Group 1

Group 1

Curriculum:

• Read Lang’s book first. When you get to Algebra 2 type stuff, use Gelfand side by side with Lang. So, read lang first, do his exercises, then do Gelfand’s exercises to make sure you can apply it.

• When you get to the Trig stuff in Lang’s book, either use Axler’s precalc book or another trig or precalc book side by side to make sure you can apply the material.

• Crack open Rudin’s book next. It will review the algebra 2 and precalc stuff in the very beginning, and introduce set theory. You can work through Rudin to learn Limits (stuff that’s sometimes taught in pre calc). It’s also a key concept in calc and, in actuality, it’s important in high school math too, especially when you think about inverse functions, domains, codomains (which range is a subset of, you’ll learn more about this later) and continuity.

• Make sure you get friends or family who know what they’re doing to test you to make sure that you know what you think you know.

• Finish Rudin side by side in Calc class.

• Take multivariable calculus at a college during a summer session (like stanford or berkeley or harvard, and surprisingly UC Santa Cruz summer math classes are open to anyone, affordable, and are surprisingly more proof based than standard or try to take a class online through an online extension school like Harvard’s extension school or UC online (UC Santa Cruz’s Math 23 is surprisingly rigorous (uses Marsden and Tromba) and way better than a standard calculus class).

• Finally, take an intro to symbolic or an intro to formal logic in the philosophy department of your school. It will be awesome. Or just read Intro to Formal Logic by Smith.

• also look at Dr. Aitken’s lecture notes when you feel more comfortable Math 378 Number Systems Aitken CSUSM(Link in resources)

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