Resources for Self-Education in Mathematics, Physics, and Engineering

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MartinLFletcher
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Resources for Self-Education in Mathematics, Physics, and Engineering

Post by MartinLFletcher » Sat Dec 31, 2022 8:02 am

Many of history’s most accomplished scientists and inventors were self-educated. Examples include steam engine pioneer James Watt, inventor and businessman Thomas Edison, and visionary Nikola Tesla.

Clearly “credentials” and a university “education” are not prerequisites for accomplishment in mathematics, the physical sciences, or engineering.

There are many resources available for anyone who has an interest in learning these subjects on their own.

A series of books that I’ve found particularly useful for self-education are the Schaum’s Outline series. These are inexpensive, large format paperbacks on a variety of topics, ranging from elementary algebra and basic electricity to tensor calculus and magnetic field theory. Each chapter has a brief review of relevant principles and theory, followed by a large number of solved problems to allow the reader to practice. When I was studying engineering I would always buy a copy of the Schaum’s Outline for any course I was taking along with the recommended textbook. They were a huge help in learning the material and I still have copies of many of them (some of first published in the 1950s and still in print today!)

Another excellent collection of books is the “...for Beginners” series by Dr. Steve Warner. These books cover such seemingly abstruse fields of mathematics such as set theory, abstract algebra, and topology—but they indeed are “for beginners.” The books are so clearly written that a motivated reader needs only an understanding of basic algebra to learn the material—illustrating one of my favorite quotes, mathematician Sylvanus Thompson’s famous dictum, “What one fool can do, another can.”

Many excellent books are also available through Dover Books, a company that publishes reprints of classic texts on mathematics, engineering, and the physical sciences. Some of their books, however, are definitely not “for beginners.” The particularly difficult ones are generally translations of Russian texts. Probably best to avoid those...

If you prefer learning through video, Amazon Prime offers the Great Courses video series. In this series, the best professors in a variety of disciplines conduct classes in their specialty. The courses are well done, the productions are professional, and the subjects range from algebra to multivariate calculus and organic chemistry. If you prefer not to deal with Amazon, the courses are also available directly from Great Courses.

Finally, there are a number of programs and apps that are extraordinarily helpful for the self-learner. One I use nearly every day is wxMaxima, a freeware Computer Algebra System. If you’re not familiar with this type of program, a CAS allows the manipulation and solution of symbolic mathematical equations. When I first used one in the 1990s, and watched the program solve a problem in seconds that would have taken me the better part of a day and dozens of sheets of paper to work out, I stared for several minutes at the screen in awe while the opening strains of “Also Sprach Zarathustra” played in my mind.

A simpler, but still powerful, app for mathematics is iHP48 by Alexis Lorca. It duplicates, on a phone or tablet, Hewlett-Packard's HP-48 calculator, the zenith of handheld calculator development.

Another very useful app is Quizlet, made by Quizlet Inc. It’s essentially a computerized flashcard system, with various features that help memorize almost any sort of material. I use it daily.

For learning chemistry, there is the Periodic Table Quiz, by Atlas Educational Software. It includes a number of games for learning properties of chemical elements, such as atomic number, atomic mass, and element symbols.

Finally, a thorough chemical reference is the Periodic Table app by Nikita Chernykh. It contains an exhaustive reference on the elements, arranged as a periodic table.

I hope this brief summary has been helpful to those interested in self-education. I hope to do a similar post on mnemonic, or memory, techniques soon.

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Jim Mathias
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Re: Resources for Self-Education in Mathematics, Physics, and Engineering

Post by Jim Mathias » Sat Dec 31, 2022 9:13 am

Thank you for this post, Martin. The book recommendations seem valuable to the homeschooler.
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MartinLFletcher
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Re: Resources for Self-Education in Mathematics, Physics, and Engineering

Post by MartinLFletcher » Fri Jan 06, 2023 10:34 pm

MartinLFletcher wrote:
Sat Dec 31, 2022 8:02 am

There are many resources available for anyone who has an interest in learning these subjects on their own.
Another great resource I neglected to mention is pdhonline.com. Licensed professional engineers are required to gain 15 "Professional Development Hours" per year, through a course taught by another P.E. I've used PDH Online courses for over a decade.

In addition to highly specialized technical courses, they have a number of courses on general engineering and engineering history that would be of interest to any technically-minded adult and would be great for an older home-school student. Some examples are:

Tucker 48: The Car of Tomorrow,
MOONSHOT: Saturn V and the Mission to the Moon,
Ford Model T: The Car That Changed the World, and
VW Beetle: Car of the People.

These courses, presented by Jeffrey Syken, P.E., are exhaustive in scope and contain a wealth of fascinating historical detail--in addition to being inspiring examples of what White men can accomplish.

The courses take 12-15 hours to complete, and have a quiz at the end. A certificate is awarded on passing.

Although the courses are typically priced at around $350, I've never paid full price. PDH Online's business strategy seems to include handing out 50% off coupons to everybody, so after the discount the courses are quite reasonably priced. If anyone is interested, the current coupon code is PDH22554. PDH2022 and PDH2023 should also be valid.

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