Ah, I think I remember bookmarking this when it was posted before. You really don't have to go very far in computing to find a frontier where most everything in described pure mathematics and so it becomes a substantial barrier for undiversified autodidacts in the field. The math in these areas can often be quite advanced and difficult to approach without the proper background and so I appreciate anyone who has made taken the time to make it less formidable to others.
I appreciate that some may find the book useful, but I personally don't agree with the presentation. There are too many conceptual errors in the book that you need to unlearn to make progress. For example, the book describes R^2 as a "pair" of real numbers. This is very much untrue and that kind of thinking will lead you even further astray.
I say this as someone with a math/cs degree and PhD having taught these topics to hundreds of students.
>For example, the book describes R^2 as a "pair" of real numbers.
I naturally auto-corrected this "(the set of) pairs of real numbers".
If that's the case, then I don't see how this differs from the actual definition.
What is the conceptual error? Is it the missing 'set of'?
> For example, the book describes R^2 as a "pair" of real numbers.
From page 15:
> The one piece of new notation is the exponent on R^2. This means "pairs" of real numbers.
Your interpretation of this quote is uncharitable at best. Using it to make a blanket assertion about the book is just silly, and quite out of the spirit of mathematics.
In particular, page 19 has an example of the kind of things that my book has that other books don't: a discussion of the soft skills of learning math and the cultural acclimation process:
> Though it sometimes makes me cringe to say it, give the author the benefit of the
doubt. When things are ambiguous, pick the option that doesn’t break the math. In this
respect, you have to act as both the tester, the compiler, and the bug fixer when you’re
reading math. The best default assumption is that the author is far smarter than we are,
and if you don’t understand something, it’s likely a user error and not a bug. In the
occasional event that the author is wrong, it’s often a simple mistake or typo, to which
an experienced reader would say, “The author obviously meant ‘foo’ because otherwise
none of this makes sense,” and continue unscathed.
The course you suggested is the sort of "grab bag of topics" course, meant to cram the basics of every topic a CS major might want to know for doing the kind of CS theory research that MIT cares about. If you find math hard, I doubt that will make it much easier, but it could be good to do alongside a book like mine if you find my book too easy.
