離散數學

Discrete mathematics is the foundation of engineering, computer science and many related fields. This course will hopefully offer you theoretical tools that will remain useful in the rest of your academic life and beyond

nono

All material will be provided on E3

12 Quizzes will give you 80% of the grade Midterm and Final projects will give you the remaining 20%

Discrete Mathematics Applications and Its Applications Kenneth H. Rosen 8th Edition

時間

Each week we will cover one chapter in the book. Accordingly, we will have: Chap 1: Logic and Proofs 1. Proposition Logic 2. Applications of Propositional Logic 3. Proposition Equivalences 4. Predicates and Quantifiers 5. Nested Quantifiers 6. Rules of Inference 7. Introduction to Proofs 8. Proof Methods and Strategy Chap 2: Sets, Functions, Sequences, Sums, and Matrices 1. Sets 2. Set Operations 3. Functions 4. Sequences and Summations 5. Cardinality of Sets 6. Matrices Chap 3: Algorithms 1. Algorithms 2. The Growth of Functions 3. Complexity of ALgorithms Chap 4: Number Theory and Cryptography 1. Divisibility and Modular Arithmetic 2. Integer Representations and Algorithms 3. Primes and Greatest Common Divisors 4. Solving Congruence 5. Applications of Congruence 6. Cryptography Chap 5: Induction and Recursion 1. Mathematical Induction 2. Strong Induction and Well-Ordering 3. Recursive Definitions and Structural Induction 4. Recursive Algorithms 5. Program Correctness Chap 6: Counting 1. The Basics of Counting 2. The Pigeonhole Principle 3. Permutations and Combinations 4. Binomial Coefficients and Identities 5. Generalized Permutations and Combinations 6. Generating Permutations and Combinations Chap 7: Discrete Probability (skipped) Chap 8: Advanced Counting Techniques 1. Applications of Recurrence Relations 2. Solving Linear Recurrence Relations 3. Divide-and-Conquer Algorithms and Recurrence Relations 4. Generating Functions 5. Inclusion-Exclusion 6. Applications of Inclusion-Exclusion Chap 9: Relations 1. Relations and Their Properties 2. n-ary Relations and Their Applications 3. Representing Relations 4. Closures of Relations 5. Equivalence Relations 6. Partial Orderings Chap 10 Graphs 1. Graphs and Graph Models 2. Graph Terminology and Special Types of Graphs 3. Representing Graphs and Graph Isomorphism 4. Connectivity 5. Euler and Hamilton Paths 6. Shortest-Path Problems 7. Planar Graphs (skipped) 8. Graph Coloring (skipped) Chap 11: Trees 1. Introduction to Trees 2. Applications of Trees 3. Tree Traversal 4. Spanning Trees 5. Minimum Spanning Trees

聯絡方式

email me at stefano@nctu.edu.tw