# You will need pen and paper

# I.S.I. Entrance Problems

## ISI MStat PSB 2012 Problem 5 | Application of Central Limit Theorem

This is a very beautiful sample problem from ISI MStat PSB 2012 Problem 5 based on central limit theorem . Let’s give it a try !!

## ISI MStat PSB 2007 Problem 7 | Conditional Expectation

This is a very beautiful sample problem from ISI MStat PSB 2007 Problem 7. It’s a very simple problem, which very much rely on conditioning and if you don’t take it seriously, you will make thing complicated. Fun to think, go for it !!

## ISI MStat Entrance Exam books based on Syllabus

Are you preparing for ISI MStat Entrance Exams? Here is the list of useful books for ISI MStat Entrance Exam based on the syllabus.

## ISI MStat PSB 2008 Problem 8 | Bivariate Normal Distribution

This is a very beautiful sample problem from ISI MStat PSB 2008 Problem 8. It’s a very simple problem, based on bivariate normal distribution, which again teaches us that observing the right thing makes a seemingly laborious problem beautiful . Fun to think, go for it !!

## ISI MStat PSB 2004 Problem 6 | Minimum Variance Unbiased Estimators

This is a very beautiful sample problem from ISI MStat PSB 2004 Problem 6. It’s a very simple problem, and its simplicity is its beauty . Fun to think, go for it !!

## ISI MStat PSB 2004 Problem 1 | Games and Probability

This is a very beautiful sample problem from ISI MStat PSB 2004 Problem 1. Games are best ways to understand the the role of chances in life, solving these kind of problems always indulges me to think and think more on the uncertainties associated with the system. Think it over !!

## ISI MStat PSB 2013 Problem 5 | Simple Random Sampling

This is a sample problem from ISI MStat PSB 2013 Problem 5 based on the simple random sampling model, finding the unbiased estimates of the population size.

## ISI MStat PSB 2013 Problem 4 | Linear Regression

This is a sample problem from ISI MStat PSB 2013 Problem 4. It is based on the simple linear regression model, finding the estimates, and MSEs.

## ISI MStat PSB 2011 Problem 1 | Linear Algebra

This is ISI MStat PSB 2011 Problem 1, based on patterns in matrices and determinants, and using a special kind of determinant decomposition. Try this out!

# Math Olympiad

## Functional Equation Problem from SMO, 2018 – Question 35

Try this problem from Singapore Mathematics Olympiad, SMO, 2018 based on Functional Equation. You may use sequential hints if required.

## Sequence and greatest integer | AIME I, 2000 | Question 11

Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2000 based on Sequence and the greatest integer.

## Arithmetic sequence | AMC 10A, 2015 | Problem 7

Try this beautiful problem from Algebra: Arithmetic sequence from AMC 10A, 2015, Problem. You may use sequential hints to solve the problem.

## Series and sum | AIME I, 1999 | Question 11

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Series and sum.

## Inscribed circle and perimeter | AIME I, 1999 | Question 12

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2011 based on Rectangles and sides.

## Problem based on Cylinder | AMC 10A, 2015 | Question 9

Try this beautiful problem from Mensuration: Problem based on Cylinder from AMC 10A, 2015. You may use sequential hints to solve the problem.

## Median of numbers | AMC-10A, 2020 | Problem 11

Try this beautiful problem from Geometry based on Median of numbers from AMC 10A, 2020. You may use sequential hints to solve the problem.

## LCM and Integers | AIME I, 1998 | Question 1

Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 1998, Problem 1, based on LCM and Integers.

## Cubic Equation | AMC-10A, 2010 | Problem 21

Try this beautiful problem from Algebra, based on the Cubic Equation problem from AMC-10A, 2010. You may use sequential hints to solve the problem.

# College mathematics

## Problem on Inequality | ISI – MSQMS – B, 2018 | Problem 2a

Try this problem from ISI MSQMS 2018 which involves the concept of Inequality. You can use the sequential hints provided to solve the problem.

## Data, Determinant and Simplex

This problem is a beautiful problem connecting linear algebra, geometry and data. Go ahead and dwelve into the glorious connection.

## Problem on Integral Inequality | ISI – MSQMS – B, 2015

Try this problem from ISI MSQMS 2015 which involves the concept of Integral Inequality and real analysis. You can use the sequential hints provided to solve the problem.

## Inequality Problem From ISI – MSQMS – B, 2017 | Problem 3a

Try this problem from ISI MSQMS 2017 which involves the concept of Inequality. You can use the sequential hints provided to solve the problem.

## Problem on Natural Numbers | TIFR B 2010 | Problem 4

Try this problem of TIFR GS-2010 using your concepts of number theory and congruence based on natural numbers. You may use the sequential hints provided.

## Definite Integral Problem | ISI 2018 | MSQMS- A | Problem 22

Try this problem from ISI-MSQMS 2018 which involves the concept of Real numbers, sequence and series and Definite integral. You can use the sequential hints

## Inequality Problem | ISI – MSQMS 2018 | Part B | Problem 4

Try this problem from ISI MSQMS 2018 which involves the concept of Inequality and Combinatorics. You can use the sequential hints provided.

## Problem on Inequality | ISI – MSQMS – B, 2018 | Problem 4b

Try this problem from ISI MSQMS 2018 which involves the concept of Inequality. You can use the sequential hints provided to solve the problem.

## Positive Integers Problem | TIFR B 201O | Problem 12

Try this problem of TIFR GS-2010 using your concepts of number theory based on Positive Integers. You may use the sequential hints provided.

# Research Tracks

## Arithmetical Dynamics: Part 6

Arithmetical dynamics is the combination of dynamical systems and number theory in mathematics. Again, we are here with the Part 6 of the Arithmetical Dynamics Series. Let's get started.... Consider fix point of \( R(z) = z^2 - z \) . Which is the solution of $$ R(z)...

## Arithmetical Dynamics: Part 5

Arithmetical dynamics is the combination of dynamical systems and number theory in mathematics. The basic objective of Arithmetical dynamics is to explain the arithmetic properties with regard to underlying geometry structures. Again, we are here with the Part 5 of...

## Arithmetical Dynamics: Part 0

Arithmetical dynamics is the combination of dynamical systems and number theory in mathematics. We are here with the Part 0 of the Arithmetical Dynamics Series. Let's get started.... Rational function \( R(z)= \frac {P(z)}{Q(z)} \) ; where P and Q are polynimials ....

## Arithmetical Dynamics: Part 4

We are here with the Part 4 of the Arithmetical Dynamics Series. Let's get started.... Arithmetical dynamics is the combination of dynamical systems and number theory in mathematics. \( P^m(z) = z \ and \ P^N(z)=z \ where \ m|N \Rightarrow (P^m(z) - z) | (P^N(z)-z) \)...

## Arithmetical Dynamics: Part 3

We are here with the Part 3 of the Arithmetical Dynamics Series. Let's get started.... Arithmetical dynamics is the combination of dynamical systems and number theory in mathematics. Theory: Let \( \{ \zeta_1 , ......., \zeta_m \} \) be a ratinally indifferent cycle...

## Arithmetical Dynamics: Part 2

We are here with the Part 2 of the Arithmetical Dynamics Series. Let's get started.... Arithmetical dynamics is the combination of dynamical systems and number theory in mathematics. The lower bound calculation is easy . But for the upper bound , observe that each \(...

## Arithmetical Dynamics: Part 1

We are here with the Part 1 of the Arithmetical Dynamics Series. Let's get started.... Arithmetical dynamics is the combination of dynamical systems and number theory in mathematics. Definition: Suppose that \( \zeta \in C \) is a fixed point of an analytic function...

## Research for School

Research projects for school students, in mathematics and data science. For advanced learners who are in love with mathematical science.

## Arithmetical Dynamics: Two possible problems

Today, we are going to discuss two possible problems for Arithmetical Dynamics in this post. 1.1. Existence of (pre)Periodic Points. These are the topics expanding on I.N. Baker’s theorem. Related reading: (1) Silverman Arithmetic of Dynamical Systems: p 165....