Thread 16672714

-Calculus: Stewart, Apostol.
-Linear Algebra: Lay, Friedberg.
-Vectorial calculus: Marsden-Tromba.
-Differential equations: Zill, Tenenbaum.
-Complex variable: Ahlfors.
-Probability and Statistics: Evans.
-Topology: Munkres.
-Analysis: Sherbert, Apostol.
-Physics: Sears.
-Thermodynamics: Callen.
-Programming Language: C, by Ivor Horton and Herbert Schildt.
-Mechanics: Landau-Lifshitz.
-Abstract Algebra: Fraleigh.
-Differential geometry: Do Carmo.
-Galois theory: Rotman.
-Electromagnetism: Reitz.
-Optics: Hecht.
-Quantum Physics: Eisberg.
-Electric circuits: Nilsson.

Discuss (other better books, opinions, experiences, etc).

we already have a textbook thread
see >>16666400

>>16672714 (OP)
>Thermodynamics: Callen
>Mechanics: Landau-Lifshitz
>Electromagnetism: Reitz
>Quantum Physics: Eisberg
this is the worst physics textbook list i've seen maybe ever

>>16672714 (OP)
>Physics: Halliday, Resnick, & Krane
>Electromagnetism: Griffiths
>Mechanics: Taylor
>Electric Circuits: Horowitz & Hill
>Thermodynamics: There are no right answers, basically every thermo/stat text is equally shit.

>>16672960
>basically every thermo/stat text is equally shit.
>t. has never had the pleasure of perusing Schroeder

>>16673022
Schroeder is mid. Some of the explanations are fine, and it does an *okay* job of diving into some of the stat material, but the problems are fucking useless. Less an assessment of your understanding of the concepts and problem-solving strategies and more an exercise in tedium.
>Chapter 3, Problem 4, Part N: Repeat the problem again, but this time use the values from the twelfth column of Table 3.72 instead of the eleventh.

>>16672714 (OP)
3/10 list
I feel like you just tried to make it 100% Jewish

>>16672714 (OP)
>2 calc books
this is how I know you fags don't actually read books. You aren't an LLM, you don't need to read 2000+ pages, most of them repeating the same shit, to grasp fucking calculus. Amann Escher and Zorich both cover Analysis and Calc very extensively in about 1200 pages
Also the complete lack of any more advanced math texts is just the cherry on the top: where's K-theory? commutative algebra? Algebraic topology or geometry? Actual differential geometry (no, do carmo is not a text on diff geo)? Functional analysis? PDEs? Lie theory? Rep theory? QFT? Stat phys? etc.
And why only take Landau for mechanics and not electrodynamics and QM too? It's not like the books you've listed cover much more

>>16673027
joyless cretin

>>16672714 (OP)
Any online sources?

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>>16681651
>>16680491
>>16679029
KYS Nigger you already were told there's another thread for this

>>16672714 (OP)
>-Physics: Sears.
Bro why are you buying a physics textbook from a bankrupt appliance retailer?

>>16672714 (OP)
>Vectorial calculus
At least get the name right

I corrected your selection to better books, there's plenty of room and there's plenty of more to explore but i am in a fucking train to Netherlands so i couldn't remember and come up with all the good shit:
-Calculus: Spivak, Hille/Salas, Piskunov and maybe Apostol
-> Special mentionening Munkres and Spivak for Calculus and/or Analysis on Manfolds, maybe also Hubbards "Vector Calculus, Linear Algebra, and Differential Forms"
-Linear Algebra: Hoffmann/Kunze, Halmos for Linear transformations, Mirsky
-Vectorial calculus: Murray Spiegel (Watch at his other Schaums),
-Differential equations: Tennenbaum and Pollard, Boyce DiPrima
-Complex variable: Ahlfors, Kunihiko Kodaira, maybe also Cartan, and Stein & Shakarchi
-Probability and Statistics: Dwass, for Probablity only Kolmogorov and Kiyoshi Ito, for more mathematical Eisen
-Topology: Munkres, Threllfall
-Analysis: No such a thing like "Analysis", it can be Real Analysis, Advanced Calculs.. You call it. At this point: Princeton series in Analysis by Stein and Shakarchi, special Mention Choquets "Lectures on Analysis", and the german goat Amann and Escher
-Physics: Sears & Zemansky, Halliday & Resnick if you want it to be a huge ass motherfucking single book. Anything else go for a series:
-> Feynmann lectures
-> Pauli Lectures
-> Sommerfeld
-> Landau/Lifschitz
-> Berkley physics course
-> If you know German: Demtroeder and Willhelm Macke
-Thermodynamics: Enrico Fermi (There's only a tiny dover paperback), including Statistical Mechanics maybe also Reif
-Programming Language: The C Programming language by Kernighan, Ritchie
-Mechanics: Classical Dynamics of particles and systems by Marion
-Abstract Algebra: Dummit & Foote
-Differential geometry: Kobayashi, Loring Tu, Spivak, Do Carmo
-Galois theory: Literally useless, but get Artin instead
-Electromagnetism: Either Griffiths or Jackson
-Optics: Max Born,
-Quantum Physics: Dirac, Albert Messiah, Cohen-Tannoudji, Sakurai, Bethe

>>16685670

-Piskunov: avoid.
-Any huge huge ass motherfucking single book: not needed, better if organized in volumes.
--Galois theory: useful in criptography, quantum physics', to classifying complex algebraic structures in geometry, etc.
-K&R: kind of outdated, but still useful.

>>16672714 (OP)
>Electric circuits: Nilsson
This is a great introduction and quite essential.

>>16672714 (OP)
>Physics: Sears.
>-Thermodynamics: Callen.
No, just, no

Signal Processing:

>>16672960
>Mechanics: Taylor

>>16690653
i really don't understand how people learn from these dense textbooks. it's informational overload.
i learn much better doing a thing.

>>16672714 (OP)
>Mechanics: Landau-Lifshitz
Those books are trash.

>>16691957
Read paragraph, absorb it, understand it, move to the next paragraph, this can take years, I saw a man who learned multiple languages using books and instruction pampleths, once you understand language you understand were it all goes, is not violence

>>16692362
agreed

>>16672714 (OP)
-Everything: Knuth

And for everything else, there's Master Card.

>>16690653
Interesting

>>16691957
A lot of denser textbooks are intended as a reference material, something to use for finding specific, deeper analysis or information than a primary text can or should. Horowitz and Hill's Art of Electronics, for example, is regarded as one of the best and most thorough reference texts on the subject of electronics, and almost any electrical engineer you talk to would agree that having a copy on your shelf is the equivalent of an English professor owning a dictionary.

... but, it's also fucking *appalling* as a primary text for actually learning fundamentals of, or even advanced topics in, electronics; it's too dense and it's not structured for it, and the authors even spell this out in the preface, and yet, in spite of this, I know several instructors who insist on using it as a primary text for teaching electronics to undergraduates.

>>16685670
>Anything else go for a series:
>-> Feynmann lectures
>-> Pauli Lectures
>-> Sommerfeld
>-> Landau/Lifschitz
>-> Berkley physics course
Saved

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>>16672714 (OP)
>Galois theory: Rotman
Finally a decent recommendation

>>16685670
>Reif
I rather enjoyed Reif
>Electromagnetism: Either Griffiths or Jackson
That's just standard fare, going through Griffiths in undergrad and then Jackson in grad and I'm inclined to agree with some of the criticisms of Jackson.

>>16677890
>Any online sources?
hownew.ru

>>16692359
explain maybe

>>16686309
>Piskunov avoid
Why? I have this book with me kek, and my only issue that for understanding it you already have to know how to do proofs lol

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Pic related the only textbooks u need for undergrad math major

>>16672714 (OP)
wot bout this one?

>>16702770

>Why? [...] kek

-Poor esthetics

-Bad definitions from the very beginning; almost no inequalities, no sequences

-Bad order of contents

-Worst definitions of functions, limits

-No deep understanding of integrals: the question 'is this function integrable or not?' doesn't appear

-The book works with obsolete, poor definitions in general

Any recommendations for number theory?

I feel like every algebraic topology textbook I've ever looked at kinda sucked. Does anyone here have any recommendations?

>>16705300
Maunder maybe, there is a Dover reprint. Also Munkres has a book on Algebraic topology which i've found ok

>>16701399
NTA but that shit was written in the 60s and covers the bare minimum
>inb4 Goldstein
Trash as well, but for the diametrically opposite reason. Tries to cover way too much and some chapters (relativity, action-angle variables, canonical perturbation theory, field theory) are unreadable useless garbage as a result.

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>>16672714 (OP)

As a nuclear engineer, I'd add Todreas and Kazimi since it's the bible of thermohydraulics and nuclear reactor design, and it has everything about heat transfer that a person would possibly need for any PWR analysis

Now for reactor physics. If you are studying nuclear engineering and reading this, just don't be a pussy and go with Duderstadt and Hamilton. All tears will be of joy

>>16706760
Thanks

>>16672714 (OP)
- Vector Calculus: Schaum's Outline for practice
- Topology: Munkers is a great starting poiny
- Analysis: Spivak Calculus, Terence Tao
- Thermodynamics: Blundell, Garg-Bansal-Ghosh
- C: don't use Schildt, worst possible books. Use K&R or Modern C.
- Mechanics: Takwale-Puranik, Berkeley Physics
- Electrodynamics: Griffiths
- Quantum: Eisberg, Resnick
- Electronics: Millman, Halkias

>>16690653
Great references

The OG

>>16712275

In one of Newtons famous letters to Richard Bentley he talks about gravity as if it is "absurd".

<<[...]The last clause of the second position I like very well. It is inconceivable, that inanimate brute matter should, without the mediation of something else, which is not material, operate upon and affect other matter without mutual contact, as it must be, if gravitation, in the sense of Epicurus, be essential and inherent in it. And this is one reason why I desired you would not ascribe innate gravity to me. That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of any thing else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe no man, who has in philosophical matters a competent faculty of thinking, can ever fall into it. Gravity must be caused by an agent acting constantly according to certain laws; but whether this agent be material or immaterial, I have left to the consideration of my readers. [...]>>

>>16712275
this too

Some of my favorites.

-Klenke's book I like because it is not handwaving the measure theoretic aspects away and you get a handle on the nitty gritty. Don't read the whole book, some of the later chapters are better developed in other books. And I don't like some of his proofs. On the spectrum of Rudin's elegant but coming out of nowhere proofs on one side and straightforward but ugly proofs on the other side, Klenke falls too much on the latter side IMO.

-Aluffi is a hard book, but I like how category theory is used to streamline arguments. Some of it can feel unmotivated or needlessly abstract at first, but that was my mediocre algebra background probably. This book introduces you to how modern mathematicians think about algebra supposedly.

-Le Gall I like because Karatzas & Shreve was too hard for me honestly ha. The construction of Brownian motion via white noise is elegant IMO, though not classical.

-Boyd & Vandenberghe. Really nice examples and intuition. I understand it's not a definition theorem proof type book but I would like it to be slightly less conversational and prove some more things because results can drop out of nowhere.

-Stroock is a peculiar and also difficult book, he presents some unique viewpoints and results and his writing style is funny to me. If nothing else, the prefaces are entertaining. E.g. : "My decision to publish a third edition was motivated in part by the hope that its contents might cause indigestion in the memory bank of an AI system (...)".

-Wainwright I like because the classical asymptotic results felt inadequate to me, statistics is a fundamentally empirical discipline so we cannot always rely on asymptotics. You also get a nice but not overly reductive overview of the subject.

>>16672870
I'm curious what the other versions were because the thread says "V1.3" anyone know?

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Looks like the usual places to download stuff are being attacked.
https://open-slum.org/
A lot of them are down. On top of shitton of DMCA.

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>>16716450
When you say attacked, do you mean law firms acting on behalf of publishers or the publishers themselves working with authorities are requesting take downs or are there people sad enough to ddos servers and shit?

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>>16690653
EEchads rise up

>>16712275
>>16712734
Classics

>>16686309
>Piskunov: avoid
Why?

>>16716450
RIP Libgen

>>16716450
The fake libgen with harmful popup ads (Library Genesis +) also fails from time to time these days. The publishers are pretty serious imo.

>>16722955
>it's real
fuck

>>16673704
nobody "reads" a calc book tho. you learn on it. You don't understand something on it, check another one on same topic.

>>16673123
are all those jew names? lol

>>16672714 (OP)
The best research paper I read was Slepian on the concept of "indistinguishable".

I found it easy to read. If you dont I am probably smarter than you.

>>16729167
Applied math slant. Who made this?

>Set theory: Kunen
>Model theory: Marker
>Computability theory: Robič
>Category theory: Awodey

>>16727300
Why do people say Basic Mathematics by Lang is a meme?

Any recommendations for an algebra book? I will attempt to learn calculus from Lagrange’s Theory of Analytic Functions. Why were his algebraic methods not adopted?

>>16731988
Have you read the book? I personally don't think it does a good job preparing students for a real calculus book like spivak. Basically, smarter kids don't need that book, and dumb ones/adult learners need more.

>>16672714 (OP)
what's the book that is basically diff eq for retards?

>>16732298
No such thing. But I like Tenenbaum's ODE book reprint from Dover. Iirc it was complete and straightforward.

>>16732248
Then which one is a good replacement?

>>16714224
Now probability books are mentioned.
If, big IF, I want to learn chaos theory... what books should I study?
What books are included in the Chaos Theory core library?

>>16732913
You don't want "chaos theory", you want Dynamical systems and related topics

>>16732674
AOPS.

Complex Analysis:

>>16672714 (OP)
Of the English language textbooks I had, the ones I liked the most were "Calculus: a complete course" by Adams and Essex; "Linear algebra and its applications" by Lay, Lay and McDonald; "Numerical analysis" by Sauer; and "Mathematical statistics with applications" by Wackerly, Mendenhall and Scheaffer.

I studied only at the undergraduate level and most textbooks I had were at a quite basic level. Of the English language textbooks I had, the ones I liked the most were "Calculus: a complete course" by Adams and Essex; "Linear algebra and its applications" by Lay, Lay and McDonald; "Numerical analysis" by Sauer; and "Mathematical statistics with applications" by Wackerly, Mendenhall and Scheaffer. Good explanations, many examples, many exercises with answers provided to most of them.

Did somebody red books from multiple authors on same subject to compare them?

>>16734550
Yeah. It’s called procrastination.

>>16672870
threads missing

>>16732913
Strogatz would be a good primer for what you're looking for.

>>16716450
And annas is down. Book piracy is definitely under attack.

>>16672951
>this is the worst physics textbook list i've seen maybe ever
I was going to say this!

>>16734550
I don't fully read books from different authors on the same subject, but I do use different books to supplement. If I find some definition or theorem puzzling, I compare definitions and explanations or proofs with other books. This is often helpful because different authors stress different aspects and word things differently in a way that might match your own thinking better. You can then distill these different viewpoints into your own "canonical" understanding of the object.

Does anyone have something which I can pair with Axler for learning about the Singular Value Decomposition (SVD)?
I have an exam on proof based LinAlg exam in a little under 2 months
All I found was Roman which looks like it would be a bit too much to chew on

>>16673704
This.
Anyway, since you mentioned it, some decent math books are:
>Algebra
Jacobson I and II or Lang
>Commutative algebra
Atiyah-Macdonald, Matsumura or Eisenbud
>Algebraic topology
Novikov, May or Fomenko-Fuchs
>Differential geometry
Lee or Tu
>Functional analysis
Kosaida or Bourbaki
>PDEs
Evans
>Algebraic geometry
EGA, Hartshorne, or Vakil
>Lie groups, Lie algebras and algebraic groups
Bourbaki, Hall, Tauvel-Yu, Borel, Humphreys, Milne, Onishchik-Vinberg
>Representation theory
Fulton-Harris
>K-theory
Rosenberg, Weibel
>Hodge theory
Voisin

>>16741994
Trefethen's Numerical Linear Algebra.

>>16716450
Z lib was down too just now. And more buggy lately.

How much benefit would there be in going through Rudin? I had been following Forster (a German textbook for Analysis) and bombed my exam today
Lost points from dumb mistakes but really I just don't know how to prove very abstract statements involving theorems like the EVT/MVT

Is Rudin worth it? I have my second analysis exam in a month and 10 days

>>16742463
>bombed analysis exam
You should give up.
You lack the divine spark necessary to comprehend mathematics. No book will ever allow you to reach what true souls already passively intuit.

>>16742584
Thanks anon, nice talk

>>16672714 (OP)
Hello /sci/, I was directed here from a /wsr/ thread and am hoping someone here might be able to help.
I am looking for a recommendation for a good introductory book on sets and set theory, something with proofs as well. My issue is that books involving proofs oftentimes skip steps when laying out the proof, assuming instead that you know how the jump from one step to the next came about. At least, that's how it feels to me. I want something that instead is relatively easy to understand for a beginner, but one that is also clear enough in its proofs. For context, I'm interested in modal logic. To be able to understand a lot of what goes on there, foundational knowledge in set theory seems necessary. I tried going through An Introduction to Classical and Modal Logics by Adam Bjorndahl and I became stuck very quickly since even the set theory that's explained in that book is done in a way that is a bit above my level, or is at least not as simplistic in its layout of proofs. I would appreciate any assistance in finding a book that works for me.

>>16743827
just google the between stuff if you lack the mental hygiene to figure it out.

>>16743839
Not necessarily about mental hygiene. I just don't have a strong background in math (nothing past calc 2 and linear algebra, which is nothing)

>>16732674
I'm doing Stewart's Precalc
Grinding through hundreds of exercises for every simple concept but that's the fun part
But you will also need "How to Prove it" before heavy calc like Spivak or Apostol.
At least ChatGPT told me so and I'm planning to, once I finish this monstrosity

>>16685670
>>16708418
>K&R
Stop recommending K&R it is horribly outdated.
Yes the exercises are decent, but you will need to read an actual book about modern C after you finish K&R to actually learn the language
And there are better sources for good exercises these days

>>16743827
It's hard to recommend books because anons have all sorts of different backgrounds.
One of my favorite self-learner-level starter books is Susanna Epp's "Discrete Math with Applications".
It's not laser focused on your interests, but it does include some of the basics while providing a gentle introduction to more rigorous mathematical thinking. Please do give it a look, and apologies in advance if I've underestimated where you're at.

A more general tip for reading: It's an unspoken assumption of most mathematical authors that you will be reading their proofs and/or examples carefully and critically, and puzzling out the fine details of any steps you're unsure on (as in, with a pencil and paper). So even once you find a book that matches your level, you should expect to have to wrestle with it a little.

>>16743854
I definitely appreciate the recommendation. I might look into it to see if it has what I want. I'm not opposed to trying to figure things out, but with very little background in terms of proofs (and the one time I took a discrete mathematics course, I didn't understand it well), it can feel impossible. Thank you, in any case

>>16743857
>>16743843
If you've only done the standard sort of "calculus and LA for science and engineering" courses that most schools run, I think that Epp may be where you want to start, especially since you keep writing as if "proof" itself is a new concept to you.
If this is the case, you want experience as much as you want specific knowledge. So I'll be a little more forceful and recommend Epp (or something like Epp) in its entirety. Yes, even the topics that seem unrelated. They will all contribute to your future success.

>>16742463
Basically people like Rudin because it's clear (and terse). And it has a good selection of exercises.
In your case, my advice is to do more problems.
Can you even solve the homework problems? Be honest. Time it. See how long it takes. Compare it with the model solution. Identify what's wrong. Make a note.
The same with the exam you just bombed. Rinse and repeat with old exams, textbook problems, problem books and so on.

Doing more problems is the most effective and efficient way to learn math at this level. But it's hard so laxy retards don't do it.

Stop looking for that perfect book, video, article. And just do problems.

>>16743861
Proof isn't a new concept to me but a thing that I've struggled with when I was still in university. I didn't do calculus for engineers but just the standard one in case that changes anything. I will definitely take a look at the Epp book. You might be right that I just need more exposure to it before I tackle any set theory stuff (to which I am not entirely new but in which I have not been terribly engrossed besides basic statistics courses and introductory logic class). Thank you again for the recommendation

half of that shit can be done with youtube videos and paul's online math notes lol
>muh textbooks
start studying math and doing the exercises right now instead of hoarding books

>>16743956
Stop larping. It's off-putting.

>>16673704
>he has never went to the library, gotten 5 different calculus books, and compared proofs and explanations to find the best one to learn
I bet you just memorized you professor's calc book like a good boy without giving two shits about actual studying?

>>16744076
>Putting that much effort into the dullest and easiest course in a math major, which most people already did in high school
Embarrassing tbqh

>>16744101
Sorry I got confused. In my country we actually do real analysis instead of calculus. Also, since calculus tools are basically 50% of the maths people will need (with the other half being linear algebra), it's actually the most important thing to learn right

>>16744106
Imagine being such a loser that you need to brag about a course's name.

>>16744076
No but I also didn't need to compare that many when my focus wasn't math. Don't see why you're attacking me when all I want is to learn, though

>>16744136
>the difference between real analysis and calculus is just a name
I knew you probably didn't even set foot in university, but this is just sad

>>16744345
What a loser. Literally bragging that your calculus course was called “analysis”.

>>16744347
My real analysis course was called analysis, yes

>>16716450
And this is just months after the AI piracy fiasco.

>>16672714 (OP)
Sounds like a phonebook of Tel Aviv.

>>16729181
I think you meant:
>The concept ‘indistinguishable’
>Simon Saunders
https://doi.org/10.1016/J.SHPSB.2020.02.003

>>16746212
Goyim like you just don't have what it takes to work on the same level as [math] \mathbb{THE~PHENOTYPE [/math]

>>16746212
Goyim like you just don't have what it takes to work on the same level as [math] \mathbb{THE~PHENOTYPE} [/math]

>>16716450
And now Annas and the fake libgen+ are down. Dark times ahead.

>>16749940
This is probably the only chart with non-meme book recommendation i've seen in all my 4chan life (been an oldfag since 2005)

Congratulations Anon, those books are hidden gems

>>16750192
>non-meme book recommendation
>The very first recommendation is Aluffi

>>16750201
>>The very first recommendation is Aluffi
Ah, anon, you got filtered by Aluffi? Maybe McDonalds is better suited for you. Ganbatte!

>>16750429
>Filtered
No. It's a meme book. Taking a categorical perspective for a first course in algebra is retarded.

>>16750439
Pal, you just got filtered. Enjoy making some fries!

>>16750449
>Understand everything in the book
>Recognize that the book is a meme
>"Lmao you got filtered by it"
You're retarded.

>>16750453
I am sorry, mate. I didn't want to insult you! But you seem like an intellectual dwarf. I think you can do it, anon, you'll make great burgers!

>>16750192
>hidden gems
Did you even go to school?

Don’t buy modern Springer books. They fired all of their technical editors most likely. Filled with typos and nonsense.

>>16690653
>Signal processing
I’m here to bring the hurt

>Fundamentals
Lyons is the best for absolute beginners
Vetterli for people from a math background
Proakis or Oppenheim for most well rounded

>Stochastic/Kalman
Widrow wrote the Bible to adaptive filters
Simmons wrote the Bible for state estimation, though I prefer Shalom for his many examples

>Wavelets
Mallet even if it’s just for that beautiful cover, Vetterli’s is again very good here

>Detection/Estimation
Can Trees or Kay, pick one and stick with it

>Communications
Proakis again for the fundamentals
Goldsmith/Rappaport for wireless
Lin wrote the Bible for forward error correction, but I prefer Moon
For more general network theory, Bertsekas

>>16672714 (OP)
>Calculus: Stewart, Apostol.
I've also heard good things about Spivak.
Stewart on the other hand is just drilling exercises from what I understand, without understanding proofs and the theory
I really don't know which one to pick.
Apostol is the middle ground?
But really I need all 3 right?

>>16754459
Understanding is a meme.
Do problems.

>>16754459
If you want proof-ridden calculus you need to aim for a "real analysis" or "mathematical analysis" or "analysis" book. Calculus books are usually without much of any kind of proof

>>16754541
Kind...

>>16754541
What "Real analysis" book do you recommend then?

>>16755892
Rudin.

>>16743853

What is your recommendation? Interested in knowing.

I don't recommend K&R to internet strangers only. I recommend it to people who are actually close to me.

>>16673704
If anything, I'd be more likely to think they read the books than one listing ones from the subjects you list simply because they're more accessible and likely to be studied in a reasonable time frame. I genuinely don't get why anyone would expect to put something from K-theory in their list of essentials and would be biased towards your interests. There is not a single thing about combinatorics or number theory listed here, for instance and those have their own advanced math on top and it's this avalanche of specialized books that'd make no sense in a basic post like this.

>>16755892
People will say Rudin and it's good but it has this terse feeling and leaves things unmotivated, but it's great for working through and doing analysis, but need already some level of mathematical maturity, especially if you are self studying. Abbot or Pugh I think treats the concepts a bit more bite sized and conceptually.

Overall I'd say Rudin is good if you want to get your hands dirty and are a tad masochistic. Just read through both a bit to get a feel of what works better for you.

>>16701159
That image is the most compelling argument I've ever seen for esoteric techno-fascism.

>>16755892
Royden

>>16755892
R. P. Burn. You honestly don’t need more.

>>16690653
Got a collage for information theory?

>>16752577
should I or is it meme

>>16754459
Apostol is best if your course use it or find a study group.
If not, go with Spivak.

>>16760582
nta but start with picrel

>>16760582
What are the prerequisites for information theory?

>>16765156
also, is information theory more fundamental than physics?

Post one for aerospace engineering with a focus on airplanes please.

Astrophysics: Carrol/Ostlie
Mechanics: Taylor
Physics: Young/Freedman

>>16705300
yeah, start with the lectures first, then go through Hatcher

https://www.youtube.com/playlist?list=PLOROtRhtegr7DmeMyFxfKxsljAVsAn_X4

like it's a great textbook, but you only really start to appreciate it after the fact, once you know what's important and have some basic intuitions. it feels like one of those rare cases where you can't really get into the topic through pure self study, you need a lecturer sherpa because so many things are handwavy. but in the end it's totally worth it.

it struck me recently that you can actually think about programming from the perspective of algebraic topology: program states or modules are like nodes, calls and state changes are edges, invariants are loops, and continuity corresponds to computability. that means you can give absolute definitive reasons behind architectural decisions, for example where to put things in modules using the van kampen theorem, or even derive your own algorithms by starting from trivial cases and working through homologies to get the desired results. shit is whack. as far as i know, no one has done this before, it's ripe for research

voids*

>>16765156
Pretty much just an understanding of linear algebra and data structures & algorithms
>>16765174
Only Elon thinks that

>>16769915
Aluffi, Hatcher, and Shafarevich belong in undergrad.
Thinking that any grad student is reading those foundations books besides MacLane's is ridiculous.
Also, how the fuck did you pick the wrong Lee for manifolds?

>>16769923
>Shafaverich and Hatcher in undergrad

What are you on.

>>16769941
They are books for undergrad courses. Grad courses should use something like Hartshorne for AG and Fomenko & Fuchs or May for AT.

>>16769915
I know French. Should I start with Nicolas Bourbaki ?

>>16769956
>Bourbaki
Its very encyclopedic, although its considered classic i wouldn't recommend it. I'd say get some stuff from Jean Dieudonné who was also part of Bourbaki, he wrote a series called Éléments d'Analyse

>>16686309
>Any huge huge ass motherfucking single book: not needed, better if organized in volumes.
pls do an infographics or list a bunch of good books that fit this criteria

>>16697201
>>16691957
Can we get another list of shorter books made for learning instead of thick ass reference books

>>16769949
They really aren't lol. I checked through a bunch of graduate course syllabus (Ivy leagues and others) and Hatcher was a common choice for the textbook (yes, including University of Chicago from which Peter May's book was written for). In any case it is relatively ludicrous to consider algebraic topology or algebraic geometry as 'undergraduate courses' and are listed as graduate courses almost always. It would be however beginning graduate or upper undergraduate if you're looking at a really good math university.

A second pass in more intermediate algebraic topology down the line may use the books you mention. But I'd feel like May would just be included as a supplemental reference to Hatcher and then a second pass would go into more specific topics. Can't speak on algebraic geometry as much.

>>16705324
What do you recommend then for physixxxx

>>16770949
Ngl I'm convinced many are just larping when they give books like these.

>>16724077
No calculus or physics... dogshit meme infograph.. no thx

>>16770968
Applied math infographics please, no memes

>>16770977
im just a purefag

>>16757735
What's your purpose?
To learn programming or to learn C specifically as someone who already knows programming?

>>16770964
Nobody that's not female or black is getting into a math PhD without knowledge of either algebraic topology or algebraic geometry.
Graduate courses generally are second or third passes at a subject.

>>16770949
A lot of books by Japanese authors are quite good in this regard. For instance
>Matsumura - Commutative Ring Theory
>Wakimoto - Infinite Dimensional Lie Algebras
>Kato - The Heart of Cohomology

>>16771089
Some casual bigotry too yay.

Even if what you say about a math PhD is the case (which I feel varies university to university), the algebraic topology and algebraic geometry courses would still be considered graduate courses in practically any university (lets take Harvard: 231A is the course code for algebraic topology: 200 is course code for graduate courses-they list Hatcher: https://scholar.harvard.edu/sites/scholar.harvard.edu/files/fanye/files/syllabus_math231a.pdf). In reality, your first pass through topology is in general topology which may include some algebraic concepts. Then your second pass is full on algebraic topology, which here is Hatcher. Then third idk more specialized topics.

While algebraic topology and algebraic geometry are definitely strong fundamental tools with many ties to areas of math, its worth noting that there are a lot of subjects one in math can specialize in: functional analysis, PDE, mathematical logic, combinatorics, number theory which depending on your area may prove more valuable. Depending on university, PhD qualifying exams may or may not demand as much from algebraic topology or algebraic geometry and the exam is in special selected topics relevant to ones study of interest, which again may or may not include algebraic topology or algebraic geometry.

>>16672960
>>Physics: Halliday, Resnick, & Krane
My nigga.

>>16771128
Pointing out admissions processes is not bigotry.

>>16732361
how the fuck do you go through 800 pages. i don’t understand the authors. why do they write books so thick they can’t even stay open. how did you slog through Tenenbaum??

>>16672960
what about Susskind for thermo/stat mech

>>16771356
Not him, but I loosely followed Tenenbaum for a course I taught, and it's a pretty easy read.
>Ignore chapter 1 - it's just an overview, and doesn't say anything precise
>Glance at chapter 2 - it's basically just some manipulation techniques to convert the problem into integration
>Ignore chapter 3 - don't need to worry about applications
>Chapter 4 is where things properly start, but it's mostly just linear algebra, so going through it is a breeze
>Ignore chapter 5 - Laplace transform is mostly garbage, and has no place being introduced so early on
>Ignore chapter 6 - it's just more applications
>Chapter 7 is back on track, but since it's basically just a different perspective of chapter 4, and again mostly linear algebra, it's a leisurely read
>Ignore chapter 8 - just more applications
>Chapter 9 is one that should be read through carefully; it is one of the essential parts of a first run-through of diffy queues. That said, it skips over the main difficult proof on which it relies, making it a relatively easy read
>Glance at chapter 10 long enough to realize how disgusting numerical methods are, and then move on
>Chapters 11 and 12 can be inserted at any point you like, but there's much better sources for those proofs, so I would simply skip them.

>>16765156
Information theory can be understood on a lot of different levels. Cover and Thomas is a great entry level text on the topic and requires little beyond calculus and linear algebra based probability (though, occasionally does pull out some calculus of variations and real analysis).

In comparison, Polyanksy and Wu's more recent information theory text requires a very strong understanding of measure theoretic real and functional analysis to really study from properly.

>>16765174
Not sure how to answer that question. Shannon's concept of information is more general than the information theory you see in physics. More "pure math," yes. More rigorous, probably. More "fundamental." I'm not sure.

>>16767158
You probably don't know much of information theory beyond the very basics. It's an incredibly general discipline with applications and extensions to all sorts of different topics. Information geometry, as an example, uses Fisher's information metric to provide quite general and powerful results about the kinds of functions that can be probability distributions.

>>16752808
Yaakov's purple book is perhaps the best "introductory" kalman filtering book I've ever seen. His coverage of parameter estimation is definitely lacking in comparison to Kay or Van Trees, in comparison.

>>16771383
What aspects of information theory do you find to be the most intriguing?

>>16771382
based!

>>16771382
What are good follow ups in terms of:
1. dynamical systems
2. pde
also, is Lie theory a meme when it comes to solving ODE as a general method?

>>16672960
what about this

>>16770984
Recommend for both scenarios.

I want to check them out.

>>16757735
>>16771424
Modern C by Jens Gustedt. It's the gold standard IMO.

>>16771424
Well if you wanna learn programming stick to the default recommended path.
Do a Python or Java course/book/whatever, then start making things.
There really is no other way, than to do projects constantly.
Then grind leetcode to learn problem solving and master the basic algorithms.
If you master the basics you can learn frontend and databases too. Nothing feels better than making your own little app/website and seeing the fruits of your labor on your screen. That's what kept me going in the beginning, not staring at a console.

K&R is not a book for beginners. It assumes you already know how to code well and basic algorithms.
If you wanna master C then sure read K&R first and then probably King to get updated on the modern stuff.
But you have to realize C is not used to "make apps". It's not what most programmers use.
It's either used for embedded programming, or Linux, or libraries where performance is critical, like for example an ML library.

But it's pretty bad as a first language imo cause you need to implement everything yourself and you will get stuck in memory management.
But as a second or third language it's probably invaluable to learn how computers really work.

Once you've learned all this you will be a competent programmer, but if you wanna be even more competent or a "Computer Scientist", you gotta start reading textbooks like CLRS, SICP, books for networking, architecture etc etc.

>>16771445
Thanks. I have been programming for 6+ years, and 4+ years professionally.

I also recommend people to start with Python/Javascript as the ability to build stuff will keep them going.

I read K&R after I learned to program in basic C, and learned Python. Another reason I picked up the book was that it was highly recommended by smart people, and I could find it for real cheap as a student. And it was thin. It was a very good decision.

I later did an MS in CS.

I am a Programming Language "hopper", akin to a distro-hopper. I exclusively use Python in my work, though. And I think C knowledge is really valuable. It is also really good to learn in college as that's when you can dedicate time to learn regularly. If you know C, you can pick up Python/JS as an adult with responsibilities in a reasonably short time. But learning C+computer arch becomes harder at this stage.

One unconventional path I recommend to kids of my friends and colleagues is to start with Raspberry Pis. They or I create the circuit with a buzzer, a bunch of LEDs, etc. 8-15 year olds are fascinated that they can turn lights on-off or make a sound by writing code!

>>16771436
Will check it out. Thanks.

>>16672960
peak picks, griffiths quantum reads great too

hi guys i'm looking for some good reading on economics and the math behind optimal bidding, in particular for energy markets.

is this a good start?

anyone got a study plan chart for cryptography with an emphasis on cryptanalysis? like abstract algebra -> algebraic number theory -> cryptography kinda thing

>>16771128
>Some casual bigotry too yay

>>16771452
Yeah the reason I did not recommend K&R is because I was memed by /g/ to read K&R to learn programming as a noob
And it sucked

Are the AoPS books good if you’re well past the K-12 stage?

I have seen this recommended here before, but I'm not sure what to make of it? A meme, a reference book or can I actually learn something from this?

>>16772666
I wouldn't aim for it, its just a thick book compilation about some calculus, linear algebra, some minor tensor/vectoranalysis stuff, differential equations

If you already got books about that, avoid it. If you want a further reference, get it!

At this point i'd rather recommend Boas (Picture related)

>>16772914
What are the other books you have? Nice little shelf you got there

>>16771403
>Dynamical systems
Maybe the book by Arnol'd, Geometric Methods in the Theory of ODEs is good. Arnol'd is a notoriously good expositor.
If you want to do things from the right point of view, then I would recommend reading through this book by Marsden, Raitu and Abraham called Manifolds, Tensor Analysis and Applications. This is a lengthy book, but a good deal of it is just generalizing familiar statements (at least they should be if you're set on taking this approach) to Banach spaces.
The best book - especially if you want to get your hands on dynamical systems as soon as possible - is the one by Katok and Hasselblatt. It is very long, but you could simply treat part 1 as a nice 250 page book of its own.
>PDEs
No clue. I can't look past Evans, which unfortunately is a tome.
The issue with both PDEs and dynamical systems is that they are so vast, and trying to approach them from the correct perspective can take years of prerequisites before even touching the subjects themselves. You're probably better off looking for lecture notes from courses given in those subjects instead of textbooks - the same goes for ODEs as well. The notion of textbooks being reference books is especially pertinent when dealing with anything related to differential equations, simply due to the difficulty and vastness of the topic.
I would say Lie theory is essential for aiding your understanding of the ideas in differential equations, and might help for solving certain specific problems, but if what you care about is just solving differential equations, and don't care so much about the underlying structures, then you shouldn't worry too much about it - just learn the basics, and pick up bits as you need them. An excellent book on the applications of Lie groups to differential equations is the one by Olver.

>>16716450
Z library removed a lot of books because of DMCA. Even popular mainstream textbooks. The future is grim.

Real Analysis:

>>16775406
>Kumar
>Malik

>>16673704
Jumping right into Analysis after baby math is ridiculous. I'm so tired of this meme. You have *not* worked through any of the 3 volumes of Amann Escher.

bump

>>16774325
grim deez nuts. anna's archive servers has em even if z-lib goes down.

>>16776914
Annas literally was down recently.
The wait time links still don’t work.
Ipfs links don’t work.
Libgen is dead.
Libgen+ is semi-dead.
This is a concerted attack against piracy. Most people only heard about mangadex. Zlib silently removed shitton of books because of DMCA.
It is grim.

>>16776988
Libgen.li works.

>>16776988
>This is a concerted attack against piracy.
There's been a concerted attack on piracy for 20 years now.
It's gonna be fine.
Rus and Chink dgaf about such bullshit so they will figure out a solution.

Classical Mechanics: