This post is mainly for our alumnis - those who have cleared one of the three entrances (Indian Statistical Institute, Chennai Mathematical Institute or Institute of Mathematics and Applications), and pursuing an undergraduate mathematics course.
It is very important to choose the right books. Once you are in college, you may face two kinds of challenges regarding books.
The first is the challenge of plenty. There are thousands of books written on a single topic and your college library will have many of them. Even after a couple of months through a semester you may find yourself shuffling amongst multiple books on a single topic without really 'doing' any one of them.
The second is the challenge of cliche. In India, (and elsewhere in the world), mathematics honors students have some 'cliche' books, or rather 'rule of the thumb' book which are supposed to 'contain all the theorem' and 'exam type exercises'. These books are generally 'manual type' in nature. Since they are devoid of any intuitive discussion (and approach), they are sufficient to destroy independent and creative mathematical thinking (which should be your aim if you have taken up mathematics as your honors).
As a remedy to these challenges we provide 'first layer' and 'second layer' books on five important papers (usually taught in the first semester of a Math Honors undergraduate course).
First Layer
Analysis - Bartley Shebert, Precalculus by Tarasov
Linear Algebra - Bronson De Costa
Probability - Ross
Discrete Mathematics - Rosen
Abstract Algebra - Herstein
Second Layer
Analysis - Rudin
Linear Algebra - Lang
Probability - Probability through Problems by Marek Capinski
Discrete Mathematics - Krishnamurthy
Abstract Algebra - Artin
Apart from a through reading and problem solving using the above mentioned books, you may also solve the Berkeley Book on Problems. It will help you to perform better in entrances for graduate schools (like TIFR, IMSc, IISc, etc)
It is very important to choose the right books. Once you are in college, you may face two kinds of challenges regarding books.
The first is the challenge of plenty. There are thousands of books written on a single topic and your college library will have many of them. Even after a couple of months through a semester you may find yourself shuffling amongst multiple books on a single topic without really 'doing' any one of them.
The second is the challenge of cliche. In India, (and elsewhere in the world), mathematics honors students have some 'cliche' books, or rather 'rule of the thumb' book which are supposed to 'contain all the theorem' and 'exam type exercises'. These books are generally 'manual type' in nature. Since they are devoid of any intuitive discussion (and approach), they are sufficient to destroy independent and creative mathematical thinking (which should be your aim if you have taken up mathematics as your honors).
As a remedy to these challenges we provide 'first layer' and 'second layer' books on five important papers (usually taught in the first semester of a Math Honors undergraduate course).
First Layer
Analysis - Bartley Shebert, Precalculus by Tarasov
Linear Algebra - Bronson De Costa
Probability - Ross
Discrete Mathematics - Rosen
Abstract Algebra - Herstein
Second Layer
Analysis - Rudin
Linear Algebra - Lang
Probability - Probability through Problems by Marek Capinski
Discrete Mathematics - Krishnamurthy
Abstract Algebra - Artin
Apart from a through reading and problem solving using the above mentioned books, you may also solve the Berkeley Book on Problems. It will help you to perform better in entrances for graduate schools (like TIFR, IMSc, IISc, etc)
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