Mathematics provides the formal structures and reasoning tools that underpin computer science. Mathematical Foundations for Computing introduces core topics essential for problem-solving, algorithm design, and theoretical computing. You will explore sets and set theory, number systems and bases, functions, and relations—building a toolkit to model data, describe systems, and reason about computational processes. Each module connects abstract mathematics to practical computing contexts, from binary representation and function mapping to relational models.
By the end of the course, you will not only understand these concepts theoretically but also know how to apply them to programming, algorithms, and data structures. This course is part of the Essential Mathematics for Computer Science specialisation, preparing you for advanced topics in logic, algorithms, and computational complexity.
This week you will be learning about two key concepts: the definition of a set, set notation, and membership tables.
涵盖的内容
9个视频6篇阅读材料9个作业
显示有关单元内容的信息
9个视频•总计70分钟
Introduction to the specialisation and this course•5分钟
The definition of a set•8分钟
The listing method and rule of inclusion•9分钟
The powerset of a set•10分钟
Set operations•10分钟
The representation of a set using Venn diagrams•5分钟
De Morgan's laws•9分钟
Laws of sets: Commutative, associative and distributives•11分钟
Partition of a set•4分钟
6篇阅读材料•总计80分钟
Course structure and navigation•15分钟
How to learn effectively on this course•15分钟
Course Syllabus•10分钟
The definition of a set•10分钟
Laws of sets: Commutative, associative and distributives•15分钟
Module 1 summary•15分钟
9个作业•总计245分钟
The definition of a set•30分钟
The listing method and rule of inclusion•30分钟
The powerset of a set•15分钟
Set operations•30分钟
The representation of a set using Venn diagrams•30分钟
De Morgan's laws•30分钟
Laws of sets: Commutative, associative and distributive•30分钟
Partition of a set•30分钟
Check your understanding: End of module 1•20分钟
Module 2: Number Systems and Bases
第 2 单元•小时 后完成
单元详情
In this module, we will cover three key concepts: an introduction to number bases, the conversion of non-integer numbers, and operations with binary numbers. You will gain an understanding of how number bases work and learn how to perform arithmetic in different bases.
涵盖的内容
8个视频4个作业
显示有关单元内容的信息
8个视频•总计59分钟
Introduction to number bases•14分钟
Conversion of integer numbers between different bases•8分钟
Conversion of non-integer numbers between bases•15分钟
Operations with binary numbers – addition•3分钟
Operations with binary numbers – subtraction•5分钟
Operations with binary numbers – multiplication•4分钟
Number representations•8分钟
Topic 1 – looking back •2分钟
4个作业•总计110分钟
Introduction to number bases – conversion to decimal•30分钟
Non-integer numbers conversion•30分钟
Operations with binary numbers•30分钟
Check your understanding: End of module 2•20分钟
Module 3: Functions and Their Properties
第 3 单元•小时 后完成
单元详情
This week you will learn about four key concepts: the definition of a function; properties of one-to-one and onto functions; proving correctness if a function is one-to-one or onto; and plotting functions.
涵盖的内容
7个视频3篇阅读材料8个作业1个非评分实验室
显示有关单元内容的信息
7个视频•总计77分钟
The definition of a function•12分钟
Plotting functions•9分钟
Injective and surjective functions•15分钟
Function composition•4分钟
Bijective functions•12分钟
Logarithmic functions•12分钟
The floor and ceiling functions•12分钟
3篇阅读材料•总计40分钟
Injective and surjective functions•15分钟
Functions problem sheet and solutions•10分钟
Module 3 summary •15分钟
8个作业•总计230分钟
The definition of a function•30分钟
Plotting functions•30分钟
Injective and surjective functions•30分钟
Function composition•30分钟
Bijective functions•30分钟
Logarithmic functions•30分钟
The floor and ceiling functions•30分钟
Check your understanding: End of module 3•20分钟
1个非评分实验室•总计20分钟
2D Graphing Calculator: Plotting some functions•20分钟
Module 4: Relations
第 4 单元•小时 后完成
单元详情
In this week you will learn about three key concepts: the definition of a relation and how it is different from a function; a relation digraph; and reflexive, symmetric, anti-symmetric and transitive relations.
涵盖的内容
7个视频2篇阅读材料7个作业
显示有关单元内容的信息
7个视频•总计53分钟
Definition of a relation: relation versus function•8分钟
Matrix and graph representations of a relation•10分钟
The properties of a relation: reflexive, symmetric and anti-symmetric•15分钟
Relation properties: transitivity•5分钟
Equivalence relations and equivalence classes•7分钟
Partial and total order•7分钟
Course summary•1分钟
2篇阅读材料•总计25分钟
Topic summary•15分钟
Mathematical Foundations for Computing: Course Summary•10分钟
7个作业•总计155分钟
Definition of a relation: relation versus function•20分钟
Matrix and graph representations of a relation•20分钟
The properties of a relation: reflexive, symmetric and anti-symmetric•20分钟
Relation properties: transitivity•20分钟
Equivalence relations and equivalence classes•25分钟
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