Mathematics Smorgasboard Textbook List

Why do brainlets like you assume no one has read them? Stop projecting

Pinter is a high school level text. Pressley's text can be read by anyone who has done multivariable calculus. After doing H&K and analysis, someone would be more than ready than to do a real algebra book like Artin and a real differential geometry book like Lee's smooth manifolds or Spivak's differential geometry books. Trudeau graph theory book is at the high school level so someone wanting more discrete math would get barely anything out of it. They should get Bondy&Murty/Diestel/Bollobas instead if they are looking for more depth. It makes ZERO sense to read another calculus book after finishing one so Apostol is out of place as fuck. Stein's 4 Princeton Lectures in Analysis should be in cat 4.

The whole list looks like something a CS major cooked up and doesn't realize what he's doing.

>Elementary Algebra – H. S. Hall & S. R. Knight
Shit book.
If you want to be autistic, Chrystal is better, and even that book sucks.
>Higher Algebra – H. S. Hall & S. R. Knight
Shittier.
>Kiselev
Actually good.
>Loney
Shit.

Don't know about the stats book. Just read Basic Mathematic, holy fuck.

>Pinter is a high school level text. Pressley's text can be read by anyone who has done multivariable calculus.

I'll shuffle Pinter and Pressley into category 3 and think about adding another algebra text to supplement Pinter in category 4. I get your issue with difficulty but I also am concerned about the applied v. pure distinction as well.

>Trudeau graph theory book is at the high school level so someone wanting more discrete math would get barely anything out of it. They should get Bondy&Murty/Diestel/Bollobas instead if they are looking for more depth.

This is good advice. Considering that the other books in the category don't cover graph theory, it is still a good "introduction" text IMO that complements the other texts for a survey of discrete mathematics.

>. It makes ZERO sense to read another calculus book after finishing one so Apostol is out of place as fuck.

Which is why I considered making it optional. Besides, if you just finished doing only quantitative problems without understanding the rigor in your calculus classes (*cough* Stewart *cough*), then you'll still get enormous benefit from Apostol. it's good proofing practice and you'll gain in-depth understanding of what you've done before. And if you're an applications-oriented person (let's say, focused in other STEM pursuits than pure math), then it's a good way to get your feet wet in pure math without too much commitment or lack of relevancy.

>Shit book.
>If you want to be autistic, Chrystal is better, and even that book sucks.
>Higher Algebra – H. S. Hall & S. R. Knight
Shittier.

What don't you like about those books?

At this point, I'm just thinking about just having Gelfand's first book on algebra, Kiselev, Stitz-Zeager, and then call it a day for "pre-math" grade school stuff,

>Don't know about the stats book. Just read Basic Mathematic, holy fuck.

Basic Mathematics is full of errors. Precalculus by Stitz-Zeager is more comprehensive and overall a better book.

Because people keep reposting that shitty list.

>Basic Mathematics is full of errors
reddit.com/r/math/comments/322hz5/serge_langs_basic_mathematics_errata/

...

>reddit.com/r/math/comments/322hz5/serge_langs_basic_mathematics_errata/

Exactly. It's still a good book, but there are better ones for its purpose.

That's why the Veeky Forums list needs an overhaul.

Thanks! This looks good. I tried Khan Academy and it was too simple.

>implying we haven't all read a list equal to this
lmao brainlet

Nice troll

>random signals and noise
no matter how many times I see this, it always makes me kek

awesome thread

lurking

Fuck I just realized that I butchered the formatting to this post.

Have you guys read all of these books?

thank you for the notes.

i never really understood "where it was all going" so to speak, which gave me great difficulty in deciding what is a key idea and what is a detail that i could spend time understanding later

who's more digestable for someone fresh out of an introductory calculus course, apostol or spivak?

>Ctrl+F, Zorich
>0 results
It's shit, senpai

How do i transition from CS into mathematics?

I can program, think up systems within an object oriented framework, i understand functional dependencies and stuff, and i'm interested in number theory, but i just become bewildered when i study even just the basics of discrete math (currently in a course and i'm probably going to pass with a D or C). also i have no one to talk to about math since all other CS majors hate math

>think up systems within an object oriented framework

Your mind is fucked up beyond repair.

Brilliant.

>what is ZFC

If it makes you feel better, I considered Zorich but decided against it.

Why did you consider against it? Zorich was essential to my understanding of analysis. I found it superior to rudin both in clarity and coverage of topics (depth and breadth, exception being Lebesgue integral). I was seriously amazed that russians have such high-quality texts.

Could replace Terrance Tao's work. I just thought that Tao's series on analysis was more comprehensive.

really disagree about pressley
of course we had this argument 100000 times
but I really really think you need analysis and ODEs at least to really grasp it

technically you can start tackling most introductions to higher level mathematics either after high school or after completing your first year round of calculus/multivariable calculus/linear algebra/difEQ rotation

but that almost never happens and besides topics get tangled into each other so more mathematical maturity is often a good thing

is this better than Veeky Forums's reading list? why or why not?

Another good book is Bass' Real Analysis for Grad Students, it's a crash course in analysis for somebody getting a PhD in math who will be tested on analysis they might have forgotten bass.math.uconn.edu/real.html

Thomas' Calculus, 3rd (or 4th) edition is still the best Calculus book you can ever get your hands on. If you want to do it in max hard mode get the second version, which has some grad level shit in it. I believe they sell this as the "Classic" version these days but getting harder to find.

After the 4th version they ripped out most of the rigor and replaced it with pablum. Don Knuth said that book made him a mathematician when he first took calculus in university, it's also why he chose Addison-Wesley as his publisher since he liked Thomas' Calculus so much

Pinter is approachable but it does cover algebra up to an introduction in group theory. It sounds like your only issue with it is that it's pleasant to read.

I think category 3 is appropriate, 4 is a stretch.

Fuck it, I decided to go for my /mathminor/ autodidact project using this list:

Pre-Calculus - Carl Stitz & Jeff Zeager
Calculus: A Modern Approach - Jeff Knisley & Kevin Shirley
Linear Algebra and Its Applications - David C. Lay
Calculus of Several Variables - Serge Lang
Ordinary Differential Equations – Morris Tenenbaum

An Introduction to Formal Logic - Peter Smith
A Book of Abstract Algebra - C. C. Pinter
Concrete Mathematics - R. L. Graham, D. E. Knuth, & Oren Patashnik
Introduction to PDEs with Applications - E. C. Zachmanoglou & D. W. Thoe
Introduction to Graph Theory - R. J. Trudeau

How to Think Like a Mathematician - Kevin Houston
How to Prove It - D. J. Velleman
The Art and Craft of Problem Solving - Paul Zeitz
Calculus Vol. I & II - T. M. Apostol
Analysis I & II - Terrance Tao

Is this a good idea?

Good choices. Some core stuff with branching out into more proofing and abstraction based mathematics.

If this is in order, I would put paragraph 2 ahead of paragraph 3.

this

The first 3 you have you should do in that order. I wouldn't do Lang anything until you have a good grasp on proofs. So after the first 3, do the first 2-3 in the third paragraph, the introduction to formal logic, then Pinter, Trudeau, and then sans the book I removed, do it in that order

Shit I meant paragraph 3 ahead of paragraph 2.

Replace Lang's book with Thomas Calculus 2nd-4th Edition for Multivariable calculus. More problems, better scope, solid presentation.

This is a much better order, with the last section having no particular order (your personal preference). Honestly you can probably end your /mathminor/ study project after you finish both the first and second sections because you'll start having diminishing returns on the other subjects when it comes to applications to other STEM, learning proofing skills and handling abstractions, etc., because by the time you finish Apostol thoroughly, you wouldn't need much more skill in that area unless you want to study pure mathematics. But by all means continue if you like the challenge.

Pre-Calculus - Carl Stitz & Jeff Zeager
Calculus: A Modern Approach - Jeff Knisley & Kevin Shirley
Linear Algebra and Its Applications - David C. Lay
Thomas's Calculus 2nd-4th Edition (Multivariable Chapters)
Ordinary Differential Equations – Morris Tenenbaum

How to Think Like a Mathematician - Kevin Houston
How to Prove It - D. J. Velleman
The Art and Craft of Problem Solving - Paul Zeitz
Calculus Vol. I & II - T. M. Apostol

Analysis I & II - Terrance Tao
An Introduction to Formal Logic - Peter Smith
A Book of Abstract Algebra - C. C. Pinter
Concrete Mathematics - R. L. Graham, D. E. Knuth, & Oren Patashnik
Introduction to PDEs with Applications - E. C. Zachmanoglou & D. W. Thoe
Introduction to Graph Theory - R. J. Trudeau

I keep seeing Thomas calculus (older editions) and Calculus: A Modern Approach - Jeff Knisley & Kevin Shirley popping up. Are they really that good? What advantages do they have over your typical Stewart book?

Thank you for putting this list together. I am starting a HEP PhD this october and I am going to need some group theory for the theory classes we have to take.

I have some knowledge of this from previous particle physics courses (SU(2), SU(3), generators etc) but I have basically no physical intuition about these and definitely no deep understanding of them other than that they represent some symmetry of a Lagrangian.

Does anyone have any good textbooks for intro to group theory, or maybe something more applied to groups and representations in particle physics that are good for a beginner? Cheers

>Analysis Now
fucking lol

No handwaving without going into analysis intro. You'll develop the intuition instead of being told what works and what doesn't.

faculty.etsu.edu/knisleyj/calculus/Crisis.htm

faculty.etsu.edu/knisleyj/calculus/facing.htm

faculty.etsu.edu/knisleyj/calculus/plan.htm

They're also easily found as free .pdfs so yeah. Check them out if you're curious.

Veeky Forums-science.wikia.com/wiki/Mathematics#Group_Theory_Teaser
Tinkham - Group Theory and Quantum Mechanics (Dover Books on Chemistry)

Thomas Calculus & Analytic Geometry version 3 and 4 and probably the best there is on the subject in terms of rigor, clear concise explanations and building intuition. Version 1 is just lecture notes from his course, and Ver 2 is lecture notes on steroids where a lot of crazy rigor is thrown in. Ver 3 and 4 are the most well rounded and complete, plus they teach you linear algebra.

I couldn't find an older pdf version of Ver 3 so I had to buy it off Abe Books, which wasn't cheap. Ver 4 is like $200 or something if you can find it, though any local library prob has a copy.

Does it cover multivariable calculus?

Yes but depends on the printing you get, some are split into 2 parts and other combined into one book. The second part deals with linear algebra, functions of several variables, infinite series, vector analysis, and differential equations.

My 3rd edition is both books combined and it looks like the vast majority of 4th editions I've seen avail are both combined too with like 800 pages.

You want the version by "George B. Thomas, Jr.", 3ed or 4th version (3 is best), and not any of the versions co-authored by Finney which are the neutered brainlet versions. If you can find the Classic version, it's actually the second edition which is the hardest version. Here's one on Amazon you can find cheaper copies a.co/at82CTZ

>a.co/at82CTZ

Is there a version I can preview?

Also what about this calculus book? It seems like it was written by the same guy without Finney.

www3.nd.edu/~mregan9/Teaching/calc2.pdf

The library maybe. So-called "open library" has a copy of the 4th edition with a waiting list openlibrary.org/books/OL22723401M/Calculus_and_analytic_geometry

Alternatively you can just buy Calculus 3rd version from the 60s by Thomas, it's Mutli Variable and DIfferential Eq too a.co/fYETE14 for only $10 (doesn't include the 'analytical geometry')

>a.co/fYETE14
Ignore that, it's the Finney reprint damnit I screwed up ISBNs.

They just used his name it's almost completely different.

The way these later version work is Thomas leased out the text copyright, and the other authors rewrite his orig Calculus (Or Calc w/Analytic Geometry) text to make it brainlet friendly. Then they attach his name to the book as it's famous and then go con universities into making them mandatory texts with new versions every single year that just rearrange the exercises and change the pictures. There's like no rigor left from the original book.

The only good version are "Calculus w/Analytic Geometry", 2-4 ed.

>I'll compile a list of books my school had me read as an undergrad into arbitrary tiers and post it on Veeky Forums
Can we stop doing this? No one cares, especially when the vast majority of textbooks there are just awful.

Thanks everyone. I've decided to finalize my /mathminor/ autodidact reading list with these books:

Pre-Calculus - Carl Stitz & Jeff Zeager
Calculus: A Modern Approach - Jeff Knisley & Kevin Shirley
Linear Algebra and Its Applications - David C. Lay
Calculus of Several Variables - Serge Lang
Ordinary Differential Equations – Morris Tenenbaum

How to Think Like a Mathematician - Kevin Houston
How to Prove It - D. J. Velleman
The Art and Craft of Problem Solving - Paul Zeitz
Calculus Vol. I & II - T. M. Apostol

A Book of Abstract Algebra - C. C. Pinter
An Introduction to Formal Logic - Peter Smith
Concrete Mathematics - R. L. Graham, D. E. Knuth, & Oren Patashnik
Introduction to PDEs with Applications - E. C. Zachmanoglou & D. W. Thoe
Introduction to Graph Theory - R. J. Trudeau
Analysis I & II - Terrance Tao

I lied, one last revision:

Pre-Calculus - Carl Stitz & Jeff Zeager
Calculus: A Modern Approach - Jeff Knisley & Kevin Shirley
Linear Algebra and Its Applications - David C. Lay
Calculus of Several Variables - Serge Lang
Ordinary Differential Equations – Morris Tenenbaum

How to Think Like a Mathematician - Kevin Houston
How to Prove It - D. J. Velleman
The Art and Craft of Problem Solving - Paul Zeitz
Calculus Vol. I & II - T. M. Apostol

A Book of Abstract Algebra - C. C. Pinter
An Introduction to Formal Logic - Peter Smith
Concrete Mathematics - R. L. Graham, D. E. Knuth, & Oren Patashnik
Introduction to Graph Theory - R. J. Trudeau
Introduction to PDEs with Applications - E. C. Zachmanoglou & D. W. Thoe
Introduction to Probability - D. P. Bertsekas & J. N. Tsitsiklis
Nonlinear Dynamics and Chaos - S. H. Strogatz

Analysis I & II - Terrance Tao

fucking christ man

Do you really think it's a good idea?

Is Pre-Calculus - Carl Stitz & Jeff Zeager really the best there is for pre-calculus?

this is embarassing.

because this list is shit and anyone actually interested in any of these topics would find better written and better presented books within 5 minutes on google or by simply talking to a professor in the field

>within 5 minutes on google

where do you think these books were found?

>by simply talking to a professor in the field

"pay me $200 for the latest edition of my textbook!"

Good one faggot

yep. you deserve that list of books OP posted. enjoy your undergrad studies.

Kek

>hurr durr I'm going to offer vapid criticism instead of suggesting better books

You deserve AIDS. Thanks for bumping a list you hate.

>doesn't sage shit threads
so this... is the power... of undergrads........

I don't understand why you insist on not following your own advice.

>doesn't know how sage works
keep posting please

This thread is getting bumped.