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Mathematical Foundations for Computing

Mathematical Foundations for Computing

This course is part of Essential Mathematics for Computer Science Specialization

Instructor: Omar Karakchi

Included with

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4 modules

Gain insight into a topic and learn the fundamentals.

Beginner level

Recommended experience

2 weeks to complete

at 10 hours a week

Flexible schedule

Learn at your own pace

4 modules

Gain insight into a topic and learn the fundamentals.

Beginner level

Recommended experience

2 weeks to complete

at 10 hours a week

Flexible schedule

Learn at your own pace

What you'll learn

Develop a strong understanding of sets, subsets, and set operations, applying them to data representation and computational modelling.
Convert numbers across decimal, binary, and hexadecimal systems, and apply base conversions to programming and computer architecture.
Analyse and interpret functions and their properties, including mappings and inverses, to understand their role in algorithms and computing.
Explore relations and their properties, using them to describe structured connections and dependencies in computational systems.

Skills you'll gain

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Build your subject-matter expertise

This course is part of the Essential Mathematics for Computer Science Specialization

When you enroll in this course, you'll also be enrolled in this Specialization.

Learn new concepts from industry experts
Gain a foundational understanding of a subject or tool
Develop job-relevant skills with hands-on projects
Earn a shareable career certificate

There are 4 modules in this course

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.

Module details

This week you will be learning about two key concepts: the definition of a set, set notation, and membership tables.

What's included

9 videos6 readings9 assignments

9 videosTotal 70 minutes

Introduction to the specialisation and this course5 minutes
The definition of a set8 minutes
The listing method and rule of inclusion9 minutes
The powerset of a set10 minutes
Set operations10 minutes
The representation of a set using Venn diagrams5 minutes
De Morgan's laws9 minutes
Laws of sets: Commutative, associative and distributives11 minutes
Partition of a set4 minutes

6 readingsTotal 80 minutes

Course structure and navigation15 minutes
How to learn effectively on this course15 minutes
Course Syllabus10 minutes
The definition of a set10 minutes
Laws of sets: Commutative, associative and distributives15 minutes
Module 1 summary15 minutes

9 assignmentsTotal 245 minutes

The definition of a set30 minutes
The listing method and rule of inclusion30 minutes
The powerset of a set15 minutes
Set operations30 minutes
The representation of a set using Venn diagrams30 minutes
De Morgan's laws30 minutes
Laws of sets: Commutative, associative and distributive30 minutes
Partition of a set30 minutes
Check your understanding: End of module 120 minutes

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.

What's included

8 videos4 assignments

8 videosTotal 59 minutes

Introduction to number bases14 minutes
Conversion of integer numbers between different bases8 minutes
Conversion of non-integer numbers between bases15 minutes
Operations with binary numbers – addition3 minutes
Operations with binary numbers – subtraction5 minutes
Operations with binary numbers – multiplication4 minutes
Number representations8 minutes
Topic 1 – looking back 2 minutes

4 assignmentsTotal 110 minutes

Introduction to number bases – conversion to decimal30 minutes
Non-integer numbers conversion30 minutes
Operations with binary numbers30 minutes
Check your understanding: End of module 220 minutes

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.

What's included

7 videos3 readings8 assignments1 ungraded lab

7 videosTotal 77 minutes

The definition of a function12 minutes
Plotting functions9 minutes
Injective and surjective functions15 minutes
Function composition4 minutes
Bijective functions12 minutes
Logarithmic functions12 minutes
The floor and ceiling functions12 minutes

3 readingsTotal 40 minutes

Injective and surjective functions15 minutes
Functions problem sheet and solutions10 minutes
Module 3 summary 15 minutes

8 assignmentsTotal 230 minutes

The definition of a function30 minutes
Plotting functions30 minutes
Injective and surjective functions30 minutes
Function composition30 minutes
Bijective functions30 minutes
Logarithmic functions30 minutes
The floor and ceiling functions30 minutes
Check your understanding: End of module 320 minutes

1 ungraded labTotal 20 minutes

2D Graphing Calculator: Plotting some functions20 minutes

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.