University Calculus 1 Preparation Course
Contact: Tigran Petrosian
As a mathematician, I’ve been blessed with a gift for teaching very advanced mathematics to younger students and children, and turn it into a world that is very fun, exciting and meaningful, revealing the beauty of mathematics.
PURPOSE OF COURSE
A major problem with high school Calculus is that it fails to provide a deep basic foundational understanding. For example, not providing simple proofs of Theorems and Laws and heavily relying in robotically following steps or an algorithm without understanding what is happening in the steps. Calculus, in it of itself is a higher level Mathematics course for the general high school level and more complex than Grade 12 Advanced Functions, Algebra/Geometry and Probability/Statistics.
Students often earn higher grades in Calculus than the other grade 12 math courses not because they have a better understanding of Calculus but ironically because they follow the robotic steps better than the other math courses. Memorizing procedures mechanically, at least 99% of students having completed Calculus can not give the rigorous definition of what a “limit”, “derivative” and why the “product rule” and “the quotient rule” of derivatives work. Students earning a grade of 90% or higher in high school Calculus never truly gras why and how the layers work underneath and at least 95% of these students struggle at university Calculus 1 because they never have internalized the “why” behind each step, specially the basics, foundation, some theory and simple proofs. In response, I’m launching a novel, experimental approach—one I’ve been envisioning for over a decade—and now I’m bringing it to life with subtle Christian Theology connected to Calculus.
HOW THIS COURSE WILL BE TAUGHT AND WHAT IS COVERED
In this course, I will teach a full University Calculus I (Differentials) specifically to Grade 12 students and students who have completed Grade 11 Mathematics, using the exact same textbook I have used and learned Calculus (Differentials and Integrals) in The University of Waterloo —“Calculus: Early Transcendentals, 5th Edition” by James Stewart.
The syllabus follows a university structure, divided into four chapters:
There will be 4 chapters and 50 lectures. The course will be taught to 4 students.
- Functions and Models (Prerequisites), 8 Lectures
- Limits (14 Lectures)
- Derivatives (14 Lectures)
- Applications of Derivatives (14 Lectures)
Each Lecture is 90min with 30 min break.
45 minutes – 30 minutes break – 45 minutes.
CHRISTIAN THEOLOGY INTEGRATED IN THIS COURSE
I also integrate Christian Theology, specifically Christian Apologetics (Faith and Science), into the course, showing how laws of nature, mathematics especially—can relate to Christian thought in most unexpected, fascinating and transcendental ways. You do not have to be a Christian to benefit, but if you’re curious about how Mathematics connects with Christianity, then this course will be a wonderful exploration for you.
SERVICE AREAS
Scarborough and Surrounding Areas
I am Tigran Petrosian, a Follower of Our Lord and Saviour, Jesus Christ, Mathematician, Kung Fu Practitioner with a Bachelor's degree in Mathematics (focused on Pure Mathematics) from the University of Waterloo.
Since 2002, I have tutored students one-on-one—primarily in Grade 11
Grade 12:
Advanced Functions,
Calculus and Vectors
Data Management
Also some University Math Courses but very proficient.
First and Second-Year University Math Courses:
Calculus 1 (Differentials) MATH 137*
Calculus 2 (Integrals) MATH 138*
Discrete Mathematics MATH 135*
Linear Algebra 1 MATH 136*
Linear Algebra 2 MATH 235*
Probability STAT 230*
Third Year Pure Math Courses:
Introductory Group Theory (Abstract Algebra) PMATH 336*
Introductory Ring Theory (Abstract Algebra) PMATH 330*
*The University of Waterloo Math Course Codes or Equivalent University Courses in Canada, University of Toronto, McMaster University, York University,...
