A few months back, I had the privilege (along with Shekhar Borgaonkar of HP Labs India) of getting a five minute tutorial on information theory from Abraham Lempel (of Lempel-Ziv fame) at Los Angeles airport. During the course of the conversation, Abraham remarked "India was always strong in mathematics". While most educated Indians are familiar with Srinivasa Ramanujan and his contributions, India has produced a number of other good mathematicians who have not gained the same popularity. One possible reason for this is that the real value of mathematics comes from applying the results of mathematics to other disciplines and there are only a few Indians I know who are extremely good at this. One of them is Dr. M. Vidyasagar who works at TCS research in Hyderabad. Besides knowing lots of mathematics, Dr. Sagar is also very good at applying them to domains like control theory, neural networks and learning theory. He also writes in a very engaging style, a good example is this survey of problems in computational biology.

My own Math education has been limited to the Computer science-oriented Math courses I took in University (Linear Algebra, Discrete Maths, Graph theory and Numerical methods). I really liked graph theory because there are so many interesting applications of graph theory. It was only much after University that I bought Hamming's book on Numerical methods and gained some appreciation for the subject. A few years back, I tried improving my mathematics knowledge by reading some texts on real analysis, differential geometry, topology etc but soon decided that it was not the right approach.

While it is not difficult to comprehend the theorems and results, it is difficult to appreciate the results without knowing how and where they can be applied. Dr. Vidyasagar suggested to me that it is better to read textbooks written by Russian professors as they usually teach undergraduate courses (and some like AN Kolmogorov even taught in schools). I briefly taught a couple of undergrad level math courses, so I can appreciate that it might be hard to keep an undergrad or schooler engaged without explaining where the theorems are applied. If anyone reading this blog knows of Russian books on advanced math topics, please recommend some. Until a few years back, it was common to find Russian text books by Mir publishers (of Moscow) on Indian footpaths, somehow they have become harder to find in recent years.

Around a year back, I read this post by Steve Yegge and have been trying to further my knowledge of mathematics from Wikipedia. Some Wikipedia mathematics pages, such as the pages on Eigen Vectors, Singular value decomposition and Riemann hypothesis are well written and give a very comprehensive overview. The links on these pages are also extremely informative. However, a lot of Wikipedia math pages appear to be edited only by mathematicians and do not appear (atleast to me) to be of the same quality as the eigen vector page. Nevertheless, the Wikipedia approach has worked reasonably well and I am a lot more awareness of math theorems and results than I was a year ago.

Does your field of work require you to learn and use mathematics? If it does, what are your approaches to learning mathematics?