Per the title, what are some of the oldest abstract algebra books out there with (unsolved) exercises? Maybe there are some hidden gems from before the 20th century out there. I am already aware of the books of Dickson and van der Waerden.
$\begingroup$
$\endgroup$
7
asked Jul 21, 2020 at 16:37
Squid with Black Bean SauceSquid with Black Bean Sauce
1,5321 gold badge18 silver badges38 bronze badges
-
3$\begingroup$ In older books (or most non-English language books), the ridiculous "abstract" adjective was not present. $\endgroup$– YCorCommented Jul 21, 2020 at 17:11
-
1$\begingroup$ @YCor Do you prefer the timeless "modern" instead? $\endgroup$– Michael GreineckerCommented Jul 21, 2020 at 18:21
-
7$\begingroup$ A year ago you posted a large number of separate questions of this kind, asking for oldest books in various areas of math with exercises (always hoping for "some hidden gems from before the 20th century"). Please consider posting just once a big-list request for the oldest books in different areas of math with exercises, rather than all of these separate questions marching (potentially) through all areas of mathematics that are all the same question. $\endgroup$– KConradCommented Jul 21, 2020 at 22:46
-
2$\begingroup$ I agree wirh @KConrad. By the way, it might be just my ignorance, but I have difficulties to see the point of the requirement "with exercises". When you are looking for old books on various subjects, is there a specific reason why you are only interested in books that contain exercises? $\endgroup$– Jochen GlueckCommented Jul 21, 2020 at 22:53
-
2$\begingroup$ @JochenGlueck see the rationale explained in the post of the earliest question mathoverflow.net/questions/313967/…. It does not explain why there have to be repeated posts about all these different areas of math instead of one single post on the general topic. See also mathoverflow.net/questions/327697/…. $\endgroup$– KConradCommented Jul 21, 2020 at 23:13
|
Show 2 more comments
3 Answers
$\begingroup$
$\endgroup$
3
For a pre-20th century textbook: Modern Higher Algebra by George Salmon (1876) has exercises (with solutions).
If I may broaden the query from "abstract algebra" to more general "algebra", I note that Elements of Algebra by Euler (1770) has more than one hundred exercises. The exercises are discussed in The origin of the problems in Euler’s algebra.
Here is an example, from the chapter on cubic equations [source].
And another example (find an integer $x$ such that $2x^2-5$ is a cube) [source]
answered Jul 21, 2020 at 17:16
-
1$\begingroup$ Problem 10 has a typo :-( $\endgroup$ Commented Jul 21, 2020 at 20:21
-
$\begingroup$ yep, the square should be a cube, well spotted! $\endgroup$ Commented Jul 21, 2020 at 20:23
-
1$\begingroup$ It seems that the unsolved problems may not have been in Euler’s original, but rather added by a later translator. $\endgroup$ Commented Jul 21, 2020 at 20:56
$\begingroup$
$\endgroup$
Two important early 20th-century abstract algebra textbooks that were superseded by van der Waerden are:
Hasse, H., 1926. Höhre Algebra.
Haupt, O., 1929, Einführung In Die Algebra, Zweiter Band - Mit Einem Anhang Von W. Krull, Akademische Verlagsgesellschaft M. B. H., Leipzig.
For an in-depth historical account of the transition from algebra to abstract algebra (including discussions of the various textbooks) see:
Leo Corry, 1996, Modern Algebra and the Rise of Mathematical Structures, Birkhäuser Verlag.
answered Jul 21, 2020 at 17:14
$\begingroup$
$\endgroup$
2
I think the following references might be useful:
H. Weber (1895/1896): Lehrbuch der Algebra, 2 volumes. Vieweg, Braunschweig. It includes examples, but it does not have any separate exercises.
E. Artin (1938): Foundations of Galois Theory. New York University Lecture Notes, New York.
N. Bourbaki (1947): Éléments de Mathématique, Algèbre. Hermann, Paris.
I am not totally sure whether the last two references include exercises.
