What is the NO-SHORTCUT approach for learning great Mathematics?

# How to Pursue Mathematics after High School?

For Students who are passionate for Mathematics and want to pursue it for higher studies in India and abroad.

Dear parent,

One of the key contributions of modern mathematics is its tryst with infinity. As parents and teachers we can initiate thought provoking communication with our children using infinity.

Consider the following set:

N = {1, 2, 3, … }

Notice that N contains infinitely many elements.

Take a subset of N that consists of multiples of 2. Lets call it $N_1$.

$N_1= \{2, 4, 6, …\}$

Notice again that N1 contains infinitey many elements. Next consider a subset of N1 that contains only the multiples of 3. Lets call that N2.

$N_2= \{6, 12, 18, 24, … \}$

Student may say: Isn’t 9 a multiple of 3? Should it not be in $N_2$?

No. Because we are taking those multiples of 3 which are in $N_1$. Hence they must be simultaneously multiples of 2 and 3.

Proceeding like this we can create infinitely many sets: $N, N_1, N_2, N_3, …$
These sets are nested! That is $N$ contains $N_1$ contains $N_2$ contains $N_3$ etc. Moreover each of them contains infinitely many terms.

QUESTION: What is in the intersection of all of these sets? That is : what is common in all of them?

This question provokes the child to really think about infinity. For the finite case it can also make a nice combinatorics problem using method of inclusion and exclusion: how many numbers from 1 to 1000 are multiples of 2 or 3 or both.

In fact this last sentence makes the student worry about the word ‘or’. It is is nice place to introduce exclusive or.

Dr. Ashani Dasgupta

Founder, Cheenta

(Ph.D. in Mathematics from University of Wisconsin, Milwaukee, USA. Research Interest: Geometric Group Theory)

## What to do to shape your Career in Mathematics after 12th?

From the video below, let's learn from Dr. Ashani Dasgupta (a Ph.D. in Mathematics from the University of Milwaukee-Wisconsin and Founder-Faculty of Cheenta) how you can shape your career in Mathematics and pursue it after 12th in India and Abroad. These are some of the key questions that we are discussing here:

• What are some of the best colleges for Mathematics that you can aim to apply for after high school?
• How can you strategically opt for less known colleges and prepare yourself for the best universities in India or Abroad for your Masters or Ph.D. Programs?
• What are the best universities for MS, MMath, and Ph.D. Programs in India?
• What topics in Mathematics are really needed to crack some great Masters or Ph.D. level entrances?
• How can you pursue a Ph.D. in Mathematics outside India?
• What are the 5 ways Cheenta can help you to pursue Higher Mathematics in India and abroad?

## Want to Explore Advanced Mathematics at Cheenta?

Cheenta has taken an initiative of helping College and High School Passout Students with its "Open Seminars" and "Open for all Math Camps". These events are extremely useful for students who are really passionate for Mathematic and want to pursue their career in it.

To Explore and Experience Advanced Mathematics at Cheenta

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# Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy