Thread: Old book's. Still good?

I have PDF's of two math book's. They both seem to explain their subjects clearly. I certainly understand the subject's better from these book's than other more recent works. However they are both fairly old, having initial publication dates in the first half of the twenty'th century.

Should they still provide an adequate foundational base for their subject's?
And has the relevant symbology changed much?

They are; Calculus Made Easy, by Silvanus P. Thompson, 2nd edition 1914.
And; Vector Analysis, by Edwin Bidwell Wilson, Founded upon the lectures of, J. Willard Gibbs, Published 1901.

Originally Posted by GiantEvil

I have PDF's of two math book's. They both seem to explain their subjects clearly. I certainly understand the subject's better from these book's than other more recent works. However they are both fairly old, having initial publication dates in the first half of the twenty'th century.

Should they still provide an adequate foundational base for their subject's?
And has the relevant symbology changed much?

They are; Calculus Made Easy, by Silvanus P. Thompson, 2nd edition 1914.
And; Vector Analysis, by Edwin Bidwell Wilson, Founded upon the lectures of, J. Willard Gibbs, Published 1901.

I am not familiar with those particular books, but I have a general idea what they mght be like.

At the elementary level mathematics as it relates to calculus and vector analysis has not changed all that much since their publication.

What has happened is that the understanding of what really makes calculus work has grown. This is reflected in the development of point-set topology and differential forms since then (in the early 1900's). I doubt that the calculus book provides a rigorous development of the subject, but most modern calculus books don't either and you see it done rigorously for the first time in an introductory class on real analysis.

Were I you, I would read those older books and then take a look at some more modern treatments of mathematics. But I most certainly would not discard the older books.

Sweet. I'm glad those books are still relevant. For whatever reason, I find their treatment of the subject matter clearer than many other works. I took a quick look at a PDF book of differential equations "DE Complete". Differential equations appear to be the Calculus of fields. Speaking of Calculus, I know that trigonometry is vital to Calculus. There seem's to be less material available on trigonometry than most other mathematical disciplines. I got a couple minor work's on trigonometry, and they are not very large. Is trigonometry a "small" genera of mathematics?

Originally Posted by GiantEvil

Sweet. I'm glad those books are still relevant. For whatever reason, I find their treatment of the subject matter clearer than many other works. I took a quick look at a PDF book of differential equations "DE Complete". Differential equations appear to be the Calculus of fields. Speaking of Calculus, I know that trigonometry is vital to Calculus. There seem's to be less material available on trigonometry than most other mathematical disciplines. I got a couple minor work's on trigonometry, and they are not very large. Is trigonometry a "small" genera of mathematics?

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Trigonometry is usually treated either as part of "college algebra" (really about the junior or senior year in high school) or as a short one-quarter class. There is not all that much to it.

However, trigonometry is essential to calculus and to basic vector analysis, as in mechanics. It is a fairly old subject -- ancient Greeks, 5th century in India, well developed by 10th century in the Middle East.

If you are not familiar with trigonometry, you need to get that under your belt before you take on calculus.

I am a little familiar, but not proficient with, trigonometry. I am glad that I have confirmation of it's compactness. Thank's.

Speaking of old book's. I have considered reading translations of Euclid's Elements, and Newton's Principia. Do you think I would gain anything by this?

Originally Posted by GiantEvil

I am a little familiar, but not proficient with, trigonometry. I am glad that I have confirmation of it's compactness. Thank's.

Speaking of old book's. I have considered reading translations of Euclid's Elements, and Newton's Principia. Do you think I would gain anything by this?

yes. Probably a bad headache. Get a big bottle of aspirin.

Eudlid is fairly pedantic, The Principia is extremely difficult to read. Newton did not use the usual Liebniz notation in calculus and his reasoning is rather difficult to follow. They are nice books to have if you something of a buff of the history of science, but difficult to read.

Have you had the usual high school geometry class ?

I remember "graphing" in high school. I can't say I had any specific geometry classes though.

Considering what I've heard about the historical Mr Newton, I can imagine that his writing style is not very effectual. I have heard that he was a "crappy" professor. That his classes were very boring.

Originally Posted by GiantEvil

I remember "graphing" in high school. I can't say I had any specific geometry classes though.

Considering what I've heard about the historical Mr Newton, I can imagine that his writing style is not very effectual. I have heard that he was a "crappy" professor. That his classes were very boring.

I have no idea where you would have heard such a thing. It may be true, but any classes were taught about 300 years ago.

I am a bit stunned that you did not have a class in Eudlicean geometry in high school. That is typically the first introduction to proofs. It is an important course. You also need to know something of geometry to understand the usual treatment of trigonometry. Trigonometry is heavily reliant on triangles and arguments involving triangles.

I read the stuff about Mr Newton in some science book somewhere. I have also heard that when Newton said "On the shoulder's of giant's" he actually meant it as an insult to Robert Hooke.

School was some time ago. I remember learning the basics of geometry, lines, rays, segments. I remember bisecting angles. I have a DVD series on geometry. I think I'll watch some of that tonight. Geometric proofs are not a thing I am very familiar with. There's a section on it in my DVD set though. So I have resources.

Don't fall for those 'calculus made easy books.' You'll go through them really easily, however, at the end of it all, you won't have gained an in depth understanding of the subject matter. In fact, you probaly won't even be able to solve difficult integrals, which doesn't require in depth knowlege of the calculus. The absolute best calculus book is Calculus by Spivak. It's a rigorous approach to calculus, which could be used for an intro analysis/advanced calculus book. This book will teach you about mathematics and what it is.