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/sci/ - Science & Math

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9264414 No.9264414 [Reply] [Original]

What's the best, most rigorous and comprehensive book covering the topic of "basic math" (below Calculus)?

>> No.9264418

Derive it all yourself, there's a reason they call it basic

>> No.9264423

>>9264414
>Basic Mathematics by Lang
>Precalculus with Unit Circle Trigonometry by Cohen
>Precalculus, Prelude to Calclus by Axler
>Precalclus, Stitz & Zeager

>> No.9264456

>>9264414
https://www.amazon.com/Algebra-Elementary-Text-Book-2-set/dp/0821819313
https://www.amazon.com/Algebra-Elementary-Textbook-Secondary-Colleges/dp/0821816489/
https://www.amazon.com/Algebra-Elementary-Textbook-Secondary-Colleges/dp/0821816497/

>> No.9264493

https://en.wikipedia.org/wiki/%C3%89l%C3%A9ments_de_math%C3%A9matique

>> No.9264526

>>9264493
I was looking through Bourboki earlier to see if they offered anything like this, but somehow missed this gem. ty

>> No.9264626

>>9264414
better question. Are any of them free online?

>> No.9264631

>>9264626
All of them are if you're not a drooling wojack.

>> No.9264633

>>9264626
Yes, Stitz and Zeager is legally free (there's more, but Stitz is the best). But I'm looking at purchasing a physical copy as a desktop reference.

>> No.9264712

Numbers and Geometry by Stillwell

>> No.9264781

>>9264418
>there's a reason they call it basic
But not because it's easy.

Reminder that it took humans over 200 millennia to develop everything before calculus, and only 400 years to get everything else.

>> No.9264931

>>9264781
yeah that guy was an idiot

>> No.9264937

>>9264781
Euler fuckin pulled some serious weight man, he's da real mvp

>> No.9264971

Don't go with Lang, I tried to use it when I started but then I found Allendoerfer and Oakley, it's basically the same as Lang but with better proofs/explanations and even some really small introduction to some cool math, you can find it on libgen, pretty much the book you need right now.

>> No.9265013

>>9264971
>Allendoerfer and Oakley

Which one?

>> No.9265051

Where is this guy?:

Pre-Calculus - Carl Stitz & Jeff Zeager
Calculus: A Modern Approach - Jeff Knisley & Kevin Shirley
The Art and Craft of Problem Solving - Paul Zeitz

>Chapter 2: Introduction to Entry-Level Mathematics, P. II
Linear Algebra and Its Applications - David C. Lay
Calculus of Several Variables - Serge Lang
Applied Differential Equations by Vladimir A. Dobrushkin

>Chapter 3: Introduction to Proofs and Survey of Higher-Level Mathematics
How to Think Like a Mathematician - Kevin Houston
How to Prove It - D. J. Velleman
Mathematics: Its Content, Methods and Meaning - A.D. Aleksandrov, A.N. Kolmogorov, & M.A. Lavrent'ev

>Chapter 4: Bringing It All Together: The First Test of Mathematical Maturity
Calculus Vol. I & II - T. M. Apostol
Analysis I & II - Terrance Tao
??

>> No.9265056

>>9264414
The most comprehensive for basic elementary math would be "What is Mathematics" by Courant. Get the 'revised' Stuart second edition, all he did was add a prologue and an extra last chapter everything else is untouched.

Axler is good because his precalc book comes with "Student Solutions Guide" so you have every second exercise completely worked out to see what he's done.

However I advise you to do neither. What I would do is find the math book you actually want to do, in my case it was a George Thomas calculus text. Anytime I ran into something I didn't understand, I simply went into Axler's book and looked it up or Khan Academy. By the end of Thomas' book I had a solid understanding of written proofs, and a lot of analytical geometry which I knew nothing of before starting the book.

Other books to just take by the seat of your pants are Knuth's Concrete Math, which is totally doable even for highschool level math ability. Spivak's Calculus is another book like that, made for self-studying and challenging enough that if you slog through it you'll make up for whatever you missed in high school.

I did go back and do "What is Mathematics?" anyway but that was just because I found it such a good book and had some free time on holiday, so I read that.

>> No.9265065

>>9265056
>What is Mathematics?
This was also on my list of books to skim over tomorrow, but I thought it was more conversational judging solely by it's name.

I'm not actually looking to go through the entire book, just doing something similar to what you're recommending; having a convienent desktop reference/review. I'm getting ready for my upper division courses and feel that I'm still way to shaky on my algebra/trig and don't know how I've made it this far desu, so I really wanted to go through some high school math like I'm preparing for the olympaids or something, lol. I can see why one might advise against spending too much time on the fundementals, but I'm a full on neet right now so I'm doing this in addition to working through some analysis text, in my (proactive) defense.


I'm leaning towards Axler's atm, so I'm very happy to have your attention since you've read both. If you could buy one for my use case, which would it be?

>> No.9265068

what level math is this to understand this page?

https://en.wikipedia.org/wiki/Gr%C3%B6bner_basis

like what person would have to google this specific thing when doing an assignment. or (eep) project?

>> No.9265073

pls get out of my thread

>> No.9265081

>>9265068
>What level math?
Commutative algebra at the level of Eisenbud. So around 2nd-ish year grad student in America.
>What person?
Someone who is interested in doing computational algebraic geometry.

>> No.9265091

>>9265065
you can get both free on libgen.io

prob axler is the best for directly looking up things, What is Mathematics is best for gaining insight into all fields like topology, number theory ect.

>> No.9265318
File: 2.11 MB, 4125x2400, 1508120571662.png [View same] [iqdb] [saucenao] [google]
9265318

lelz not posting this yet.

>> No.9265369

>>9265318
I wanted to read Enderton book on logic, and he makes a few references to topology.
After Enderton book on set theory, I'm I good to go to study point-set topology?

(Also, is topology without tears a good book?)

>> No.9265499

>>9264414
>pre-calc
>rigor
Are you an absolute fucking retard? If you have to study basic math there's a million things you need to worry about before "rigor".

>> No.9265694

>>9265091
Ok, i've got both. I guess I'll read through each and find out which one is worthy of physically purchasing :-)

>>9265499
lol stay mad

>>9265318
this guide sucks huge balls

>> No.9265758

>>9265369
no it's terrible, just get munkres

>> No.9265759

>>9265369
And studying topology is unmotivated if you havent done any real analysis, and complex analysis is an even better motivator for algebraic topology

>> No.9265801

>>9265758
Can you tell why it's terrible? I see a lot of people recomending Munkres, but from what I heard it excpects you to already have taken an analsys course.

>>9265759
I'm fine for now with "unmotivated". For now I rather this than studying something with arguments that I haven't learn yet.

>> No.9266113

>>9265801
nigga what do you think unmotivated means, it's precisely that it uses arguments that you haven't learned yet. The most important type of topological space is a metric space which, surprise surprise, is the object of study in analysis.

Munkres doesn't expect you to have anything, it literally starts with the definition of a set and unions and intersections. It has plenty of helpful diagrams, while Top without tears has basically no diagrams, the content isn't very well organised, and doesn't give you the "bigger picture".

Also you can find online most of the solutions to Munkres (at least the core chapters), eg: https://drexel28.wordpress.com/tag/munkres/

>> No.9266124

>>9265801
If you'd rather learn from some other source, here's a lecture course on topology from one of the best universities in the world, with exercises and hints and some solutions

https://www.dpmms.cam.ac.uk/~twk/Top.pdf

>> No.9266155

>>9266113
>>9266124
Thank you kind anons.

>> No.9266804

ok boys lets get back to the featured topic in the OP

>> No.9266844

There seem to be a few math books here, but the link is very slow. It has Lang's book, Courant's Pure Matematics, and the book Feynman learned from, Calc for the Practical Man, and a few others.

http://uw43tal2d7wwziju.onion/

>> No.9266866

>>9264414
Maybe read the gucking sticky?

>> No.9266913

>>9266866
maybe i already have and thoguht it was kinda shit for precalc recs?

>> No.9266916

>>9266913
>Obviously hasn't actually read the sticky

>> No.9267032

>>9264414
"Principles of Mathematics" by Oakley and Allendoerfer

>> No.9267591

>>9266916
I've referred to the sticky like a thousand times faggot

>>9267032
I really don't trust this one, can you make a case for it over some of the others mentioned ITT?

>> No.9267642

>>9265318
You have anything like that for physics and CS? Thanks, will follow this.

>> No.9267650

>>9264626
>not wanting a nice HARDCOVER book with that wonderful old book smell

>> No.9267713

>>9267642
How advanced are you in CS? There are so many solid guides out there for CS idiot. Here's a few:
https://functionalcs.github.io/curriculum/
https://teachyourselfcs.com/
https://github.com/ossu/computer-science

of course if you want memes, consult the /g/ wiki (installgentoo wiki)


For physics, try the theoretical minimum.

>> No.9267906

>>9267642
http://4chan-science.wikia.com/wiki/Computer_Science_and_Engineering
http://4chan-science.wikia.com/wiki/Physics_Textbook_Recommendations

>> No.9268200

>>9265056
OP here. Thanks for the "What is Mathematics" recommendation, I think it's just what I was looking for (something that can be meaningfully read by both high schoolers and graduate students).

>> No.9268201

>>9268200
Also, any similar recommendations would be great (I was the one who posted "Numbers and Geometry by Stillwell, since it falls into a similar category).

>> No.9268227

>>9268201
http://4chan-science.wikia.com/wiki/Mathematics#Overview_of_Mathematics

>> No.9268251

>>9268227
>http://4chan-science.wikia.com/wiki/Mathematics#Overview_of_Mathematics
I've read this but wasn't looking for basic / overview books last time, so thanks. Also, "Elements of Mathematics, From Euclid to Godel" by Stillwell is a great overview and read if anyone is looking for something similar :^)

>> No.9268379

>>9264456
damn son these are solid af, where's the equivalent for geometry and trig?

>> No.9268385

>>9268379
Euclid's Elements of Geometry (Dover books)
Hartshorne's Geometry: Euclid and Beyond (Undergraduate Texts in Mathematics)

>> No.9268387

>>9268385
Sweet, I have Euclid's and was planning Hartshorne afterward.

>> No.9268395

>>9268385
Would the study of Chrystal's algebra, Euclid's and Hartshorne's Geometry provide a more rigorous, in depth and comprehensive version of what high school (pre calc and below) is intended to provide?

>> No.9268399

>>9268395
Probably talking to myself here but I don't think Chrystal, Euclid and Hartshorne would cover the details of functions and trig (in terms of cos(x), sin, etc) like a precalc text would... Or am I mistaken?

>> No.9268403

>>9268395
You get more rigorous, in depth and comprehensive by moving on and studying college level math.

>> No.9268412

>>9268403
I'm in college atm and have taken discrete math, the Calculus series including vector calc, and applied lin alg, and I'm studying analysis on my own time. I don't go to a great school though and still feel there would be a lot for me to gain by developing my roots a bit more thoroughly. So I don't know why you're withholding recommendations, as I'm simply looking to improve and fill in the gaps that solely Chrystal, Euclid and Hartshorne would leave in sub high school level math.

>> No.9268514

>>9268395
bump, don't fai me now /sci/, need a rigorous text that isn't agebra or geometry but covers the rest of precac

>> No.9268519

>>9268514
https://www.amazon.com/Advanced-Trigonometry-Dover-Books-Mathematics/dp/0486432297

>> No.9268521

>>9268514
i'm honestly considering wilderbergers divine proportions

>> No.9268525

>>9268395
In wondering this too. I want my foundation to be firm.

>> No.9268531

>>9268519
>https://www.amazon.com/Advanced-Trigonometry-Dover-Books-Mathematics/dp/0486432297

more choices?

>> No.9268532

>>9268525
yeah, I mean I'm keeping up with my college courses but always feel I'm both lacking the bigger picture and building on top of a loose foundation.

>> No.9268671

bamp


>>9268514

>> No.9268676

>>9268531
https://www.amazon.com/Plane-Trigonometry-Loneys-Original-Classic/dp/1452898499/

>> No.9268678

>>9264418
fpbp

>> No.9268713

>>9268395
Euclid's proofs have holes in them and hartshornes's book doesn't rigorously prove the basics of geometry. Get Geometry by Moise instead and then read a trigonometry book

>> No.9269015

>>9268713
do you have a trig boook you'd recommend?

>> No.9269919

>>9269015
gelfand

>> No.9270509

>>9269919
Gelfand is a weirdo tho

>> No.9270818
File: 2.61 MB, 4125x2400, guide.png [View same] [iqdb] [saucenao] [google]
9270818

>>9265318
>tfw someone edited out the anime girl from my guide
REEEEEEEEEEEEE

>> No.9270821

>>9264414
[math]
\int_{0-}^{\infty} f(t).e^{-st}.dt \in C
[/math]

>> No.9270823

>>9270821
[math]
\int_{0-}^{\infty} f(t).e^{-st}.dt | s \in \C
[/math]

>> No.9270833
File: 2.52 MB, 5000x8000, real foundational approach.jpg [View same] [iqdb] [saucenao] [google]
9270833

>>9270818
I was in the thread, someone edited it out and another made their own, this is 1 iteration of it.