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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.

Winter PUMP Sessions

The Winter PUMP sessions are designed for adult learners therefore registration will not be accepted for students currently enrolled in high school. This is structured to facilitate the pace of the group and is directly impacted on by the group dynamics.

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 extra hard, especially in the first three weeks .

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. Properties.
  • 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 ivnerse of an exponential function. Logarithmic functions and their graphs. Properties of the logarithms. Exponential and logarithmic equations and inequalities. Exponential growth and decay. Applications.
  • 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 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.

How is PUMP run?

The summer PUMP session of 2014 will run in the evenings of Mondays and Wednesdays from 4:00pm-7:00pm.  The winter PUMP session of 2014 will run on Wednesdays from 6:00 pm - 9:00 pm once a week. Students are encouraged to attend one of the listed tutorial.  Additional problem solving and quizzes will take place in these sessions.

PUMP has regularly scheduled tests and quizzes that reflect university standards. Students will have the opportunity to measure their own progress throughout the course. At the end of the program, each student will receive a written assessment of his/her performance.

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Current/Upcoming Sessions

Sessions Days Course Start Date Course End Date Application
Deadline Date
Summer 2014 Mondays & Wednesdays July 7, 2014 August 20, 2014 extended to June 13, 2014
Winter 2014 Wednesdays January 8, 2014
April 2, 2014
January 15, 2014

Class Information

Class Times

Sessions Lectures Tutorials Math Aid Centre Quizzes
Winter 2014 Wednesdays
6:00 - 9:00 pm
Room:  MC 254 (see map below)*
Tuesdays or Thursdays:  6:00pm-9:00pm
Room:  MC 252 (see map below)*
N/A (Included in Tutorial Sessions)
Summer 2014 Mondays & Wednesdays
(4:00 - 7:00 pm)

Group 1: Mondays 12:00-3:00pm;
Group 2: Tuesdays 1:00-4:00pm;
Group 3:  Wednesdays 1:00pm-4:00pm
Thursdays 7:30-8:30pm;
All students in the course can attend this session for extra help
(Included in Tutorial Sessions)

Winter 2014 Session Class Locations
*Click here for a searchable map of the campus*



Summer 2014 Session Class Locations
*Click here for a searchable map of the campus*



Textbooks/Teaching Aids

Winter 2014 Textbook:  Precalculus, Enhanced WebAssign Edition (with Mathematics and Science Printed Access Card and Start Smart), 6th edtion. The ISBN# for the bundle is 9781133594765.  Please note as well that we have a special price in place for this bundle for U of T so it is important that this ISBN is the one that is ordered.

Summer 2014 Textbook:  TBA

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Financial Information

What is the cost?

The fee is $600.00

How do you register for PUMP?

You can get a copy of the Registration form at the bottom of this page.

Complete the Registration form and submit it with your payment to the address on the form.  Payment can be made by personal cheque, money order, cash (in person only!), Visa or MasterCard. Cheques and money orders should be made payable to "PUMP-University of Toronto". Visa or MasterCard orders should include the card type, number and expiry date along with the cardholder's signature. The fee is not tax-deductible.


Winter Partial Refund Deadline Date -  January 17, 2014
Summer Partial Refund Deadline Date -  July 18, 2014

If you withdraw from the program by January 17, 2014 (for Winter PUMP) or July 18, 2014 (for Summer PUMP), $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. No refunds of any kind will be made after the deadline date. Please budget a minimum of two weeks for receipt of refund cheque.


Bursary assistance is available for students with financial need. To apply for bursary assistance, please contact Magdalene Cheung. Application deadline:  extended to June 16, 2014.  Please note that bursaries are not offered in the winter session.

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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:

214 College St. 
Toronto, ON M5S 1A1
(416) 978-8045
(416) 978-1616 (fax)

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Contact Information

*We strongly encourage you to contact us by e-mail
Payment and Financials

Ms. Magdalene Cheung
Assistant Registrar
Faculty of Arts and Science
Sidney Smith Hall, Room 1006
100 St. George Street
(416) 978-7466

Academic Content and General Program Inquires

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

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Registration Form

Please note this form must be mailed or faxed to the address indicated on it, email submissions are not accepted at this time

Click here for the registration form

Last Updated: January 15, 2014