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⇱ Mathematical Foundations for Computing | Coursera

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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
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.

Details to know

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Recently updated!

February 2026

Assessments

28 assignments¹

AI Graded see disclaimer
Taught in English

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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.
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  • Gain a foundational understanding of a subject or tool
  • Develop job-relevant skills with hands-on projects
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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.

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.

What's included

9 videos6 readings9 assignments

9 videos•Total 70 minutes
  • Introduction to the specialisation and this course•5 minutes
  • The definition of a set•8 minutes
  • The listing method and rule of inclusion•9 minutes
  • The powerset of a set•10 minutes
  • Set operations•10 minutes
  • The representation of a set using Venn diagrams•5 minutes
  • De Morgan's laws•9 minutes
  • Laws of sets: Commutative, associative and distributives•11 minutes
  • Partition of a set•4 minutes
6 readings•Total 80 minutes
  • Course structure and navigation•15 minutes
  • How to learn effectively on this course•15 minutes
  • Course Syllabus•10 minutes
  • The definition of a set•10 minutes
  • Laws of sets: Commutative, associative and distributives•15 minutes
  • Module 1 summary•15 minutes
9 assignments•Total 245 minutes
  • Check your understanding: End of module 1•20 minutes
  • The definition of a set•30 minutes
  • The listing method and rule of inclusion•30 minutes
  • The powerset of a set•15 minutes
  • Set operations•30 minutes
  • The representation of a set using Venn diagrams•30 minutes
  • De Morgan's laws•30 minutes
  • Laws of sets: Commutative, associative and distributive•30 minutes
  • Partition of a set•30 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 videos•Total 59 minutes
  • Introduction to number bases•14 minutes
  • Conversion of integer numbers between different bases•8 minutes
  • Conversion of non-integer numbers between bases•15 minutes
  • Operations with binary numbers – addition•3 minutes
  • Operations with binary numbers – subtraction•5 minutes
  • Operations with binary numbers – multiplication•4 minutes
  • Number representations•8 minutes
  • Topic 1 – looking back •2 minutes
4 assignments•Total 110 minutes
  • Check your understanding: End of module 2•20 minutes
  • Introduction to number bases – conversion to decimal•30 minutes
  • Non-integer numbers conversion•30 minutes
  • Operations with binary numbers•30 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 videos•Total 77 minutes
  • The definition of a function•12 minutes
  • Plotting functions•9 minutes
  • Injective and surjective functions•15 minutes
  • Function composition•4 minutes
  • Bijective functions•12 minutes
  • Logarithmic functions•12 minutes
  • The floor and ceiling functions•12 minutes
3 readings•Total 40 minutes
  • Injective and surjective functions•15 minutes
  • Functions problem sheet and solutions•10 minutes
  • Module 3 summary •15 minutes
8 assignments•Total 230 minutes
  • Check your understanding: End of module 3•20 minutes
  • The definition of a function•30 minutes
  • Plotting functions•30 minutes
  • Injective and surjective functions•30 minutes
  • Function composition•30 minutes
  • Bijective functions•30 minutes
  • Logarithmic functions•30 minutes
  • The floor and ceiling functions•30 minutes
1 ungraded lab•Total 20 minutes
  • 2D Graphing Calculator: Plotting some functions•20 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.

What's included

7 videos2 readings7 assignments

7 videos•Total 53 minutes
  • Definition of a relation: relation versus function•8 minutes
  • Matrix and graph representations of a relation•10 minutes
  • The properties of a relation: reflexive, symmetric and anti-symmetric•15 minutes
  • Relation properties: transitivity•5 minutes
  • Equivalence relations and equivalence classes•7 minutes
  • Partial and total order•7 minutes
  • Course summary•1 minute
2 readings•Total 25 minutes
  • Topic summary•15 minutes
  • Mathematical Foundations for Computing: Course Summary•10 minutes
7 assignments•Total 155 minutes
  • Check your understanding: End of module 4•20 minutes
  • Definition of a relation: relation versus function•20 minutes
  • Matrix and graph representations of a relation•20 minutes
  • The properties of a relation: reflexive, symmetric and anti-symmetric•20 minutes
  • Relation properties: transitivity•20 minutes
  • Equivalence relations and equivalence classes•25 minutes
  • Partial and total order•30 minutes

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¹ Some assignments in this course are AI-graded. For these assignments, your data will be used in accordance with Coursera's Privacy Notice.