/sci/ - Science & Math » Thread #13383352

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Anonymous Mon 12 Jul 00:50:07 2021 No.13383352 View Reply Original Report

Quoted By: >>13383537 >>13383551 >>13383574 >>13384121 >>13386314 >>13386590

Hey sci, I have been trying to relearn math ever since 2020 happened. I love Elements by Euclids' ground up logical approach to deriving geometrical theorems and principles, can you recommend other books that take a similar approach in other branches of math and Physics?

Anonymous

Anonymous Mon 12 Jul 2021 01:28:36 No.13383444 Report

Quoted By: >>13383471

hoffman and kunze

Anonymous

Anonymous Mon 12 Jul 2021 01:40:23 No.13383471 Report

Quoted By:

>>13383444
I dont think I'm ready for Linear Algebra, is there something like this for calculus or algebra?

El Arcón

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El Arcón Mon 12 Jul 2021 01:57:44 No.13383537 Report

Quoted By:

>>13383352
>other books that take a similar approach in other branches of math and Physics?

Fractional Distance: The Topology of the Real Number Line with Applications to the Riemann Hypothesis
https://vixra.org/abs/1906.0237
>Recent analysis has uncovered a broad swath of rarely considered real numbers called real numbers in the neighborhood of infinity. Here we extend the catalog of the rudimentary analytical properties of all real numbers by defining a set of fractional distance functions on the real number line and studying their behavior. The main results of are (1) to prove with modest axioms that some real numbers are greater than any natural number, (2) to develop a technique for taking a limit at infinity via the ordinary Cauchy definition reliant on the classical epsilon-delta formalism, and (3) to demonstrate an infinite number of non-trivial zeros of the Riemann zeta function in the neighborhood of infinity. We define numbers in the neighborhood of infinity as Cartesian products of Cauchy equivalence classes of rationals. We axiomatize the arithmetic of such numbers, prove all the operations are well-defined, and then make comparisons to the similar axioms of a complete ordered field. After developing the many underling foundations, we present a basis for a topology.

Anonymous

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Anonymous Mon 12 Jul 2021 02:01:33 No.13383551 Report

Quoted By:

>>13383352
Check out Geometry: Euclid and Beyond by Robin Hartshorne. It follows Euclid at the start giving exercises and a guide to some of the books, but then later it goes beyond, just as the title says.

Anonymous

Anonymous Mon 12 Jul 2021 02:10:28 No.13383574 Report

Quoted By:

>>13383352
Elements of Set Theory by Enderton

Anonymous

Anonymous Mon 12 Jul 2021 06:21:51 No.13384074 Report

Quoted By: >>13384145 >>13384177 >>13386309

Bump...
I really need a book for calc

Anonymous

Anonymous Mon 12 Jul 2021 06:46:48 No.13384121 Report

Quoted By:

>>13383352
Someone here recommended this:

https://archive.org/details/ElementsOfAlgebraLeonhardEuler2015

Anonymous

Anonymous Mon 12 Jul 2021 06:57:12 No.13384145 Report

Quoted By:

>>13384074
google "free calculus textbook" and its probably at least decent

Anonymous

Anonymous Mon 12 Jul 2021 07:08:55 No.13384177 Report

Quoted By: >>13386417

>>13384074
Apostol Calculus is the best.

Anonymous

Anonymous Mon 12 Jul 2021 23:02:44 No.13386309 Report

Quoted By:

>>13384074
Start with Zorich
If you're looking for plug and chug calculus don't bother with textbooks and just start with 18.01SC

Anonymous

Anonymous Mon 12 Jul 2021 23:04:54 No.13386314 Report

Quoted By:

>>13383352
I've heard Goldstein has a nice flow to its exposition, but that's a graduate book, you might want to start with standard undegrad material like 8.01SC

Anonymous

Anonymous Mon 12 Jul 2021 23:42:01 No.13386417 Report

Quoted By: >>13386457 >>13386616

>>13384177
Would you suggest Apostol over Spivak?

Anonymous

Anonymous Mon 12 Jul 2021 23:55:14 No.13386457 Report

Quoted By:

>>13386417
no

Anonymous

Anonymous Tue 13 Jul 2021 00:51:53 No.13386590 Report

Quoted By:

>>13383352
I'm currently reading picrel
Am I meant to be reading the commentary as a novice?
there are something like 70 pages written on the definitions in book 1 alone

Anonymous

Anonymous Tue 13 Jul 2021 01:05:20 No.13386616 Report

Quoted By:

>>13386417
Spivak is wonderful, and well written. If your goal is pure mathematics I'd suggest Spivak. For anyone else Apostol is the best suggestion. It has more applications, and more exercises with calculations. Also Apostol covers more material, the part on multivariable calculus is the best there is at that level.

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