Infocus Academy

Philosophy

In my extensive career as a professor, tutor, entrepreneur, and engineer, I have always had a deep passion for teaching, coaching, and guiding students and mentees to their fullest potential. It is without doubt one of the most rewarding work I do. In the same vein, math has been my cornerstone for intellectual pursuit and enjoyment. Teaching math is the happy intersection.

As a tutor, my teaching methodology has imbibed skills from each one of my professions. I begin with a thorough assessment of my student’s grasp of fundamental concepts and identify their strengths and weaknesses. I use various visual aids to help my students build an intuition for new or difficult concepts. Additionally, I work with the students to find a method of study that works for them so they continue to learn effectively once they graduate from my tutelage. My students consistently show a significant improvement in their grades, and more importantly a new positive take on Math as a subject.

Pricing

Note: Due to the Covid crisis, all sessions will be conducted over Zoom calls. Students must have a notebook, pencil, calculator (if applicable), any relevant course materials, and a laptop or desktop with a good internet connection.

Credentials

I am a graduate with a Master’s degree in engineering from Delhi College of Engineering, Delhi, India. I started my career as a Professor in Engineering College at Jalgaon (India) teaching Engineering subjects in 1989. As I moved ahead in my career with additional family responsibilities, I founded Rosh Tutoring centre where I provided in home tutoring in Math and Science to middle school and High school students. Later, I worked as Senior Design Engineer at Engineering Consultancy Company designing Effluent treatment plants and plumbing services for commercial and residential buildings. Eventually, I worked as an Environmental Engineer at the Central Polution Control Board (the EPA equivalent in India).

Tutoring young minds has been a recurring theme in my career. I found myself drawn back to it as there is some satisfaction to be found in witnessing a young mind finally grasp a concept that seemed, at one point in time, to be well beyond their reach. And so, in 2006, I found myself returning to tutoring and helping students improve their appreciation and knowledge of Mathematics. I achieved that by working with Brainfuse, a New York based Company.

In 2007, I began a new venture Enviva Engineering Consultants. In 2010, I added a second venture, Enviva-Lights for every mood. I was the CEO of these two Companies with 7 employees and an annual revenue of $225,000.

In 2019, I relocated and once again, I have started a new venture. I am in the process of setting up and running a Sign and Business Centre- Signarama franchise in Washington. At the same time, I tutor students in Math, ACT and SAT. I am also on the rolls of a reputed Company based in Atlanta as a tutor for Math, SAT, ACT. My teaching philosophy is the key to my students’ successes, and it has been the key to the success of Infocus Academy.

My motto: Doubt kills more dreams than failure ever will.

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Explorations

Math is something you improve on the more you play with numbers. Take squares of numbers ending with 5, for example: \begin{align} 5^2 &= 25 \\ 15^2 &= 225 \\ 25^2 &= 625 \\ 35^2 &= 1225 \end{align} Notice any patterns? They all end in 25 is a good start. What else? If we ignore the 25, we get a sequence: \(0,2,6,12,20, ...\). A good way to play with numbers, especially sufficiently small ones, is to break them down into their prime factors. So, the previous sequence, \(S\) becomes: \begin{align} S &= & 0, && 2, &&2*3, && 2^2 *3,&& 2^2 *5,&\quad&... \\ &= &0*1, && 1*2, &&2*3, && 3*4, && 4*5, &\quad&... \end{align}
Now, we have something! To square any number ending with a 5, we omit the 5, multiply it with one digit greater than what it had before, and append 25. So, for \(25^2\), we omit the 5 and are left with 2. We multiply that with 3 to get 6 and append 25 to get 625. But, can we prove it works for ALLnumbers ending with 5? Lets try. We define a number \(N\) that ends with 5 as: \[N = 10x + 5\] In the above, when \(x=2, N=25; x=3,N=35\) and so on.
So, what do we get when we square it? \begin{equation} \begin{split} N^2 & = (10x+5)^2 \\ & = 100x^2 + 25 + 2*5*10x \\ & = 100x^2 + 100x + 25 \\ & = 100x(x+1) + 25 \end{split} \end{equation} Since we haven't put any constraints on x, this trick actually works for all numbers that end in 5 (although it does get harder to calculate \(x(x+1)\) for larger values of x.
A great way to build curiosity for math is to look at sequences of numbers like these and to look for patterns, build hypotheses, and try to prove the results.

Happy calculating!