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Precalculus in a Nutshell is a beautiful little book by George F Simmons, which pretty much captures everything you need to know to undertake the study of calcu
by dougabug 7y ago
Precalculus in a Nutshell is a beautiful little book by George F Simmons, which pretty much captures everything you need to know to undertake the study of calculus. https://www.maa.org/press/maa-reviews/precalculus-mathematics-in-a-nutshell-geometry-algebra-trigonometry https://www.maa.org/press/maa-reviews/precalculus-mathematic...
Linear algebra is quite a beautiful, approachable subject; and a certain amount of it is necessary to make the leap from single variable to multi-variable calculus. Without a good grip on calculus, you can’t really what’s going on under the covers with linear algebra. What you need to do is precalculus (Simmons) -> single variable calculus -> very introductory / elementary linear algebra -> multi variable calculus (Apostol) -> less introductory linear algebra but still fairly basic (Gilbert Strang Intro to Linear Algebra) -> mathematical analysis (Apostol) -> linear algebra done right (Axler). You have to apply a spiral method where you return to subjects as you gain the tools you need to understand them better. You’ll never be done understanding geometry, algebra, or analysis.
Also, math is a problem solving art, and you can’t solve problems by reading, you solve them by thinking. Seek out problems that challenge and consolidate your understanding. You should be able to prove everything in Simmons and it should seem totally natural and intuitive. Then you’re ready to struggle with calculus, which is a subject humanity struggled with for centuries before getting a rigorous handle on. You probably want to get a handle on the mechanics and intuition, first, and for that I’ve heard that “Calculus Made Easy” by Silvanus Thompson is good.
Don’t try to eat too much all at once, you’ll make yourself sick. Don’t try to cheat yourself of the patient struggle to understand, confusion is completely natural when striving to really know something.
- graycat 7y agoSimmons? WOW! He's a serious mathematician, e.g., as in his George F. Simmons, Introduction to Topology and Modern Analysis. I studied it one summer in an NSF program at Vanderbilt. Then I concluded that he is one heck of a good math writer.
- dougabug 7y agoHe has elementary textbooks on calculus and differential equations, as well, so you get an entire development from precalculus all the way to topology and analysis from the coherent viewpoint of a legit (but sympathetic) mathematician.