Course: Precalculus: the Mathematics of Numbers, Functions and Equations

Increasing and decreasing functions, even functions, symmetry

The Cartesian plane, coordinates, affine functions, slope

The following exercises are solved in this step. We invite you to try to solve them before watching the video. In any case, you will find below a PDF file …

Definition, domain, range, sums, products, quotients, composition

The following exercises are solved in this step. We invite you to try to solve them before watching the video. In any case, you will find below a PDF file …

Proof of the formula presented in the first lecture, sigma notation

The following exercises are solved in this step. We invite you to try to solve them before watching the video. In any case, you will find below a PDF file …

Definition of absolute value, laws, distance, decimal representation, the number pi

The following exercises are solved in this step. We invite you to try to solve them before watching the video. In any case, you will find below a PDF file …

Arithmetic, intervals, means (average), complements, inequalities

The following exercises are solved in this step. We invite you to try to solve them before watching the video. In any case, you will find below a PDF file …

Fractions, rational numbers, negative integers, the square root of 2 is not rational, the real line.

When Gauss, who later became a famous mathematician, was still in school, his teacher asked him to sum the integers from 1 to 100. The teacher probably wanted to punish …

The following exercises are solved in this step. We invite you to try to solve them before watching the video. In any case, you will find below a PDF file …

In this video, Francis introduces counting numbers, sets, set operations, the induction principle, divisibility, and primes. You can access a copy of the slides used in the video in the …