What's the most efficient way to study for a math exam?
I have a calculus final in two weeks and I need to improve my grade significantly. I've been reading the textbook and highlighting but it doesn't seem to help. How do math students study? Should I just do practice problems over and over? Are there any specific techniques for retaining formulas? I know them during study but forget during the test.
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Carl Sagan's 'Cosmos' explains stuff like this better than any textbook. If you can find the old TV series or the book, watch or read it. He had a gift for making the universe make sense without dumbing it down. Highly recommend.
7 Answers
Carl Sagan's 'Cosmos' explains stuff like this better than any textbook. If you can find the old TV series or the book, watch or read it. He had a gift for making the universe make sense without dumbing it down. Highly recommend.
I'd recommend the book 'A Brief History of Time' by Stephen Hawking, or for the math side, 'The Joy of x.' Your library has them. They're written for curious regular people. You don't need a degree to understand the big ideas.
This is actually a much deeper question than it appears on the surface. The simple answer most textbooks give is technically correct but misses a lot of nuance. Let me try to explain it in a way that captures the full picture.
This is something I struggled with until a professor explained it using an analogy that finally clicked. The real world is messy and doesn't always fit neatly into the simplified models we learn in textbooks.
I'm a physics grad student and this is one of my favorite questions to explain. The key insight is that our everyday intuition doesn't always apply at extreme scales — very small (quantum), very large (cosmological), or very fast (relativistic).
I teach high school science and I get this question every year. The textbook explanation is a simplification — a useful one, but a simplification. The real answer involves stuff you'd cover in a college course, but I can give you the gist.
Don't feel bad for not getting this right away. Some of the smartest people in history spent their whole lives on questions like this. The fact that you're curious enough to ask puts you ahead of most people. Keep asking why.
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