**Proofs and Ideas: A Prelude to Advanced Mathematics**

**Prof Sethuraman, could you tell us what was the inspiration for the book?**

Most people view mathematics as a formidable edifice built using reams upon reams of mysterious symbols, decipherable only to the chosen few who have dedicated their lives to it. While this view has partial justification, it fails to capture the essence of the subject: mathematics is a *beautiful* subject, full of the most delectable patterns, many of which can be appreciated by anyone who has studied the subject in high school. It is an arena for play, for exercising our creativity. It can bring joy. It can evoke a deep sense of wonder. All it requires is patience and a willingness to push our minds to their furthest.

**Why is this book the need of the hour?**

Unfortunately, a lot of school mathematics is geared towards getting students ready for the applications of mathematics to physics and engineering, and this essence of mathematics is lost among all the symbol pushing and manipulation needed. Therefore, this essence needs to be re-captured when studying for a degree in mathematics, for there, one has to go beyond mere symbols and get down to the heart of the subject.

**What is the premise of the book?**

This book focusses on some core ideas that are needed for studying mathematics, ideas that are quite accessible to anyone with exposure to high school mathematics. For instance, how do you show that given any six arbitrary natural numbers, the difference of some two of them must end in 0 or 5? Or, how do we capture the fact that the kind of infinity represented by the natural numbers is the same as that represented by the rational numbers (the set of reduced fractions), but is different from the kind of infinity represented by the real numbers (the numbers represented by lengths along a line)? The ideas behind these are all simple and yet deep.

**How do some ideas in the book find expression in the Krea curriculum?**

I have used the material in this book for the Core and Skills course at Krea “Mathematical Reasoning,” and have also used it for the required mathematics department course “Discrete Mathematics” (soon to be re-named as Introduction to Proofs and Mathematical Thinking).

**When did you start work on the book and how do you feel now that it is officially launched?**

The project started several years ago at my previous university, California State University Northridge, where I designed the text for their version of the Introduction to Proofs course. While the core was conceptualized and developed there, much of the book was written after moving to India, and in particular, the last portions were written at Krea (and used for courses here). It was delayed by Covid (and my own laziness), but I am glad that it is finally out.

**About Prof. Bharath Sethuraman**

**Professor of Mathematics, Krea University**

Prof. Bharath Sethuraman has nearly thirty years of experience as a mathematician and a teacher. He received his B.Tech in Mechanical Engineering from IIT Madras, but switched to pure mathematics and obtained his Ph.D. from the University of California at San Diego. He held a permanent position as mathematics faculty at California State University Northridge for over twenty-five years, teaching undergraduate and masters level students, many of whom came from less privileged backgrounds, and many of whom were first generation college learners. He has also taught at other universities in the US and in India, including at IIT Bombay, Indian Statistical Institute Bangalore, and Azim Premji University.

Besides being a committed teacher, Prof. Sethuraman has been active in research, working primarily in the fields of algebraic number theory and algebraic geometry. Prof. Sethuraman has been the recipient of several research grants from the U.S. National Science Foundation, and of other research and teaching grants from various sources.

Prof. Sethuraman has written three books for undergraduate students: Rings Fields and Vector Spaces, A Gentle Introduction to Abstract Algebra, and Proofs and Ideas: A Prelude to Advanced Mathematics. Outside of academics, he enjoys traveling, cycling, reading, and music.

Reach him at: [email protected]