Tips for self-study with just a textbook and google

Question

I'm going to be working through a textbook on discrete mathematics that has a special focus on computer science. My only resources are the textbook (which, in its defense, has answers to the odd numbered problems in the back, and "self-tests" with answers) and the great and powerful Google. Since I don't have a teacher per-se to help me, are there any things I should do to help keep myself focused and retaining the information I read? I'm planning on doing every single odd-numbered problem, but are there extra projects I could be doing (programming or whatever) to reinforce aspects of it?

The book is Discrete Mathematical Structures, 5th edition, by Kolman, Busby, and Ross. Chapters are

1. Fundamentals (covering set theory, matrices, etc)
2. Logic
3. Counting
4. Relations and digraphs
5. Functions
6. Order relations and structures
7. Trees
8. Topics in graph theory
9. Semigroups and groups
10. Languages and finite-state machines
11. Groups and coding

Answer 1

Your general plan seems good: Do a lot of exercises. An old proverb (Chinese, but maybe more general) is that you don't know something until you've practiced it ten thousand times. (Rule of 10,000).

I've found wikipedia to be quite good, but not perfect, for questions on mathematics. Be a little skeptical if anything seems a bit strange in an article there. I once came upon an article that seemed sketchy in part - just a paragraph or two in the middle of a long piece. I came back in an hour or two and it was gone. A professional isn't likely to be misled, but a student should be just a bit cautious.

Also, take notes. What are the most important three ideas in this section/chapter? Don't try to re-write the book, just abstract the gems. Highlighting has less impact since your brain is less engaged. You want to do things while self studying that are "active" enough that your neurons get rearranged. This is why the exercises are especially good.