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A Gentle Introduction to the Art of Mathematics, by Fields. View.
- Very gentle indeed, but also with nice wide margins to write in and lots of good hints with plenty of exercises. Author is a fan of Sage.
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Introduction to Proofs, an Inquiry-Based approach, by Hefferon. View.
- Very terse, but that is the point. Can you learn to prove without given examples? Why not, if the problems start basically enough? Worth approaching if you want to really learn deeply.
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Book of Proof, by Hammack. View.
- Not familiar with this one, but comes with glowing reviews from those who ought to know. From an institution with a strong record of supporting faculty writing the right books for students.
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Mathematical Reasoning: Writing and Proof, by Sundstrom. View.
- I don't know this one, but I do know the institution, which is very good at undergraduate resources of innovation, and it comes with screencasts and I believe is sometimes taught with Sage.
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The Art of Proof, by Beck and Geoghegan. View.
- I'm not as familiar with this one but it really takes the "learning by doing" seriously, and has some very interesting topics and goes at a reasonable pace. NOT (legally) PRINTABLE.
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If you want more free textbooks for various subjects, the American Institute of Mathematics maintains a carefully curated list.
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Another source for guided-inquiry lecture notes that can be used for independent study is the Journal of Inquiry-Based Learning in Mathematics.
- Documentation for Interacts. View.
- Somewhat dry but comprehensive documentation for making interacts in the notebook.
- Interact sharing website. View.
- Lots of examples here, though not as active due to some spam issues.
- Sage wiki examples of interacts. View.
- Many more examples, organized nicely by category. Some are quite complicated!
- Brief Tutorial in SageTex. View.
- This is a quite brief but useful tutorial showing the most basic uses of SageTeX.
- Embedding Sage in Latex. View.
- Somewhat rambling but definitely still useful Sage and SageTeX tutorial, focusing on use on the Mac.
- SageTeX installation. View.
- This is information about making SageTeX known to your computer. Jan will have more information for you as well.
- Official SageTeX guide. View.
- This is quite nice. The source is also available in every Sage installation.