A Spiral Workbook for Discrete Mathematics

In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values.

Combinatorics and Discrete Mathematics Mathematics

Tác giả: Harris Kwong
Nhà xuất bản: State University of New York at Fredonia
Nguồn: LibreTexts
Giấy phép: CC BY-NC-SA
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

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Mục lục· 54 mục

01: Introduction to Discrete Mathematics
1.01: An Overview of Discrete Mathematics
1.02: Suggestions to Students
1.03: How to Read and Write Mathematics
1.04: Proving Identities
02: Logic
2.01: Propositions
2.02: Conjunctions and Disjunctions
2.03: Implications
2.04: Biconditional Statements
2.05: Logical Equivalences
2.06: Logical Quantiers
03: Proof Techniques
3.01: An Introduction to Proof Techniques
3.02: Direct Proofs
3.03: Indirect Proofs
3.04: Mathematical Induction - An Introduction
3.05: More on Mathematical Induction
3.06: Mathematical Induction - The Strong Form
04: Sets
4.01: An Introduction to Sets
4.02: Subsets and Power Sets
4.03: Unions and Intersections
4.04: Cartesian Products
4.05: Index Sets
05: Basic Number Theory
5.01: The Principle of Well-Ordering
5.02: Division Algorithm
5.03: Divisibility
5.04: Greatest Common Divisors
5.05: More on GCD
5.06: Fundamental Theorem of Arithmetic
5.07: Modular Arithmetic
06: Functions
6.01: An Introduction to Functions
6.02: Denition of Functions
6.03: One-to-One Functions
6.04: Onto Functions
6.05: Properties of Functions
6.06: Inverse Functions
6.07: Composite Functions
07: Relations
7.01: Denition of Relations
7.02: Properties of Relations
7.03: Equivalence Relations
7.04: Partial and Total Ordering
08: Combinatorics
8.01: What is Combinatorics
8.02: Addition and Multiplication Principles
8.03: Permutations
8.04: Combinations
8.05: The Binomial Theorem
09: Appendices
9.01: Answers