MCC: MTH 220 - Discrete Math

MTH 220 Discrete Math is a foundational course (often for computer science/math majors) focused on logic, proofs, and non-continuous mathematical structures. Key topics include propositional logic, set theory, combinatorics, graph theory, functions, and proof techniques like induction and contradiction. The course emphasizes rigorous, abstract, and algorithmic thinking.

Mathematics

Tác giả: Judy Dean
Nhà xuất bản: Monroe Community College
Nguồn: LibreTexts
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

Đọc trực tuyến Tải PDF (nguồn mở)

Mục lục· 54 mục

1: Introduction to Discrete Mathematics
1.0 Preface
1.1: An Overview of Discrete Mathematics
1.2: Suggestions to Students
1.3: How to Read and Write Mathematics
1.4: Proving Identities
1.5: Introduction to Sets and Real Numbers
2: Logic
2.1: Propositions
2.2: Conjunctions and Disjunctions
2.3: Implications
2.4: Biconditional Statements
2.5: Logical Equivalences
2.6 Arguments and Rules of Inference
2.7: Quantiers
2.8: Multiple Quantiers
3: Proof Techniques
3.1: An Introduction to Proof Techniques
3.2: Direct Proofs
3.3: Q-R Theorem and Mod
3.4: Indirect Proofs
3.5: The Euclidean Algorithm
3.6: Mathematical Induction - An Introduction
3.7: The Well-Ordering Principle
3.8: More on Mathematical Induction
4: Sets
4.1: An Introduction to Sets
4.2: Subsets and Power Sets
4.3: Unions and Intersections
4.4: Cartesian Products
4.5: Index Sets and Partitions
5: Functions
5.1: Intro to Relations and Functions
5.2: Deﬁnition of Functions
5.3: One-to-One Functions
Preimages of Sets
5.5: Inverse Functions and Composition
5.6: Infinite Sets and Cardinality
6: Relations
6.1: Relations on Sets
6.2: Properties of Relations
6.3: Equivalence Relations and Partitions
7: Combinatorics
7.1: Intro Probability and Pigeonhole Principle
7.2: Addition and Multiplication Principles
7.3: Permutations
7.4: Combinations
7.5: Combinations WITH Repetitions
7.6: The Binomial Theorem
8: Big O
8.1: Big O
Appendices
A.1: Cardinality-additional info
Answers