第一週

• 1.1 Proposition Logic
  1.2 Proposition Equivalences
  1.3 Predicates and Quantifiers　

• 1.4 Nested Quantifiers
  1.5 Rules of Inference
  1.6 Introduction to Proofs

• 1.7 Proof Methods and Strategy
  Preliminary Test #1
  2.1 Sets　

• 2.2 Set Operations
  2.3 Functions
  2.4 Sequences and Summations

• 3.4 The Integers and Division
  3.5 Primes and Greatest Common Divisors
  3.6 Integers and Algorithms

• Preliminary Test #2
  Break

• 3.7 Applications of Number Theory
  4.1 Mathematical Induction
  4.2 Strong Induction and Well-Ordering

• 4.3 Recursive Definitions and Structural Induction
  4.4 Recursive Algorithms
  5.1 The Basics of Counting
  4.4 Recursive Algorithms

• 5.2 The Pigeonhole Principle
  5.3 Permutations and Combinations
  5.4 Binomial Coefficients

• 5.5 Generalized Permutations and Combinations
  Midterm #1 Ch 3.3~3.7 & Ch.4.1~4.4

• 5.6 Generating Permutations and Combinations
  7.1 Recurrence Relations
  7.2 Solving Linear Recurrence Relations

• 7.3 Divide-and-Conquer Algorithms and Recurrence Relations
  7.4 Generating Functions
  7.5 Inclusion-Exclusion
  7.6 Applications of Inclusion-Exclusion

• 8.1 Relations and Their Properties
  Midterm #2: Chapter 5,7 (not including 7.3)

• 8.3 Representing Relations
  8.4 Closures of Relations
  8.5 Equivalence Relations

• 8.6 Partial Orderings
  9.1 Graphs and Graph Models
  9.2 Graph Terminology and Special Types of Graphs

• 9.3 Representing Graphs and Graph Isomorphism
  9.4 Connectivity
  9.5 Euler and Hamilton Paths
  9.6 Shortest-Path Problems　

• 10.1 Introduction to Trees
  10.3 Tree Traversal
  10.5 Minimum Spanning Trees

• Break
  Final Exam Chapter 8,9,10