Prime Obsession with Math

Meet the math book you’re were craving for so long

If you are interested in math and like to have your hands dirty in nitty gritty calculations then the Prime Obsession book by John Derbyshire is just for you. Unlike other popular books on mathematics it provides a gentle and powerful introduction to all math you need to know to understand the Riemann Hypothesis (RH). Reading, I should say, working through the book you’ll learn about interesting properties of Prime Numbers, meet the Prime Number Theorem (PNT) and really understand what the Riemann Hypothesis is all about. In this book you’ll meet Gauss, Euler, Riemann, Hilbert and other renowned mathematicians that influenced the development of mathematics.

What I find most useful about this book

There are books that require a discipline to read through, there are books that are plain boring, and there are books that excite you and your imagination, books that you can’t help, but continue reading more and more. The Prime Obsession is of the latter kind.

What I most like about the book is the historical context John Derbyshire provides throughout the book in addition to his sense of humor and his ability to explain required math in a way that each mathematically inclined person can get fast. I should mention, that having an engineering degree could speed up you understanding significantly, but strictly speaking, it is not required.

In addition, the references to other books on mathematics that John provides are very useful and may provide you with additional materials to digest, like the Hardy’s A Course of Pure Mathematics.

Where to get the book?

Surely, the easiest way to get the book is to buy a copy of it in a Kindle format or a print one. I bought a used one quite cheaply, for less than a Kindle book, which generally cheaper than a hard copy. An old fashion way would be to go to a nearest library and fish for the book their.

Mathematical Modeling

A new math book each blog-post 

There are quite a few books on mathematical modeling available out there, but I want to literally and figuratively focus  on a single one, which is Mathematical Modeling by Mark M. Meerschaert.

First, a number of details about the author of the book. Mark Meerschaert is  a University Distinguished Professor in the Department of Statistics and Probability at Michigan State University. He authored a number of books among them the Mathematical Modeling.

What is special about the book?

I have a third edition of the book and I want to provide some thoughts about it. Personally, I like books that provide detailed explanations and ample of examples accompanying the theoretical parts of the book. In my opinion, author’s own view on the subject phrased in his own words, instead of strict adherence to formal definitions is a valuable aid in comprehending mathematical theory.

As for the content of the book, it is divided in three parts which reflects the fact that most of the mathematical models fall into three types 

  • Optimization Models
  • Dynamic Models 
  • Probability Models

Each chapter in the book has detailed examples and quite a few exercises for the reader to tackle. What is also nice that the book is quite practical and have examples from various fields of science and engineering.

References

mark

Math books Applied for Good

Math books and more books on math

Following the path of applied mathematics and popular science with math inclination I want to bring to your attention a couple of books that some of you may find helpful if not insightful.

Oliver Heaviside’s Maxwell’s Equations

Actually, I would rather start from a book which is an amalgam of history and mathematical physics in one and it’s a book about the self-taught mathematical physicist Oliver Heaviside who brought to you the so called Four Maxwell’s equations.

equations

book_heaviside

The book is Oliver Heaviside: The Life, Work, and Times of an Electrical Genius of the Victorian Age written by Paul J. Nahin an emeritus prof. of Electrical Engineering in University Of New Hampshire which we’ll return to later in the post.  What is interesting about the books is that it has a right amount of math for readers who are interested not only to know who Oliver Heaviside was,  but also what he did as a physicist and engineer.

 

 

 

 

Okay, the books

While reading very interesting Applied Mathematics book by David J. Logan (3rd edition, Ch. 4.4 Green’s Functions, p. 253)

step_function

I was, as always, diverged by the mentioning of the Heaviside Step function in the text that I felt an urgent surge to check a biography of this incredible person and, lo an behold, I was able to find the Paul Nahin’s book mentioned above and also quite interesting and short  article in the Physics Today magazine Oliver Heaviside: A first-rate oddity

David J. Logan

Having mentioned, David Logan I should say that I am reading the 3rd edition of his book, which is available in Scribd if you have a membership there, and even for free for 30 days trial period. It is always possible to buy the 4th edition, but the price is, quite frankly, astronomical.

logan

Applied Mathematics 4th edition by David J. Logan. What I like about this book is the detailed examples that help you understand the content of the book better, but even more I like the way David Logan explains the physical rational behind the differential equations. It helps very much to know how and why this or that math technique is applied in practice. In addition, another applied mathematician Mark H. Holmes book’s is also mentioned by David Logan which you also may find useful.

 

 

 

Paul J. Nahin

Now that’s get back to Paul Nahin. It turn’s out he produced a whole series of books on Physics, Mathematics, Electrical Engineering and Computer Science which can be called popular, but actually are an essays full of wonderful applied mathematics. Paul is able to explain things in engaging and easy to understand manner. As people like to say, I wish I had come across his books earlier in my life, but it is what it is and it’s good that I was able to find them. Thanks to the Scribd digital library I was able to glimpsed through all of his books available there and I’d recommend to math inclined readers to check the following books.

simple_physics

 In Praise of Simple Physics: The Science and Mathematics behind Everyday Questions will take you into the physics journey that you could have been missing since your school or collage years. Maybe, you weren’t able  to understand it back then or had no time, but this time it will be different thanks to Paul’s ability to explain physics in an easy to grasp way.

 

 

 

 

And one additional book that I find quite impressing 

crunchung numbers

Number-Crunching: Taming Unruly Computational Problems from Mathematical Physics to Science Fiction as all books by Paul J. Nahin this one draws examples from different areas of exact sciences and engineering that will keep you awake at night following the stories and trying to solve the puzzles yourself.

 

 

 

 

Mark H. Holmes

holmes

Remember, I’ve mentioned Mark H. Holmes so he also wrote a couple of books on applied math, and I’d recommend you to check his Introduction to Numerical Methods in Differential Equations which I find also very useful and a helper while reading aforementioned books on applied math. Unlike his Introduction to the Foundations of Applied Mathematics, which I find cryptic due to the lack of detailed examples, Introduction to Numerical Methods has quite a few of them. This makes the book kind of easy to digest.

 

 

 

Last, but not least

To make sense in this whole unfamiliar forest of applied mathematics there is a nice book that has all you need in one place classified and summarized to be your guidance on your quest to master the math and apply it for good. It is

all_of_it

The Princeton Companion To Applied Mathematics.

 

 

 

 

 

 

 

Dare think, keep on going, and be carried forward on wings of math muse.

References

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.