🧵 Non-calculus topics in math that require no prerequisites
Anonymous at Sat, 18 May 2024 16:13:40 UTC No. 16181636
I've been away from school for a while. Took calculus of a single variable and linear algebra a while ago. Most of it was hand wavy. I'd like to get back to math but I feel I don't have the mathematical maturity to truly understand calculus. What are some good resources/books for learning discrete math, number theory, etc. to build the maturity needed to tackle calculus?
Anonymous at Sat, 18 May 2024 16:56:33 UTC No. 16181707
>>16181636
>build the maturity needed to tackle calculus
The /sci/ wiki has (IMO) good advice in this regard:
https://4chan-science.fandom.com/wi
I'm in a similar position as you and have just finished working through Stewart's Precalculus after completing the exercises on Khan Academy. It took a while but I definitely feel a lot more confident now about all the math I learned in high school.
I'm now starting Chartrand's Mathematical Proofs: A Transition to Advanced Mathematics as preparation before tackling Apostol's Calculus I and continuing on from there. I'm obviously a noob but so far the wiki's guidance seems to be really good.
Anonymous at Sat, 18 May 2024 17:56:25 UTC No. 16181782
>>16181636
Name something specific in calculus that you failed to understand. If you can't just study calculus. If you can we will help you with that.
Anonymous at Sat, 18 May 2024 18:23:58 UTC No. 16181810
>>16181782
For starters why is integral from 1 to x 1/t dt logarithmic? This was also my motivation for “retreating” to discrete math, to get a better grasp of summation since they’re heavily involved in proving integral properties.
Anonymous at Sun, 19 May 2024 03:38:10 UTC No. 16182325
>>16181636
I'm a brainlet too, I just end up reviewing Khan academy YouTube material whenever I forget about statistical stuff.
Anonymous at Sun, 19 May 2024 03:39:26 UTC No. 16182326
>>16181810
The area under the curve y=1/x between x=1 and x=2 can be stretched horizontally by a factor of 2 and shrunk vertically by a factor of 2 to get the area under the same curve between x=2 and x=4. Similarly it's the same as the area under the curve between x=4 and x=8, and so on. Same thing works for a base other than 2. That's the basic insight, and with a bit of work you can show that if the integral from 1 to x (x being positive and not equal to 1, and we lose nothing by making x > 1) is a, the integral from 1 to x^y is ay. Here y can be any real number, but it's easiest to prove it for natural numbers first; then you should be able to extend it to integers, rationals, and finally real numbers.