December 22, 2022
7:00 pm
Srinivasa Ramanujan is considered to be one of the geniuses in the field of mathematics. He was born on 22nd December 1887, in a small village of Tamil Nadu during British rule in India. His birthday is celebrated as national mathematics day. In high school, he used to do very well in all subjects. In 1990, he started working on his mathematics in geometry and arithmetic series. Although he had no official training in mathematics, even then, he was able to solve problems that were considered unsolvable. He published his first paper in 1911. In January 1913, Ramanujan began a postal conversation with an English mathematician, G.H. Hardy at the University of Cambridge, England and wrote a letter after having seen a copy of his book Orders of infinity. He found Ramanujan’s work to be extraordinary and arranged for him to travel to Cambridge in 1914. As Ramanujan was an orthodox Brahmin, a vegetarian, his religion might have restricted him to travel. This difficulty of Ramanujan was solved partly by E H Neville, a colleague of Hardy. Hardy after analysing the works of Ramanujan, said, Ramanujan had produced groundbreaking new theorems, including some that defeated me completely. I had never seen anything in the least like them before.’
At the age of 32, he died of Tuberculosis. In his short life span, he independently found 3900 results. He worked on real analysis, number theory, infinite series, and continued fractions. Some of his other works such as Ramanujan number, Ramanujan prime, Ramanujan theta function, partition formulae, mock theta function, and many more opened new areas for research in the field of mathematics. He worked out the Riemann series, the elliptic integrals, hypergeometric series, the functional equations of the zeta function, and his theory of divergent series, in which he found a value for the sum of such series, using a technique he invented, that came to be called Ramanujan summation. In England, Ramanujan made further research, especially in the partition of numbers, i.e, the number of ways in which a positive integer can be expressed as the sum of positive integers. Some of his results are still under research. His journal, Ramanujan Journal, was established to keep a record of all his notebooks and results, both published and unpublished, in the field of mathematics. As late as 2012, researchers studied even the small comments in his book, as they do not want to miss any results or identities given by him, that remained unsuspected until a century after his death. From his last letters in 1920 that he wrote to Hardy, it was evident that he was still working on new ideas and theorems of mathematics. In 1976, mathematicians found the ‘lost notebook’, that contained the works of Ramanujan from the last year of his life. Ramanujan devoted all his mathematical intelligence to his family goddess Namagir Thayar. He once said, “An equation for me has no meaning unless it expresses a thought of God.” Now, we will discuss in detail all his contributions to mathematics.
SymPy is a Python library for symbolic mathematics. It aims to become a full-featured computer algebra system (CAS) while keeping the code as simple as possible in order to be comprehensible and easily extensible. SymPy is written entirely in Python.
SymPy is…
Python is an interpreted, object-oriented, high-level programming language with dynamic semantics. Its high-level built-in data structures, combined with dynamic typing and dynamic binding, make it very attractive for Rapid Application Development, as well as for use as a scripting or glue language to connect existing components together. Python’s simple, easy-to-learn syntax emphasizes readability and therefore reduces the cost of program maintenance. Python supports modules and packages, which encourages program modularity and code reuse. The Python interpreter and the extensive standard library are available in source or binary form without charge for all major platforms and can be freely distributed.
The main objective of this course is to provide a comprehensive overview of symbolic Mathematics and Computing with Python and its applications in Engineering, Sciences, and Mathematics.
This training is packed with real-life analytical challenges which you will learn to solve. Some of these we will solve together, and some you will have as homework exercises.
In summary, this course has been designed for all skill levels and even if you have no programming or computing background you will be successful in this course!
No programming experience is needed. You will learn everything you need to know.
Dr. Mehar Chand: Department of Mathematics, Faculty of Computational and Mathematical Sciences, Baba Farid College, Bathinda, INDIA
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