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Online course

Maths for Humans: Linear and Quadratic Relations

Explore interesting and practical real-world relationships hinging on the interplay between the linear and the quadratic.

Maths for Humans: Linear and Quadratic Relations

Why join the course?

What is the connection between slices of a cone and the trajectory of a football? Between the geometry of the great pyramid and the tax bracket that you might be in? Between studying the protein content of bugs and comparing internet speeds? In this course we explore a range of interesting and practical real-world relationships hinging on the interplay between the linear and the quadratic.

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. These real-world interconnections can be studied using algebra and visualised concretely using graph paper and pencil, along with modern technologies such as graphing calculators and interactive graphing software.

Linear and quadratic functions and their graphs allow us to make predictions, evaluate actions and test theories about many things - such as the maximal grade of railways, the trajectory of a football, the relationship between supply and demand in economics, and the difference between momentum and kinetic energy in physics. Linear and quadratic relations are balanced between algebra and geometry, with numerous connections to real life.

Explore linear and quadratic relationships

Our journey begins with the fundamental idea of direct proportionality. In the first week you’ll meet lots of examples of linear relationships in the world around us. Then you’ll learn to represent these relationships algebraically and graph them geometrically in the Cartesian plane to aid in visualisation.

In subsequent weeks, we’ll look at quadratic relations from Apollonius to Bezier. We’ll discuss the history, look at lots of practical examples, and show you how to solve an interesting variety of concrete problems.

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 more sophisticated algebraic topics such as inverse relations and power laws.

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.

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Skip to 0 minutes and 4 secondsFEMALE VOICE: UNSW Australia

Skip to 0 minutes and 8 secondsNORMAN WILDBERGER: We live in a highly complex and interconnected world. Making sense of it can be a challenge, but looking closer we can find simple connections that can be understood using high school mathematics.

Skip to 0 minutes and 23 secondsHi, I'm Norman Wildberger and we're here at the University of New South Wales. This course will show you how to use mathematics to explore relationships and answer questions about the real world. How much longer does it take to download a movie in HD? Does your city have enough gas stations? What's the connection between how much you exercise and your life expectancy? These questions are about relationships between variable quantities in our world. Some relationships are very familiar from everyday life, such as how the price of a pork chop depends on its weight. Others express important physical or mathematical laws, like the fact that the acceleration of an object is directly proportional to the force on it.

Skip to 1 minute and 7 secondsOr that the area of a planar figure scales quadratically with its size. And some correspondences surprise us, such as how populations of cities are distributed in a given country. Historically, these ideas rest on 17th century discoveries

Skip to 1 minute and 21 secondsof Fermat and Descartes: that mathematical relations can be modelled with algebraic equations and visualised with a sheet of graph paper. These insights brought together Greek geometry and Arabic algebra and set the stage for calculus and the Newtonian revolution in physics. In this course, we'll look at understanding linear, quadratic and inverse functions and their graphs, with applications to a wide variety of real life situations. You'll strengthen your skills in algebra and geometry, connect with science and economics, and solve a wide variety of interesting, fun and sometimes challenging problems. Finishing this course will be valuable to senior high school and incoming college and university students wanting to review an essential pre-calculus topic.

Skip to 2 minutes and 11 secondsIt'll be useful to high school teachers and to anyone with an interest in how the remarkable power of mathematics helps us understand the world around us.

What topics will you cover?

This online course explored the mathematics of linear and quadratic relations, and related these to a variety of real-life applications. It covered:

  • Linear relationships
  • Cartesian geometry and equations of lines
  • slopes and intercepts
  • transformations of the plane
  • tax rates, interest and conversions
  • quadratic relations and parabolas
  • zeroes and the quadratic formula
  • quadratic equations in design and architecture

When would you like to start?

  • Date to be announced

What will you achieve?

By the end of the course, you'll be able to...

  • Explore different kinds of linear and quadratic relations in a variety of real world contexts.
  • Demonstrate application of algebra to solve and interpret geometrical problems.
  • Engage with specific problems involving lines and quadratics in a Cartesian setting.

Who is the course for?

This course is aimed at:

  1. senior high school students wanting to strengthen and enrich their understanding of a core pre-calculus topic;
  2. new undergraduates wishing to review and consolidate their background in algebra and geometry in preparation for STEM studies;
  3. high school maths teachers;
  4. anyone with an interest in mathematics and a curiosity about how mathematics is intertwined with the real world.

Who will you learn with?

Norman Wildberger

Norman is a research mathematician with a strong interest in education. He is the discoverer of Rational Trigonometry, and his YouTube site (user njwildberger) has more than 30K subscribers.

Daniel Mansfield

Daniel likes to learn. Most of the time he does this vicariously through teaching Mathematics at UNSW Australia. His research interests are ergodic and dimension theory.

Who developed the course?

Established in 1949 with a unique focus on the scientific, technological and professional disciplines, UNSW is a leading Australian university committed to making a difference

Buy a personalised, digital and printed certificate and transcript

You can buy a Certificate of Achievement for this course — a personalised certificate and transcript in both digital and printed formats, to prove what you’ve learnt. A Statement of Participation is also available for this course.

Certificate of Achievement + transcript $64.00

Statement of Participation $54.00

Course highlights Get a taste of this course before you join: