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I'm looking for a big list of resources for advanced undergraduate - beginning graduate (and even beyond, really) with a particular feature. Namely, I really like solving "project"-like problems that include the general direction of the proof. I think it helps keep me motivated and learn more by solving multi-step problems with some direction.

Here are a few specific examples:

Dummit & Foote, pg. 96:

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Dummit & Foote, pg. 268-269

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Bartle, Elements of Real Analysis, p. 273

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Generally, these problems are few and far between (probably for good reason) but I was hoping there were some books (from any subject area!!) that go out of the way to include problems like this.

Obviously I am familiar with Dummit & Foote and Bartle's Elements of Real Analysis. I know Rudin's PMA also has quite a few problems in the same vein. Which do you know?

Thanks,

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  • $\begingroup$ If you're interested in computer science, I recommend The Elements of Computing Systems by Nisan and Schocken. The whole book is a project to create a computer from scratch (starting from nand gates). The individual chapters are projects to create things such as a CPU, an assembler, a compiler, etc. Brilliant book. $\endgroup$ – littleO Jun 14 at 16:49
  • $\begingroup$ @littleO since this is a community wiki/big list feel free to add that as an answer :) $\endgroup$ – graeme Jun 15 at 12:39
  • $\begingroup$ See also this question which is asking for similar types of books: math.stackexchange.com/questions/1104996/… $\endgroup$ – graeme yesterday
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Strom J - Modern Classical Homotopy Theory.

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Anthony Knapp's Basic Algebra (presumably his Advanced Algebra as well) has several problems like this in every chapter, introducing new important concepts, extending ideas from the text, or investigating applications. Here is an example project:

Knapp's Basic Algebra

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