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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 winter PUMP session of 2016 will run on Wednesdays from 6:00 pm - 9:00 pm once a week.  The summer PUMP session of 2016 will run on Mondays and Wednesdays, 11:00am-2:00pm.  Students are encouraged to attend one of the listed tutorial.

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 Registration OpensRegistration
Winter 2016 Wednesdays January 13, 2016 April 6, 2016 October 26, 2015 extended to January 11, 2016
Summer 2016 Mondays & Wednesdays June 27, 2016
August 17, 2016
April 4, 2016
June 20, 2016

Class Information

Class Times

Sessions Lectures Tutorials Math Aid Centre Quizzes
Summer 2016 Mondays and Wednesdays
Locations sent by email to registered students.
Group 1: TBA
Group 2: TBA
TBA (Included in Lecture Sessions)
Winter 2016
6:00 - 9:00 pm
Room:  MC252 (see map below)*
Room: LM157
(Included in Lecture Sessions)


Summer 2016 Session Class Locations
*Click here for a searchable map of the campus*



Winter 2016 Session Class Locations
*Click here for a searchable map of the campus*


Lectures are located in MC252 - Mechanical Engineering Building, 5 King's College Road, Room 252.

As of March 14th tutorials are located in LM157 - Lash Miller Building, 80 St. George Street, Room 157.

Textbooks/Teaching Aids

Summer 2016 Textbook:

Title: Precalculus: Mathematics for Calculus 7th edition; Author: James Stewart, Lothar Redlinm, Saleem Watson; Publisher: Brooks Cole; ISBN: ISBN-13: 978-1305071759

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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 certified cheque or money order only. Certified cheques and money orders should be made payable to "PUMP-University of Toronto". The fee is not tax-deductible.


Summer Partial Refund Deadline Date -  Tuesday July 5, 2016 by 4:30pm
Winter Partial Refund Deadline Date
-  Friday January 22, 2016 by 5:00pm

If you withdraw from the Summer 2016 session of PUMP by Tuesday July 5, 2016 at 4:30pm, $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 date.


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 guaranteed and 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

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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Registration Process

Please fill out the form found at the bottom of this page.  The registration fee is by certified cheque or money order only - payable to "U of T - Pump". 

The form and the payment can be submitted to:

Ashley Armogan
Department of Mathematics
University of Toronto
40 St. George Street, Room 6290
Toronto, ON M5S 2E4

Registration Form


Last Updated: April 2016