Month: February 2020

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.

Planning in Software and QA Engineering

During my years at the college of engineering I had a short conversation with a PhD 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