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Intro Math Old Mathematical Books

  1. Apr 23, 2015 #1
    Anyone else use mathematical textbooks from around 1950?

    I do... by accident...

    Tend to pick them up in thrift stores where they just get dropped, discarded...

    But, I find them engaging! Many of them are around 1950. It is also a little fun to see how mathematics has progressed. For example, my General Mathematics Volume 1 assumes there is no simple divisibility test for 7.

    Well, he was wrong.

    I was just wondering if anyone else even uses these volumes now. Let me know if any of these sound familiar.

    Algebra for Beginners including Easy Graphs by Hall and Knight - 1950
    Calculus made easy by Sylvanus P. Thompson F. R. S. - 1948
    General Mathematics Volume 1 by C. V. Durell - 1952
    and Elements of Analytical Geometry by J. T. Brown & C. W. M. Manson - 1957

    Much gratitude for replies,

  2. jcsd
  3. Apr 23, 2015 #2


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    I found a couple of old intermediate algebra books from, I believe, the early 1960's. One was by "drooyan", and another I forgot who. Good books. Good discussions as instruction. No distractions on the pages. These books were very good for reviewing the course, and nearly all the topics you would expect would be there.

    I will have to recheck the publish date on one of those, because maybe one of them was from the 1950's.
  4. Apr 23, 2015 #3
    Wow, that's exactly what I love about the older books!

    Not only are they nearly all-hardback, but there are no distractions on the page, yet surprisingly simple to absorb.

    Algebra, after all, is always algebra. Alright, excluding periods before the 1600's...

  5. Apr 23, 2015 #4


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    The author of the other intermediate algebra book was, (spelling may be wrong) Siegenfry, or Siegenfrai.
  6. Apr 23, 2015 #5


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    I learnt my mathematics from German textbooks, and the old ones are simply marvelous. I sometimes have the impression they were be written with much more love not only for the subject but also for the way, how to explain things. One example, I know there's an English translation, is the two-volume book on mathematical methods for physicists by Courant and Hilbert.

    Another thing is that there is a clear cut in the writing style between the era before and after Bourbaki. As great as this idea of very dinstinguished mathematicians were to write an axiomatic presentation of all of mathematics, for the writing style of textbooks it was a disaster (in my humble opinion as a math-loving theoretical physicist). Even a topic as exciting as Lie-group theory can be written in such a dull way that it's not only utmost boring but much harder to understand than if it is written in the "old-fasioned" style. I also think that they were not less rigorous than the modern ones. Fortunately this too large Bourbakian influence on the writing writing style of math textbooks seems to become weaker with the years, and there are again great textbooks written more recently.
  7. Apr 23, 2015 #6


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    the divisibility test for 7 has been known of course for a very long time, certainly before that book was written. also silvanus p thompson's book dates from about 1907 i believe. there is probably nothing in any of those books that was not known in the 1800's. the algebra book i recommend most is by euler, he died in 1783, and it covers up through the cubic and quartic formulas, which are unlikely in any of those books, and further. one of the best analysis books (advanced calculus and de) is in the series by goursat from about 100 years ago. courant is a hugely popular highly rigorous calc book today and was written in the 1930's.

    good for you for finding these gems. keep looking. if you just want a good basic calc book, the early editions (1950's) of thomas can often be found for $1 or less online.
  8. Apr 23, 2015 #7


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    I use such books all the time; that is what I studied in school.

    Courant & Hilbert has been mentioned above. Morse & Feshbach is another extremely valuable 2 vol set. Courant's Diff & Int Calculus is very well done. I also use Adv Calc by Kaplan.

    Mathematics of Modern Engineering (1936) by Doherty & Keller (2 vols) is an excellent applications set.

    Vector & Tensor Analysis by Lass is a well done book.

    Mathematics of Physics & Modern Engineering by Sokolnikoff & Redheffer is a great book.
  9. Apr 24, 2015 #8
    Trigonometry looney, kisselev planimetry/sterometry, thomas calculus, Euler algebra book. There is one I am forgetting which covers number theory.
  10. Apr 24, 2015 #9
    Was it this one?
    "An introduction to the theory of numbers"- G.H.Hardy and E.M.Wright (first published in 1938)
  11. Apr 24, 2015 #10
    Correct. A bit to advanced for my current level. Although it is very well written.
  12. Apr 24, 2015 #11
    It's basically a classic in number theory.You'll usually find it on the reading list of an undergrad. taking a course in number theory. But most of the times it's just used as an intro. to a sub-field. You could try reading the first few chapters..... they're not too difficult.
    From the preface:-"This book is written for mathematicians but it does not demand any great mathematical knowledge or technique. In the first eighteen chapters we assume nothing that is not commonly taught in schools, and any intelligent university student should find them comparatively easy reading."
  13. Apr 24, 2015 #12
    As for introductory calculus textbooks, how about books written by Moise and Bers?
  14. Apr 25, 2015 #13
    True, however to fully appreciate the value of the book (it is a very good one), I should read naive set theory by halmos and how to prove it by velheim? Both are in my library. I havnt gotten a chance to read them. I have 2 not so great professors where the classes are basically teach yourself. Not unfair by any means but the test are killer, because the teachers can not convey there knowledge to layman students.
  15. Apr 25, 2015 #14
    I'll still recommend that you dig right into it......... don't regard it as a gem, play with it, struggle with it.......carry it around, and if you get stuck, don't give up, post your problems online (math stackexchange and mathoverflow are excellent sites) if the professors won't help you or get the solutions from them and work out the logic yourself, this is very important in pure mathematics, then you'll start having affections for the book, and that is when it becomes a gem :) I've always tried to avoid reading prerequisites because you'll find that more often than not that sort of motivation is short lived :) you'll lose interest halfway (or if you're like me after 2 chapters) so I would especially not recommend it for a book that doesn't demand any.
    It's difficult to find someone interested in number theory on sites like PF.
    Cheers :)
  16. Apr 25, 2015 #15
    My word! Such a large following. My analytical geometry and calculus books seem to go a little over my head too... despite one being simplified. I am just surprised that so many people are enjoying these little classics, while they can be found in shops, simply discarded!

  17. Apr 25, 2015 #16
    It's just a proof of the fact that a price has never been and never will be put on knowledge............
    P.S. did you know that algebra is actually derived from the word al-jabr which in turn is a shorthand of Al-Khwarizmi's book "Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabla" (the compendious book on calculations by completion and balancing) which is generally considered to be the first book containing the systematic solutions of linear and quadratic equations and along with Diophantus has earned Al-khwarizmi the title of the "father of algebra". This book was published first in 820 A.D.
    Cheers :)
  18. Apr 25, 2015 #17
    Wow, certainly! And to think, I'm reading a book on Arabic science and I didn't guess that... Oh man...

    There was me thinking it emerged from the alchemist Al-Jabir.

  19. Apr 25, 2015 #18
    That book by Thompson is nothing but dumped down lol. Quite a challenging little book. Maybe pick up a copy of thomas calculus 3rd edition? I think thomas was alot easier to follow.
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