## MAT102 Tutoring: Intro to Mathematical Proofs

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

#### Topics and Examples of Sub-topics

• Inequalities: trivial, AGM, triangle
• Sets: double set inclusion
• Functions: domain, codomain, range
• Fields: axioms, method of exhaustion
• Logic: symbols, truth tables
• 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 2-3 lessons per week, depending on availability
• Time will be spent on the subject matter, homework, preparation for tests, 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

• A decade of educational experience in mathematical proofs and contests
• University of Toronto graduate in math
• 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

#### Prerequisites

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

#### Technology

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
• The all-inclusive cost of this university-level training is $60 CAD per lesson, meaning it 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-on-1 coaching call is available upon request so that you may experience our teaching. This is a$60 CAD value offered for free!