Date: 20th April 2023
I joined the Bachelor of Mathematics (B.Math.) program at ISI Bangalore in December 2020. Through the 3-year program, I studied various introductory courses in pure mathematics, probability, statistics, and physics. Here are some of the additional readings, that I have undertaken, and also some of my favorite books.
‘An Introduction to Measure Theory’ by T. Tao. This book was my first introduction to "advanced topics" in mathematics. I took a course on Measure theory at the NPTEL platform, taught by Prof. Inrdava Roy, IMSc.
'Functional analysis' by W. Rudin. I studied the first few chapters of this book as a part of the Functional analysis course, delivered by Dr. Soumyashant Nayak, which I audited in February 2022. At the end of the course, I studied the chapter from the same book on Schwartz's theory of distributions.
‘Interpolation And Sampling In Spaces Of Analytic Functions’ by K. Seip. As a part of the Summer Research Fellowship Program (SRFP) 2022, I studied under the guidance of Dr. Purvi Gupta, at IISc. I wrote a detailed report on the first two chapters of this book, which I will link here.
‘Complex Analysis: A Functional Analytic Approach’ by F. Haslinger. During the second half of my SRFP, I studied several functional analytic topics that arise in complex analysis from this book, which include Frechet spaces of holomorphic functions, Bergman spaces, the d-bar operator, the d-bar complex, etc.
'Category Theory in Context' by E. Riehl. I read the first couple of chapters of this book in a leisurely fashion just to get a grasp of what category theory is about. The material has helped during my algebraic geometry course in the final semester of B.Math.
'A Basic Course in Partial Differential Equations' by Q. Han. I studied this textbook as a part of a winter project under Prof. Dr. Sandeep K, TIFR CAM.
- Aprameya