Looking for old mathematics textbooks (high school to undergrad level)

Where can I purchase old mathematics textbooks on Advanced level (16-18 year olds) or undergraduate mathematics? I am ideally looking for books from the 1920’s to 1980’s.

Can you tell us why you are looking for such books? In mathematics, we have a pre- and a post-Bourbaki era, i.e. roughly speaking: a time when most contents were presented in words, and a time when people switched to more formulas and technical descriptions.

So do you want to learn subjects in a different way than by modern treatment, or are you just interested in old books? E.g. the Springer's GTM series dates partially way back.

I like the the following books from Edwin E. Moise:

Geometry (not the elementary geometry from an advance standpoint). Elementary Geometry From an Advance Standpoint is an excellent book, but it is university level, and not high school.
The author is Moise/Downs

Calculus. The green covered book contains volume 1 and 2.
The calculus book is like a mixture between Stewart and Courant. Great balance.

I also like Thomas Calculus 3rd edition. An applied Calculus book with great insights.

matqkks said:

Where can I purchase old mathematics textbooks on Advanced level (16-18 year olds) or undergraduate mathematics? I am ideally looking for books from the 1920’s to 1980’s.

I got some good ones from the Waterstones web site. They are reasonably priced but shipping adds on, depends where you are.
There is a book link on pf too somewhere. Amazon? Edit: the thread is called ' Support PF buy your textbooks here.' You can always key in the edition/ year to get your specific 1970s/80s copy if you know the title author and edition.
This is why I love second hand book shops and charity shops. You can come across a gem, just takes a lot of time. Fun time though. Google second book stores in your area, the charity shops. Oxfam tend to be pretty good. Happy hunting!

matqkks said:

Where can I purchase old mathematics textbooks on Advanced level (16-18 year olds) or undergraduate mathematics? I am ideally looking for books from the 1920’s to 1980’s.

I forgot about the library sales, a lot of chaff in there but worth a go before spending money on shipping for E bay, Amazon and Waterstones. Depends if you like spending time in libraries, old book shops and charity (thrift) shops.
I picked these up there.

For algebra, Hall and Knight is popular. I believe it's available in PDF for free online. It has a long list of miscellaneous problems at the end that I very much enjoy. I think the 9th problem is a weird radical expression that you're supposed to simplify. I thought I was strong at algebra until I struggled for months with this!

There seem to be two questions here: what are some recommended old books, and where can they be purchased? The standard marketplace for used books is Advanced Book Exchange, abebooks.com. That requires you to know the name and author of the book. Some recommendations for specific books can be found in the thread "Should I become a mathematician?" in the STEM academic advising forum here.

These comments are meant for someone who wants to compare the approach to geometry in the book of Moise and Downs to that in the original book of Euclid, or the modern book of Hartshorne, expounding and completing Euclid's approach.

I liked the suggestion above of books by Moise because in my experience his writing on advanced topics, such as in his more advanced geometry book, is exceptionally accurate mathematically, although not easy. In reference to the more elementary geometry book suggested above by Moise and Downs, (paradoxically NOT the one with the word "elementary" in the title), I would remark that, according to reviews, it apparently follows the approach of Birkhoff, rather than Euclid, in that it assumes the real numbers as a more fundamental concept than geometric lines, and defines geometric concepts in terms of the real numbers. In my personal opinion, this is somewhat backwards, not only historically but logically and intuitively, since the real numbers are much more sophisticated than are basic geometric concepts, so it is to me unlikely that the student of the Birkhoff approach will actually have a good understanding of them in advance.

Nonetheless, this approach can "work" just because many students think they know what real numbers are, and taking them for granted does make many geometric proofs easier. Thus one is making the arguments easier by assuming a great deal more content up front. I prefer Euclid's approach myself, since I think it makes one more able to understand how the concept of real numbers arose out of geometry historically, and not vice versa. (The deepest property of real numbers is their "completeness" which corresponds to the geometric property that every separation of a line into two "sides" is caused by the removal of a unique point. The real numbers version, that every non empty bounded set of reals has a least upper bound is, to me at least, much more difficult, and not understood by essentially any students. This is not fully needed in Euclidean plane geometry, only a much weaker assumption, that lines and circles which look as if they intersect, actually do so. I.e. one does not need the full intermediate value theorem allowing one to solve equations with any continuous function, just the ability to solve certain quadratic equations. For this reason, Birkhoff geometry covers essentially only one of the infinite family of Archimedean geometries covered by Euclid's axioms, although it is the one needed by calculus students. Birkhoff also often assumes a rather sophisticated "similarity" principle. Finally, the Birkhoff approach does not work at all for non Archimedean geometry, while Euclid's does, suitably understood.)

Having said this, the Birkhoff approach is logically valid, it just assumes more sophisticated concepts to begin with, but it can be made to work well in class, and I would imagine that Moise is an excellent choice for an expositor of it. Further, since the Birkhoff approach is often found in modern texts for high schoolers, it seems well to learn it from an authoritative source like Moise. (Although I have not read the actual book by Moise and Downs, I respect the former's reputation.)

mathwonk said:

These comments are meant for someone who wants to compare the approach to geometry in the book of Moise and Downs to that in the original book of Euclid, or the modern book of Hartshorne, expounding and completing Euclid's approach.

I liked the suggestion above of books by Moise because in my experience his writing on advanced topics, such as in his more advanced geometry book, is exceptionally accurate mathematically, although not easy. In reference to the more elementary geometry book suggested above by Moise and Downs, (paradoxically NOT the one without the word "elementary" in the title), I would remark that, according to reviews, it apparently follows the approach of Birkhoff, rather than Euclid, in that it assumes the real numbers as a more fundamental concept than geometric lines, and defines geometric concepts in terms of the real numbers. In my personal opinion, this is somewhat backwards, not only historically but logically and intuitively, since the real numbers are much more sophisticated than are basic geometric concepts, so it is to me unlikely that the student of the Birkhoff approach will actually have a good understanding of them in advance.

Nonetheless, this approach can "work" just because many students think they know what real numbers are, and taking them for granted does make many geometric proofs easier. Thus one is making the arguments easier by assuming a great deal more content up front. I prefer Euclid's approach myself, since I think it makes one more able to understand how the concept of real numbers arose out of geometry historically, and not vice versa. (The deepest property of real numbers is their "completeness" which corresponds to the geometric property that every separation of a line into two "sides" is caused by the removal of a unique point. The real numbers version, that every non empty bounded set of reals has a least upper bound is, to me at least, much more difficult, and not understood by essentially any students. This is not fully needed in Euclidean plane geometry, only a much weaker assumption, that lines and circles which look as if they intersect, actually do so. For this reason, Birkhoff geometry covers essentially only one of the infinite family of Archimedean geometries covered by Euclid's axioms, although it is the one needed by calculus students. Birkhoff also often assumes a rather sophisticated "similarity" principle. Finally, the Birkhoff approach does not work at all for non Archimedean geometry, while Euclid's does, suitably understood.)

Having said this, the Birkhoff approach is logically valid, it just assumes more sophisticated concepts to begin with, but it can be made to work well in class, and I would imagine that Moise is an excellent choice for an expositor of it. Further, since the Birkhoff approach is often found in modern texts for high schoolers, it seems well to learn it from an authoritative source like Moise. (Although I have not read the actual book by Moise and Downs, I respect the former's reputation.)

Yes, it is a very nice and easy going book. Two critiques I would say about the book are:
1) The exercises are a bit too easy.
2)Constructive proofs are nonexistent or relegated to a section very near to the ending of the book. However, from memory (been 7 years since I read it), it gives an explanation on impossible constructions. Ie., trisecting an angle. I don't recall if it does it rigorously.

What I do like: great exposition of topics. Explains clearly what an axiom, definition, theorem, corollary, lemma are. No dreaded two column proofs. Explains clearly what existence and uniqueness means. The book can also be used as an intro to proofs course.

I would say that my ability to read, understand, and do proofs came from this book.

Moreover, I also purchased Moise's problem book involving real analysis and topology. I forget the name, but its great preparation for review, practice for entrance exams, and overall testing ones understanding of intro analysis/topology.

Hopefully one day you write an insights article on geometry, its many areas, resources to learn, and overall how to become a geometer. I remember sending you a pm once regarding geometries, and Dedekind Construction of Real Numbers, and your response was extremely insightful. I was able to also learn about the cool book Geometries and Groups.

matqkks said:

Where can I purchase old mathematics textbooks on Advanced level (16-18 year olds) or undergraduate mathematics? I am ideally looking for books from the 1920’s to 1980’s.

Usually easily found at library used-book sales. Prices are often excellently low.

a bit of an edit: What may be found at any booksale/library sale will vary from time to time and from place to place. One simply should go to a few of such sales in the local area.

matqkks said:

Where can I purchase old mathematics textbooks on Advanced level (16-18 year olds) or undergraduate mathematics? I am ideally looking for books from the 1920’s to 1980’s.

matqkks said:

Where can I purchase old mathematics textbooks on Advanced level (16-18 year olds) or undergraduate mathematics? I am ideally looking for books from the 1920’s to 1980’s.

My father passed away recently and I have a large number of math/physics and math related books that belonged to him, that I am looking to rehome.
Please let me know where you are and if you may be interested. Warm regards, Rebecca

Dover is great https://store.doverpublications.com/by-subject-mathematics.html

Some cities have Half price books. I bought several there. I have had to use this chain since brick and mortar technical bookstores vanished.

agirlinthesky said:

My father passed away recently and I have a large number of math/physics and math related books that belonged to him, that I am looking to rehome.
Please let me know where you are and if you may be interested. Warm regards, Rebecca

Consider making a list and sharing it on PF; there may be interest in buying or at least providing good homes for the books.

If they are too many to list, maybe take photos of the shelves.

There are many PFr's who appreciate books.

EDIT: to be fair, give @matqkks first crack at them

matqkks said:

Where can I purchase old mathematics textbooks on Advanced level (16-18 year olds) or undergraduate mathematics? I am ideally looking for books from the 1920’s to 1980’s.

Bookfinder.com is a great aggregator of many used book sites