/sci/ - Science & Math

[Anonymous No.9848951]

ITT: name your math/science objective/goal and anons post textbooks that would guide you to this goal.

For example: anon 1:
>I want to learn about topological K-theory, and I know the basics of topology and abstract algebra

anon 2:
>read up on the chapters of Munkres Topology about Urysohn lemma / tietze extension and paracompactness
>read the intro chapters on (co)homology in any algebraic topology book (easiest is Hatcher)
>read Hatcher's vector bundles and k-theory or Atiyah's k-theory (or both concurrently)

Example 2: brainlet anon:
>I'm a shitter high school drop out, I want to learn calculus

patrician anon:
>baby rudin is all you need

[Anonymous No.9848958]

>>baby rudin is all you need
Rudin is a meme.

[Anonymous No.9848960]

>>9848958
brainlet anon spotted

[Anonymous No.9848971]

In my country, Calculus is only taught at Universities.

I want to learn:

>calculus
>algebraic topology
>set topology
>set theory

I'm not in STEM, though. I want to learn it by myself.

I also want to self study Astrophysics too. What do I need?

[Anonymous No.9848981]

>>9848971
by what you've written, I can immediately guess you don't know what you're talking about, and probably just liked the fancy names. I'm going to assume you only really actually want to learn the set theory you need.

Pedagogically, the best way to learn would be calc to point-set topology to algebraic topology with the set theory you need learnt just before topology.

Of course, that assumes you actually have some maturity, which you probably don't have at all. In that case, I would recommend:

>Hammack, book of proof
>Halmos, Naive set theory
>Apostol, Calculus volumes
>Munkres, Topology (includes almost everything you need to know about set theory in its first chapter)
>Hatcher, Algebraic topology

[Anonymous No.9848982]

>>9848951
>easiest is Hatcher

[Anonymous No.9848985]

>>9848982
>implying there's an easier book

[Anonymous No.9848995]

>>9848985

[Anonymous No.9849007]

I want to learn Iwasawa theory. I don't have much background beyond undergrad math and some algebraic number theory (the stuff in pic related), what should I focus on to learn this? I want to go deeper into algebraic number theory.

[Anonymous No.9849015]

>>9849007
look into this trilogy

[Anonymous No.9849028]

>>9849015
Fuck ya, modular forms look sexy af. Thanks anon

[Anonymous No.9849037]

>>9848951

Not sure if this is irrelevant, but I'm interested in learning how the internet works. Not just some superficial overview, but how the signals are actually communicated and the math underlying it

I'm in college for CS right now, but still at a somewhat amateur level

[Anonymous No.9849297]

>Number Theory in general?
I've breezed through the Principia Mathematica a couple times, but what all should I read?

[Anonymous No.9849302]

>>9848951
I'm a physics student, I want to build a yacht out of composites.

[Anonymous No.9849306]

>>9849302
Wew boy...

[Anonymous No.9849307]

I want to learn analysis, and have Rudin's Principles of Analysis, and have done Calculus through multivariable and a proof based linear algebra class (all at a top 3 university in the US). Do I really need to go through a more rigorous Calculus book like Apostol before starting analysis? Should I do all the exercises or just skim both volumes in a month? From people with more experience in math, what are your thoughts?

[Anonymous No.9849308]

I want to learn basic differential geometry, so far I only know calculus and linear algebra. I guess I have a long way to go but I'd appreciate to be put on a somewhat right track.

[Anonymous No.9849309]

>>9849306
Yachts are cool.

[Anonymous No.9849310]

Try Spivak's Calculus. It worked well enough for me.

[Anonymous No.9849311]

>>9849307
To clarify, I haven't started Rudin, but I have the book and know that this is where I'm going to start. My goal is to skip the intro proof class and take analysis in the fall, so that next summer I can take intermediate analysis and abstract algebra abroad (can't dedicate a lot of credits to math during the year since I'm an electrical engineering major).

[Anonymous No.9849312]

>>9848971
>>9849310
Sorry, meant to reference you in that.

[Anonymous No.9849325]

>>9848971
http://4chan-science.wikia.com/wiki/Mathematics#Proofs_and_Mathematical_Reasoning
http://4chan-science.wikia.com/wiki/Mathematics#Group_Theory_Teaser
http://4chan-science.wikia.com/wiki/Mathematics#Introductory_Set_Theory
http://4chan-science.wikia.com/wiki/Mathematics#Calculus
http://4chan-science.wikia.com/wiki/Mathematics#Linear_Algebra
http://4chan-science.wikia.com/wiki/Mathematics#Point-set_Topology

http://4chan-science.wikia.com/wiki/Physics_Textbook_Recommendations#High_School
http://4chan-science.wikia.com/wiki/Astronomy_Textbook_Recommendations

[Anonymous No.9849332]

I want to have a strong understanding of complex analysis. I'm about halfway through Ahlfors, and while his style is good for rigor, I sometimes feel like I'm missing out on an intuitive understanding of what's going on. I'm skimming through "visual complex analysis" for better intuition but I'd like to hear what other people have to say about other texts at that level, as well as what I should look at after.

I also think my abstract algebra is weak, any recommendations for something rigorous that covers the basics of "stuff you're just expected to know"? I feel like I'm missing some stuff there. I grabbed a copy of Dummit & Foote but jesus christ it's like 1000 pages, idk what parts are skippable.

[Anonymous No.9849471]

>>9848958
It's a book with concise and clear explanations. Not a difficult read. I think people usually complained about the problems. Some students were not ready.

[Anonymous No.9849483]

>>9849332
D&F is just super slow
you can get the same content in fewer pages, from other introductory algebra tests
there's rotman, artin, herstein...

[Anonymous No.9849491]

>>9849332
>I also think my abstract algebra is weak, any recommendations for something rigorous that covers the basics of "stuff you're just expected to know"? I feel like I'm missing some stuff there. I grabbed a copy of Dummit & Foote but jesus christ it's like 1000 pages, idk what parts are skippable.

Just read Artin or Herstein

[Anonymous No.9849504]

>>9849037
Try "Computer Networks" by Larry Peterson, you can decide how far to go and it's a nice read.

[Anonymous No.9849505]

>calculus
>differential equations
>linear algebra (this I want to master)

as >>9848971 anon, calc is taught only at uni and I'm also self-studying

[Anonymous No.9849512]

>>9849307
You can go the Rudin way and get "Real Mathematical Analysis" by Charles Pugh, which is like a slower version of Rudin, both books are pretty alike but Pugh takes a bit of extra time to give you some intuition.

Alternatively you could read Tao analysis 1, Chapter 5 of Tao is like Rudin's Chapter 1 and I'd say it's even better than both, Rudin or Pugh, since it starts from the naturals with just Peano axioms and builds everything from there so you don't have to just assume things like commutativity and construct the integers and rationals. There's also Analysis 2 by him and it's just as good.

[Anonymous No.9849514]

>>9849332
>>9849483
Allufi is amazing, really fun and it helps a lot with intuition.

[Anonymous No.9849516]

>>9848951
learn real algebra and category theory (i'm a memester)

[Anonymous No.9849615]

>>9849297
You want to start with elementary number theory - David Burton's book is quite complete for that, covering all of the theory and some of it's most relevant applications. It's readily available online, to the point that the first result on Google for "david burton elementary number theory" should be a pdf.

[Anonymous No.9849640]

>>9849308
differential geometry of curves and surfaces by Do Carmo is perfect for that background, assuming you already have a handle with proofs. To learn any more differential geometry, you need topology, in which case there are several routes/books after that:

topology from munkres (just the important chapters, not all of it)

then you can take smooth manifolds by Lee up to your heart's desire (it's massive)
alternatively Tu's book is pretty good, or if you liked the style of Do Carmo, then that (he also has a Riemannian geometry book that is pretty good)

[Anonymous No.9849641]

>>9849307
>Do I really need to go through a more rigorous Calculus book like Apostol before starting analysis

Fuck no. Read Apostol's Mathematical Analysis book if you want a supplement to Rudin.

[Anonymous No.9849649]

>>9849505

apostol's volumes 1 and 2 covers all three things that you want, but you won't master linear algebra from it. Instead, you can read (after apostol) Axler's linear algebra done right, and if you really want to 'master' linear algebra, you need to learn category and homological algebra and some other stuff, which you might reconsider after you've read axler

>>9849516
memesters learn from categories for the working mathematician by maclane

[Anonymous No.9849731]

>>9849649
>categories for the working mathematician by maclane
what if i'm unemployed tho?

[Anonymous No.9849745]

I am an undergrad studying math & phil and aiming to go into grad school to specialize in foundations of math, specifically HoTT.

Is there any set list of material one needs to cover to properly understand UF? Outside of basic stuff like type theory, algebraic topology, mathematical logic

[Anonymous No.9849750]

>>9849731
If MacLane weren't dead he would be annoyed with you for misusing the book, but nowadays you can freely read it even if you're a NEET

[Anonymous No.9849859]

I want to learn about the mathematical relationship between enzyme active sites and their substrates meaning how the congruence of a substrate and an enzyme's active site can be quantified.

[Anonymous No.9849871]

>>9848951
Compsci student here, any compsci kiddo with physics experience or physicist that can help me make sand simulations? My goal is to simulate it in real time and also want to simulate the effect that water has on it.
I know linalg and a bit of calc.

[Anonymous No.9849872]

>>9848951
I'm doing chemistry, starting to do some undergrad research into nanochemistry/nanotech and materials science.

Any math/chemistry/physics textbooks or subjects anyone would recommend?

Advice is greatly appreciated

[Anonymous No.9850026]

i want to ace linear algebra course.

[Anonymous No.9850057]

I want to learn calculus 3

[Anonymous No.9850134]

>>9850026
linear algebra done right by axler if it's a "theoretical course", otherwise linear algebra by strang

>>9850057
stewart or apostol, depending on the level of rigor you want (stewart for shit rigor, apostol for the opposite)

[Anonymous No.9850155]

Is Paul's online calculus good enough?

[Anonymous No.9850167]

>>9850134
Thanks, what does rigor mean here? For context I'm a engineering sophomore

[Anonymous No.9850170]

>>9850167
with this new information, you should read stewart. In short, rigor is the autism added to mathematics

[Anonymous No.9850172]

I want to learn about electronic materials with a whole bunch of math, mainly materials side.

[Anonymous No.9850179]

>>9850170
Thanks.

[Anonymous No.9850205]

I want to review integrals then study line integrals, vector fields and line integrals green's theorem, surface integrals and stokes' theorem.

[Anonymous No.9850206]

>>9850205
apostol volume 2

[Anonymous No.9850208]

>>9849649
I was considering Courant & Fritz (mixed approach between pure and applied math) but I guess I'm going to use both with Apostol's as the main one. thanks, anon! btw, which would be good self-study oriented books to learn category and homological algebra? do I have to know something different than calc and linear algebra as prerequisite to learn these?

[Anonymous No.9850238]

>>9850208
I don't know what your definition of mastering linear algebra is, but you shouldn't attempt it until you have a solid grasp of abstract algebra. For starters, calculus is completely unnecessary for it. You need to learn module/ring theory to be able to get to the point of serious linear algebra. The best book that I know of that is pretty "concise" in getting to that point (which I very much like) is Aluffi's Algebra chapter 0. But I wouldn't recommend Aluffi without having first had a first course in abstract algebra though... (try Topics by Herstein first)

[Anonymous No.9850252]

I want to learn on what shit was Schrodinger high with when he developed his Wave Function. I'm a graduated high school studying (gap year) for college.

My background in physics is 101 for everything. I.e. just finished freshman physics courses.

[Anonymous No.9850256]

>>9850238
For starters, calculus is completely unnecessary for it.
I disagree with you, anon, I think that the concepts taught in Calculus are nice to know for LinAlg

[Anonymous No.9850258]

>>9850256
true, a wealth of examples comes from calculus in lin alg. But you do not need them to develop the theory

[Anonymous No.9850262]

>>9850238
I did an entire book, LinAlg and its applications, a shitty book, but still, without any knowledge of rings or even groups.

[Anonymous No.9850310]

I just want to learn how to evaluate integrals and then be good at it.

[Anonymous No.9850317]

I want to be able to tutor in college but I only know up to algebra 2 right now

[Anonymous No.9850332]

>>9850262
you are retarded if you think what you did is advanced linear algebra

[Anonymous No.9850372]

I have a pretty good understanding of undergraduate abstract algebra and point set topology. Will reading all of Atiyah-MacDonald be enough to understand Hartshorne?

[Anonymous No.9850377]

>>9850238
>calc with Apostol
>linear algebra with Axler
>intro to abstract algebra with Herstein
>module and ring theory with Aluffi
is this the right route? after all that I will be able to learn category and homological algebra?

[Anonymous No.9850392]

>>9850377
module/ring theory, category and homological algebra and advanced linear algebra are all in aluffi, which is why it's so good. Regardless, don't take it all so religiously. Doing just the first three books will take you a while, and you may reconsider what you like, etc

[Anonymous No.9850397]

>>9849007
>Michael Rosen
Nice.

[Anonymous No.9850398]

>>9850392
thanks, anon. I genuinely appreciate your replies and the time you spent helping me

[Anonymous No.9850583]

>>9850397
Super nice. One of the most enjoyable textbooks I've ever read. If that was mainly due to Rosen then I'll have to check out his other work.

[Anonymous No.9850705]

i'm a software engineer building games and i want to learn graph theory in well connected graphs (every node has a geometric maximum of connections, like a square node has four connections according to adjacent nodes)

[Anonymous No.9850720]

>>9850172
Goddammit each thread there is not a single reply to my post. What the fuck guys?

[Anonymous No.9850724]

I want to solve P =?= NP

[Anonymous No.9850746]

>>9848951
>objective
I'd like to dive into DSP. That aside, I'd just like to learn the most broadly applicable mathematics for engineering/physics (am a CS major currently)

>currently reading
>Calculus of Several Variables by Serge Lang
>Abstract Algebra by Pinter
>Software Defined Radio for Engineers by like four different guys

[Anonymous No.9850762]

>>9850720
this is a math board, newfag

[Anonymous No.9850787]

>>9850762
>ITT: name your math/science objective/goal

[Anonymous No.9850806]

>>9848951
A-any books on practical chemistry, I want set up a lab at home without killing myself...

[Anonymous No.9850811]

i want to repair my horrible bases and also get motivated with examples

[Anonymous No.9850817]

theres a book about mathematics that doesnt need exercises? something too just read about the topic and its uses and tracendance

[Anonymous No.9850826]

>>9850817
janich topology

[Anonymous No.9850847]

>>9850746
Oh, I also want to look into coding theory

[Anonymous No.9850993]

I want to learn stochastic calculus

[Anonymous No.9850996]

>>9850993
Edit: I know Calc, LA, and differential equations and basic set theory and proof writing/reading skills

[Anonymous No.9851019]

I want to get good at algorithms and algorithm analysis for competitive programming.

[Anonymous No.9851061]

Which Stewart calculus book should I start with? (For calc 3)

[Anonymous No.9851169]

>>9850724
Build a craft using this
8ch dot net/pdfs/res/315.html#9711
and ask the people upstairs, because I don't wanna type (it's late)

[Anonymous No.9851826]

>>9850817
Depends on what you want to study, but sounds like you'd like to read something like Mathematics: It's Content, Methods and Meaning. It's basically an anthology of most of modern mathematics as it was in the late 1950s, when it was written. It's formal enough to count as reading mathematics yet casual enough for a general audience. If you get it digital (it's a three volume behemoth) it's fun to skim through chapters while commuting or in trips

[Anonymous No.9851833]

>>9848951

>I want to learn race realism, the arguments against it, and the arguments for it, to the extent that I can perfectly replicate an ideal proponent of either side

E,g, Sean Last was able to humorously model a race 'denier' on April Fool's Day.
https://www.youtube.com/watch?v=3-JoZbLAuT8&t=325s

[Anonymous No.9851837]

>>9850817
Hardy and Wright has no exercises. Ryder's quantum field theory is physics but has some glances at mathematics and no problems.

[Anonymous No.9851860]

>>9850996
It's gonna be steep. Definitely get an in-depth understanding of elementary probability (basically everything in Feller's introduction to probability theory vol. 1: combinatorics, *independence and conditioning*, random variables, law of large numbers, markov chains, martingales), learn some measure theory and real analysis with a view towards probability theory (say in Rudin and Billingsley) and then get started with continuous-time processes (martingales, Brownian motion) and then you can start

[Anonymous No.9851886]

I wanna learn biophysics.

[Anonymous No.9851959]

I would like to create an algorithm and duel data structure combo that experiences and memorizes experiences, and makes intelligent decisions, but works on modern commercial processors. The ideal housing for this system would be a home user deskto, likely with a multi tasking processor. The avergae use case would be an intelligent boot useable in gaming or other information based tasks.

[Anonymous No.9852411]

I want to study neuroscience and I am a fresh CS graduate going for an A.I. master at a shitty uni, so I know next to nothing about the subject. I also just memorized for biology in highschool, so I remember jack shit.

[Anonymous No.9852414]

I want to learn more about astrophysics and space so I can have a better understanding and bring that to industry.

[Anonymous No.9852546]

I'm an Engineering student and I asked a while ago to help me find good books on Logic. Some anon helped me a lot and I read his recommendations. I want to thank whoever that was for that, it was very nice to read.

Now I'm getting into Albert Menne's Introduction to Logic. It's really interesting how you could read up a lot on really basic logic books and still get something out of them.
So yeah, really cozy, thanks anon.

[Anonymous No.9852570]

>>9852411
>neuro
protip: your strongest strength going into neuro will be ur A.I./CS stuff. you really dont need to bother with the biology unless you want to do neuroanatomy/neurophysiology. A.I. is important in neuro. if u wna do cognitive neuro thats not hard reading/learning.

[Anonymous No.9853225]

I'm a mathematics grad student that has not taken a physics course since 10th grade.

I'd like to develop a broad, but not very deep, understanding of basic physics. By "physics", I mean the kind of things an undergrad student in theoretical physics would know (mechanics, relativity, electromagnetism, quantum mechanics, etc.)

What's the most efficient way to go about this? I don't have the time or desire to work through a 300 page book on every topic.

[Anonymous No.9853252]

>>9853225
Why do you want to? Almost none of undergrad physics is relevant to math. Undergrads don't even get to quantum field theory, which is a prerequisite to most of the interesting stuff in modern physics. I can give some recommendations for just learning qft if you're interested.
Know basic mechanics, stuff from first year physics. Read the first 4 chapters of Schutz's general relativity, best place to learn special relativity and tensors in physics. Read the first half or so of Shankar's quantum mechanics, it's a clear intro but the later chapters aren't very good, also I think it covers enough classical mechanics but if not look at Goldstein's chapters on lagrangians and hamiltonians. Read the first 4 chapters of Sakurai's quantum mechanics. Now you should be able to read qft books like Lahiri and Pal, Ryder, Peskin and Schroeder, and Srednicki.
For further reading, some interesting books are Bertlmann's anomalies in qft, Coleman's aspects of symmetry, Atiyah's geometry and physics of knots, Hori's mirror symmetry, Ammon's gauge/gravity duality, Becker's string and M theory, Francesco's conformal field theory, Zinn-Justin's qft and critical phenomena

[Anonymous No.9853287]

>>9853252
Thanks for all the detail.

Motivation is mostly just curiousity and feeling like it's something I ought to know at least a little of (like not knowing how to fry an egg, or something like that).
As far as I know my work has no relation to physics.

I'd assumed that the higher-octane areas of physics would be inaccessible to somebody without any physical background; if it's possible to just dive straight into quantum field theory without serious issues I'd be interested in recommendations.

[Anonymous No.9853326]

>>9853287
There are books on physics for mathematicians. I'm not a mathematician so I'm not sure what books would be best but I can list a few that seem well received. There's takhtajan's quantum mechanics. Folland's or Ticciati's qft. Haag's local quantum physics. Deligne et al's quantum fields and strings. Hori's mirror symmetry is geared for both audiences. For most mathematicians I know this path would be much harder than what physicists do, the sheer breadth and specificity of the required math is too much. If you care about rigor, I think topological qfts and 2d conformal field theories are the best places to start but I can't recommend anything.

[Anonymous No.9853411]

>>9853225
pic related is a fast intro to physics for mathematicians

[Anonymous No.9853616]

I want to learn maths that are applicable to designing real-time interactive 3d simulations

[Anonymous No.9853624]

>>9853411
Пиздeц. Tы c yмa coшeл, Apнoльдa coвeтoвaть?

[Anonymous No.9853706]

I wanna review/brush up the basics for series (our prof went over it because we ran out of time). I also want to get a good beginner's grasp on complex analysis ( I have lang's complex analysis. are there any better ones?) and wanna be able to solve elementary geometry problems, which I have been having difficulty with. thanks

[Anonymous No.9853729]

>>9853706
Even Ahlfor's is more accessible than Lang. Consider Marsden/Hoffman w/ skimming through Needham for accessible basics.

[Anonymous No.9853738]

>>9853706
>I have lang's complex analysis. are there any better ones?
All of them are better, Lang is a meme.

[Anonymous No.9853783]

>>9853729
Ahlfor's is my course's book (haven't been there yet, I'm preping). Is it not beginner friendly? I assume the other ones are complex analysis too, or are they not?

>>9853738
why?

[/ No.9853807]

>>9853411
What about Spivak's Physics book?