Interview: SCIMS Lecturer publishes book on Hilbert Spaces


Dr. Ittay Weiss is a Lecturer in Mathematics at SCIMS. He recently published a book in mathematics in the area of topology called A Premier on Hilbert Spaces. Below is his interview conducted by SCIMS Newsletter team.

Question: Can you give a brief background of your book and its application?

The topic of Hilbert spaces forms the mathematical foundations of quantum mechanics and thus underlies modern physics. The mathematics of classical Newtonian mechanics is calculus and thus in a sense Hilbert spaces are the necessary replacement of calculus if one is to tackle modern physics. However, it is notoriously so that while calculus is accessible at the first year of studies, the mathematics of Hilbert spaces is hardly accessible at the fourth year, due to a strong reliance on non-trivial topological considerations.

There are several excellent introductory level textbooks on Hilbert spaces but they are require quite an advanced level of maturity from the student. The book I wrote, together with Prof. Carlo Alabiso, is the first such book to include all the prerequisites at the undergraduate level and also the first such book to be written jointly by a physicist and a mathematician. This is important since the main target applications of Hilbert space theory are in modern physics, and thus the book offers a unique perspective on the subject, appealing to physicists and mathematicians

Question: Title and publisher of your book?

“A Primer no Hilbert Space Theory”, Springer-Verlag. 

Question: How did you get the publisher interested in this book?

Due to the unique content level, expository style, and appeal to a large body of students, Springer-Verlag was happy to sign the contract. 

Question: Who is the target of your book? Is it for students or researchers?

The main target audience is student, both physicists and mathematicians. The book is also a good resource for practitioners seeking to strengthen their grasp of the mathematical foundations of modern physics, as the book is a very detailed and rigorous account of these foundations. 

Question: Why is your book important to the field of research  and community?

The contribution of the book is in making the mathematics of modern physics more accessible by creating a single self-contained source of information geared towards Hilbert spaces. 

Question: What motivated you to write this book?

The collaboration with Prof. Carlo Alabiso, which makes this book very unique, was the initial primary motivation. As the project unfolded and the book was taking form, we both saw that we are creating a truly new addition to the existing literature, and one that we hope will be appreciated by others.

Question: What are the challenges you faced during the writing journey?

 Co-authorship offers plenty of friction points. At times we disagreed on things and needed to spend some time convincing each other and adapting our points-of-view. Aside from that, the writing of a book requires extreme care and diligence, reading, proof-reading, and re-reading page after page after page. 

Question: What is your message to aspiring writers?

 I will just offer the quote: “What the poet laments holds for the mathematician. That he writes his works with the blood of his heart.”
— Ludwig Boltzmann.

Question: Can this book be used in Fiji as a text book for any university courses?

Yes, certainly. This book can be used at the advanced undergraduate or beginning postgraduate level for mathematics and physics students. The book, or chapters in it, can also supplement undergraduate courses on analysis and linear algebra, providing a perspective geared towards higher studies.

Question: Any other comments?

I will gladly accept any comments, corrections, or general remarks from anybody reading the book, so please feel free to email me!

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