Maths for Humans: Inverse Relations and Power Laws (FutureLearn)

Maths for Humans: Inverse Relations and Power Laws (FutureLearn)

Strengthen your algebra, geometry and thinking skills by learning about fascinating mathematical relations from daily life.

Class Deals by MOOC List - Click here and see FutureLearn's Active Discounts, Deals, and Promo Codes.

What’s the connection between the size of a city and the number of gas stations in it? How would you describe this relationship? How would you try to visualise and understand it?

Study real-world connections using algebra and geometry
In this free online course, we’ll look at a wide spectrum of interesting, and often surprising, mathematical relationships in our everyday world. We’ll be studying inverse relations, which complement direct relationships; power laws that occur in economics, physics and biology; as well as curious applications of the logarithm function. We’ll visualise these real-world interconnections using graph paper and pencil, and also modern graphing software such as GeoGebra and Desmos.
The functions and graphs in this course help us to make predictions, evaluate actions and test theories about population distributions, the frequencies of common words in texts, scaling laws in biology and much more. We’ll even see some applications to detecting fraud!

Explore inverse and power relationships
In Week 1 you’ll meet hyperbolas and inverse relations, which are complementary to the direct proportionality that we studied in Maths for Humans: Linear and Quadratic Relations. You’ll learn to represent such relationships algebraically, and understand them geometrically in the Cartesian plane in a direct visual way.
In subsequent weeks, we’ll look at Zipf’s law and Benford’s law, check out applications in engineering and physics, investigate power relations and higher degree polynomials, and explore allometry in biology. You will see the history, look at lots of examples, and get useful insights into: lifespans, whether exercise really is good for you, the distribution of wealth, and the crazy claw of the Fiddler crab. And lots of other juicy applications of advanced high school mathematics.

Gain valuable skills for further study
Understanding basic mathematical relationships is vital to many fields of study: biology, engineering, business, economics, political science and design. By the end of this course, you’ll have hands-on experience with a wide range of explicit examples, be familiar with a core area of pre-calculus mathematics, and be ready to go on to more advanced study of calculus or linear algebra.
Whether you’re encountering these topics for the first time or brushing up on your high school mathematics, we hope you’ll actively join our community on this journey through some fascinating and practical topics that have contributed much to our understanding of the world around us.

Go to Class
MOOC List is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

Related Courses

Aléatoire : une introduction aux probabilités - Partie 1 (Coursera) Coursera
École Polytechnique

Aléatoire : une introduction aux probabilités - Partie 1 (Coursera)

Ce cours d'introduction aux probabilités a la même contenu que le cours de tronc commun de première année de l'École polytechnique donné par Sylvie Méléard. Le cours introduit graduellement la notion de variable aléatoire et culmine avec la loi des grands nombres et le théorème de la limite centrale. Les notions mathématiques nécessaires sont introduites au fil du cours et de nombreux exercices corrigés sont proposés.

Oct 5th 2026
5-12 Weeks
World Class Maths: Asian Teaching Practice (FutureLearn) FutureLearn
Macmillan Education

World Class Maths: Asian Teaching Practice (FutureLearn)

Learn how to create lessons plans based on Asian maths teaching methods, and develop your maths teaching practice. Integrate world-class maths teaching methods into your own teaching practice. Get an introduction to Asian maths teaching methods for primary education, with this course from Macmillan Education and University of Southampton.

No sessions available
4 Weeks
Information Theory (Coursera) Coursera
The Chinese University of Hong Kong

Information Theory (Coursera)

At the completion of this course, the student should be able to: demonstrate knowledge and understanding of the fundamentals of information theory; appreciate the notion of fundamental limits in communication systems and more generally all systems; develop deeper understanding of communication systems; apply the concepts of information theory to various disciplines in information science.

Oct 5th 2026
13-24 Weeks
Cracking Mechanics: Further Maths for Engineers (FutureLearn) FutureLearn
University of Bristol

Cracking Mechanics: Further Maths for Engineers (FutureLearn)

Practise the maths, learn the physics, and find out how engineers use both to solve real world problems. The aim of this free online course is to introduce you to some of the physics and maths that engineers find useful. The content comprises: parts of A-level maths and further maths (mechanics); the physical laws which this maths is used to model; and examples of how these skills are employed in mechanical, aerospace, civil, environmental, materials and electrical engineering.

No sessions available
5-12 Weeks
Combinatorics: Strategies and Methods for Counting (FutureLearn) FutureLearn
University of Padova

Combinatorics: Strategies and Methods for Counting (FutureLearn)

Explore the wonderful world of combinatorics with this course exploring simple and efficient ways to count. See combinatorics made simple and how to avoid errors in counting principles. Combinatorics is an area of mathematics primarily concerned with counting. Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry. On this free online combinatorics course, you’ll discover a simple and efficient method to translate a combinatorial problem into counting the elements of a reference mathematical structure.

Self Paced
4 Weeks
Analytic Combinatorics (Coursera) Coursera
Princeton University

Analytic Combinatorics (Coursera)

Analytic Combinatorics teaches a calculus that enables precise quantitative predictions of large combinatorial structures. This course introduces the symbolic method to derive functional relations among ordinary, exponential, and multivariate generating functions, and methods in complex analysis for deriving accurate asymptotics from the GF equations. All the features of this course are available for free. It does not offer a certificate upon completion.

Oct 5th 2026
5-12 Weeks
Introduction to Mathematical Thinking (Coursera) Coursera
Stanford University

Introduction to Mathematical Thinking (Coursera)

Learn how to think the way mathematicians do - a powerful cognitive process developed over thousands of years. Mathematical thinking is not the same as doing mathematics – at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself.

Oct 5th 2026
5-12 Weeks
Studying in Italian - Science and Mathematics: a MOVE-ME Project Course (FutureLearn) FutureLearn
The Open University,Università per Stranieri di Siena - UniStraSi,NUI Galway

Studying in Italian - Science and Mathematics: a MOVE-ME Project Course (FutureLearn)

Study Science and Maths in Italian and develop the skills you need when you take part in a European student mobility programme. Each year thousands of students travel across Europe to study in a foreign language like Italian. This can be daunting, even for those who are fluent. This online course from UniStraSi will help, guiding you through the peculiarities of academic discourse in Italian, and enabling you to understand and produce written and aural academic texts.

No sessions available
5-12 Weeks
Scratch to Python: Moving from Block- to Text-based Programming (FutureLearn) FutureLearn
Raspberry Pi Foundation

Scratch to Python: Moving from Block- to Text-based Programming (FutureLearn)

Learn how to apply the thinking and programming skills you've learnt in Scratch to text-based programming languages like Python. Discover how you can transition from block to text-based programming. Block-based programming languages like Scratch make it simple to learn and teach programming. But once you and your students have mastered it, it’s time to move on to a text-based programming language such as Python. This online course will show you how.

Mar 6th 2023
4 Weeks