## Mission and Vision

My goal is to help students to become better thinkers by teaching them about the most impenetrable form of human knowledge: mathematics. I envision providing a transformative learning experience for students who want help with excelling within school curricula by teaching them in a focused one-on-one environment. Over the past several years, this vision has been implemented, with approximately one hundred Canadian students benefiting from working closely with me. By gaining a true understanding of mathematics, they were able to raise their math grades at school.

## History and Biography

Existsforall Academy is an online school for students of mathematics. The origins of the academy go back to Samer’s high school years when, in the midst of training for the Canadian Mathematical Olympiad, he started an after-school club for sharing his mathematical knowledge with fellow students. He earned an undergraduate degree in higher mathematics from the University of Toronto, during which time he held two research grants, wrote several papers, attended conferences, and was elected as the President of the undergraduate Mathematics Union. Upon graduation, he moved to San Diego, California to contribute to a leading company in the US education sector. After several years of gaining experience in the industry, Samer returned to his hometown in the Greater Toronto Area, where he founded this academy. His recent contributions to the Canadian mathematical community have included being a guest editor of the Canadian Mathematical Society’s problem-solving journal, Crux Mathematicorum, sitting on the University of Waterloo CEMC’s committee for the Problem of the Month, teaching courses at the University of Toronto’s math outreach program, Math+, and serving as a trainer of Team Canada for the International Mathematical Olympiad.

## Educational Philosophy

At the core of my pedagogical philosophy lies the following question:

*What is the interplay of intuition and rigour in mathematical activity?*

Mathematical intuition is creative freedom and mathematical rigour is structured reinforcement. Both are essential to the practice of mathematics, and indeed all analytical fields. I make an effort to emphasize both aspects of mathematics. Here are more specific details about my approach towards teaching and learning:

**Teaching Philosophy**

- When reasoning intuitively, I use diagrams, try out examples, and do concrete computations.
- When reasoning rigorously, I always dig deep by asking myself and asking students “What does this mean?” and “Why is this true?”
- I try to assign work to students that is meaningful so that they will be more inspired. When assigning computations, I explain the origins of the associated formulas or processes.
- When needed, I prefer to communicate the main idea instead of pedantically pointing out every minor detail that the student could independently verify. Envisioning the forest is more important than counting the leaves of every tree.
- I am as truthful as possible with my students by clearly stating any assumptions, deficiencies or omissions, in order to give a precise picture of my level of exposition.

**Learning Philosophy**

- Don’t avoid pattern recognition but focus on recognizing heuristics that are widely applicable instead of superficial characteristics such as formulas that apply to only niche scenarios. Examples of famous heuristics are to work on a simpler question or to work backwards.
- While some schools are pro-memorization or anti-memorization, I recommend that students gain a general sense of the relevant theorems, and write up personal notes that can be consulted for the details. Some degree of memorization is needed for exams, but constant usage of theorems often results in naturally remembering how to apply them.
- Learning is never complete and no version of a theorem or proof is the final word on it. Always be ready to be surprised by new light being shed on an old idea.