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Online course

Precalculus: the Mathematics of Numbers, Functions and Equations

Get an introduction to the essential mathematical knowledge and skills required to take a first course in calculus.

Precalculus: the Mathematics of Numbers, Functions and Equations

Get an introduction to precalculus fundamentals

This course is the first of two precalculus courses from the University of Padova, providing you with an introduction to the fundamental mathematical skills required to complete a first course in calculus.

You’ll get familiar with the basic precalculus required for college or undergraduate-level studies, notably: factoring and division; sets and set operations; reasoning and proofs; functions and graphs; and equations and inequalities.

Through this course you’ll gain the foundation to support further mathematical studies, or improve your use of mathematics in everyday life.

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Skip to 0 minutes and 10 secondsIf 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 secondsTrue, 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 secondsWe'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?

  • Available now

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?

Francis Clarke

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.

Carlo Mariconda

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

Alberto Tonolo

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.

Valentina Franceschi

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

Francesco Mattiello

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?

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.


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  • Access to this course for 7 weeks
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  • Unlimited access to this course
  • Includes any articles, videos, peer reviews and quizzes
  • Tests to validate your learning
  • Certificate of Achievement to prove your success when you're eligible
  • Download and print your Certificate of Achievement anytime

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