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Contents
Fundamentals of Mathematical Logic
1 Propositions and Related Concepts
2 Conditional and Biconditional Propositions
3 Rules of Inferential Logic
4 Propositions and Quanti ers
5 Arguments with Quanti ed Premises
6 Project I: Digital Logic Design
7 Project II: Number Systems
Fundamentals of Mathematical Proofs
8 Methods of Direct Proof I
9 More Methods of Proof
10 Methods of Indirect Proofs: Contradiction and Contraposition
11 Method of Proof by Induction
12 Project III: Elementary Number Theory and Mathematical Proofs
13 Project IV: The Euclidean Algorithm
14 Project V: Induction and the Algebra of Matrices
Fundamentals of Set Theory
15 Basic De nitions
16 Properties of Sets
17 Project VI: Boolean Algebra
Relations and Functions
18 Equivalence Relations
19 Partial Order Relations
20 Functions: De nitions and Examples
21 Bijective and Inverse Functions
22 Recursion
23 Project VII: Applications to Relations
24 Project VIII: Well-Ordered Sets and Lattices
25 Project IX: The Pigeonhole Principle
26 Project X: Countable Sets
27 Project XI: Finite-State Automaton
Introduction to the Analysis of Algorithms
28 Time Complexity and O-Notation
29 Logarithmic and Exponential Complexities
30 - and -Notations
Fundamentals of Counting and Probability Theory
31 Elements of Counting
32 Basic Probability Terms and Rules
33 Binomial Random Variables
Elements of Graph Theory 201
34 Graphs, Paths, and Circuits
35 Trees
