to C...

This is Unit 6 from Saylor.org's Discrete Structures course.

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Introduction to Probability

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Mathematics for Computer Science: “Counting I”

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The Algebra of Combinations

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Mathematics for Computer Science: “Conditional Pro...

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Mathematics for Computer Science: “Independence”

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Lists, Decisions, and Graphs: Unit CL: Counting an...

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Lists, Decisions, and Graphs: Unit DT: Decision Tr...

### Unit 7: Recursion

This is Unit 7 from Saylor.org's Discrete Structures course.

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Mathematics for Computer Science: “Recurrences”

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Mathematics for Computer Science: “Sums and Approx...

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McCarthy’s 91 Function

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The Ackermann Function

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Lists, Decisions and Graphs: Unit DT: Decision Tre...

### Unit 8: Graphs and Trees ...

This is Unit 8 from Saylor.org's Discrete Structures course.

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Graph Theory

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Handshaking Lemma

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Types of Trees

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Graph Theory: Problem Set 5

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Graph Theory: Problem Set 5: Solution Set

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Basic Concepts in Graph Theory

### Unit 9: Regular Expressio...

This is Unit 9 from Saylor.org's Discrete Structures course

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Formal Languages

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Polish Notation

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Languages Defined by Regular Expressions

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Order of Precedence Rules

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Deciding Whether Regular Expressions Define the Sa...

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Finite State Automata

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Automaton and Accepted Language

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Designing a Finite State Automaton

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Simplifying Finite State Automata

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Regular Expressions and Finite-State Automata: Ass...

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Regular Expressions and Finite-State Automata: Ass...