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CIT206Sciences2 Unitsintermediate

Discrete Structure

This course introduces students to the fundamental concepts of discrete structures and their applications in computer science. It covers essential topics such as set theory, logic, proofs, relations, functions, graph theory, and Boolean algebra. Students will learn to apply these concepts to solve problems in computer science, develop logical reasoning skills, and understand the mathematical foundations of computing. The course also explores matrices, counting principles, and discrete probability.

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120h
Study Time
13
Weeks
9h
Per Week
intermediate
Math Level
Course Keywords
Discrete StructuresSet TheoryLogicGraph TheoryBoolean Algebra

Course Overview

Everything you need to know about this course

Course Difficulty

Intermediate Level
Builds on foundational knowledge
65%
intermediate
📊
Math Level
Moderate Math
📖
Learning Type
Theoretical Focus

Course Topics

Key areas covered in this course

1

Set Theory

2

Logic

3

Proofs and Induction

4

Graph Theory

5

Boolean Algebra

6

Matrices

7

Counting Principles

8

Discrete Probability

Total Topics8 topics

Requirements

Knowledge and skills recommended for success

Basic Mathematics

Introduction to Computer Science

💡 Don't have all requirements? Don't worry! Many students successfully complete this course with basic preparation and dedication.

Assessment Methods

How your progress will be evaluated (3 methods)

assignments

Comprehensive evaluation of course material understanding

Written Assessment

tutor-marked assessments

Comprehensive evaluation of course material understanding

Written Assessment

final examination

Comprehensive evaluation of course material understanding

Computer Based Test

Career Opportunities

Explore the career paths this course opens up for you

Software Developer

Apply your skills in this growing field

Data Analyst

Apply your skills in this growing field

Network Engineer

Apply your skills in this growing field

Database Administrator

Apply your skills in this growing field

Systems Analyst

Apply your skills in this growing field

Industry Applications

Real-world sectors where you can apply your knowledge

Computer ScienceInformation TechnologyTelecommunicationsData ScienceSoftware Engineering

Study Schedule Beta

A structured 13-week journey through the course content

Week
1

Module 1: Introduction to Discrete Structures

3h

Unit 1: Set Theory

3 study hours
  • •Read the introduction to mathematical statements and understand statement definitions.
  • •Practice identifying atomic and molecular statements.
  • •Work through examples of logical connectives.
Week
2

Module 1: Introduction to Discrete Structures

3h

Unit 1: Set Theory

3 study hours
  • •Study set notations and operations on sets.
  • •Solve problems involving union, intersection, and complement of sets.
  • •Practice using Venn diagrams to represent set operations.
Week
3

Module 1: Introduction to Discrete Structures

3h

Unit 2: Proofs and Induction

3 study hours
  • •Learn basic proof techniques: direct proof, proof by induction, and indirect proofs.
  • •Practice constructing direct proofs for simple mathematical statements.
  • •Understand the initial and inductive steps in proof by induction.
Week
4

Module 1: Introduction to Discrete Structures

3h

Unit 2: Proofs and Induction

3 study hours
  • •Work through examples of proof by induction, including sums and divisibility.
  • •Understand proof by contrapositive and proof by contradiction.
  • •Solve tutor-marked assignments on proofs and induction.
Week
5

Module 1: Introduction to Discrete Structures

3h

Unit 3: Logic

3 study hours
  • •Study propositional logic and logical connectives.
  • •Construct truth tables for logical expressions.
  • •Learn about logical equivalence and De Morgan's laws.
Week
6

Module 1: Introduction to Discrete Structures

3h

Unit 3: Logic

3 study hours
  • •Apply deduction rules to determine the validity of arguments.
  • •Understand first-order logic and its applications.
  • •Solve tutor-marked assignments on logic.
Week
7

Module 2: Boolean Algebra and Graph Theory

3h

Unit 1: Boolean Algebra and Lattices

3 study hours
  • •Learn about partially ordered sets and lattices.
  • •Distinguish between least upper bound (LUB) and greatest lower bound (GLB).
  • •Understand the properties of lattices.
Week
8

Module 2: Boolean Algebra and Graph Theory

3h

Unit 1: Boolean Algebra and Lattices

3 study hours
  • •Study Boolean algebra and its axioms.
  • •Understand complemented and distributive lattices.
  • •Solve problems involving Boolean algebra and lattices.
Week
9

Module 2: Boolean Algebra and Graph Theory

3h

Unit 2: Graph Theory

3 study hours
  • •Learn about vertices, edges, and types of graphs (directed, undirected).
  • •Understand isomorphic graphs and subgraphs.
  • •Study bipartite graphs and their properties.
Week
10

Module 2: Boolean Algebra and Graph Theory

3h

Unit 2: Graph Theory

3 study hours
  • •Apply the Handshaking Theorem to solve problems.
  • •Learn about Euler paths and circuits.
  • •Study adjacency matrices and their applications.
Week
11

Module 3: Matrices, Applications to Counting and Discrete Probability

3h

Unit 1: Matrices

3 study hours
  • •Study matrix operations: addition, subtraction, multiplication.
  • •Understand determinants and their properties.
  • •Learn about special matrices: transpose, symmetric, skew-symmetric, singular, non-singular.
Week
12

Module 3: Matrices, Applications to Counting and Discrete Probability

3h

Unit 2: Applications to Counting

3 study hours
  • •Apply the product and sum rules to solve counting problems.
  • •Understand permutations and combinations.
  • •Learn about combinatorial identities and Pascal's triangle.
Week
13

Module 3: Matrices, Applications to Counting and Discrete Probability

3h

Unit 3: Discrete Probability Generating Function

3 study hours
  • •Apply the inclusion-exclusion principle and pigeonhole principle.
  • •Understand discrete probability generating functions (PGFs).
  • •Use PGFs to calculate mean, variance, and probabilities.

This study schedule is in beta and may not be accurate. Please use it as a guide and consult the course outline for the most accurate information.

Course PDF Material

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Study Tips & Exam Preparation

Expert tips to help you succeed in this course

1

Review all unit objectives and key concepts

2

Practice solving problems from each unit

3

Focus on understanding proofs and logical arguments

4

Create concept maps linking different topics

5

Allocate sufficient time for studying graph theory and Boolean algebra

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