Все как обычно

Как обычно

День начинался как обычно: дверь в комнату была крепко заперта, окна плотно закрыты, шторы пропускают лишь малый лучь света. Боб как всегда, сидит за столом и первым делом проверяет последние новости на компьютере. Да, все как всегда, и это придает увереность в завтрашнем, ну, и сегодняшнем, дне.

– Итак, – подумал Боб. – Что же там новенького происходит на просторах нашего мира?

Первым делом он открыл сайт Си-Эн-Эн, так как это был один из самых известных новостных каналов, новостям которму он доверял больше всего. Крупный заголовок вверху страницы красным цветом сообщал: “В США зарегистрирован первый случай особенно странной аномали, жена коснулась руки своего мужа!” Не веря своим глазам, Боб нервно перечитал сообщение еще раз.

“Данные пока скудны, но по всей вероятности, идет речь о самом черезвычайном проишествии в истории США, а может даже и всей планеты. Пока, еще рано впадать в панику, но по всей видимости, речь идет о пока что невстречавшемся вирусе, который скорее всего и паразил женщину, совершившую этот немыслимый поступок.”

Боба охватила дрожь, и он почувствовал, как струйки пота потекли у него по спине.

– Этого не может быть! – с ужасом подумал Боб. – Ведь еще вчера, такого никто не мог себе представить. Все шло своим чередом. Как всегда, все члены семьи передвигались по дому только по одиночке, строго по заранее устоновленному расписанию, тем самым предотвращая малейшую возможность физического контакта. Все внутренние камеры наблюденя встроенные в двери и стены дома, только помогали соблюсти этот распорядок. Малейшее движение регистрировалось, и было показано в виде трехмерной голлограмы, заменившей экраны, еще десятилетия назад.

Боб украдкой посмотрел в щель между штор. На как всегда пустынных улицах только дроны доставки создавали до боли знакомый фоновый шум, который воспринимали микрофоны по периметру дома и передавали на динамики в комнате Боба. Дроны точно свора пчел жужжали и летали в разных направлениях. – Ну, хоть это еще как обычно.

– Интересно, что пишут про это зарубежные сайты, – подумал Боб. Он открыл новую страницу и набрал имя сайта КНР.сом, того самого, который довольно подробно и точно овсещал пару лет назад экономический кризис в США, что отбросил страну в своем развитии на десятки лет назад. – Да, теперь Китай занимает то место в мире, что США так долго удерживали несколько столетий подряд.

-Черный заголовк на английском гласил: “Камеры наблюдения в доме, где был зафиксирован этот невообразимй случай физического контакта между людьми, также записали отклонения в обычном поведении женщины. На протяжении последних дней, она пыталась внести изменения в программу планирования перемещений по дому, с неясной целью. Объяснить эту аномалию пытаются лучшие ученые по всему миру. Всемирная Организация Здравоохранения в замешательстве. Некоторые ученые, робко, высказывают мнение, что, возможно, только новый тип компьютерного, быстромутирующего вируса мог вызвать такие изменения в психике женщины. Но как такой вирус мог возникнуть в рядовом американском доме остается загадкой.”

-Этого не может быть, – подумал Боб – Компьютерные вирусы, способные заражать людей, хотя и существовали, но были строго запрещены, как особо опасное биологическое оружие, которое охранялось за семью замками.

-Как вообще такой вирус мог попасть в сеть, и как он попал в самый обыкновенный дом? И вообще, что Боб знал о компьютерных вирусах, способных используя, вездесущие трехмерные репликаторы, в народе, известные как 3D-принтеры, создавать свои биологические копии, способные паражать живие организмы.

-Все научные разработки по этой теме были засекречены, ведь так? И только несколько человек во всем мире, имели доступ к этой технологии, но это только основываясь на общедоступных данных, – вспомнил Боб.

Что делать?

Размышления Боба прервал пронзительный вой донесшийся из динамиков. Это был из ряда вон выходящий случай, уже второй за сегодня, – в испуге подумал Боб.

Этот сигнал значил то, что всемирная система слежения за состоянием сети регистрирует изменения в поведении сразу множества людей. Искуственный интеллект, который контроллировал  всех роботов отвечающих за производство товаров потребления и дронов, которые их доставляли адресатам, также вел тотальную, но незаметную, слежку за тем, как вели себя люди день ото дня. Люди не догадывались о том насколько она была тотальной, но даже зная это, они бы только были спокойнее, что не только они стоят на страже соблюдения абсолютной физической изоляции. Даже дети наизусть знали и тысячи раз репетировали, что требовал протокол самоизоляции в таких случаях: требовалось срочно одеть защитный скафандр, до того как система безопасности дома включит насосы для откачки, и так фильтруемого, воздуха. На все приготовления отвдилось несколько минут, чтобы быстро вытащить, уже заранее готовый скафандр, совмещенный с гермошлемом. Боб молнией метнулся к шкафу в стене, пулей вскочил в скафандр и быстро закрыл его. Послышалось мерное шипение кислорода, который стал закачиваться внутрь. Потный, и тяжело дыша, Боб включил беспроводную трансляцию последних новостей прямо на стекло гермошлема. Благо, что перчатки были ненужны, так как управлять изображением можно было лишь с помощью мыслей, благодаря датчикам, встроенным в шлем, который плотно прилегал к голове Боба.

Главная новость в Си-Эн-Эн вогнала Боба в штопор.

-По последним данным что мы имеем, доселе неизвестный вирус поразил многие тысячи людей и с каджой минутой идет экспоненциальный рост зараженных. Система слежения за поведением людей регистрирует множество физических контактов между людьми, таких как касания, робкие прикосновения и, даже, обятия! Да вы не ослышались, самое страшное о чем мы и не могли помыслить еще вчера произошло. Люди обнимаются, и как дальше будут развиваться события никто толком предсказть не может, – сказал диктор.

-Искуственный интеллект, уже остановил передвижение всех дронов. Идет проверка возможности включения системы автоматического усыпления, существующей в каждом доме, чтобы предотвратить эту эпидемию, гразящую изменить наш мир.

-Да, ситуация из ряда вон выходящая. Президент и правительство делают все возможное, чтобы оценит опастность ситуации и принимают меры для предотвращения далнейшего распостранения вируса.

– Главное, без паники!

– Ну, а пока, послушайте хит сезона – “Все как обычно”.

Drums Lead The Way

josh-sorenson-MjIMc6uhwrE-unsplash

Photo by Josh Sorenson on Unsplash

Unexpected turn of events

If you didn’t know it turns out that I play drums a little bit. So after watching quite a few videos on the YouTube, I decided that there may be a merit to share the best of them with other musicians or people who just like to listen to good music. So, I created a public Facebook group called Drums Lead The Way

What this group is all about?

The main purpose of this group is to share useful information mostly about the world of drums, such as helpful drum tutorials from YouTube, Drumeo etc. but also share good music and other stuff related to drums. It seems if you are interested in drums, it’s worth to give it a try and maybe even contribute by providing your own tips and tricks.

So take care and keep drumming!

Now it is the best time to get to the basement and keep on drumming, while the virus is doing its nasty thing outside. 

How To Do It. Is the best type of a blog post

Connected world

In this post I want to thank all the people who took part in creating the Internet. And this is because thanks to the Internet I am where I am, doing the work I do and writing these words right now, which later will be read by people just like you thanks to the Internet.

What is nice about the Internet is that it allows you to make unexpected connections throughout the world with almost anyone you can imagine. You can meet your favorite sci-fi author, or maybe an inventor, the scientist you always admired or maybe reconnect with your friends and family. In addition, Internet allows you to find a job, apply for a job and do your work, surely, it depends on the type of the work, but it’s hard to imagine any type of work that doesn’t require some rudimentary access to the Internet.

How to do it yourself

This kind of long introduction brings me to the title of this post. In my opinion, the most useful, helpful and effective way of communicating on the Internet is by producing How To Do It, Fix It, Create It etc. posts. Think for example, about millions of video tutorials on YouTube, be it music, drawing, cooking, fixing machinery and what not. The same goes about written tutorials through out the web, that could potentially teach you almost everything about anything.

Personally, based on the statistics of the posts I wrote on this blog the most viewed ones were posts related to programming, Machine and Deep Learning. It’s not surprising I think, since theses posts were about How To install such an such software library, such and such book on Machine Learning, such and such tutorials on how to get things done.

I remember back in Ukraine when I had no Internet we went to a number of libraries trying to win a crossword contest held by a local newspaper. It was kind of tedious process. Nowadays, it is possible to solve any crossword fast and easy using the Internet. 

Get to the bottom of it

The main point is that writing, filming or whatever simple and short How To tutorial may be beneficial in the long run to some person out-there, who’ll be very thankful to accomplish things that were not possible without you sharing your knowledge and experience. I myself used quite a few tutorials on the Internet that helped me fix my car, fix cell phones, tablets, computers. It helped me install or remove software, find very exciting things in life, find an interesting job and be in touch with incredible people coming from around the globe. So, when next time you postpone sharing things that can make life easier to somebody, think again and get to the bottom of it and create a nice tutorial explaining how to stop procrastinating and get going.

Important ingredients in How To Do posts

Judging by the posts I wrote, that resonated with readers I think what the How To Do post should contain is a number of ingredients.

  • First of all, the topic of the post should resonate with yourself and be interesting to you.
  • Second, you shouldn’t be an expert about the topic of the post, but you should be excited about it enough to be able to learn what it requires to explain it in simple terms and clear steps.
  • Third, if the posts can make even a single person more happier by fixing his or her situation, then it’s worth investing time and effort in preparing it in the first place.

 

So, if you want to share some piece of knowledge that can help others, do not hesitate and share it. In the end, it may even help you later, when you’ll forget how to do it.

Planning can change your life

Planning may be annoying, but it works

This post about the virtue of planning before taking any action or no action. 

Do you plan your actions beforehand? Do you have any goals in life? Do you have dreams that are still dreams? Then you are not alone. Do you know, that making a habit of planning your actions may drastically improve the chances of you achieving your goals, if you have ones, or helping you to come up with some in the first place.

Planning in the self help movement

There are plenty of books and courses on self-help that promote planning, and I have to say that this thing is actually, useful and helpful in the short and long runs. The planning exercise is quite simple. 

  1. Decide what you want to achieve in near term. Think of a dream you have for a long time or some goal that is somehow at the background currently.
  2. Write down these goals on a piece of paper or using other convenient means. While doing so state the goals to be achieved in the terms of answering  Who, What, Where, When and How  to be more precise, since it helps in visualizing a possible way of action. The goal should be framed in the present tense in a positive way.
  3. Think what you can action right away to start moving towards your goals.
  4. Each day review the list of the goals your composed and revise it if needed with new goals, new details.

Here comes an example

Say the goal is to proceed with acquiring working knowledge of applied mathematics. Then I write:

Goal: advancing in Applied Mathematics

  1. Starting today I work on the book Mathematical Modeling on evenings, at least for an hour-two, while solving as many tasks for each chapter as possible.
  2. When not working through that book,  I read the book on Applied Mathematics  and solve the tasks in it too.
  3. While being outside I carry at all times another popular book on mathematics for not to waste time.
  4. I aggregate and classify useful material on applied mathematics that I come across, for it to be easily retrieved when needed.

Planing in Software and QA Engineering

During my years at the college of engineering I had a short conversation with a doctor in Electronics Engineering who was a scientist and engineer. We talked about the differences of scientific and engineering approaches. Then he said that simply put scientist are interested in the edge cases where theory may not work and fail, while engineers are quite opposite and interested in things that work most of the time without failing. This crucial difference also applicable to the field of Software development and testing.

  • Software engineers being engineers are mostly concerned with the cases when software should work, while tending to put less emphasis on the edge cases or more precisely, boundary conditions and unexpected events.
  • Software testing engineers or tester on the other hand, are just like scientist more interested in checking unusual cases, when the software possibly could fail, break or behave unexpectedly.

How is that related to planning you may ask? Planning in software or hardware worlds allows you make less mistakes before actually carrying out the work. Thoroughly thinking about requirements with stakeholders, be it waterfall or scrum way of accomplishing projects, is invaluable instrument.

Just like in the example for achieving good understanding of  applied mathematics, planning in Software helps by framing the purpose of each functionality to be implemented in the form of Who, What, Where, When and How questions.

 

The solution is quite simple

  1. Decide what you want to achieve
  2. Clearly describe it on a piece of paper  with as much details as possible
  3. Each day review you goals and take action to move towards them
  4. Then you’ll surprise yourself

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

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.