/sci/ - Science & Math

[Anonymous No.5857900]

Hi /sci/,
I'm looking to formalize a course of books in the mathematics course outlined in the sticky. A few of the books are obvious, but some of the suggestions have only the author named, and some of the suggestions list only a subject. I want to formalize the course, so we can add it to the sticky, and so I can know what to study for the next few years. My hope is that we can add this more precise list to the sticky because the prospect of studying math is very exciting!
Here is the course, to be completed in order, that is presented in the picture, as best as I can gather:
1. "Single Variable Calculus: Early Transcendentals" by James Stewart
2. "How to Prove It: A Structured Approach" by Daniel J. Velleman
3. "Calculus" by Michael Spivak
4. A multivariable calculus textbook
5. A vector calculus textbook
6. "Linear Algebra and Its Applications" by Gilbert Strang
7. A differential equations textbook
8. Some textbook by Richard Courant
9. Some textbook by Tom M. Apostol
10. An abstract algebra textbook
11. "Linear Algebra and Its Applications" by David C. Lay
12. "Principles of Mathematical Analysis" by Walter Rudin
13. "Real and Complex Analysis" by Walter Rudin

... and then you're ready for the math GRE. It seems like this would be roughly equivalent to a standard undergraduate degree in mathematics. If anyone knows how to fill in the gaps of this list, please do. If we can complete this list confidently, it will make the sticky much better AND I will know what to study for the next few years (because med school might not let me in and I want to have lots of things to talk about at parties).

[Anonymous No.5857940]

>>5857900
http://www.ocf.berkeley.edu/~abhishek/chicmath.htm

[Anonymous No.5857941]

>>5857900
do not get Apostol's books on calculus and linear algebra, they are godawful.

[Anonymous No.5857951]

>>5857900
>1. "Single Variable Calculus: Early Transcendentals" by James Stewart
>3. "Calculus" by Michael Spivak
Crap

>4. A multivariable calculus textbook
>5. A vector calculus textbook
These are practically the same thing (at this level)

>7. A differential equations textbook
Tenenbaum's Dover book is good. Arnold is great when you're older.

>9. Some textbook by Tom M. Apostol
Use his calculus book to replace 1 3 4 5. His Analytic Number Theory book is good too.

>10. An abstract algebra textbook
Artin no question. Herstein's Topics in Algebra if you want a second view on the subject.

>13. "Real and Complex Analysis" by Walter Rudin
Not as universally loved as baby Rudin. You're better off reading separate books like Stein's set and come back latter to test whether you've mastered it when preparing for your oral exam.

>6. "Linear Algebra and Its Applications" by Gilbert Strang
>11. "Linear Algebra and Its Applications" by David C. Lay

What's with Lay book? His book isn't good or well known and irrelevant once you've work through Strang. Did you buy into what that troll said the other day?

Also where's the theoretical Linear Algebra slot? You really should read Shilov, Axler, or Halmos's books.

[Anonymous No.5857955]

Calculus Vol I & II by Apostol
Linear Algebra and Its Applications by Strang
Ordinary Differential Equations by Tenenbaum
A Transition to Advanced Mathematics by Smith
Elements of Set Theory by Enderton
A Mathematical Introduction to Logic by Enderton
Generatingfunctionology by Wilf
A First Course in Probability by Ross
Linear Algebra by Shilov
Complex Variables by Fisher
Applied Partial Differential Equations by Haberman
Partial Differential Equations by Strauss
Numerical Analysis by Burden
Algebra by Artin
Geometry by Brannan
Topology by Munkres
Principles of Mathematical Analysis by Rudin
Counterexamples in Analysis by Gelbaum
Differential Geometry of Curves and Surfaces by Do Carmo
Ordinary Differential Equations by Arnold
Algebraic Topology by Hatcher
Fourier Analysis; Complex Analysis; Real Analysis; Function Analysis by Stein
Partial Differential Equations by Jost
Basic Algebra I & II by Jacobson
Modern Graph Theory by Bollobás
A Classical Introduction to Modern Number Theory by Rosen
Introduction to Analytic Number Theory by Apostol
Enumerative Combinatorics by Stanley
Probability and Random Processes by Grimmett and Stirzaker

[Anonymous No.5857996]

Read Stillwell's "Mathematics and Its History" for culture
get a few books on PDEs
get a book and set theory and a book on mathematical logic. (Enderton has great books for both)
get a book on Probability theory (Grimmett & Stirzaker, Ross's books, Feller's set, Baclawski & Rota unfinished book)
get a book on Number Theory
get actual Linear Algebra books (Shilov/Halmos followed by Roman)
get a college level Geometry book
get a book on Differential Geometry
get a book(s) on Graph theory and/or Combinatorics
get a book on Numerical analysis

[Anonymous No.5858040]

>>5857951

>Implying Early Transcendentals isn't the goat Calc 1-3 textbook

Stay pleb

[Anonymous No.5858041]

>>5858040
>learning calc 3 from stewart
okay.

[Anonymous No.5858045]

OP, wouldn't it be a lot easier to just go to some university's website and see what courses they have and what books they use in those courses?

>>5857996
>get a college level Geometry book
Could you name an example?

[Anonymous No.5858047]

>>5858041

>tfw James Stewart has a PhD in mathematics and you dont

[Anonymous No.5858048]

First, you can probably get a 90% on the math GRE without knowing anything besides engineering level calc and differential equations. It doesn't test real math that much.

Also, these lists are pretty stupid because math isn't a linear thing. If you wanted to become an algebraist you could probably get by for a long time without knowing baby level analysis and calculus. I think it would be best for people to just focus on what they like, and learn the rest when they have to for classes. The only stuff in there that's truly universal is linear algebra, and I agree that Axler or some other theoretical book would probably be better.

[Anonymous No.5858057]

>>5858047
whats your point?
there are better books written about the material.

[Anonymous No.5858061]

>>5858045
Geometry by Brannan is fairly standard.

Basically anything that covers Affine, Projective, Inversive, Hyperbolic, and Elliptic Geometries as well as how they all are interrelated is good.

[Anonymous No.5858064]

>>5858040
>the goat
what?

[Anonymous No.5858063]

>>5858048
No, graduate level math is all very interconnected and you're going to end up seeing at least everything taught in undergrad no matter what sub-field you go into.

[Anonymous No.5858068]

>>5858040
>>5858047
>>5858064

blatant spee trolling pls go

[Anonymous No.5858082]

>>5858063
Except you're wrong.

[Anonymous No.5858089]

>>5858082
give an example

[Anonymous No.5858098]

>>5858089
A lot of people doing more applied things can get by without knowing any algebra (besides linear algebra)

As for things in more pure undergrad math that are very easy to avoid later on, Galois theory and Riemann integration come to mind. If you do something like combinatorics you can probably get by pretty well without knowing what a derivative is.

Anyway I don't actually advocate skipping all the undergrad math curriculum, I just think that people might be better served trying to go deeper and seeing what modern math looks like. It's not like you can't go back and learn the details of differential forms when they actually come up.

[Anonymous No.5858100]

>>5858098
>If you do something like combinatorics you can probably get by pretty well without knowing what a derivative is.
That's a pretty bad example.

[Anonymous No.5858111]

>>5858100
Only if by applied math you mean the CS kiddie pool discrete math.

>combinatorics you can probably get by pretty well without knowing what a derivative is.

Analytic Combinatorics

[Anonymous No.5858112]

>>5858111
meant to quote >>5858098

[Anonymous No.5858141]

>>5858111
I said you can avoid it. Obviously you can choose a field that uses both.

Maybe you should practice your own logic before insulting CS kids. You seem no better.

[Anonymous No.5858143]

>>5858064

>2013
>not knowing what goat is

shig

[Anonymous No.5858163]

>>5858141
Generating functions and Analytic Combinatorics play a big ass role in real combinatorics outside of petty discrete math books.

[Anonymous No.5858405]

Advanced Calculus by Fitzpatrick is a very good undergraduate Real Analysis text; I recommend it.

[Anonymous No.5858670]

>>5858405

understanding analysis

[Anonymous No.5858704]

>>5858405

Up until the last few chapters, where he clearly stops giving all fucks about what's being printed.

(but seriously, it's a great book)

[Anonymous No.5858852]

>>5858163
They also don't play a big role in a lot of real combinatorics.

[Anonymous No.5859663]

OP here.

I'm not a math major, so that is why I am so interested in having a logical curriculum for undergrad level math. I'm teaching myself, and I don't have any professors or advisors, so it's just easier to be like, "Now do linear algebra..."
Thanks a lot, I'll type this out into an ordered list later, even though that's not necessary. I never trust anyone though, especially on the internet (or my mother).

[Anonymous No.5859784]

>>5859663
why are you not using this then

"How to Become a Pure Mathematician (or Statistician)" @ Sci's Sticky?

[Anonymous No.5859835]

>>5859784
Wow that is perfect, maybe that should be a little more obvious on the sticky rather than having that tiny incomplete guide for majors at the top of the mathematics page.

[Anonymous No.5859904]

>James Stewart.
For a book about applying Calculus, you are going to want at least use Thomas'.

[Anonymous No.5859922]

>>5858163
>>5858141
Yeah, this. You can't go too far without learning about Generating Functions.

[Anonymous No.5859940]

>>5857951
I agree. Once you go through LA a first time, Shilov's book will step up your game greatly for minimal price.

[Anonymous No.5859954]

>>5857900
why dont you just formulize a course from all the homework threads?

[Anonymous No.5859952]

>>5857955
> "A First Course in Probability" by Sheldon Ross

NO NO NO NO. Fuck that book.

[Anonymous No.5860156]

Bumping for props to OP for the effort; looking forward to this.

I'm watching this thread but there better be a sticky or something soon.

[Anonymous No.5860179]

>>5860156
Agree dude, this is gold.

[Anonymous No.5860246]

>>5859663
Hey OP -
I actually am working on a project remarkably similar to this, albeit slowly. You can check out a bit of what I've done in the sticky over at https://sites.google.com/site/scienceandmathguide/subjects/mathematics/calculus

My goal is to partition each subject into logical subtopics, each with links to multiple resources (lectures, practice problems, video lectures, relevant textbook sections, practice exams, etc etc). The idea here would be that this would give a fair amount of structure to those people who want to learn this stuff outside of the hallowed halls of academia.

Anyway, just thought I would let you know that some similar work is underway, and we should totally join forces.

[Anonymous No.5860285]

>>5860246
>This is becoming good

[Anonymous No.5860313]

>>5860285

>>5860246 here
For what its worth, my lofty goal is to extend this idea to Chemistry and Physics as well.

[Anonymous No.5860333]

I did the same thing for physics and maths for a couple of years before starting a physics degree. It's probably the best thing I've ever done.

There are also plenty of lectures on the internet, so use them. The real analysis lectures from Harvey Mudd College were great for supplementing Rudin's mathematical analysis. For physics, search for lectures from the Perimeter Institute video library.

[Anonymous No.5860398]

>>5860333
I added these to a list of resources to sift through and compile - plus, these might actually help in my upcoming classes. Thanks!

[Anonymous No.5860873]

>>5857900
Lord have mercy that looks like a painful way to learn mathematics.

[Anonymous No.5861209]

Since we have this thread, does anyone know any good material with multivariable integrals, (no surface or line integrals) with a lot of non-trivial excercises with solutions worked on?

[Anonymous No.5861225]

>>5857900

>4. A multivariable calculus textbook
>5. A vector calculus textbook

This won't be enough, but there's a book "Geometrical Vectors" by Weinreich that's not very well known that covers vector calculus amazingly, better than any textbook I've ever read. I don't know if it has problems though, but if this is for self study then I strongly suggest it for the insight.