Mathematics after engineering

In this post, I will be telling you about my preparation journey for all the entrance exams like JAM, GATE, TIFR and NBHM. For those who wanted to know about my journey from engineering to mathematics can have a look ( Journey ). First, starting with the list of books. For every book below, you will also find the reason why I chose that particular book. 1. A Basic Course in Real Analysis by S.Kumarsen : This book is written in a way that students of different caliber, students preparing for different exams and interviews can refer it and this book will serve their purpose.  Each question in this book comprises of 2 parts : First is strategy which deals with how to approach the question and the second is the formal mathematical solution of the question which is motivated by the strategy.  For engineers it is like you develop an algorithm for your code. Let me give you an example : suppose you want to find limit x as x tends to a. In strategy part you would find something like when x is