Discrete structures course information  (Page 3/6)

In Chapter 1, we also study sets, relations between sets, and operations on sets. Sets are the basis of every theory in computer science and mathematics.

In Chapter 3, we learn recursive definitions and mathematical reasoning, in particular induction. There are sets, operations and functions that can be defined precisely by recursive definitions. Properties of those recursively defined objects can be established rigorously using proof by induction.

Then in Chapters 6 we study relations. Relations are one of the key concepts in the discussion of many subjects on computer and computation. For example, a database is viewed as a set of relations and database query languages are constructed based on operations on relations and sets. Graphs are also covered briefly here. Graphs are an example of discrete structures and they are one of the most useful models for computer scientists and engineers in solving problems. More in-depth coverage of graphs can be found in Chapter 7.

Finally, back in Chapter 1 again, we briefly study functions. Functions are a special type of relation and basically the same kind of concept as the ones we see in calculus. However, functions are one of the most important concepts in the discussion of many subjects on computer and computation, such as data structures, database, formal languages and automata, and analysis of algorithms, which is briefly covered in Chapter 2.

Instructional sequence

Unit 1

Task 1: Read the following:

• Introduction to Discrete Structures
• Problem Solving Framework
• Problem Solving Example 1

Unit 2

Task 1: Read the following:

• Problem Solving Examples

Unit 3

Task 1: Read the following:

• Introduction to Logic
• What is Proposition
• Elements of Propositional Logic
• Truth Table
• Connectives
• Construction of Proposition
• Converse and Contrapositive

These materials can also be found in Textbook 1.1 - 1.2.

Task 2: Do the following exercises: These exercises are NOT homework questions. They are for helping you understand the materials of this unit.

• Textbook p. 11 : 1 all
• Textbook p. 11 : 3 all
• Textbook p. 11 : 7 a c e g
• Textbook p. 12 : 9 b d f h
• Textbook p. 13 : 19 all
• Textbook p. 13 : 21 a c e
• Textbook p. 13 : 23 d f
• Reading Material: Chapter Logic - Exercise 16-21

Unit 4

Task 1: Read the following:

• Variations of if_then
• From English to Proposition

These materials can also be found in Textbook 1.1 - 1.2.

Task 2: Do the following exercises: These exercises are NOT homework questions. They are for helping you understand the materials of this unit.

• Textbook p. 12 : 15 all
• Textbook p. 12 : 17 all
• Reading Material: Chapter Logic - Exercise 22-23

Unit 5

Task 1: Read the following:

• Introduction to Reasoning
• Identities of Propositions and Dual
• Example of Use of Identities

These materials can also be found in Textbook 1.1 - 1.2.

Task 2: Do the following exercises: These exercises are NOT homework questions. They are for helping you understand the materials of this unit.

• Textbook p. 19 : 1 a d f
• Textbook p. 19 : 5
• Textbook p. 20: 9 b d f
• Textbook p. 20: 11 a
• Textbook p. 20: 20 all
• Textbook p. 20: 25
• Reading Material: Chapter Logic - Exercise 24-29