Theoretical Foundations of Computer Engineering

Cpr E 310 Theoretical Foundations of Computer Engineering

Course catalog page: Course catalog

Syllabus: PDF

Textbook: Discrete Mathematics and Its Applications, Kenneth Rosen, 7th ed.

Lectures

Introduction

1.1 Propositional_Logic

1.2 Propositional Equivalences

1.3 Predicates and Quantifiers

1.5 Rules of Inference

1.6 Introduction to Proofs

1.7 Proof Methods and Strategy

2.1 Sets

2.2 Set Operations

2.3 Functions

2.4 Sequences and Summations

3.1 Algorithms

3.2 The Growth of Functions

3.3 Complexity of Algorithms

4.1 Mathematical Induction and 4.2 Strong Induction and Well-Ordering

4.3 Recursive Definitions and Structural Induction

4.4 Recursive Algorithms

5.1 The Basics of Counting

5.3 Permutations and Combinations

5.4 Binomial Coefficients

7.1 Recurrence Relations

7.2 Solving Linear Recurrence Relations

7.3 Divide-and-Conquer Algorithms and Recurrence elations

7.4 Generating Functions

8.1 Relations and Their Properties

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

Homework Problems

HW1

6th Edition Problems (from 1.1): 10, 28, 52, 60, (from 1.2): 29, 32, 52, 54

7th Editiom Problems (from 1.1): 14, 32, (from 1.2): 12, 32, (from 1.3): 29, 32, 52, 54

HW2

6th Edition Problems (from 1.3): 10, 40, 56, 62, (from 1.4): 26, 28, 30, 40, (from 1.5): 4, 12, 14, 30

7th Edition Problems (from 1.4): 10, 40, 56, 62, (from 1.5): 26, 28, 30, 40, (from 1.6): 4, 12, 14, 30

HW3

6th Edition Problems (from 1.6): 8, 18, 40, (from 1.7): 12, 20, 34

7th Edition Problems (from 1.7): 8, 18, 40, (from 1.8): 14, 22, 36

HW4

6th Edition Problems (from 2.1): 6, 8, 20, 36, (from 2.2): 48, 50(a), (from 2.3): 2, 24, 40, (from 2.4): 20

7th Edition Problems (from 2.1): 8, 10, 22, 44, (from 2.2): 50, 52(a), (from 2.3): 2, 28, 44, (from 2.4): 36

HW5

6th Edition Problems (from 3.1): 24, Read Example 6 and do problem 56; (from 3.2): 20, 22, 60; (from 3.3): 8, 26

7th Edition Problems (from 3.1): 24, Read Example 6 and do problem 56, (from 3.2): 26, 28, 70, (from 3.3): 14, 36

HW6

7th Edition Problems (from 4.1): 32, 34, (from 4.5): 6, 32 (from 4.6): 2, 18

HW7

7th Edition Problems (from 4.3): 32, 54; (from 4.2): 30; (from 4.4): 6 (a), (c) , 16; (from 4.6): 26

HW8

7th Edition Problems (from 4.2): 26, 28; (from 4.4): 38, 46 (read Def 2 and Example 11 on page 283); (from 4.6): 30, 32 (read pages 302-303)

HW9

7th Edition Problems (from 5.1): 4, 34, 74; (from 5.2): 4, 14, 34; (from 5.3): 6, 12, 18, 26, 50.

HW10

6th Edition Problems (from 9.1): 14, 18, 30; (from 9.2): 4, 10

7th Edition Problems (from 10.1): 14, 18, 32; (from 10.2): 4, 10

HW11

6th Edition Problems (from 9.3): 24, 58(a); (from 9.4): 12, 14, 48, 54.

7th Edition Problems (from 10.3): 24, 58(a); (from 10.4): 12, 14, 58, 64.

HW12

6th Edition Problems (from 9.5): 2, 4, 10, 32, 36, 38; (from 9.7): 6, 12, 14, 16

7th Edition Problems (from 10.5): 2, 4, 10, 32, 36, 38; (from 10.7): 6, 12, 14, 16.