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TIFR Ph.D.

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IIT JAM

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College Mathematics Portal

College Mathematics Portal contains problems, discussions, and information on Masters and Ph.D. entrances. It also contains research-oriented mathematical discourse that is supplemental to our main program.

Problem Garden

This repository contains papers and problems from challenging Mathematics contests and entrances for college students. These include a wide range of advanced topics such as group theory, multivariable calculus, topology, and linear algebra.
Tata Institute of Fundamental Research

Tata Institute of Fundamental Research (TIFR) – Integrated Ph.D. and Ph.D. in Mathematics Entrance

Chennai Mathematical Institute M.Sc.-Ph.D. Entrance

Indian Statistical Institute – M.Math and JRF Entrance

National Board of Higher Mathematics – M.Sc. and Ph.D. scholarship tests

IIT JAM

IIT JAM – Math Entrance for IIT’s and Indian Institute of Science

Spanning matrix space by niltopent matrices: TIFR 2018 Part A, Problem 15

This problem is a cute and simple application of spanning matrix space by niltopent matrices in the linear algebra section. It appeared in TIFR GS 2018.

Calculating eigenvalues through geometry:TIFR 2018 Part A, Problem 14

This problem is a cute and simple application of calculating eigenvalues through geometry in the linear algebra section. It appeared in TIFR GS 2018.

Direct product of groups: TIFR 2018 Part A, Problem 9

This problem is a cute and simple application of the direct product of groups in the abstract algebra section. It appeared in TIFR GS 2018.

Real Symmetric matrix: TIFR 2018 Part A, Problem 6

This problem is a cute and simple application of the real symmeric matrices in the linear algebra section. It appeared in TIFR GS 2018.

Integration of nonnegative function: TIFR 2018 Part A, Problem 4

This problem is a cute and simple application of the integration of nonnegative function in the analysis section. It appeared in TIFR GS 2018.

Application of L’Hopital: TIFR GS 2018 Part A, Problem 2

This problem is a cute and simple application of the L’Hopital rule in the analysis section. It appeared in TIFR GS 2018.

I.S.I. M.Math Entrance 2019 (PG) Solutions, Hints, and Answer Key

This is a work in progress. Please suggest improvements in the comment section.Problems Objective I.S.I. M.Math Subjective 2019 Objective Section (Answer Key)  1. C 2. D 3. B 4. C 5. A 6. D 7. B 8. D 9. D 10. D 11. A 12. B 13. B 14. A 15. C 16. A 17. C 18. A 19....

Clocky Rotato Arithmetic

Do you know that CLOCKS add numbers in a different way than we do? Do you know that ROTATIONS can also behave as numbers and they have their own arithmetic? Well, this post is about how clocks add numbers and rotations behave like numbers. Consider the clock on earth....

What is the boundary?

Boundaries are controversial. Ask the politicians! Mathematicians, on the other hand, have an interesting way of thinking about the boundary of the space. It is less controversial for sure.

A Proof from my Book

This problem is a cute and simple application of the L’Hopital rule in the analysis section. It appeared in TIFR GS 2018.

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