Synopsis Of Pure And Applied Mathematics Pdf

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Start your review of A Synopsis of Elementary Results in Pure and Applied Mathematics: Volume 1: Containing Propositions, Formulae, and Methods of Analysis, with Abridged Demonstrations

I discovered this book when it was mentioned in a video on YouTube, uploaded by the channel Tibees, entitled "The book that Ramanujan used to teach himself mathematics" (https://www.youtube.com/watch?&v=...).

Srinivasa Ramanujan was said to have read this book when he was 16 years old, being one of the key factors in awakening his genius. This book may not have been the best choice, but it was what Ramanujan could get his hands on. He was quite poor and a friend lent him a library copy of this book. The author, G.S. Carr, was a private tutor for students preparing for exams such as the Cambridge University Mathematical Tripos, and the book was written to be an aid for these students in preparing for the exam, it was not intended to be a stand-alone teaching resource.

The book is huge, and starts off with some basic algebra. Factors are the very first thing that is mentioned, but then it accelerates through the theory of equations, trigonometry, geometry and conics. It lays a foundation for differential and integral calculus and differential equations. It covers some advanced ideas that Toby (from the Tibees YouTube channel) doesn't understand, and there are words, such as "cissoid", "lemniscate", "cassinian" and "conchoid" that she hasn't seen before.

On p. 359, we can see where Ramanujan likely first learned about the gamma function, which went on to feature a lot in his work, so much so that he mentioned it as one of the results he was most proud of in his first letter to Hardy. There's also a mention of things like infinite series and their convergence or divergence, which might have been important to Ramanujan's thinking, and perhaps this is where he first got inspired.

Toby doesn't recommend reading this book as she does not think there is anything particularly special about it, and in the case of Ramanujan, what was special was the reader. The best book to learn mathematics from, she says, is the one that you can get your hands on, whether it's from the local library or from a second-hand book shop or lent from a friend like in the case of Ramanujan.

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