PUMP 2010
Preparing for University Math Program
2010 Spring, January 12 - March 30, 2010
An Initiative of the Department of Mathematics
Faculty of Arts and Science, University of Torontohttp://www.math.utoronto.ca/PUMP

What is PUMP?
PUMP is a non-credit course specially designed to prepare students for entry-level mathematics courses, like calculus and linear algebra, at the University of Toronto.

Who is PUMP for?
PUMP is for those who want to close any existing gap between high school math and university level math courses. It covers algebra, geometry, trigonometry and calculus at the high school level. PUMP would also be beneficial to those who wish to review high school math before attempting university-level math or other science 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 an 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?
PUMP runs from January 12 - March 30, 2010 inclusive. It meets Tuesday 6:00 p.m. - 9:00 p.m. for lectures, and Thursday 6:00 p.m. - 8:00 p.m. tutorials and problem-solving sessions.  PUMP emphasizes class efficiency.  Homework and assignments will be kept to an absolute minimum.
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.

Lectures location:
TBA

Tutorials location:
TBA

Textbooks/Teaching Aids
The text will be Pre Calculus by Stewart - EWA Edition.

How do you register for PUMP? What is the cost?
You can get a copy of the Registration form by clicking here. Complete the Registration form and submit it with your payment to the address on the form. The fee is $600.00. 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.

Refunds
If you withdraw from the program by January 21, 2010,  $500.00 will be refunded. You must inform 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 January 21, 2010. Please budget a minimum of two weeks for receipt of refund cheque.

Questions about payment?

Ms. Kelly Jay , Associate Registrar                    
Faculty of Arts and Science
Sidney Smith Hall, Room 1006
100 St. George Street
416-978-3393
kelly@artsci.utoronto.ca

Need more information about the program?
Contact:

Click here to get to the PUMP Registration Form

We encourage you to contact us by e-mail