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

Fixing a broken zipper slider. Fill your boots

slider_bigger

Do it yourself

This post is a little be unexpected, but nevertheless it may be useful to some of the readers of this blog.

The issue is that last weekend while having fun with my family outdoors I was skillful enough to brake the zipper slider of one of my beloved winter boots. Even though the boots weren’t new and showed early signs of wear and tear replacing them with a new pair of similar ones would cost me about 115 CAD. I knew that throwing the old boots only because of a broken slider wasn’t an option, so I resorted to trying to reattach it myself without first watching how to do it on the YoutTube. The result wasn’t encouraging, so I watched a couple of videos there, the most useful, I’ve attached at the bottom of the post. Following the video advice I ended up with a zipper slider in a really broken state as in the image above.

A fork stuck in the road

Having found myself and the boots in this awkward situation, the options were to buy a couple of new zipper sliders of varying sizes. The issue was I wasn’t sure what slider to chose on the Internet, since there were quite a few, and frankly speaking, I’m not a shoemaker expert. I was curious enough to notice that some descriptions for sliders had a Vislon term in them. So I searched for it and hooray a number of posts clarified that a zipper is more then meets the eye, and there are some things to know about them before any purchase.

Zipper sciences

Zippers have a number of distinct physical parameters:

  • Type
  • Size
  • Markings or absence of which
  • Lock mechanism

Below comes a more detailed description of each parameter.

Types

It turns out that there are two kind of zippers: Vislon and Coil. While the Vislon zipper has distinguishable teeth, the Coil more resembles a coil, hence its name.

zippers_shape

 

Sizes

As for the sizes, zippers are numbered starting from #1 to #10. The sizes are measured in inches or millimeters.  When the size is measured in a following fashion as it’s shown in the image below

size_zippers

To find a mapping from zipper number to zipper size, and vice versa, in inches/mm search the Internet.

Roughly it’s

Markings

If you think that determining the size of your zipper is easy, it’s yes or no.

Best case scenario – good markings

There are zippers, such as YKK that have proper markings on the back side of the zipper slider. Where the number, for example 5, stands for the zipper size number and CN or VS/V post-fixes stand for the zipper type. CN stands for Coil type and V/VS stands for Vislon type. In the image below it’s size number 5, Coil type YKK zipper slider.

ykk_marking

So – so scenario – some markings in unexpected places

Some zippers have no apparent markings, but upon thorough investigation it can be found at the front side of the slider like on the image below, which has size number 8 shown (though it resembles a letter B in this case)

marking_on_the_side

 

No markings – use your engineering skills, i.e. the ruler

Since the slider on my boots was a stealth one, it had no markings, I resorted to measuring the size using a good old ruler. And it measured to about 6.5-7 mm which could be size #6 or #7.

Locking mechanism

Some zipper sliders have a retractable pin or other means to lock the slider in place to prevent it from sliding. Other zippers can’t have this functionality and are plain non-locking sliders. My broken slider had the pin configuration as in the image below.

lock_pin

 

An ideal solution

Having watched on the YouTube a couple of video tutorials on how to reattach a slider or attach a new one, I got that it wasn’t gonna be an easy task. So I searched a little bit more and found a kind of ideal solution.

As you would expect the robust solution should be adjustable and easy to install zipper slider. The good news are that there is such a thing already in three sizes to rule them all. It’s a FixnZip.

This FixnZip consists of two metal parts that are easily install-able and work just like it should provided you had a correct size for the boots in hand. Actually, it is applicable to jacket, bags and other kinds of zippers. 

So in the end having the small size FixnZip for 25 CAD saved me about 90 CAD spared on not buying a new pair of boots. The lesson is do it yourself, and be happy.

shoes

 

References

Building your own computer language

Just code it

If you wanted to build your own computer language, but didn’t know how to start or thought you didn’t have time and skills to do this, then look no harder then the Crafting Interpreters book by Bob Nystrom on building a computer language from scratch. That’s it from the very beginning to the full fledged object oriented stuff.

Where do I find it?

Just visit this web page where Bob has a free of charge web book, still in the process of writing, were you can start to build you own language. You can call it BestLangEver or even something like Jabba, etc. The book is very detailed and explains thing in a clear and easy to understand manner. Thanks to the book I was able to understand how a Mark-and-Sweep garbage collector works and can be quite easily implemented. Bob has done a great work of bringing the art of language design to the masses.

What are you waiting for?

Start reading.

 

Read as if you edit. Editing Imbalanced Classification with Python

Reading can be hard, but rewarding

I like to read books. They provide me with the opportunity to discover new worlds and learn new things. Unlike other sources, e.g. YouTube tutorials, which I find a little bit distracting, books don’t seduce you to click on them, instead they lay on a flat surface and don’t care. In addition, it’s quite hard to jump from a book to a book in haphazard way reading them in parallel physically. But when you find an interesting book, say a novel, it can draw you attention and hold you captive until you finish reading it. And there are books that are interesting and at the same time require from a reader a certain amount of concentration and work that needs to be done to get the most out of reading a book.

I call such a reading a workout. It’s similar to physical exercises, that can be unpleasant at times, but it has a reward of deeper understanding and grasp of concepts. It also resembles editing a book, call it testing, even alpha testing if you have a software background. By reading a book, as if you edit it, and as such need to pay attention to details and working on it from A to Z, you are bound to better understand the information that the book tries to convey. 

Read as if you edit

With the recent wave of high interest in Machine and Deep Learning there are a lot of books published on the subject to satisfy hungry readers. The books are ranging from popular explanations for a general audience to technical books, that teach readers how to apply Machine Learning to day to day practical applications. Machine Learning Mastery web site provides a number of such books, that are written with a hands on experience first approach. This makes the books perfect candidates for the Read as if you edit approach, since it is the best way to get actual practical experience in Machine Learning by actually applying examples from each chapter in these books. For readers, who aren’t familiar with Machine Learning Mastery books, all of them (books) are structured  in a similar way, where each chapter has just enough theory to get you started using practical code samples.

It is possible to only read through the books, without running a single code sample having a feeling of understanding how things work and being happy with yourself. The issue is, this approach brings almost zero value and provides you with no real experience. Instead, think of yourself as an editor or a tester, who was tasked with finding mistakes, omissions, unclear explanations or wrong code samples. Doing this will help you get the most out of  the book since it forces you to actually run the code, play with it by adjusting it. It also helps you to get better understanding of the material by cross-referencing unclear points by searching on the internet or in other books. 

Don’t you think that read as if you edit approach is only applicable to Machine Learning books. I find it also useful in reading books on mathematics, physics and engineering. Actually, it can be applied to any source of written information, only then it becomes a critical reading approach, where you don’t blindly trust what you read, but instead analyze it and verify the information.

So how was it editing Imbalance Classification with Python book?

I very much liked editing this recent book, since it had enough theory, math and new machine learning concepts to get me excited to work with the book from start to finish. The book has about 450 pages of actual content and it took me about three hours a day for nine days to finish it. I can’t say that it was smooth and easy. The content, at least for me, required cross-checking it with other sources. The code samples required, not once, a need to reference Python libraries documentation and quick dives into sources about imbalanced classification, statistics and information theory.

All in all, reading this from A to Z made me realize the importance of knowing that the data could be imbalanced, as in case of anomaly detection, and one cannot train a model assuming an equal distribution between positive and negative classes, since such a model will tend to classify incorrectly in practice.

 

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.

On importance of a good pen

A pen is here to stay. Isn’t it?

Now days, that using computer programs to document various everyday activities from to-do lists to studies, one can ask whether there is still a need to have a pen in your arsenal. What’s the value of having such a heavy companion that requires paper to be functional and can’t be that easily corrected or deleted as a text in a word processor? It seems like there is no obvious answer that satisfies everyone, but definitely there’s one for me. Personally, I like to use a pen for writing to feel how I actually produce words in an antiquated analog way, instead of using discrete machines, except for this post. Text written with a pen does not require electricity to be useful, though it requires light to be seen. 

A pen to stick to

Having stated my affection to pens I personally recommend to stick with a pen that is durable, has a long lasting refill and has a beautiful embodiment. I think about fifteen years ago I found such a pen in the form of one of Parker’s low end models that are quite inexpensive, but deliver on refill longevity and durability. The pan in hand was Parker Jotter Originals Ballpoint Pen since 1954.

It’s slim and thin for touch, it’s small in size and its refill lasts almost forever even if you document lectures on history at the university. To these days I have one, but I actually prefer an older brother of this one.

A fountain pen, won’t last long enough

Generally speaking pen refills have a number of main types which are

  • Fountain using a refillable liquid ink
  • Ballpoint uses oil based ink
  • Rollerball uses water based ink

It was funny to actually try to write with a fountain pen such as, low end similar to Sonnet Stainless Steel.

What’s nice about a fountain pen is that it feels like writing in XIX century, but with the style come a number of drawbacks. The quality of written text  depends on the angle of the pen tip to the paper. A fountain ink is easily solvable by water drops which is unfortunate and the ink doesn’t last long enough, to say the least.

Is there anything else?

The true love of mine is another low end Parker pen which is a thicker version of the Jotter Originals one, and it’s Parker IM. It’s a little bit heavier than Jotter, but actually it feels nicer to handle it. It’s thicker and doesn’t press very hard against the fingers. And it has fancier finish than the Jotter. All in all this is the pen I value the most.

 

Does it really matter what pen it is?

In my opinion, what is the make and model of a pen doesn’t matter that much, but consider this.

  • The pens described in this post are reusable ones that are durable and can be used for dozen of years if not longer in comparison to plastic ones that get thrown to the garbage most of the time.
  • The refills that they use come in metal containers that can be recyclable or can degrade naturally unlike plastic ones, that again most of the time thrown into garbage.
  • Lastly, they may provide you with a real satisfaction from the writing process unlike the simpler plastic ones that merely do the task in hand.

Can you learn anything from books on Apollo program?

What this post is about?

If you are interested in Apollo Moon program and curious what books are worth reading on the subject, probably this post may help you.

So far, I’ve read more than a dozen of books on U.S. Apollo program which were written by people coming from all walks of life. There were flight directors and controllers, engineers, surely, astronauts, historians and journalists. As such, I tend to classify the books on Moon program into four main categories based on the background of the authors.

Books classification 

  • Engineers and scientists
    • Books written by engineers, including flight directors and controllers who took part in the Apollo program. These tend to be more technical and down to earth with lots of details for technically inclined readers
  • Scientists and engineers beyond Apollo
    • Books written by authors with scientific background who were not part of Apollo program
  •  Astronauts
    • Books written by astronauts. These ones range from technical to more emotional ones
  • Historians and journalists
    • Books written by historians and journalists

Examples

  • Engineers and scientists
    • Flight: My Life in Mission Control by Christopher Kraft

    • Failure Is Not an Option: Mission Control From Mercury to Apollo 13 and Beyond by Gene Kranz

    • Go, Flight!: The Unsung Heroes of Mission Control, 1965–1992 by Rick HoustonMilt Heflin, et al. 

    • Safely to Earth: The Men and Women Who Brought the Astronauts Home by Jack Clemons

    • Sunburst and Luminary: An Apollo Memoir by Don Eyles

    • Left Brains for the Right Stuff: Computers, Space, and History by Hugh Blair-Smith

  • Scientists and engineers beyond Apollo
    • Digital Apollo: Human and Machine in Spaceflight by David A. Mindell

    • The Apollo Guidance Computer: Architecture and Operation by Frank O’Brien

    • The Apollo Chronicles: Engineering America’s First Moon Missions by Brandon R. Brown

  •  Astronauts
    • Technical 
      • Two Sides of the Moon: Our Story of the Cold War Space Race by David Scott and Alexei Leonov
    • Emotional 
      • Carrying the Fire: An Astronaut’s Journeys by Michael Collins 

      • The Last Man on the Moon: Astronaut Eugene Cernan and America’s Race in Space by Eugene Cernan

  • Historians and journalists
    • Historians
      • A Man on the Moon: The Voyages of the Apollo Astronauts by Andrew Chaikin

      • First Man: The Life of Neil A. Armstrong by James R. Hansen

    • Journalists
      • Apollo 8: The Thrilling Story of the First Mission to the Moon by Jeffrey Kluger

      • Apollo 13 by Jeffrey Kluger

      • Disaster Strikes!: The Most Dangerous Space Missions of All Time by Jeffrey Kluger

 

Personal viewpoint

I personally, liked the most books from first and second category written by engineers and scientists who took an active part in the program and others who were influenced by the Apollo events and became engineers and scientists themselves fascinated with Lunar program. 

What I like about more technical books is the explanation of how certain systems were envisioned and designed. How did they worked in practice and what challenges engineers faced throughout the systems’ life and how they were tackled. 

Why should you care about technical books?

If you are a technically inclined person, reading the technical books on Apollo program may bring you enjoyment of learning how various types of obstacles were solved by people working day to day on the most challenging aspect of then never done before and exciting endeavor. You also may trace the beginnings of the U.S. space program that can be felt to these days in managing International Space Station (ISS), unmanned space vehicles traversing our solar system and beyond and private space companies.