Discussions Related to A Book on Mathematical Physics

PREFACE

The twentieth century saw great discoveries and growth in all sciences, particularly physics. The amount of core, or basic physics a student has to learn before reaching a research or advanced graduate level has become several times than what used to be about fifty years ago. Despite this, the number  of years available to a student after 10+2 school level years has remained the same: three years at undergraduate level and two at the graduate or MSc
level.

In order to cope with this situation, universities have been including more and more of the recent developments in the syllabi at the cost of the fundamental concepts and methods which require more time to absorb. The students quickly learn the tricks to somehow manage, hoping to get a fuller understanding later on. That hope, sadly, is not fulfilled due to demands of work.  It has been our experience that with the inclusion of more content, a great  harm is done to the teaching of basic mathematical and experimental skills  to the physics student. Of these two, learning mathematics demands more time. Usually, there is just one course on mathematical methods in the initial  semester of the 4-semester MSc Physics program. The topics included in the course are usually chosen for immediate use in the core physics part, while new tools are needed in teaching the advanced topics. This leads to a basic gap in the training.

In this book we try to bridge this gap. The book starts at the undergraduate level when a student enters the MSc program and goes up to the tools needed for advanced courses.  Such a book will be useful to students, and to their teachers as well, for all the four semesters. It will be more like a companion reader, because  different methods crop up in different courses, and there is no reason that a student has to learn all the methods in just the first semester. Such a book can result in a massive, dull, and forbidding encyclopedia of a book, whereas what we are attempting is not a book for reference but a book iii  primarily for inspiring students to learn and appreciate mathematical tools. There are a great many, exhaustive, books in the tradition of Courant- Hilbert, Morse-Feshbach, B. Simon, W. Thirring, Choquet-Bruhat-DeWitt- Morette-Bleick or V. Balakrishnan, to name just the few most venerable authors. And our task is to prepare the student to approach those books with confidence.

An analogy might help to illustrate our purpose. Being a good citizen does not mean having to read all the law books in order to be on the right side of law. There must be a minimum set of guidelines and public instructions to avoid going astray. This book on mathematical physics will be such a set of instructions. And  the book should be fun to read! We know from our experience as teachers that many physics students, and  even senior researchers, feel hesitation and discomfort when approaching mathematical topics. Our idea is to make them overcome that feeling. If this book succeeds in doing that, it would have served its purpose.

Pankaj Sharan and Ashok K. Kapoor