Tag Archives: Online Articles

Practical Matrix Mathematics in Canada

This past week I answered a reader’s question to Decoded Science with the online article, “Practical Uses of Matrix Mathematics“. That reader wanted to know about using matrices in daily life; but so much depends on one’s own day-to-day life.

"Matrix" image by Lakeworks via Wikimedia Commons
“Matrix” image by Lakeworks via Wikimedia Commons

Learn to Apply Matrix Math

Actually there are many, many fields in science that use matrix arithmetic. These include statistical applications (from sociology through “hard sciences”), chemistry and physics, and electrical engineering. As well, the discipline of mathematics studies how matrix math works: the rules, the tricks, and the relationships with other disciplines.

Before applying matrix mathematics, you have to learn the math; and also learn about the discipline to which it applies.

I just glanced over some courses offered by the University of Waterloo, where I earned my B.Math degree several decades ago. The Math faculty introduces matrix mathematics in the linear algebra courses; this provides a strong theoretical basis for matrix math. Meanwhile, an Electrical Engineering class approaches matrices from the practical side, where you solve simultaneous equations to analyze electrical circuits. In my view, the University of Waterloo remains one institutions of higher learning in Ontario.

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So if you’re heading for university in some discipline, check the course lists for topics like “matrix” or “vectors and matrices”; “linear algebra”; or “simultaneous equations”. If that’s part of your future, plan to enjoy manipulating rows and columns in matrices.

Thirsty for more information on this topic? Start with the paperback “Linear Algebra for Dummies” from Amazon Canada or Amazon USA. Mary Jane Sterling introduces vectors and matrices, simultaneous equations, and explains how to compute determinants and eigenvectors. Plus, she finishes with “real-world applications”… which is just what my Decoded Science reader wanted.

Professional Writing by DeHaan Services

DeHaan Services writes web site or advertising copy for clients. Our skills are demonstrated in online articles in Decoded Science, Decoded Pregnancy, and DeHaan Fitness. That’s why we highlight these online articles on this blog page.

Read my writing tip in “Quick Response for Matrix Math Application Examples“, in my Blog of Writing. I based this writing tip on my preparation for the Decoded Science article.

To only see our Toronto events (for things to do in Toronto) or fitness articles, please click on the appropriate category in the “Categories” section at the bottom of the right-hand margin.

Thank you for reading about practical matrix mathematics in Canada.

One SMART Goal for Toronto Mayor Rob Ford is Fitness

Once again Toronto Mayor Rob Ford placed the spotlight on his personal quest for fitness and a healthy weight loss. My recent online article in DeHaan Fitness, “Toronto Mayor Rob Ford Avoids SMART Goal for Fitness“, explains how Mayor Ford’s approaches to losing weight compare with following SMART goal methods.

"Toronto Mayor Rob Ford campaigns with puppet in 2010" image by Shaun Merritt
“Toronto Mayor Rob Ford campaigns with puppet in 2010” image by Shaun Merritt

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Will Toronto Mayor Rob Ford Lose More Weight This Time?

My online article starts by explaining the SMART acronym; then it moves on to compare the 2012 “Cut the Waist” campaign with Mayor Ford’s current fitness announcement.

I’d covered “Cut the Waist” back in 2012, which was a friendly contest between the mayor and his brother, Toronto City Councillor Doug Ford. Let’s hope Mayor Ford has more success over then next half year than he did in 2012.

Certainly his approach is different. In my view, the biggest improvement is that he has “a team” to advise and support him. (Whether he’s chosen the best team is a matter of some speculation). The next six months should reveal whether he loses more weight with his current strategy. And it would be interesting if he reveals whose long-term advice and coaching he follows…if anyone’s.

Whatever his politics, whatever substances he uses or stops using, and whatever successes he finds in any future political campaigns, let’s hope he can succeed in his personal quest for better health through fitness.

Professional Writing by DeHaan Services

DeHaan Services writes web site or advertising copy for clients. Our skills are demonstrated in online articles in Decoded Science, Decoded Pregnancy and DeHaan Fitness. That’s why we highlight these online articles on this blog page. I’ve also publicized the main article in “New Approaches by Toronto Mayor Rob Ford and DeHaan Fitness“, where my Blog of Writing offers a free writing tip.

Are you a Canadian trying to lose weight, or just to check your weight accurately? The “Smart Weight DVS150 Digital Scale”  measures up to 330 pounds, but you can switch to metric kilograms. Save battery life with its automatic “Step On” to turn it on; it powers off after 10 seconds of inactivity. The CR2032 lithium battery is a small button cell, available online at The Source and in other retail stores in Canada. It has a perfect 5-star review at Amazon.ca based on a handful of reviews.

And if you are trying to lose weight for a second or third time, it’s smart to get advice and support.

To only see things to do in Toronto, or fitness articles, please click on the appropriate category in the “Categories” section at the bottom of the right-hand margin.

Thank you for reading about Toronto Mayor Rob Ford’s renewed fitness goal of November 2013.

From Kurt Godel to God via Modal Logic

My recent Decoded Science article, “How Modal Logic Proved Godel was Right, and God Exists“, explains the basics behind a brief but bold claim by 20th century mathematician Kurt Gödel.

"Kurt Godel" via Arithmeum Museum in Bonn
“Kurt Godel” via Arithmeum Museum in Bonn

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Introducing Gödel’s “God Theorem”

Gödel’s “God Theorem” garnered news internationally in the past month because German researchers succeeded in running a variety of computer programs that verified the “modal logic” which the theorem used.

My article summarizes the logic of Gödel’s God Theorem, and then puts the focus on modal logic. (The very quick synopsis: modal logic deals with “possibility” and “necessity” on top of more common logical terms such as “true/false”, “for all”, “if-then”, and “there exists”).

Gödel is most famous for his “Incompleteness Theorem”, which states that sufficiently powerful mathematics can not possibly be “complete”. (Such a powerful mathematics cannot generate every statement which is true within its own framework).

Earlier, Gödel had proven a “Completeness Theorem”: sufficiently simple math can generate all true statements within its framework. (For example: if you start with the number ‘1’, and only allow addition, and allow {1+1=2, (1+2=3, 2+1=3), (1+3=4, 2+2=4, 3+1=4),…}, then eventually you will generate any “n+m=[n+m]”. Simple, yes? Almost too simple).

For this DeHaan Services article, I tried to find a Canadian connection for Gödel. The closest relationships that I found were essays written at Canadian universities, such as the PDF “Kurt Gödel and Computability Theory” from the University of Calgary.

In another promotional article, my “The Proof of God: a New Niche for Kurt Godel” includes a niche writing tip.

Learn More about Kurt Gödel and his Incompleteness Theorem

Learn more about the man behind the Incompleteness Theorem, in the Canadian or American version of “Incompleteness: The Proof and Paradox of Kurt Gödel” via Amazon Kindle.
Hofstadter’s “Godel, Escher, Bach: An Eternal Golden Braid” is a fun and easy-to-read explanation of the Incompleteness Theorem. Amazon sells the paperback to Canadians and Americans.

Professional Writing by DeHaan Services

DeHaan Services writes web site or advertising copy for clients. Our skills are demonstrated in online articles in Decoded Science, Decoded Pregnancy and DeHaan Fitness. That’s why we highlight these online articles on this blog page.

Thank you for reading about Kurt Gödel’s proof that God exists.