Monday, June 30, 2014


After reading my first book, I switched books with Morgan Sparber and read my second book titled Love and Math: The Heart of Hidden Reality by Edward Frenke. While discussing first books in class, Morgan's account of this book piqued my interest by depicting the book to be the journey of a young man going through his studied and his love of mathematics that drives him. Obviously being a math lover myself, I related well to this aspect. What I did not expect, however, was to find a part of math that I had not discovered myself; Frenke helped me fall in love with this part. He depicts math as more of an art and more creative rather than black-and-white as those starting off in mathematics sees it as.

Tuesday, June 17, 2014

Newton and Mathematics

Sir Issac Newton (1642-1727), though is largely attributed towards the advancement in physics, was a key contributor to the advancement of mathematics as well. It is said that the beginning of his education focused on law and it was not until he picked up an astrology textbook in which he did not understand the mathematics contained in it, that he became interested in math. Newton - though proclaimed to be predominantly self-taught - studied underneath mathematicians such as William Oughtred and John Wallis, and Descartes. He is greatly known for contributions such as differentiation and integration, at the time known as method of fluxions and inverse method of fluxions (later on Leibniz would ultimately define these methods as differentiation and integration).

The famous Leibniz vs. Newton dispute concerned who exactly came up with these fundamental calculus ideas. Followers of Newton claimed that Leibniz had glimpsed Newton's notes of his fluxions in 1676 during a visit which then lead to Lebniz publishing this pleigerized work in 1684, stealing the thunder from Newton.

Newton also came up with the Binomial Theorem, which states,

General Form: 

He discovered such a way to expand any binomial, fractions, complex, etc., when he exiled himself to keep from contracting the plague. His general form contains works of Pascal in which (n  / k) relates to numbers in Pascal's Triangle. The general Binomial Theorem form is present on Newton's tombstone in Westminster Abbey.

Monday, June 9, 2014

e : the Story of a Number (a review)

     Unlike a typical stiff, boring, Mathematics textbook one might come across in a classroom setting, e: the Story of a Number by Eli Maor (1994) humanizes the number e in way of depicting its long history in which it was "invented" (or discovered, whichever you believe). It balances equations and - as the book puts - pure mathematics with applied mathematics and the history of the mathematicians that have formed mathematics as we know (and love) today.

     I was (pleasantly) surprised that the book not only covered the number e and its brother ln (which I was expecting) but also covered various trigonometric topics, differentiation, anti-differentiation,  and other famous numbers such as pi and i. This book is very well rounded and very well written: most ideas written in layman's terms.

     Since most (including myself) have learned math through a series of building blocks, it is refreshing to explore along with Maor how those long ago learned mathematics. Also, reading of the lives of mathematicians was rewarding as well; it allowed the static "characters" in a typical math textbook to be more dynamic and relate-able. I would easily recommend this book even to those with average math background and skills, especially if one were newly starting their journey in the subject; the book does a fantastic job of giving a deeper explanation of how different mathematics links together.

     To conclude, I cannot say with confidence that I was eager to start this book, but come the end of it I was in full math-nerd mode, happy that I did.


Extensions/Aspects I Found interesting:

-The "log base 10" being the normal base came from the mathematician Henry Briggs who suggested 

-“The logarithm function remains central to almost every branch of mathematics” (Maor 16). I have noticed this substantially while studying mathematics myself throughout these past few years. There have been many-an-equation in which log was included.

- That e can be written as

- logarithmic spiral: First studied by Descartes in 1638 and then by Jakob Bernoulli, the logarithmic spiral is quite interesting. For example, I had not known before that every straight line through the origin intersects the spiral at the same angle. This is the only curve that does this.

Also, that inverting the logarithmic spiral causes a mirror reflection upon itself. Though I have studied The Golden Ratio and Fibonacci's numbers before, I had not realized that the logarithmic spiral and the formers were the same. This got me to explore the logarithmic spiral in nature:

- Euler's Formula and Identity fascinated me. We discussed the topic in class however the book divulged much more information. Chapter Thirteen is titled most appropriately:

The talk about how amazing Euler's Identity was had me searching the web for their reactions to the famous identity:

(1) I like this video for it shows a way to describe the famous identity to those without much mathematical background
(2)This Video shows all of the components of such a nice equation.