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About the Preparing for University Math Program (PUMP)

What is PUMP?

The Preparing for University Math Program (PUMP) is a non-credit course designed for students who have not taken the appropriate high school mathematics prerequisites for university calculus and linear algebra. It equips students with the necessary background knowledge required to succeed in first year mathematics courses. PUMP may also be taken by individuals who wish to close any existing gap between high school math and University level math courses or any one who wish to review high school math before attempting University level math or other science courses.

Programs that Require Calculus before Admissions

Ontario high school students applying on the 101 application form are expected to present MCV4U - Calculus and Vectors for admission to all science, math and commerce programs in the Faculty of Arts and Science, St. George Campus. PUMP cannot be used as a replacement for this admission requirement.

Students already enrolled in the University of Toronto, may use PUMP to upgrade their mathematics skills in order to prepare for the first year math courses.

What is the required background for PUMP?

Even though PUMP covers pre-university level math material, a certain background knowledge is required. In general terms, a student must have a working knowledge of basic high school algebra, linear quadratic functions and elementary analytic geometry.

Students who do not have the above-mentioned background may still take PUMP and do well provided they are prepared to work hard.

What does PUMP cover?

PUMP focuses on the mathematical background needed for entry-level university science courses, expanding and developing relevant skills and techniques of reasoning. It includes a thorough review of primary algebraic, geometric and trigonometric results and methods as well as an introduction to the fundamental ideas underlying calculus, its elementary properties and applications.

Topics to be covered:
  • Fundamental algebraic background: sets, operations and properties; Numbers, fractions, exponents and rational expressions; Factorization and reduction; Completing the square; Binomial expansion; Operations with general algebraic expressions.
  • Equations, inequalities and systems: equations in quadratic form; Absolute value, rational and radical equations; General equation solving; Polynomial, rational and absolute value inequalities; General solving and graphing of algebraic inequalities; Systems of linear equations; Gaussian elimination; Non-linear systems and systems containing inequalities; General system solving; Setting up equations; inequalities and systems; Working with word problems; Applications.
  • Fundamental trigonometric background: The number p; Radians and degrees; Trigonometric functions and their graphs; Generalizations and inverse trigonometric functions; The algebra of trigonometric identities and equations; Right triangle trigonometry; The law of sines and the law of cosines; Applications.
  • Exponential and logarithmic functions: the number e; Exponential functions and their graphs; The inverse of an exponential function; Logarithmic functions and their graphs; Properties of the logarithms; Exponential and logarithmic equations and inequalities; Exponential growth and decay.
  • Analytic geometry and introductory calculus: rectangular and polar co-ordinates; Basic formulas, equations and graphing; Lines, parabolas, circles, ellipses and hyperbolas; The tangent line problem. Limits and derivatives; Computing limits and the algebra of limits; Continuity; Computing derivatives and the algebra of derivatives; Derivatives of trigonometric, exponential and logarithmic functions; The chain rule and implicit differentiation; Antiderivatives; Basic applications of derivatives and antiderivatives.
  • Additional topics (if time permits): Sequences and series; Complex numbers and vectors; Mathematical induction; Matrices and determinants.
What are the advantages of PUMP?

PUMP has regularly scheduled tests and quizzes that reflect university standards. Students will have the opportunity to measure their own progress throughout the course.

PUMP provides the necessary mechanical foundations upon which the greater generality and abstraction of university mathematics is based.

PUMP is a non-credit course; it eliminates the stress associated with competing for grades and allows each student to fully concentrate on his/her own critical shortcomings.

PUMP participants will be exposed to an inside view of what to expect in their future university math courses, how to cope with the demands of courses, and what their prospects are.

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Current/Upcoming Sessions

For the Summer 2017, PUMP will be offered at two different paces.  The regular paced version will run for 12 weeks with four hours of lecture per week.  The accelerated paced version will run for 7 weeks with 6 hours of lecture per week.

PUMP at a regular pace is ideal for:

  • High school students who will be starting a university level education in an upcoming semester and who need grounding in pre-calculus topics.
  • University level students engaged in studies outside the field of mathematics who desire to becom functionally literate in mathematics.
  • Students intending to register for calculus courses that are analogous to MAT135H1 or MAT133Y1.

PUMP at an accelerated pace is ideal for:

  • High school students who want a quick review to pre-calculus followed by an exploration of topics that will prepare them for a more challenging course analogous to MAT137Y1.
  • Any student who intends to register for MAT137Y1.


Sessions Course Start Date Course End Date Course ScheduleRegistration OpensRegistration
Summer - Regular Pace 2017 Tuesday May 9, 2017 Thursday August 3, 2017
Tuesdays and Thursdays
6:00 - 8:00 pm
March 1, 2017
April 20, 2017
Summer - Accelaterated Pace 2017 Tuesday, July 4, 2017 Thursday August 17, 2017 Tuesdays and Thursdays
6:00 - 8:00 pm
May 9, 2017
June 19, 2017
Winter 2017 Tuesday, January 10, 2017 Thursday March 30, 2017 Tuesdays and Thursdays
6:00 - 8:00 pm
October 6, 2016 extended to January 6, 2017

The location of lectures will be emailed to you upon registration.  In addition to lecture hours, there will be four hours of tutorial per week as well as math aid centre hours.  The tutorial and math aid centre schedule will be announced in the lecture.

Textbooks/Teaching Aids

Fall 2016 Textbook:

Title: Precalculus: Mathematics for Calculus 7th edition (Webassign Version); Author: James Stewart, Lothar Redlinm, Saleem Watson; Publisher; Nelson  ISBN 9781305618152. 

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Financial Information

What is the cost?

The fee is $600.00 and is payable by Visa or Mastercard only.


Fall Partial Refund Deadline Date -  Monday, September 19, 2016 by 5:00pm
Winter Partial Refund Deadline Date
-  Monday, January 16, 2017 by 5:00pm
Summer Partial Refund Deadline Date - 
Tuesday, May 23, 2017 by 4:30pm

If you withdraw from the PUMP sessions on/or before the partial refund deadline, $500.00 will be refunded.  You must inform the office of your plans to withdraw as soon as you decide. Non-attendance is not accepted as proof of withdrawal. Please budget a minimum of two weeks for receipt of refund cheque.

No refunds of any kind will be made after the deadline dates.


Bursary assistance is available for current University of Toronto students based on financial need. 

Criteria to apply for bursaries:

-Bursary applicants must be returning or newly-admitted students to U of T (non-U of T students are NOT eligible).

-Returning students must be eligible to register (must not be suspended).

-Newly-admitted students must have accepted an offer of admission and must have registered in the Fall/Winter session (enrolled in courses and paid/deferred fees for the Fall/Winter).

-The student must demonstrate financial need.

-The student must present valid reasons for taking the course.

-The student must not have fees owing to U of T.

To apply for bursary assistance, please pick up a form at the main office BA 6290 - Bahen Centre, 40 St. George Street, Room 6290.  The application deadline is June 3, 2016.  Late applications will not be accepted.  Please note that assistance is not guarantee.



A new online regsitration system is available.  To register for PUMP, please click here.

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Are you coming from out-of-town?  Do you need accommodations?

If you require accommodation for the duration of PUMP, please contact the University of Toronto Housing Service at:

Koffler Student Services Centre
214 College St., Room 203
Toronto, ON M5T 2Z9
(416) 978-8045
(416) 978-1616 (fax)

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Contact Information

Academic Content and General Program Inquires

Donna Birch
Student Advisor
Department of Mathematics
40 St. George Street, room BA 6290
(416) 978-5082

*We strongly encourage you to contact us by e-mail
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Last Updated: December 20, 2016