• University of Padova

Precalculus: the Mathematics of Numbers, Functions and Equations

Gain an introduction to the essential mathematical knowledge and skills required for your first calculus course

23,884 enrolled on this course

algebraic equations written on a blackboard

Precalculus: the Mathematics of Numbers, Functions and Equations

23,884 enrolled on this course

  • 5 weeks

  • 6 hours per week

  • Digital certificate when eligible

  • Intermediate level

Find out more about how to join this course

Get an introduction to precalculus fundamentals

This course is the first of two precalculus courses from the University of Padova that will provide you with an introduction to the fundamental mathematical skills required to complete your first course in calculus.

You will learn the basic precalculus required for college or undergraduate-level studies, including factoring and division, sets and set operations, reasoning and proofs, functions and graphs, and equations and inequalities.

On this online precalculus course, you will gain the foundation to support further mathematical studies and improve your use of maths in everyday life.

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Skip to 0 minutes and 10 seconds If we are going to do this precalculus course, it’s going to be really a lot of work. True, but imagine how much we’re going to learn in doing this! And I guess those who take the course will learn something too. Who will be taking the course, do you think? Oh, there are lots of people who need such a course, for example those who want to prepare a college course, calculus, say, or statistics, or if you are taking an admission test, to get into business school. And people of good taste who simply want to be better informed about mathematics. And besides, mathematics is good for the brain, and keeps you young also. Oh definitely, look at us!

Skip to 0 minutes and 54 seconds True, and lots of people need to brush up on their mathematics. As long as they have some high school maths, they should be able to follow the course. What material would we put into the course, do you think? Well, I suppose we’ll put in the basic stuff that people usually know, you know, at the end of high school or beginning university. Things like numbers, the various types. And functions. And their graphs. Some algebra, radicals, how to solve equations… Yes, right! Beautiful stuff! But, algebra? Don’t people tend to be intimidated by algebra? I’ve heard that in some occasions, you know… Personally, I believe algebra is really a lot of fun. Oh, you’re right!

Skip to 1 minute and 39 seconds We’ll have to find a way to show them that,once you know a few operations, it’s a very natural thing, algebra. Yes, let’s hope you can do that in the lectures. But we’ll also need to prepare lots of good exercises to go along with those lectures. Yes, and we need to work out how to present problems and solutions in a new and interesting way. Well, if we’re gonna do this, we better get started pretty soon…

What topics will you cover?

  • Numbers: integers, rationals, real numbers, absolute value, induction.
  • Functions: graphs, integer powers, roots and radicals, rational powers.
  • Algebra: polynomials and their roots, quadratic polynomials, polynomial division, finding roots, binomial coefficients.
  • Equations: types of equations, equivalence, polynomial equations, equations involving a radical, equations with several radicals/with absolute values, equations in several variables.
  • Inequalities: linear and polynomial inequalities, inequalities involving radicals and absolute values.

When would you like to start?

Start straight away and join a global classroom of learners. If the course hasn’t started yet you’ll see the future date listed below.

  • Available now

Learning on this course

On every step of the course you can meet other learners, share your ideas and join in with active discussions in the comments.

What will you achieve?

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

  • Describe the basic arithmetic of numbers, including absolute value and radicals
  • Identify the standard notation for sets and set operations
  • Explain the elements of mathematical reasoning and proofs
  • Classify the types of functions and their graphs
  • Solve polynomials: roots, factoring, and division
  • Solve equations and inequalites

Who is the course for?

This course is for anyone who wants to brush up on their basic mathematical skills, particularly students in the last year of high school, or at the beginning of undergraduate studies, who intend to take a first course in calculus.

Who will you learn with?

I am a professor of mathematics at the University of Lyon. In previous lives I have held tenured positions at the University of British Columbia and the University of Montreal.

I am professor of mathematical analysis at the University of Padova. Among my interests: magic, tango, photography, innovative teaching, technology and e-learning.

I am a professor of algebra at the University of Padova and I teach at the science and engineering faculties. I like very much math and classical music.

I am Postdoc researcher at Inria Paris. My research field is mainly sub-Riemannian geometry. Among my interests: photography, swimming and science communication.

I'm a mathematician expert in the fields of homological algebra and applied category theory.
I'm also interested in photography, bike and powerlifting.

Who developed the course?

University of Padova

The University of Padova is one of Europe’s oldest and most prestigious seats of learning; it aims to provide its students with both professional training and a solid cultural background.

Endorsers and supporters

supported by

Dipartimento di Matematica, University of Padova

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Ways to learn

Choose the best way to learn for you!

Subscribe & save


Automatically renews

Develop skills to further your career

  • Access to this course
  • Access to 1,000+ courses
  • Learn at your own pace
  • Discuss your learning in comments
  • Tests to boost your learning
  • Digital certificate when you're eligible

Cancel for free anytime

Buy this course

$134/one-off payment

Fulfill your current learning need

  • Access to this course
  • Learn at your own pace
  • Discuss your learning in comments
  • Tests to boost your learning
  • Printed and digital certificate when you’re eligible

Limited access


Sample the course materials

  • Access expires 23 May 2024

Find out more about certificates, Unlimited or buying a course (Upgrades)

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