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# Category Archives: Learning Math

## Determinants in Matrix Algebra: Why are they important?

I had a difficult time making sense of this topic. Good mathematicians frequently have trouble teaching math—I’m guessing—because they have mastered the art of thinking in numbers but are unable to translate that into English. Or perhaps—I’m also guessing—a subject … Continue reading

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## Matrix Multiplication Algebra

I wouldn’t wish pencil and paper matrix multiplication algebra on my worst enemy. Well, on second thought…… Anyway, Michael Kelley describes it as, “The trickiest thing you’ll need to do with matrices.” In Kelley’s Algebra, Chapter 9, pg 118-120, he … Continue reading

Posted in A Series about learning, APL and J, Do It Yourself Learning, Dr. Kenneth Iverson, Learning Math, Self Education
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## Matrix division and Cramer’s Rule

In this post, we will demonstrate how you can apply Cramer’s Rule in J, using a sample problem in Michael Kelley’s in his Algebra, pg. 126 Chapter 9. The original system of equations: … Continue reading

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## Matrix Division made simple

The following might be a somewhat advanced topic for some of you. But, don’t be intimidated, I actually think you’ll get it. Gary Helzer wrote An Encyclopedia of APL for I-APL Limited, which was part of British APL. Dr. … Continue reading

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## The Shape Command in J with Squares and Roots

Previously, I mentioned that W. Michael Kelley in his Algebra Book suggested you should memorize the first fifteen perfect squares. Then, in his Pre-Algebra book on pg 278, he suggests you memorize the first twenty square roots. I’ve never really … Continue reading

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## Exponents and Proofs in J

While I was writing the post on the first five cubes, I had to brush up again on the rules for multiplying exponents in Chapter 3, pg 34 of Michael Kelley’s Algebra. I didn’t remember the rules on why you … Continue reading

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## Cubes and Exponents

Remember in the post on Perfect Squares and Exponents that W. Michael Kelley in a sidebar on page 155 of his book on Algebra recommended memorizing the first 15 perfect sqaures. On that same page, he also recommended memorizing the first … Continue reading

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## Perfect Squares in J

In his book on Algebra, W. Michael Kelley has a sidebar note in Chapter 12, pg. 155, in which he suggests that students should memorize the first 15 perfect squares. Examples of a perfect square—a number multiplied times itself—would be … Continue reading

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## Millions, Billions, Trillions, What’s the Difference?

In the early years of my Community College teaching career, I read a book by John Allen Paulos, Innumeracy, showing the extent and the effects of poor math skills. I was all too aware of the high price one pays … Continue reading

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## Experts predict death toll in the thousands in L.A.; 7.5 magnitude earthquake likely before the end of the 21st century.

So says Dr. Lucy Jones, seismologist with the U.S. Geological Survey and Professor at Cal Tech, in Pasadena, California. She was interviewed by Melissa Crise of Fox News for a story published May 13, 2014. Dr. Jones is a familiar figure … Continue reading

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