MAT 310 Bridge to Advanced Mathematics

This book will initiate you into an esoteric world. You will learn and apply the methods of thought that mathematicians use to verify theorems, explore mathematical truth and create new mathematical theories. This will prepare you for advanced mathematics courses, for you will be better able to understand proofs, write your own proofs and think critically and inquisitively about mathematics.

Mathematics

Tác giả: Richard Hammack
Nhà xuất bản: Virginia Commonwealth University
Nguồn: LibreTexts
Giấy phép: CC BY-NC-ND
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

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Mục lục· 110 mục

01: Sets
1.01: Introduction to Sets
1.02: The Cartesian Product
1.03: Subsets
1.04: Power Sets
1.05: Union Intersection Difference
1.06: Complement
1.07: Venn Diagrams
1.08: Indexed Sets
1.08: Sets That Are Number Systems
1.09: Russells Paradox
02: Logic
2.00: Statement
2.01: And Or Not
2.02: Conditional Statements
2.03: Biconditional Statements
2.04: Truth Tables for Statements
2.05: Logical Equivalence
2.06: Quantifiers
2.07: More on Conditional Statements
2.08: Translating English to Symbolic Logic
2.09: Negating Statements
2.10: Logical Inference
2.11: An Important Note
03: Counting
3.00: Lists
3.01: The Multiplication Principle
3.02: The Addition and Subtraction Principles
3.03: Factorials and Permutations
3.04: Counting Subsets
3.05: Pascals Triangle and the Binomial Theorem
3.06: The Inclusion-Exclusion Principle
3.07: Counting Multisets
3.08: New Page
3.09: New Page
04: Direct Proof
4.01: Section 1-
4.02: Section 2-
4.03: Section 3-
4.04: Section 4-
4.05: Section 5-
4.06: Section 6-Exercises
05: Contrapositive Proof
5.01: Section 1-
5.02: Section 2-
5.02: Section 3-
5.04: Section 4-
5.05: Section 5-
5.06: Section 6-
06: Proof by Contradiction
6.00: Section 1-
6.01: Section 2-
6.02: Section 3-
6.03: Section 4-
6.04: Section 5-
6.05: Section 6-
07: Proving Non-Conditional Statements
7.00: Section 1-
7.01: Section 2-
7.02: Section 3-
7.03: Section 4-
7.04: Section 5-
7.05: Section 6-
08: Proofs Involving Sets
8.00: Section 1-
8.01: Section 2-
8.02: Section 3-
8.03: Section 4-
09: Disproof
9.00: Section 1-
9.01: Section 2-
9.02: Section 3-
9.03: Section 4-
9.04: Section 5-
9.05: Section 6-
10: Mathematical Induction
10.00: Section 1-
10.01: Section 2-
10.02: Section 3-
10.03: Section 4-
10.04: Section 5-
10.05: Section 6-
11: Relations
11.00: Section 1-
11.01: Section 2-
11.02: Section 3-
11.03: Section 4-
11.04: Section 5-
11.05: Section 6-
12: Functions
12.00: Section 1-
12.01: Section 2-
12.02: Section 3-
12.03: Section 4-
12.04: Section 5-
12.05: Section 6-
13: Proofs in Calculus
13.00: Section 1-
13.01: Section 2-
13.02: Section 3-
13.03: Section 4-
13.04: Section 5-
13.05: Section 6-
14: Cardinality of Sets
14.00: Section 1-
14.01: Section 2-
14.02: Section 3-
14.03: Section 4-
14.04: Section 5-
14.05: Section 6-