MAT102 Tutoring: Intro to Mathematical Proofs

For information, call: +1 (416) 876-1248 (Canada)

See the Testimonials page for reviews from past students and parents

Scroll down or click here for the application form.

Topics and Examples of Sub-topics

  • Quadratics: formula, discriminant, Vieta
  • Inequalities: trivial, AGM, triangle
  • Sets: double set inclusion
  • Functions: domain, codomain, range
  • Fields: axioms, method of exhaustion
  • Logic: symbols, truth tables
  • Proofs: contradiction, contrapositive
  • Induction: regular, strong, sums, products
  • More functions: bijection, injection, surjection
  • Cardinality: equal size, Schröder-Bernstein
  • Divisibility: GCD, FTA, Bézout, Euclid’s lemma
  • Relations: equivalence, classes, modularity

Included in the Commitment

  • A total of approximately 40 lessons, with 3 lessons per week, scheduled by availability
  • Time will be spent on the subject matter, homework, preparation for assessments, and training based on practice materials
  • Each lesson will consist of 1 hour of individual live instruction
  • The instructor will use Zoom Pro and an interactive pen tablet to teach online
  • Homework will be assigned weekly and personalized feedback will be provided
  • Help is available by email contact

Instructor: Samer Seraj

Samer Seraj

About the Instructor

  • A decade of educational experience in mathematical proofs and contests
  • University of Toronto graduate as a mathematics specialist
  • Crux Mathematicorum journal guest editor
  • University of Waterloo CEMC Problem of the Month committee member
  • University of Toronto Math+ instructor
  • USRA and UTEA research grant winner
  • Canadian Mathematical Olympiad qualifier


Students should be in the final year of high school or undertaking university studies. They should currently be taking or have already taken the following Ontario courses or their equivalent:

  • Grade 11 Functions
  • Grade 12 Advanced Functions
  • Grade 12 Calculus and Vectors
Familiarity with math contest-style counting, number theory, and geometry will be an asset, though these are not strictly required.


Lessons will be delivered in live online sessions via Zoom. Students will need to provide the following for themselves:

  • A stable internet connection
  • A computer or tablet
  • Headphones or speakers
  • A microphone (many computers have one in-built)
  • A free Zoom account on your device
  • Phone camera or scanner for submitting handwritten homework


Please apply using the form below and we will respond by email to begin a conversation about the student’s needs.

  • The all-inclusive cost of this university-level training is $65 CAD per lesson, which includes the preparation time before class, the 1-hour lesson, and the time required for providing feedback on homework after class.
  • Payments are done via INTERAC e-transfer at the beginning of each month for that month. After each payment, a refund will not be processed. The student may choose to cease to partake in the program at the end of any month.
  • For students who are new to Existsforall Academy, a free 1-hour long 1-on-1 coaching call is available upon request so that you may experience our teaching. This is a $65 CAD value offered for free!

Note: we do not write tests for students and we are not affiliated with the University of Toronto Mississauga.

Thank you for your interest!