Your favorite math reference book(s)?

[pier4r]

Follow up of "Your favorite book (genre: STEM )?" (thanks to the new forum, everyone can still contribute there!)

I have some calculators (although not many as others). I see them and I am pushed to use them, somehow. Often I find problems that I would like to explore by myself, some other times I have no ideas and I fall back on a very old todo of mine: refreshing basic math. Math from, say, school to the math needed to complete an Engineering course. Computer engineering or Electrical engineering. One day (always one day... damn me) I will have to do this todo properly, with proper notes, but until then I pick this or that topic and I do some exercises.

Lately, since our company gave us a safaribooksonline account (see n1), I stumbled upon Precalculus with Calculus Previews 6th Edition, Zill, Dewar (woah it is 92 euro? How can students afford it?)

It is not bad at all. It is not that exhaustive either. For example proofs are missing, or also some explanations of subtleties (the famous "the exercise is left to the reader", that I dislike). The book tends to be practical and it is ok. The exercises are nice but for what I read, they are nothing difficult as well. I like the applications though, that shows how this or that concept can be applied outside the exercises, producing some interest in the reader.

So I would recommend it as reference to refresh some basic math.

Which math book(s), to refresh math or to get deep in some topics would you recommend?

I cannot really recommend any other book because either they are in italian only, especially high school books approved by the Italian minister of education. I liked them but they are unlikely translated in other languages, or I was happy with the notes taken during the lessons. Therefore at the end I used no other reference except some internet searches. Internet communities for those topics were good enough already after 2002, as far as I remember.

n1: I would say that a safaribooksonline account may be somewhat valuable for sysadmin or programmers, but not even that much, at least if one does not have much time to read. For mathematics it is a bit dry. I expected more choice but maybe my searches were poor. Though, I found the "story of e" that is interesting.

edit1: little rant against the google search engine. It indexed the hpmuseum threads in a very curious way because getting useful threads that talk about books using the "book" word is, well, hard. Either this or there were few threads about books.

[Maximilian Hohmann]

(12-28-2017 04:36 PM)pier4r Wrote:  ...Precalculus with Calculus Previews 6th Edition, Zill, Dewar ... (woah it is 92 euro? How can students afford it?)

When I was studying, we were required to buy Bronstein/Semendjajew: Taschenbuch der Mathematik (= Handbook of Mathematics). Don't know if an English translation exists, the original is in Russian and was translated into German to be used in the German Democratic Republic. From there it found it's way to Western German universities as well because nothing better existed then. The book cost roundabout 50 DM then, my student's appartment cost 200 DM per month. So that book cost about one week's rent. Our son started at university last fall and pays in excess of 500 Euros for his room. With that in mind those 92 Euros for your "Precalculus" can be considered a bargain as it equates only 5 days of renting :-) (and by the way, our son studies law where there are no textbooks which cost only 92 Euros ...)

And regarding the thread, my answer would most probably be the already mentioned "Bronstein".

[Dieter]

(12-28-2017 06:10 PM)Maximilian Hohmann Wrote:  When I was studying, we were required to buy Bronstein/Semendjajew: Taschenbuch der Mathematik (= Handbook of Mathematics).

For our friends living between the Atlantic and Pacific ocean: The relevance of this book is comparable to that of the "Abramovitz & Stegun". It even has its own Wikipedia page: Bronshtein and Semendyayev. This quote may give an impression of the very comprehensive integral tables:

Quote:Due to Bronshtein and Semendyayev containing a comprehensive table of analytically solvable integrals, integrals are sometimes referred to as being "Bronshtein-integrable" in German universities if they can be looked up in the book (in playful analogy to terms like Riemann-integrability and Lebesgue-integrability).

;-)

Dieter

[SlideRule]

(12-28-2017 06:10 PM)Maximilian Hohmann Wrote:  … required to buy Bronstein/Semendjajew: Taschenbuch der Mathematik (= Handbook of Mathematics). Don't know if an English translation exists…

YES, try Handbook of Mathematics 6e (Authors: Bronshtein, I.N., Semendyayev, K.A., Musiol, G., Mühlig, H.) ISBN 978-3-662-46221-8
from the URL
This guide book to mathematics contains in handbook form the fundamental working knowledge of mathematics which is needed as an everyday guide for working scientists and engineers, as well as for students. Easy to understand, and convenient to use, this guide book gives concisely the information necessary to evaluate most problems which occur in concrete applications. In the newer editions emphasis was laid on those fields of mathematics that became more important for the formulation and modeling of technical and natural processes, namely Numerical Mathematics, Probability Theory and Statistics, as well as Information Processing. Besides many enhancements and new paragraphs, new sections on Geometric and Coordinate Transformations, Quaternions and Applications, and Lie Groups and Lie Algebras were added for the sixth edition.

BEST!
SlideRule

ps: have both

[Maximilian Hohmann]

(12-28-2017 08:33 PM)SlideRule Wrote:  YES, try ...

Wow. 129$ (or 99$ for the eBook). Didn't know all those years what a precious book I own :-)

Later I also got a copy (literally: done on a photocopier!) of Abramowitz and Stegun. But I didn't look into that one very much. Not even in the electronic version on my iPad. Once Bronstein, always Bronstein...

[Nigel (UK)]

“An Elementary Treatise on Differential Equations” by Piaggio. Here’s a link: online book. I found this book so useful as a physics student! Very readable and not unnecessarily mathematical.

Nigel (UK)

[SlideRule]

My favorite depends on the branch of mathematics I'm interacting with, however, my most frequent, universal reference is CRC Standard Mathematical Tables & Formulae.

BEST!
SlideRule

[matthiaspaul]

(12-28-2017 09:27 PM)Maximilian Hohmann Wrote:  Wow. 129$ (or 99$ for the eBook). Didn't know all those years what a precious book I own :-)

Interestingly, the current German edition (the 10th edition reworked by Musiol/Mühlig, 2016) is still very affordable:

- ISBN 978-3-8085-5789-1 (book) 30.80 EUR
- ISBN 978-3-8085-5790-7 (book with CD-ROM) 40.80 EUR

https://www.europa-lehrmittel.de/t-1/tas...tein-2658/

Greetings,

Matthias

[Accutron]

Practical Mathematics, edited by Reginald Stevens Kimball. There are many different editions, including single volume editions with about 1300 pages, a four volume set and a periodical format released in over a dozen issues, but I think the content is pretty much the same across all versions. The book covers many important topics in both academic and applied mathematics, and presumes that the reader is using nothing more elaborate than a slide rule or maybe a mechanical adder. Topics include algebra, plane and solid geometry, statistics, differential equations, calculus, accounting and finance, chemical equations, radio and electrical calculations, thermodynamics, structural engineering, gunnery calculations, log tables, and of course a section on how to operate a slide rule. I consider it an absolutely essential reference book.

[Gamo]

I like Number Theory this particular book cover all the elementary number theory in general.
This book simply called "Number Theory by George E. Andrews"
This can be found in Google Play Book

Gamo

[pier4r]

(12-29-2017 12:11 AM)SlideRule Wrote:  My favorite depends on the branch of mathematics I'm interacting with, however, my most frequent, universal reference is CRC Standard Mathematical Tables & Formulae.

BEST!
SlideRule

You can mention many if you want

[SlideRule]

(12-29-2017 08:02 AM)pier4r Wrote:  You can mention many if you want

Currently, I'm scanning a multitude of math & math-related books, such as Pi, e, Measurement Uncertainties in Science & Technology, the Uncertainty in Physical Measurements, Analyzing Uncertainty in Civil Engineering … & various related publications.
I"m looking for validation of a curious aspect of number theory I was taught in Engineering; namely the answer to the question "What do ALL numbers have in common?"
… I'm still researching.

BEST!
SlideRule

[Felix Gross]

Had the same experience with Bronstein as Maximilian. Great book, still use it.

Good are also:

The VNR Concise Encyclopedia of Mathematics: The design is straight from the 60ies but its very handy for quickly getting into a new topic or for relearning. More explanation than Bronstein. Lots of numerical examples. Do not know if that is still in print. The original version came from East Germany.

NIST Handbook of Mathematical Functions: Superseded Abramowitz & Stegun.

Oldham et al.: An Atlas of Functions. The first edition had algorithms for programming. Nice graphics.

Emde, Jahnke: Tables of Functions with Formulae and Curves. Precursor to Abramowitz & Stegun. Wonderful graphs drawn without computers.

Felix

[matthiaspaul]

A recommendable German title comprehensively covering all kinds of school math (and a bit beyond) is "Kleine Enzyklopädie Mathematik" edited by W. Gellert, H. Küstner, M. Hellwich and H. Kästner. Originally published by the former East-German Bibliographisches Institut, Leipzig, 1968, it was also licensed for publication by Western publishers like Pfalz Verlag and Verlag Harri Deutsch. Newer German editions exist (some under the title "Meyers kleine Enzyklopädie Mathematik"), but I haven't used them myself so I cannot comment on them. However, I have been told they are heavily reworked. I am not aware of an English translation of this book.

Another work I can recommend is Vladimir Smirnov's "Lehrgang der höheren Mathematik" in seven volumes, an expanded translation of the Russian original "Курс высшей математики" published by the former East-German Deutscher Verlag der Wissenschaften, Berlin as volumes 1-6 of their series "Hochschulbücher für Mathematik", and licensed by Verlag Harri Deutsch for Western distribution. Last revised in 1994/1995, it is still available from Europa-Lehrmittel today (ISBN 978-3-8085-5572-9). Apparently, an English translation exists under the title "A Course in Higher Mathematics".

Yet another "classic" is Gregor Fichtenholz's "Differential- und Integralrechnung" (ISBN 3-8171-1418-4) in three volumes (as volumes 61-63 of the "Hochschulbücher für Mathematik" series). There never was an English translation, unfortunately.

Greetings,

Matthias

[pier4r]

While I appreciate the sources from Germany (since sooner or later I will master the German language), I wonder why they are, well, all from East Germany (or Russia through East Germany). Impressive.

[matthiaspaul]

(12-29-2017 08:28 PM)Felix Gross Wrote:  The VNR Concise Encyclopedia of Mathematics: The design is straight from the 60ies but its very handy for quickly getting into a new topic or for relearning. More explanation than Bronstein. Lots of numerical examples. Do not know if that is still in print. The original version came from East Germany.

Thanks for the hint. So an English translation of "Kleine Enzyklopädie Mathematik" exists as well.

Quote:NIST Handbook of Mathematical Functions: Superseded Abramowitz & Stegun.

I can recommend this one as well. However, what I don't like about (AS and) NIST is their use of some misleading nomenclature, like prefixing inverse hyperbolic functions with arc- (as if for arcus) rather than ar- (for area).

Quote:Oldham et al.: An Atlas of Functions. The first edition had algorithms for programming. Nice graphics.

Owning the second edition, I agree, this is a really nice book.

Greetings,

Matthias

[SlideRule]

(12-30-2017 12:06 AM)matthiaspaul Wrote:  … lehrbuch der hoeheren mathematik ISBN 978-3-8085-5572-9 … Apparently, an English translation exists under the title "A Course in Higher Mathematics"… Matthias

from the preface of A Course of Higher Mathematics (vol 5)

Code:

THIS is the final volume of Prof. Smirnov's five-volume course of
higher mathematics, about whose history some remarks were made
in the Introduction to Vol. I of the present English edition.
The first Russian edition of this volume, published in 1947, enjoyed
the distinction of being the first book in any language on the theory
of integration and the elements of functional analysis to be written
specifically with the needs of theoretical physicists in mind. Indeed
nearly twenty years after its publication its only rivals would appear
to be works by other Russian authors.

Pergamon Press 1964

BEST!
SlideRule

[Felix Gross]

Checked http://www.eurobuch.com (meta search engine for antiquarian booksellers):

The VNR Concise Encyclopedia is available. It covers many engineering math and pure math topics (number theory, measure theory, group theory etc.) at least briefly. Get the second edition.

If you are interested in old math books: archive.org offers many famous math handbooks as (mostly) very good pdf scans. Just for curiosity check out Briggs Log Tables from 1706.

Regarding the arcsinh terminology I checked out several reference. arcsinh is used quite often, as is sinh^-1 (that is real bad, since it is not 1/sinh(x)) and arsinh. No real consensus. The HP Prime manual uses ASINH which seems almost Solomonic.

[Pekis]

(12-30-2017 12:37 AM)SlideRule Wrote:  THIS is the final volume of Prof. Smirnov's five-volume course of
higher mathematics...

BEST!
SlideRule

Famous vodka indeed

[pier4r]

(12-30-2017 10:52 AM)Felix Gross Wrote:  Checked http://www.eurobuch.com (meta search engine for antiquarian booksellers):

The VNR Concise Encyclopedia is available. It covers many engineering math and pure math topics (number theory, measure theory, group theory etc.) at least briefly. Get the second edition.

If you are interested in old math books: archive.org offers many famous math handbooks as (mostly) very good pdf scans. Just for curiosity check out Briggs Log Tables from 1706.

Nice pointer! I still want to replicate some math tables by myself.

Has anyone an idea why a lot of good books mentioned here comes from East Germany/Russia instead of being preferred to western* books?

Not that the people in the Warsaw pact were unable to do math or something (on the contrary!), rather I thought that some books were more spread than others based on cultural/political preferences.

* with west I mean countries in the sphere of influence of the US.