Textbook Thread

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>>9020114
This is a great gateway book into higher level mathematics. My favorite book so far.

After reading this cover to cover I plan to dig into abstract algebra.

>>9020332
Top tier book m80.

Here's another top tier book: https://www.math.wisc.edu/~keisler/calc.html

>>9020114
uchebnik

Understanding Analysis by Abbott

>>9020114
are you actually doing the exercises or just reading it?
also, is that 3rd edition? i have 2nd edition and it doesn't look like htat.

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>What textbook(s) are you currently reading?
read this book anon

>>9020131
>buying anything that pays homage to slavery

artin is a mess. surely you cant be serious OP

>>9020332
>>>/g/tfo

>>9020538
No thanks. I'm more interested in pure mathematics. /g/ has nothing to do with my interest nor this book. I am not a CS major and want to stay away from gamers.

>>9020351
Thanks mate. Checking it out.

>>9020519
Grad students are basically slaves so It's best I embrace slavery now. At least I'll get my own slaves if I manage to get tenure.

>>9020525
This is true. But no other (popular) basic algebra book has Artin's perspective so it's still a good book for linear algebra lovers.

>>9020525
artin is pretty cool. the emphasis on linear algebra and cohesion between topics makes it stand out as a unique book.

I prefer rotman but what don't you like about artin?

>>9020131
Qaqabaqo?

>>9020332
what edition? The newest one just is too much for me in terms of how it's written

Aluffi, Algebra Chapter 0

only half way through the second chapter but I'm finding it quite enjoyable, although the exercises are quite time consuming and he expects you to solve some with minimal machinery (for example, most, if not all, of the answers online to a similar question usually involve stuff that he hasn't covered yet), which really make the cogs turn

>>9021132
The newest one. I'm reading it cover to cover and doing major theorem / proof exercises + proving in-text exercises without looking at the solutions etc.

I'm studying it rigorously to continue my studies in number theory & abstract algebra. The next book I plan to read cover to cover will be on in abstract algebra.

The chapters on algorithms, number theory, number theory applications, graph theory, combinatorics really pique my interest to learn more.

What qualms do you find with the newest version? I found chapters 1.1-1.8 to go on forever and to be really a drag. i like logic but I felt like "how to prove it" covered those exact sections more concisely. I've been reading "how to prove it" as supplement to Rosen.

Anyway. An interesting discovery, Rosen has an older text which includes topics not in his standard discrete book: http://www.mhhe.com/math/advmath/rosen/texfiles/ - I am selectively going through some of the topics of interest from that as well.

>>9021430
It has way too many stupid useless examples (at least in the first couple of sections), way too many exercises that are "same example different numbers", and as you said, the logic part dragged way too long and it felt like it was addressing brainlets.

I'd want a book that ideally says enough, and the exercises to make you think instead of the same old format of repeating what there was earlier in the text. I feel like this is a recurring theme in newer textbooks that have a new edition every year and are an attempt to standardize the curriculum.

Anyways, for algebra, I'd recommend >>9021138 (I'm this guy), or Dummit and Foote (although both of these are 700+ pages long). Aluffi has a more abstract and categorical approach from the get-go which is an attempt to familiarize the reader with concepts that are used in modern math, while D&F is more of a standard curriculum text that covers almost everything.

Both of them are quite abstract and don't really deal with applications if that's your interest. If you'd like a 'primer' to abstract algebra, the book by Pinter (Dover, so cheap) is a really good, somewhat informal, introduction to algebra with many exercises with some applications to code theory, which are quite interesting.

>>9021481
Thanks for the recommendations on algebra. I'm certainly interested in learning category theory and this is one of my main motivations in learning abstract algebra (so that I could work with different examples of categories, e.g. categories of sets / groups / etc).

Kind of funny because right now I'm on chapter 2 of Rosen (functions) and I already see how category theory generalizes the notion of inverses with isomorphisms and injection / subjection with monomorphisms and epimorphisms.

With your recommendations I'll go with Pinter and Aluffi. I peaked ahead and the exercises at the end of chapter 2 of Pinter serve as a review of topics covered in Rosen. After Pinter I'll go D&F.

I like applications (algorithms related to CS) but I also really like pure math. ESP. areas related to what I already mentioned. I'm just beginning so I have a lot to learn.

>>9021534
Just as a heads-up, Aluffi isn't that intense on the categorical part (he doesn't introduce functors until chapter 7 or so, 400 pages in), although he does motivate it in a way that seems somewhat natural, although he does really make it seem interesting by showing through examples how things like gcd, lcm, cartesian products, disjoint unions, min, max are all interrelated as universal properties of categories.

Godspeed anon

>>9021555
Okay, good to know. Thanks anon. Really appreciate it.

>>9020114
Real mathematical analysis, by Pugh

>>9021555
>how things like gcd, lcm, cartesian products, disjoint unions, min, max are all interrelated as universal properties of categories.
This piques my interest. All of those topics seemed like clusterfucks when I learned them in discrete math.

>>9021574
It's on the first chapter of the book, should take at most 1-2 days to get to the point if you read into it and do all the exercises, or less if you're already "mature".

For any category C, and an object or a pair of objects in the category, you can create (co)slice categories, and all the examples I just gave are called terminal objects in the category, meaning every object in the category has a unique morphism into or out of the terminal object.

>>9020442
It's the 1st edition

Lol, why read boring math books? Can't you guys do something more interesting, like I dunno, playing games, watching tv-shows, making music? Math and science arent entertaining that you consume after full-time daily job, you know?

>>9021898
>a shitty boring daily job + mindless entertainment is the only way to do things
you're an idiot

>>9021905
Lol, don't tell me that math can entertain you somehow, it just a useless topic that people teach you in hs/uni, that's it. Real entertaiment looks different. And hell, every job is shitty and boring, there are no interesting job anywhere, isnt that right?

>>9020332
Joke book with too many errors

>>9021959
>don't tell me that math can entertain you somehow
it does. the shitty rote memorization 'math' for non mathematicians is not math
>there are no interesting job anywhere, isnt that right?
it's not

>>9021964
It's not a joke book. It's a solid introductory book for newbs transitioning from computational mathematics to proofs. Books at that level are like that. Rosen does a good job, albeit a bit wordy, but less so than epp IMO. Rosen is also more rigorous than epp.

If you actually followed the thread then you'd see how a fruitful conversation unfolded. Those kind of conversations highlight the best of /sci/. More experienced mathematicians helping their juniors. Don't come in here and shit all over everything.

What level of math do i need to be able to understand some of the textbooks that pop up here.

>Highest math was a little bit of Cal. long time ago.
>Working through pre-algebra to calculus right now.

>>9022001
some of the textbooks that pop up here are beyond the graduate level and into very niche research topics
if you want to learn math, ask more explicitly explaining your intentions and aspirations

>>9022001
What is your daily job? It really matters anon.

>>9022010
Maintenance tech.

>>9022007
I don't have any big intentions with math. I just found a new interest in it and trying to get gud. If i can leverage it into making more money then that's cool too.

>>9022019
precalc and calculus is the way to start. serious math will then go to real analysis and linear algebra. practical math will instead go for calculus-based study of ODEs and such

>>9022027
what are the best books to go through a rigorous basis for precalc material? stuff like trig and arithmetic work?

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Does anyone have a good copy of An Introduction to Modern Astrophysics by Carroll and Ostlie? The one on libgen has mixed up page sizes and is completely impractical to use.

>>9022035
Or, alternatively, suggest a different textbook to learn basic astrophysics.

>>9022030
there's not much rigor in that I think
uhhh basic mathematics by lang is supposed to be good? I don't really know

>>9022030
Manhattan review GRE prep books. That's all the material you need for calculus and if you study that not only will you get the benefit of doing well on the GRE math section but you'll know all your pre-read coming into calculus studies

>>9022045
Ok, I can help you with that. First of all, what is your motivation behind learning astrophysics? Is it degree or just out of curiousity?

>>9022057
Just curiosity. I've taken basic introductory physics courses (i.e. basic classical mechanics and electromagnetism) and math up through differential equations and linear algebra. I also took an astronomy course that was super dumbed-down for general education. I'd like a good, somewhat rigorous overview of the subject.

>>9022001
you need to specify which ones. One of the lower level texts (intro to inter-universal teichmuller theory) would require (from the bottom up):

>Algebra, Gelfand
>The method of coordinates, Gelfand
>How to prove it, Velleman
>Geometry: Planimetry and stereometry, Kiselev
>Trigonometry, Gelfand
>What is mathematics?, Courant
>A course in pure mathematics, Hardy
>Linear algebra, Hoffman/Kunze
>Elementary Differential equations, Boyce
>Topology, Munkres
>Calculus on Manifolds, Spivak
>Principles of mathematical analysis, Rudin
>Real and Complex analysis, Rudin
>Functional analysis, Rudin
>PDEs, Evans
>Analysis on manifolds, Munkres
>Abstract algebra, Dummit/Foote
>Algebraic Topology, Hatcher
>Intro to smooth manifolds, Lee
>Foundations of differentiable manifolds and lie groups, Warner
>Galois theory, Edwards
>Linear representations of finite groups, Serre
>A classical introduction to modern number theory, Ireland/Rosen
>Introduction to analytic number theory, Apostol
>Modular functions and Dirichlet series in number theory, Apostol
>Riemannian Geometry, Petersen
>The theory of the Riemann Zeta function, Titchmarsh
>Introduction to Teichmuller spaces, Imayoshi/Taniguchi
>A course in p-adic analysis, Robert
>Foundations of p-adic Teichmuller theory, Mochizuki
>Mochizuki's papers
>IUTT

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my thesis is on the h-cobordism theorem. so yeah.

>>9022195
what's cobordism? (you can assume knowledge of basic differential geometry)

>>9021898
Most of us also engage in other entertainment, but we don't really value them as much as math since we can't get a job doing it. And since getting a job that uses math is hard, mostly due to how much math needs to be known, we have to study a lot of math by necessity.

>>9022001
Try reading Calculus Made Easy by Thompson. If you like it then move on to books like Spivak's calculus, Rosenlicht's analysis, Axler's or Hoffman and Kunze's linear algebra.

>>9022333
not him, but two surfaces are cobordant if their union is the boundary of some compact manifold of higher dimension

https://app.pluralsight.com/library/

I use this website to study computer science while I listen to music and play video-games.

>>9021898

I'm a math neet right now

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Currently self studying pic related but US edition..not really for a course I am in yet (EE junior this fall) but planning on applying to a undergrad research position over photonics and hoping to gain some useful knowledge

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>>9022734
Also getting this book by mail next week and plan on studying through it just for extra knowledge. Only got third edition tho because less $$$.

>>9022459
could you elaborate a bit? is it up to iso/homotopy? then what does this h-cobordism theorem says?

>>9020114
>What textbook(s) are you currently reading?
Hartshorne's Alg. Geom.

>What is your favorite textbook of all time?
Janich's Topology, I have never encountered another math textbook that is so intuitive and technical at the same time.

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t. hischool newb

>>9022333
When [math]M[/math] an oriented n-mfldand [math]{\Sigma_i}[/math] oriented (n-1)-mflds, then [math]M:{\Sigma _1} \to {\Sigma _2}[/math] cobordism if [math]\partial M \cong {\Sigma _1}\coprod {\Sigma _2}[/math], where the isomorphism is some orientation preserving diffeomorphism.

>>9022505
Lol, don't say that you don't have a job, and instead of enjoying your life, (via dating a girl, meeting friends, watching some good tv-shows, play cool games) you ' re doing math problems? That's like really weird, and you should consider changing your life style. Take a fresh air outside, look around ya, and start living your life with full potential.

>>9022968
Math is more fun than all the things you listed though? I don't really understand what you're trying to say.

>>9020114
great first advanced math book. I liked it a lot, and supplemented with a text with a more abstract approach gets you totally ready for most topics in algebra.

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>>9020114
I will be glad to learn more about modern and abstract algebra, as well as intermediate topics in linear algebra. I hardly know anything about algebra.

>>9022978
No, I'm saying exactly the opposite, than math is much more boring and useless than girls' dating, games' playing, show's wacthing, and that you should do that instead of math.

>>9022968
>sitting in front of a tv or monitor like a consumerist zombie is "living your life with full potential"

I do agree though that having friends and girlfriends is more important than math. Just slightly, though.

Just downloaded this. I haven't actually opened it yet but I intend to. Has anyone read it? Is there a better book?

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>>9023461

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>>9022748
A cobordism between [math]M[/math] and [math]N[/math] is a compact manifold [math]W[/math] such that [math]\partial W \cong M \sqcup N[/math], everything is in the smooth category, so [math]\cong[/math] means differomorphism. You have also oriented cobordism, framed cobordism and what not, everytime you get some equivalence relation on the set of all compact manifolds with a given dimension. An h-cobordism is a special case when the inclusions [math]M \hookrightarrow W[/math] and [math]N \hookrightarrow W[/math] are homotopy equivalences. The theorem then says that if all manifolds are simply connected, than the cobordism is trivial, i.e. [math]W \cong M \times I[/math] which immediately implies [math]M \cong N[/math]. A notable consequence of the h-cobordism theorem is the Poincaré conjecture in dimension 5 and above, I hope I will get to that.

>>9023461
you mean artin?
it's good, it's a classic. has a strong tendency towards linear algebra, which gives it a very particular flavor that sets it apart from other introductory algebra books.

>>9023120
You're right that going out with friends and having a girlfriend is great and important. But watching TV ? Are you retarded ? Do you also think lifting is more boring and useless than watching TV ? go to /fit/ and tell them.

>>9023583
It is quite nice! I lost a detail, when you write M \sqcup N you mean the space that you get by eventually identifying some diffeomorphic boundaries, as in the image? So from two cylinders you get a solid cylinder or torus, while from two S^2 (only simply connected compact 2-manifold) your (connected)cobordism is a ball without a ball inside, hence S^2×I.. and since it is homotopic to the two manifols they must be homotopic too; why the dimension 5 for Poincaré anyway? And what tools are you using to prove this stuff? (is this the reason you are working with smooth and not continuous arrows?)

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>>9023737
[math]M \sqcup N[/math] means disjoint union, just the two manifolds sitting next to each other. Naturally you picture cobordism as some very tangled "tube" with [math]M[/math] the entrance and [math]N[/math] the exit. The general idea goes as follows: every cobordism essentially looks the "trivial tube" [math]M \times I[/math] but with "handles" attached to it. Turns out that under the assumptions these handles can all be cancelled and you're left with the trivial cobordism. But to do the cancellation, you need to be able to slide the handles along the cobordism quite freely, this is why you need simple connectedness and large dimension (so you have enough room), very roughly speaking. If you're interested, google "handle decomposition", "surgery", "morse theory" and "whitney trick".

pic is somewhat related: it doesn't show cobordism, but it shows how torus is constructed by inductive handle attachment.

>>9021997
I apologise

How good is Elementary Differential Equations and Boundary Value Problems? I've been following it with my class on DE

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>>9020519
>Buying anything that doesn't

Get the fuck out

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>>9020114

>>9023461
My circuits class this fall will use this book so maybe it is alright. I think it is recommended on the wiki too

>>9023847
No problem anon! You have good humility

>>9022035
>>9022045
>>9022070
:(

>>9022035
>>9025300
I use evince for viewing djvus, and I don't have that problem when I turn off continuous mode (pages are displayed below each other in continuous mode), and when I set the size percentage to "fit page" (the page is automatically resized to optimally fit the screen area inside the reader). When I turn on dual mode (two pages are displayed side-by-side), I do get the error, so it's not like the reader I'm using is innately better at displaying the document. You could try using similar settings in your djvu viewer of choice, or you could try using a djvu editor to correct the erroneous sizing of the document, if you're autistic enough. I will try that tomorrow, and if I'm successful, I'll upload the corrected document to libgen.

>>9025394
>>9022035
>>9025300
I've just checked, and you can do the same thing in djview4, which seems to be the program you're using, based on the colour of the background (it's the exact same shade of grey, according to gimp).

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I'm actually not reading the bottom one at the moment, but it's in my lineup. I'm reading the top two and also studying out of Peskin and Schroeder, into to QFT.

>>9025394
>>9025407
I didn't even think of turning off continuous mode. You're a lifesaver.

Fixing the document on libgen would probably be helpful for other people in the future, if you ever want to pursue that project. I probably won't do it, though.

>>9025413
Interested in reading up on QFT, what would be good things to know before hand?

>>9023779
I have seen handle decomposition while studying the classification of compact surfaces(vaguely remember conway' zippers lol), morse theory and surgery seems interesting too, but it's too hard for me right now(at least the second one); thank you for your guidance senpai