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This is something that takes a lot of practice, and many schools don't or can't teach it. Fear not, it's easier than it sounds.
First, some background:
This will introduce you to most of the historical method used today. It's quite boring, but if you're going to study history, you'll need to get used to reading some pretty dry material.
For a styleguide, use Diana Hacker's:
It will teach you everything you need to know about citations.
As far as getting better at source analysis, that's something that comes with time in class and practice with primary and secondary source documents. If you're just going into college, it's something you're going to learn naturally.
However, I do have some tips.
-The main goal of a piece of historiography is to bring you to a thesis and then clearly support that argument. All REAL historiography asks a historical question of some sort. I.E. not when and where, but a more contextual why and how.
-Real historiography is produced 99.9% of the time by a university press, NOT A PRIVATE FIRM. If a celebrity wrote it, it's probably not history.
-Most, if not all real historiography is going to spell out the thesis for you almost immediately.
-A lot of historiography is quite formulaic in terms of its layout and how it's put together on paper:
A. Introduction -- thesis statement and main argument followed by a brief review of past historiography on the subject.
B Section 1 of the argument with an a,b, and c point to make in support.
C just like B
D just like B again, but reinforces A a little more
E Conclusion, ties all sections together and fully reinforces A.
Not all works are like this, but almost every piece you will write in college is or should be.
Some history books that do real history (by proper historians) and are easy to find arguments in, just off the top of my head:
For the primer on social histories, read Howard Zinn:
What you're going to come across MORE often than books is a series of articles that make different (sometimes conflicting) points about a historical issue: (I can't really link the ones I have because of copyright [they won't load without a password], but check out google scholar until you have access to a university library)
Virtually any subject can be researched, you just have to look in the right place and keep an open mind about your thesis. Just because you've found a source that blows away your thesis doesn't mean it's invalid. If you find a wealth of that kind of stuff, you might want to rethink your position, though.
This isn't comprehensive, but I hope it helps. Get into a methods class AS FAST AS POSSIBLE and your degree program will go much, much smoother for you.
The gold standard for this sort of thing is going to be A Pocket Style Manual by Diana Hacker and Nancy Sommers. You would also do well to pick up The Elements of Style by Strunk and White.
What exists for a high quality reference equation handbook?
Specifically, I've seen these kinds of handbooks for writing:
"A Pocket Style Manual" - Diana Hacker
The layout is by subject, color coated, simple bolded items, etc.
What would be the equivalent for math?
Starting in algebra, rules of exponents, point slope, geometric equations, equations for sine wave, linear algebra and vectors, calculus formulas, etc and so on. Does anything like this exist?
The book is Diana Hacker's "A Pocket Style Manual," 6th Edition. I love this little book and use it for all my papers.