This will be especially helpful if you are planning to begin GMAT or GRE preparation soon, because then you will need to refresh your advanced high school maths.

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? This is just part of what you will learn during the free online course “Maths for Humans: Inverse Relations and Power Laws”.

## What you will learn

• Study real-world connections using algebra and geometry

In this free online course, you will look at a wide spectrum of interesting, and often surprising, mathematical relationships in our everyday world. You will 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. You will 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 will help you to make predictions, evaluate actions and test theories about population distributions, the frequency of common words in texts, scaling laws in biology and much more. You will even see some applications in 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 are 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, you will 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 will 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 are 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.

Starting date: 22 August 2016

Duration:  4 weeks, 3 hours per week

Language: English

Instructors: Norman Wildberger, Daniel Mansfield

Institutions: UNSW Australia