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.