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University of Padova

Precalculus: the Mathematics of Numbers, Functions and Equations

University of Padova via FutureLearn

Overview

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.

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.

Syllabus

  • Numbers
    • Presentation of the course
    • Integers
    • Rational numbers
    • Real numbers
    • Absolute value
    • An induction proof
    • It's quiz time!
    • Test yourself
  • Functions
    • The function concept
    • The graph of a function
    • Integer powers
    • Roots and radicals
    • Simplifying radicals
    • Rational powers
    • It's quiz time
    • Test yourself
  • Algebra
    • Polynomial and identities
    • Roots of polynomials
    • Quadratic polynomials
    • Polynomial division
    • Finding roots
    • Binomial coefficients
    • It's quiz time
    • Test yourself
  • Equations
    • Introduction: types of equations
    • Equivalence
    • Polynomial equations
    • Equations involving a radical
    • Equations with several radicals
    • Equations with absolute values
    • Equations in several variables
    • It's quiz time
    • Test yourself
  • Inequalities
    • General principles
    • The quadratic case
    • Polynomial inequalities
    • Inequalities with radicals
    • Inequalities with absolute values
    • Lines in the plane
    • Systems of linear inequalities
    • It's quiz time
    • Test yourself
    • Revision Test

Taught by

Francis Clarke

Tags

Reviews

4.7 rating, based on 49 Class Central reviews

4.4 rating at FutureLearn based on 29 ratings

Start your review of Precalculus: the Mathematics of Numbers, Functions and Equations

  • Anonymous
    I am new to MOOC and am both humbled and honoured that such esteemed professionals would provide a course like this, gratis, to anyone in the world with a computer and access to the internet. The team behind it should be justifiably proud of their e…
  • Anonymous
    It's very good course to understand basic concepts. It'll be really helpful to the students who have taken the break after their 12th grade and started the bachelor's after some break of 3 to 4 years.
  • Anonymous
    Interesting course on Precalculus (Numbers, Functions, Equations and Inequalities) with a focus on depth rather than breadth. Proofs were touched on as well. The format was great as well, there were a few (5-7) concepts for each week's topic. Each c…
  • Robert John Humphries
    I have rated this course 5 stars, although there have been times when when I was so frustrated that that I would have said otherwise. The nature of the instruction seems to be very university oriented. By that I mean the lecture component which give…
  • Anonymous
    The course is well structured and organized with topics fine-tuned for the students which want to refresh their already good knowledge from the high school. I highly recommend it.
  • Mike Lewis
    A very well-presented course which lived up to all its claims. The presentations were clear and easy to understand, and the instructors all had an easy-going and personable style (I would especially mention Francis Clark in this regard - a really good teacher). My only problem was that the course required a lot more of my time than I expected, and I had to rush through the final segments in order to finish in time.

    I'm happy to recommend this course to anyone who needs to prepare for a more advanced maths class or who (like me) simply wants to recapture what was learned (and forgotten) long ago. But make sure you have enough time in your schedule to complete all the segments.
  • Anonymous
    I did not like this class. In my opinion I did not learn anything. The expiations were unhelpful, and I disliked that not all the problems were solved in a video even though there was a pdf of the answers it would have been nice to have all of the problems in a video. I would not recommend this class.
  • Anonymous
    excellent course, with detailed explanations, thorough notations and terminology, paced well.

    I like the explanatory video, examples are well explained and questions to practice give enough material to deepen the understanding.
    Thank you!
  • Anonymous
    This was an excellent in depth course of all the concepts which are necessary before one can move on to logarithmic functions and solid geometry. The material is presented in a very compact way so I would recommend watching each video several times. The exercises and their solutions are fascinating.
  • Anonymous
    Very important course. It helps you learn and covers all calculus material in a very good way. It taught me alot with a well organized videos and important notes.
  • Anonymous
    The course il very well explained and there is plenty of material to test yourself and understand your point of weakness and strength
  • Anonymous
    The MOOC was incredibly interesting and fun. The activities weren't too difficult but not too easy that they didn't require thinking. The lecturers were some of the best, as they were informative, clear and engaging. Also, the questions in the comments would always be answered. I especially enjoyed the comedy show between the 2 researchers. I would recommend this to anyone that has or is doing their A-levels or equivalent qualifications as a reminder.
  • Anonymous
    Taken this course to refresh my knowledge before getting into Calculus and Algorithms afterwards. It is great, straight to the point. If you are looking for deep understanding it is good to solve all the examples and go along all the practice videos. If you're like me just refreshing already established but slightly blurred knowledge, it will be enough to just go through the lectures. They are very explanatory.
  • Anonymous
    I found the course difficult in some areas especially " Inequalities " and some aspects of
    "Polynomials" I have always liked maths especially the "J operator" (imaginary no's) algebra
    and Cartesian to Polar co-ordinates. Being involved in electronics I found those branches of maths very useful.
    Thank you. John H Robertson
  • Anonymous
    My school work isn't challenging enough for me, so taking this course has really stimulated my brain. I would like a career in mathematics or astrophysics. I'm sure what I've learnt recently will be useful to me in either. Thank you! P.s. the hardest part was inequalities involving absolute values. I will definitely be taking the second precalculus course.
  • Anonymous
    I thought the course was well presented and well structured. Providing a pdf copy of the key points from the presentations was much appreciated, as was the follow-up worked examples. I've completed several on-line courses, and this one was one of the best. Congratulations to everyone involved in the preparation and presentation.
  • Anonymous
    Excellent course, I highly appreciate the methodology, first the theoretical explanation and second the exercises, both in video or in pdf. I recommend to everybody that needs a refresh of the topic, or just to revise or check the syllabus in order to learn the next course. The explanations are very easy to understand, excellent work¡
  • Profile image for Stephanie Williams
    Stephanie Williams
    This is a fantastic course, really well structured and well presented. It's quite challenging but in a good way, there is lots to learn. If I'd had access to a course like this when I was young it would have made my first year at university a lot easier! Looking forward to taking the advanced course.
  • Anonymous
    This course takes a lot of time and work, you must have a pretty good base of algebra to start with as you are expected to be able to manipulate difficult equations etc easily....or be really quick at learning! I did not take the tests, however, the exercises and quizzes are really testing.
  • Anonymous
    I enjoyed this course very much. In some respects it was a refresher for me, just to check that my mathematical brain still functions, but some of the teaching was new to me. I hope to take the advanced course when I have another block of spare time. Excellent.

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