Math is in the air

Start this year the right way

New year’s time is usually a time to make some new year’s resolutions. I won’t do it and instead this year for me at least will be solely focused on applied mathematics. Math topics interest  me for a long time. But I never took it seriously to invest quality time into studying advanced math topics with enough detail. This year will be different. The plan is to start from some quite general books on math that try to approach the topic in an engaging way like Measurement book by Paul Lockhart and slowly transitioning to more technical books for applied mathematics like Elements of Applied Mathematics by Zeldovich and Myskis and  Nonlinear Dynamics and Chaos by Steven H. Strogatz.

A little bit about the books

Why these three books you may wonder? Actually, there are four books I want to focus on. What is so specially about these books is the fact that they do not simply talk about one specific field in math with a very narrow focus on the subject, but like Donald Knuth’s The Art Of Computer Programming volumes approach the subject in a more general way without being fearful to delve in fields of physics, engineering, biology etc.

To summarize the books are:

measurement

Measurement by Paul Lockhart which tries to show math as an engaging activity that resembles arts, such as music, painting where there is a place for creativity,  a joy of new discoveries or a pain of being stuck trying to get a solution.

 

 

 

 

2020-01-01 16_03_56-Elements Of Applied Mathematics _ YA. B. Zeldovich, A. D. Myskis _ Free DownloadElements of Applied Mathematics by Zeldovich and Myskis which is an old book, but it’s still relevant today, at least in many parts of it, as it was back in 1972. As authors themselves put in the foreword of the book

So our advice is: read our book and study it. But even if there is not time enough to make a deep study, then merely read it it like a novel, and it may be just the thing you will need for solving some difficult problem.

 

 

math_arnoldMathematical Understanding of Nature: Essays on Amazing Physical Phenomena and Their Understanding by Mathematicians by Vladimir Arnold. This book is a collection of applied math problems  that were drawn from various fields such as physics, engineering etc.

Note: If you’re capable of reading in Russian then this book is available in full for free here.

 

 

nonlinear-dynamics-and-chaosAnd finally there is the voluminous  Nonlinear Dynamics and Chaos by Steven H. Strogatz that makes me feel better by having hundreds of differential quotations.

Note: The older edition of this book is available for free, for example, here.

A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages.

 

Now is the best time to start

This paragraph is dedicated to myself and possibly you. Remember that now is the best time to start doing what you wanted, but postponed ad infinitum. So start by taking small steps to big results later. Or at least to having satisfaction from solving some non-trivial tasks and applying a new skill to real life problems.

Good mathematics books to read and work through

Math is entertaining when you try to play with it

If you have an interest in mathematics be it pure or applied there are plenty of books were written on the subject varying by the depth of the presented material and the need to know a certain level of math to be able to not only read the book but also gain some practical insights by working through the examples and tasks. Personally, I like more books that freely use math in the description of the examples and give tasks for a reader to accomplish. It seems like this is the only way to really understand what author tried to convey. It’s like reading a book on programming and trying right away the code samples, changing them.

Following is the description of a number of popular math books that I find very insightful, useful and entertaining, since reading them not only gives an appreciation of the beauty of math, but also makes one feel better when he or she is able to find a solution to tasks in the book.

A Mathematician’s Lament

lament-1

I want to start with the article that Paul Lockhart wrote, that later was expanded to a book with the same name which is A Mathematician’s Lament. The first part of the book is essentially the article itself. So if you read only the article you read half a book already. If you have an Amazon account you may buy a Kindle version of the book and it may take you a couple of hours to finish it. Then you may return it for refund and that’s it. You got the entire book for free.

The article and consequently the first part of the book presents readers with a very strange way that math is taught in schools using very clever analogy to how music might have been taught if it would be taught like math in most schools today. 

The second part of the book tries to show some solutions to the problems of how math is taught that were described in the first part of the book.

I recommend this book to all who disliked math and thought that it was boring and  disgusting. Maybe, you’ll change you thoughts on the subject.

From popular to more hands-on math books

primes

Recently, I’ve read the The Music of the Primes book by a mathematician Marcus du Sautoy on Riemann hypothesis. Previously I read a  book about primes and as part of my studing at college learned a thing or two about them, but I never appreciated how interesting it may be to follow the path along with mathematicians trying to prove Riemann hypothesis. This hypothesis is one of the seven problems that Clay Mathematics Institute thinks worth 1,000,000 USD for one who’s able to prove it. Though less money is given to one who will disprove it. 

 

 

The Riemann hypothesis states that all interesting solutions of the equation

ζ(s) = 0, where ζ(s) is a Riemann Zeta function, ζ(s) = 1 + 1/2s + 1/3s + 1/4s + …

 lie on a certain vertical straight line which is  Re(s) = 1/2,  Re(s) stands as for a real part of the argument s.

What I liked about The Music of the primes that Marcus wasn’t afraid to show a little bit of mathematics that was related to the saga of trying to prove the Riemann Hypothesis. He also was able to create an adventurous story that connected math and physics and such a mundane thing as RSA cryptosystems that was used in Internet secure web communications. In addition, Marcus du Sautoy mentions a large number of prominent mathematicians who deserve a separate book to be written about them.

 

Math is a pleasure to play with when it is presented in an interesting manner

The last book that I want to mention in this post is the book by Vladimir Arnold who was one of the distinguished Russian mathematician and the one who solved the Hilbert thirteenth’s problem in the age of twenty. Only a number of numerous books written by Vladimir Arnold were translated into English from Russian, but even the ones that were are still very exciting to read and include lots of tasks to be resolved by a reader. I should say that Arnold’s popular math books are actually a kind of math courses. If you’ll check one of his books you’ll understand what I mean by this. What I find appealing in the Arnold’s books is his ability to explain complex topics in a simple way that is entertaining and makes you long for more. By the way if you can read in Russian you may find all of his books and many others for free at the Moscow Center For Continuous Mathematical Education web site library.

If you like physics and applied math, then you gonna find Mathematical Understanding of Nature: Essays on Amazing Physical Phenomena and Their Understanding by Mathematicians book by Vladimir Arnold very informative and entertaining at once. In it you’ll find a number of task and solutions to them drawn from various fields of physics along with a simple to grasp explanations that makes complex things seem beautiful.

There are additional Vladimir’s books that may be found in English so if you’ll find this book useful to you then there are others you can enjoy too.

It’s only the beginning

This post is only the first one in a series of post that will accompany me while I myself read and work through the popular math books and try to report on interesting gems I find in them.