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If you look at old books like Euclid, and Archimedes it seems that there weren't any problem set exercises. They just presented the all information. There were no "end chapter" problems. In short, it seems that most ancient books were written as treatises.

However, for contemporary textbooks, they often leave exercises at the end of the chapter, often with no solutions. I wonder when did exercises were appended into textbooks. Specifically, exercises which do not contain answers/derivations.

I conjecture maybe from the the industrial revolution, but that's just my guess. I want to know the palpable answer to this. In other words, I wonder when did books begin to include exercises with omitted solutions.

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I can only talk about math books. Problems in the end of the chapters is a British-American custom. German, French and Russian books do not have them. Instead they publish separate problem books, usually by a different author. Problem books contain only problems, and in the introduction they mention which textbook(s) are recommended. British/American textbooks with problems at the ends of the chapters appear since the beginning of 20th century, perhaps there are some late 19th century but I have not seen them.

Of course, in the end of 20th century this British/American custom spreads over the world, like many other British/American customs, and you can see textbooks in other languages that follow it.

Examples from my speciality (where I know most of the existing textbooks). Whittaker-Watson (first edition 1902) has problems. K. Knopp (German, many textbooks) no problems. Separate problem books by the same author. Hurwitz-Courant (German, first ed. 1922, and many later editions) no problems. H. Cartan (French, first ed. 1963) no problems. Markushevich, Privalov, Lavrentiev-Shabat (Russian, multiple editions) no problems.

The most famous problem books in the same subject: Polya-Szego (German), Volkovyski (Russian). On the other hand, there is no such genre as a "problem book" by a British/American author, with very rare exceptions like Halmos.

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  • $\begingroup$ " Problem books contain only problems, and in the introduction they mention which textbook(s) are recommended." In other words, did these books not contain solutions? If there was no solutions in the problem book, were there solution manuals? $\endgroup$ – displayname Dec 30 '15 at 15:27
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    $\begingroup$ @thepotato: usually they did not contain complete solutions, but sometimes they did contain hints, or answers or solutions to a subset of problems. The idea was that these books could be used for HW. Existence of a solution manual makes this use impossible. $\endgroup$ – Alexandre Eremenko Dec 30 '15 at 17:26
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Here is one data point. (It does not contradict Alexandre's assertion that this is an American innovation, but does provide an earlier starting date.)

Day's Algebra (I picked this volume up in a used book store once.) Days

This textbook does have lists of exercises at the end of each section.

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  • $\begingroup$ Regarding British-American math textbooks from the 1800s, I own at least 30, I have .pdf files of well over 100, and I have probably looked at (digital or university library) several hundred, and virtually all have end of the chapter exercises. The books I'm talking about deal with arithmetic (of which I've not looked at very many), algebra, calculus, analytic geometry (here I'm also including analytic conics and geometrical conics), and trigonometry. Also, a lot of French texts also have chapter problems, such as Niewenglowski's and Bertrand's Algebra texts (the only 2 I looked at just now). $\endgroup$ – Dave L Renfro Jan 6 '16 at 20:14
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Mezopotamian and ancient Egyptian math "textbook" contains only problems and and solution. Something like "Adding a length to a square give 1. What was the number?" followed by actual computation.

It seams that their conception of mathematics was to accumulate solved problems, like astronomers accumulate observations, without never thinking of making a general theory of it.

The first to write a text-book in the modern form was Euclid.

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    $\begingroup$ You write of problem sets without a textbook (which by modern definition includes theory) and a textbook without problem sets. However, the OP is about when they were first combined. Can you modify your answer to address that? $\endgroup$ – Rory Daulton Dec 31 '15 at 14:53
  • $\begingroup$ This doesn't answer the question, as Rory Daulton points out $\endgroup$ – Cicero Jan 2 '16 at 20:41

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