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old-school math

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In preparation for an engineering course I'm taking in the fall I've been revewing my linear algebra and some calculus. I'll sit at lunch and work problems with pencil and paper. I find it enjoyable, actually - relaxing. But a recent-grad engineer I work with just chuckles at me and claims that he'd let Excel handle such calculations like the adjoint. For me, there's some value in being able to work all of the problem with pencil in hand. I joke that this makes me "old school". As I've not attended an engineering class at a university in a long time and am curious to see how things have changed.

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In preparation for an engineering course I'm taking in the fall I've been revewing my linear algebra and some calculus. I'll sit at lunch and work problems with pencil and paper. I find it enjoyable, actually - relaxing. But a recent-grad engineer I work with just chuckles at me and claims that he'd let Excel handle such calculations like the adjoint. For me, there's some value in being able to work all of the problem with pencil in hand. I joke that this makes me "old school". As I've not attended an engineering class at a university in a long time and am curious to see how things have changed.

You are on the right track. You will never need batteries or a power cord. Just a pencil and paper.

Bob Kolker

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Yes you are on the right track, and for more than just not needing batteries that may be outlawed by the viros.

As the famous applied mathematician Richard Hamming wrote in his book Numerical Methods for Scientists and Engineers, "The purpose of computing is insight, not numbers". By working out basic calculations by hand you are learning more about the relationships, seeing the relative orders of magnitudes that appear and their affects on precision in calculations, and practicing the art of estimating magnitudes as a check on the reasonableness of your results. You will often use a calculator or computer for calculations, especially lengthy, time consuming ones, and that is a great value. But every engineer should understand the nature of the numerical calculations he is making and not treat them as a "black box". There have been notorious examples of engineers making major blunders in engineering and design because they didn't realize that aspects of the patterns in results of calculations were artifacts of the numerical methods employed in a program and not representative of an important physical characteristic.

Engineering education has changed in this respect. Slide rules were replaced with simple calculators, then programmable caculators, then desktop computers, and now laptops. (The future may bring coprocessor brain implants.) Along the way the power of computers and numerical and engineering software for extensive calculations has progressively increased enormously, along with the ease of their use and the sophistication of the kinds of analysis you can now do routinely.

You will also find powerful symbolic computing programs like Maple V and Mathematica for algebraic manipulations -- like the evaluation of derivatives and integrals in basic calculus -- to obtain a closed form result. That gives much more insight than numerical results alone. But as in knowing how to do calculations of numbers by hand, you still need to know how the algebra is done for the increased understanding it provides.

When you do use a computer for general calculations, use Matlab most of the time, not Excel, especially for linear algebra and matrices. It was originally developed for matrices, and has operations like adjoints in one step. As a registered student you can get a basic version of Matlab inexpensively.

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When you do use a computer for general calculations, use Matlab most of the time, not Excel, especially for linear algebra and matrices. It was originally developed for matrices, and has operations like adjoints in one step. As a registered student you can get a basic version of Matlab inexpensively.
Yes, I was just researching that yesterday. Thanks.

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When you do use a computer for general calculations, use Matlab most of the time, not Excel, especially for linear algebra and matrices. It was originally developed for matrices, and has operations like adjoints in one step. As a registered student you can get a basic version of Matlab inexpensively.
Yes, I was just researching that yesterday. Thanks.

Yes, MATLAB is excellent for matrix manipulation and numerical solutions, but even the student edition is fairly expensive (~$100). If you want a free program that has a large portion of the functionality of MATLAB and similar syntax, try SCILAB (here).

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Yes, MATLAB is excellent for matrix manipulation and numerical solutions, but even the student edition is fairly expensive (~$100). If you want a free program that has a large portion of the functionality of MATLAB and similar syntax, try SCILAB (here).

MATLAB costs about as much as one new textbook ... but if anybody wants to tinker with another monetarily free system, the Octave project (http://www.gnu.org/software/octave/) is actually designed to be directly compatible with MATLAB syntax and is available for every major platform, though unfortunately associated with the scummy GNU organization.

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MATLAB costs about as much as one new textbook ... but if anybody wants to tinker with another monetarily free system, the Octave project (http://www.gnu.org/software/octave/) is actually designed to be directly compatible with MATLAB syntax and is available for every major platform, though unfortunately associated with the scummy GNU organization.

The cost of textbooks commonly being around $100 each is another big change in engineering education. The prices seem to have skyrocketed for no obvious reason, with even older classics, or newer editions of the older books, that used to cost around $10 now selling at ten times what they used to (with no GNU substitutes). A lot of newer books have little or no improvement in content (or worse) but are promoted with colorful plastic covers and fancy formatting -- that is sometimes useful and often a distractiing 'eye candy' -- which is now much cheaper to produce using computer publishing software.

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The cost of textbooks commonly being around $100 each is another big change in engineering education. The prices seem to have skyrocketed for no obvious reason, with even older classics, or newer editions of the older books, that used to cost around $10 now selling at ten times what they used to (with no GNU substitutes). A lot of newer books have little or no improvement in content (or worse) but are promoted with colorful plastic covers and fancy formatting -- that is sometimes useful and often a distractiing 'eye candy' -- which is now much cheaper to produce using computer publishing software.

This is certainly my experience. I have, for example, two different editions of Mechanical Engineering Design by Shigley and Mischke. The older one (a fifth edition) I purchased for less than $20, whereas the latest edition (the ninth, I believe) cost $195! The only additions were pretty, but otherwise useless, pictures and some brief sections on computational methods.

Not only are the prices rediculous, but the writing style is horrific. It is as if they go out of their way to use circumlocutions. I hope I never see "is the fact that" ever again.

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The cost of textbooks commonly being around $100 each is another big change in engineering education. The prices seem to have skyrocketed for no obvious reason, with even older classics, or newer editions of the older books, that used to cost around $10 now selling at ten times what they used to (with no GNU substitutes). A lot of newer books have little or no improvement in content (or worse) but are promoted with colorful plastic covers and fancy formatting -- that is sometimes useful and often a distractiing 'eye candy' -- which is now much cheaper to produce using computer publishing software.

Two days ago I went to the university library to rent an Inorganic Chemistry book, and the trend in those particular textbooks over the last 60 years was quite sobering. It's as if the authors slowly but surely understood the fact that they were dealing with a progressively less and less rigorously prepared audience, with increasingly smaller and smaller attention spans that had to be compensated for with thousands of graphics.

It seems that 60 years ago you would have just a single monolith published for a subject that would be all-encompassing, perfectly written, and incredibly rigorous. Now we have "Introduction to _____" as well as general intro textbooks to prepare for the "Introduction to...". I understand part of it is because of the modern cheap use of computer generated graphics, but still the decline in rigor seems evident.

As an example, I've seen cases where the introductory textbooks are so watered down in an attempt to ease comprehension that they basically destroy the integrity of the content. My girlfriend and I were both horrified the other day by the incredibly sloppy language in an introductory chemistry book when the author said "water and oil repel each other because water is polar and oil is non-polar" which is a brutal mishandling of what is actually happening with the physical mechanism because if taken literally it would make the naive student think that polar and non-polar molecules actually have a force of repulsion that causes water and oil to separate.

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The cost of textbooks commonly being around $100 each is another big change in engineering education. The prices seem to have skyrocketed for no obvious reason, with even older classics, or newer editions of the older books, that used to cost around $10 now selling at ten times what they used to (with no GNU substitutes). A lot of newer books have little or no improvement in content (or worse) but are promoted with colorful plastic covers and fancy formatting -- that is sometimes useful and often a distractiing 'eye candy' -- which is now much cheaper to produce using computer publishing software.

Part of it is because of a university enforced monopoly; a professor will write a book for the course he teaches, and that textbook will only be sold at the university bookstore.

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...but the writing style is horrific. It is as if they go out of their way to use circumlocutions. I hope I never see "is the fact that" ever again.

Which can only be a result of the fact that basic courses on English grammar, composition, etc, are all but gone in all levels of education in America (even within the curriculum of university English degrees!).

I am reminded of a conversation recently with a European, comparing our respective education systems:

Carlos: In America we are never taught grammar at all.

European: Oh come on! You mean never once in your education you were shown how to diagram a sentence, how to identify the indirect-object, etc?

Carlos: Nope, literally never at all.

European: But that's ridiculous! How can you even write?

Carlos: We can't...

This same person also noted that she was very confused to see written on each question of the chemistry tests for undergraduate students the phrase "Please write grammatically correct, complete sentences."

That you would even have to remind your students to write in complete, correct sentences seemed so unusual and redundant to her because the concept of an educated populace being completely incompetent with basic writing skills with its own language was completely alien to her.

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As a general tip for math study with respect to engineering/science, something that I've found useful is to practice working out by hand example problems or equations from memory in many different notations; it is often a very quick diagnostic tool for determining whether I remember some equation or chain of reasoning purely by blind memorization of math symbols or if I really understand the different mathematical concepts there as well as their interrelations.

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This is certainly my experience. I have, for example, two different editions of Mechanical Engineering Design by Shigley and Mischke. The older one (a fifth edition) I purchased for less than $20, whereas the latest edition (the ninth, I believe) cost $195! The only additions were pretty, but otherwise useless, pictures and some brief sections on computational methods.

Not only are the prices rediculous, but the writing style is horrific. It is as if they go out of their way to use circumlocutions. I hope I never see "is the fact that" ever again.

I have this book from my college days and use it regularly, still. That's it...I have to look up "circumlocutions" now.

A forum member suggested a book "Calculus Made Easy" and I've been playing (as opposed to "working") my way through it. I really like how it was written - back in ~1942!

Thanks all for the input regarding Matlab and cheaper options.

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