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# Problem Garden

Mathematics is not a spectator sport. In this portal, we have gathered (and are adding) problems, discussions and challenges that you may try your hands on.

## Test of Mathematics Solution Objective 401 – Trigonometric Series

Summing a sequence of trigonometric ratios can be tricky. This problem from I.S.I. Entrance is an example.

## Understanding Simson Lines

Simson lines arise naturally. Imagine a triangle as a reference frame. Let a point float on the plane of the triangle. How far is the point from the sides of the triangle?

## What if a Simson Line moves!

A beautiful curved triangle appears when we run along the circumference! A magical journey into the geometry of Steiner’s Deltoid.

## 2016 ISI Objective Solution Problem 1

Problem The polynomial $$x^7+x^2+1$$ is divisible by (A) $$x^5-x^4+x^2-x+1$$ (B) $$x^5-x^4+x^2+1$$ (C) $$x^5+x^4+x^2+x+1$$ (D) $$x^5-x^4+x^2+x+1$$ . Also Visit: I.S.I. & C.M.I Entrance Program Understanding the Problem: The problem is easy...

## Test of Mathematics Solution Objective 398 – Complex Number and Binomial Theorem

Try a beautiful problem from complex numbers and geometry. It is from I.S.I. Entrance. We have created sequential hints to make this mathematical journey enjoyable!

## ISI – CMI entrance Book List

ISI – CMI entrance book list is useful for B.Stat and B.Math Entrance of Indian Statistical Institute, B.Sc. Math Entrance of Chennai Mathematical Institute

## Test of Mathematics Solution Objective 394 Power of Complex Number

Complex numbers and geometry are very closely related. We consider a problem from I.S.I. Entrance that uses this geometric character complex numbers.

## AM GM Inequality, Euler Number – Stories in Real Analysis

A.M.- G.M. Inequality can be used to prove the existence of Euler Number. A fascinating journey from classical inequalities to invention of one of the most important numbers in mathematics!

## Homework, Duality, Euler Number and Cheenta this week!

Hello mathematician! I do not like homework. They are boring ‘to do’ and infinitely more boring to ‘create and grade’. I would rather read Hilbert’s ‘Geometry and Imagination’ or Abanindranath’s ‘Khirer Putul’ at that time. Academy Award winner Michael...

Problems and discussions from various math olympiads including RMO, INMO (India), USAMO, AMC (United States), BMC and more.

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#### Informative Articles

Selected articles on books, learning methods, and scholarship opportunities.

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#### ISI and CMI Entrance Solutions and Problems

Problems and Solutions from Test of Mathematics at 10+2 Level, previous year ISI and CMI Entrances.

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#### College Mathematics

Problems and discussions from TIFR, M.Math, Subject GRE, IIT JAM and more.

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