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Preparing for University Math Program (PUMP) offers two non-credit courses run by the Department of Mathematics on the St. George campus of the University of Toronto.

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

PUMP is a non-credit course. Because it does not count towards a degree, the stress associated with course marks is reduced and students can better concentrate on their learning.

PUMP participants are given 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. In short, successful PUMP students will have better insight into which first-year math course(s) to choose and will be generally better prepared for university.

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

PUMP is now available at two levels: PUMP Level 1 and PUMP Level 2.

PUMP Level 1 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 become functionally literate in mathematics.
- People who wish to learn (or re-learn) high school pre-Calculus
- Any student who intends to register for MAT135H1 or MAT133Y1 or MAT186H1 (or their analogues).

PUMP Level 2 is ideal for:

- People who want a quick review of high school pre-Calculus followed by an introduction to logic, problem solving and methods of proof.
- Any student who intends to register for MAT137Y1 and MAT157Y1, MAT223H1, or MAT194H1 (or their analogues).

Important Note about U of T Programs that Require Calculus for Admission:

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 Level I and Level 2 cannot be used as a replacement for this admission requirement.

A certain background knowledge is strongly recommended for PUMP Level 1. In general terms, a student must have a working knowledge of basic high school algebra, linear and quadratic functions, and elementary analytic geometry. Students who do not have this background may still enroll and can do well if they work hard.

This course focuses on the mathematical background needed for entry-level university science and math courses, expanding and developing relevant skills and techniques of reasoning. Topics to be covered include:

**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.**Basic trigonometry:**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 co-ordinates; Basic formulas, equations and graphing; Lines, parabolas, and circles; The tangent line problem. Limits.**Additional topics (if time permits):**Sequences and series; Complex numbers and vectors; Mathematical induction; Matrices and determinants.

PUMP Level 2 focuses on reading and understanding definitions and theorems, and writing basic mathematical proofs. Within each topic, students will see definitions, theorems, ways to use each, and basic proofs. There will be plenty of opportunities to write proofs in the style of each topic, explore the topic at a higher level of rigor than before, and receive feedback.

Topics include:

**Symbolic Logic and Understanding Theorems:**Basics of first-order logic, well-formed formulas, and quantifiers; Translating between mathematical theorems as logical statements; Implications, the contrapositive, converse, and inverse; Basic proof techniques including direct proof, proof by contradiction, and proving the contrapositive.**Polynomials and Other Functions:**Factoring polynomials of degree two, three, and higher; Factor Theorem; Simplifying rational expressions; Domain/Range; Injective/Surjective properties; Graphing and basic transformations.**Planar and 3-D Geometry:**Equations of lines and planes; Normal and tangent lines; Triangles, circles, rectangles; Pythagorean Theorem, distance formula between points, a point and a line, planes; Adding/Subtracting vectors algebraically and geometrically.**Trigonometry:**Definition of radians; Converting between degrees and radians - how to do it and motivation; Trigonometric rations; inverse trigonometric rations and right-angle triangle geometry; The unit circle; Sine and Cosine laws; Techniques for proving trigonometric identities; Proofs of the double/half-angle formulas and adding/subtracting formulas; Graphs of trigonometric functions and their transformations; Applications.**Exponential and Logarithmic Functions:**Definitions of "e", "In", and "log"; Exponential growth, decay, and modeling real-world problems; Inverse functions and solving exponential/logarithmic equations; Properties of logarithmic and exponential functions and their graphs.

We will be offering both levels of PUMP in the summer term at the faster (condensed) speed from July-August. Math Learning Centre hours may also be available for students.

Due to COVID-19, these courses will be delivered online until it is safe to meet in person again. Both lectures and tutorials will be delivered synchronously, so students should expect to attend class virtually at the scheduled times.

Course Level Offered |
Sessions |
Course Start Date |
Course End Date |
Course Schedule |
Registration Opens |
RegistrationDeadline |

PUMP Level 1 - Faster Speed | Summer 2020 | Tuesday, July 14 | Thurs, August 20 | Lectures: Tu & Th 11am-1pm Tutorials: Tu & Th: 3-5pm |
June 15, 2020 | Tuesday, July 21, 2020 |

PUMP Level 2 - Faster Speed | Summer 2020 | Monday, July 13 | Monday, August 24 | Lectures: Mo & We 11am-1pm Tutorials: Mo & We 3-5pm |
June 15, 2020 | Tuesday, July 21, 2020 |

PUMP Level 1 - Regular Speed | Winter 2021 | TBD | TBD | Lectures: Mo & We 6-8pm Tutorials: W 5-6pm |
TBD | TBD |

Please note for the Winter session, a minimum enrollment of 25 students will be needed in order for the Department to run the course.

Currently, PUMP is not offered in the fall.

**PUMP 1 recommended textbook (from summer 2020):**

Functions of Modelling Change: A Preparation for Calculus, 6th Edition, by Eric Connally, Deborah Hughes-Hallett, Andrew M. Gleason, ISBN: 978-1-119-49837-7

**PUMP 2 optional textbooks (from summer 2020): **

How to Read and Do Proofs: An Introduction to Mathematical Thought Processes, 6th Edition, by Daniel Solow, ISBN: 978-1-118-16402-0

Proofs and Fundamentals: A First Course in Abstract Math, 2nd Edition, by Ethan D. Bloch, 978-1-4419-7127-2

*Note: textbooks may change between terms. If you are planning on taking PUMP, please check with the course instructor to see which textbook (if any) will be used for the course.*

What is the cost?

The fee to register is $600.00 per course and is payable by Visa or Mastercard only.

Refunds

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

Session |
Partial Refund Deadline Date |

Summer 2020 PUMP Level 1 - Faster Speed | Monday, July 27, 2020 |

Summer 2020 PUMP Level 2 - Faster Speed | Monday, July 27, 2020 |

Winter 2021 PUMP Level 1 - Regular Speed | TBA |

Bursaries

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.

The deadline to submit your bursary application is Friday, July 24. **Late applications will not be accepted. Please note that assistance is not guaranteed. **

Successful candidates who receive a bursary will still be required to pay the full registration fee upfront. Then once the course has been completed with a passing grade, the student will then be reimbursed.

Bursaries are not available in the winter sessions due to the Faculty of Arts and Science funding model.

Registration for PUMP is currently closed.

For inquiries about our PUMP courses please email uginfo@math.utoronto.ca with "PUMP inquiry" in the subject line.

Last Updated: June 24, 2020