Anonymous at Sun, 19 May 2024 05:16:28 UTC No. 16182373

>>16182312
>I found two books that appeal to me,
They may be appealing, but will they provide you with "mathematical maturity"? A nice phrase that authors of advanced textbooks use to describe all of the math you're just assumed to know.

Anonymous at Sun, 19 May 2024 19:12:44 UTC No. 16183160

>>16182312
Don't be fucking stupid, heed my advice. Buy the book called Mathematics for Physicists by Altland, it's made by Cambridge. Google library genesis, click on the Wikipedia article, then click on the domain link which should be libgen.rs
Download Altland's book, then search the solution manual for the book by adding solution to its title or find it by the author, it's there because I downloaded it myself. You're gonna want to buy his book yourself though since it's nice to have a physical copy. The first chapter on set theory and group theory is the hardest chapter, it will take the longest time to learn, but keep rereading the chapter until it at makes sense to you, attempt his problems and or look at the solution manual then reattempt the problem from memory and try to understand it. The first chapter is the hardest, after the first chapter everything gets easier, you'll be proving vector spaces in the 2nd chapter, then it's regular arithmetic linear algebra, followed by calculus, then some differential equations and complex analysis, it's easy though, it's just that the first chapter is the hardest to understand until it clicks. You can finish his entire book in a year or 2 if working a full time job. After that you can try math methods by blennow his solution manual is available as well or mathematical physics by tikhonov dover book for pdes, you're all set for math after that.

Altland -> Blennow is a safe way to learn since they both have solutions manual on library genesis. You'll have all the math you need then for anything.

Anonymous at Sun, 19 May 2024 19:15:58 UTC No. 16183165

>>16182312
*Mathematical Methods for Physics and Engineering 1st Edition
by Mattias Blennow (Author)

Anonymous at Sun, 19 May 2024 19:19:37 UTC No. 16183175

>>16183165
>Mathematical Methods for Physics and Engineering
*Laughs in Analysis* Is that the follow up to Mathematical Methods for Niggers and Canadians?

Anonymous at Sun, 19 May 2024 19:28:17 UTC No. 16183186

>>16183160
Can someone tell me if this is a troll or if this advice is legit.

What about the infinitesimal/nonstandard approach recommended in the wiki?

Anonymous at Sun, 19 May 2024 19:47:20 UTC No. 16183216

>>16182373
> “mathematical maturity” describes mathematical knowledge

kek, nice larp anon

Anonymous at Sun, 19 May 2024 20:03:24 UTC No. 16183242

>>16182312
I used mit ocw materials and felt they were fine
Just use both books if you want but make sure you do most exercises if not all
I'd pick more standard texts but whatever you find engaging should be fine
Lax has a great linear algebra book so your choice might be fine

Anonymous at Sun, 19 May 2024 20:09:38 UTC No. 16183258

>>16183186
Math methods books are usually very shallow and/or fast paced, I wouldn't use them to replace a proper calculus textbook
They are great references and sources of exercises though, so consider getting one after you've learned calculus it somewhere along the way

Anonymous at Sun, 19 May 2024 21:40:53 UTC No. 16183354

>>16183216
You got filtered by "mathematical maturity", didn't you? It's ok, many such cases.
>There are no difficult proofs in this course, students are only advised to have a certain level of mathematical maturity, with the implicit assumption being a working knowledge of Calculus 1-3, Linear Algebra, Algebra , Set Theory, Probability theory, Ordinary and Partial differential equations, some contact with real and complex Analysis including exposure to concepts from Topology, Symplectic geometry, Fourier analysis etc; all of which the reader will find as part of a normal elementary education. Prior exposure to electromagnetism is helpful, but not required. Many students have also reported that prior experience interning at CERN to be beneficial, but this is also optional.

Anonymous at Sun, 19 May 2024 22:46:16 UTC No. 16183435

>>16183186
It's legit

Anonymous at Sun, 19 May 2024 22:55:22 UTC No. 16183445

>>16182312
You don't need analysis if you want to study anything that is not pure mathematics.
If you're an idiot go through algebra chapter 0 by aluffi then the big book of real analysis by Johar.

If you're smart go through mathematics for physicists by Altland then Mathematical Physics by Tikhonov or Mathematical Methods by Blennow.

Either way you're a pretty fucking stupid person if you decide to go through Aluffi then Johar, because you're dumb as shit and misconstrue Mathematical maturity as the end all to be all then just do Aluffi then Johar, then do Functional analysis by Reed and Simon then do Complex Analysis by Lang, you'll definitely learn calculus that way, dumbass.

Anonymous at Sun, 19 May 2024 22:58:45 UTC No. 16183451

>>16183186
You're stupid if you are worrying about this, it's all the same, don't even try studying Calculus if you're worried about something as non-trivial as this.

Anonymous at Sun, 19 May 2024 23:09:28 UTC No. 16183466

>>16183186
That wiki is over a decade old and hasn't been updated since, it's not even good advice

Anonymous at Sun, 19 May 2024 23:39:33 UTC No. 16183529

>>16183466
>a decade old
Oh no. YIKES! Physics and mathematics doesn't go "out of date" like this years iPhone faggot.
>>16183445
>You don't need analysis if you want to study anything that is not pure mathematics.
Opinion immediately discarded with extreme prejudice. You'll never be white, you will never be a woman.

Anonymous at Sun, 19 May 2024 23:49:17 UTC No. 16183544

>>16182312
Algebra Chapter 0 by Aluffi -> Mathematics for Physicists by Altland -> Real and Complex Analysis by Rudin. You'll know everything about calculus once you finish these books.

Anonymous at Mon, 20 May 2024 00:27:29 UTC No. 16183603

>>16183354
NTA but Mathematical maturity isn't about knowledge of specific fields. It's actually all about reps in the gym, i.e., have you spent time trying to learn difficult mathematical subjects?

You can spend the next 40 years reading every single Springer UTM/GTM textbook line by line, but you'll never develop any mathematical maturity if you don't actually spend time trying to figure out the problems.

Anonymous at Mon, 20 May 2024 00:35:21 UTC No. 16183617

>>16183354
> there are no difficult proofs; students are only advised to have a certain level of mathematical maturity, *with* an assumption they’re exposed to XYZ

Scratching my head rn trying to understand why you’re trying to make my point for me lmfao.

Sorry, but I’m placing an undergrad with a 60 on the Putnam who hasn’t taken a course higher than Diff Eq above a graduate student who’s struggling with their topology homework in terms of mathematical maturity. It’s about the familiarity and ease with which you construct mathematical arguments, not the content knowledge, retard.

Anonymous at Mon, 20 May 2024 01:15:52 UTC No. 16183666

>>16183603
Yes, notice I specified "working knowledge".
>>16183617
>Scratching my head rn trying to understand why you’re trying to make my point for me lmfao.
It's alright if you're stupid, not everyone needs to be smart.

Anonymous at Mon, 20 May 2024 01:17:06 UTC No. 16183670

>>16182312
Why do so many of you autists reject the Stewart Canon?

Precalculus: Mathematics for Calculus - Stewart

Calculus: Early Transcendentals - Stewart

You don't need anything else.
You don't want anything.
Just read these two books and then an intro to logic/proofs book and then start analysis.

Anonymous at Mon, 20 May 2024 01:19:12 UTC No. 16183672

>>16183670
Because he was a gay leaf.

Anonymous at Mon, 20 May 2024 01:24:44 UTC No. 16183679

>>16183672
Doesn't matter, it's the best way for the vast majority of people, including literally everyone who asks this kind of question on /sci/. There is a reason even top tier school follow that path in undergraduate programs.

You're not some special hyper intelligent autist nor are the pseuds recommending dogshit books from the past. Believe it or not retards, pedagogy has advanced since the fall of the soviet union.

Read Stewart.

Anonymous at Mon, 20 May 2024 01:27:17 UTC No. 16183681

>>16183679
>You're not some special hyper intelligent autist
Wrong.
>pedagogy has advanced since the fall of the soviet union.
Probably wrong, but somewhat right, in that it's now designed to cater to niggers.

Anonymous at Mon, 20 May 2024 01:28:30 UTC No. 16183682

>>16183666
Well yes but "working knowledge" doesn't mean you have some incredibly broad set of subjects that you have studied.

One of the most brilliant professors I've ever had the pleasure of working with never took a Lebesgue integration focused probability theory course and yet his 30+ years of linear algebra and convex analysis experience allowed him to solve really challenging probability problems without this "basic" set of skills you'd acquire in your first year of grad school today. Reps in the gym doesn't mean you have a broad knowledge base, it means you know how to use the knowledge base you have, regardless of its breadth.

Anonymous at Mon, 20 May 2024 01:30:27 UTC No. 16183683

>>16183682
>Well yes
I accept your concession. Didn't read the rest.

Anonymous at Mon, 20 May 2024 01:37:38 UTC No. 16183689

>>16183679
>There is a reason even top tier school follow that path in undergraduate programs.
There is a reason, and it's the power of the textbook lobby. A good book doesn't need to go up to edition 23 or whatever they're at now. Yet their is a financial incentive to reorder the questions around and demand students buy a whole new textbook instead of acquiring it from the secondary market. They get away with this shit because fucking retards like you buy into "muh pedagogy" (more like pedal-to-goy-agy). Lol sealed book, online access code inside, and the nigger cattle actually pretend they love it. ahahahahahahaha

It's not used at top schools in the honours programs, if it is, the prof is a nigger.

Anonymous at Mon, 20 May 2024 01:44:53 UTC No. 16183693

>>16183683
> Didn't read the rest.

Not surprising. You got filtered by one of the most straightforward concepts in all of mathematics education.

Anonymous at Mon, 20 May 2024 01:47:16 UTC No. 16183694

>>16183693
The rest was just some anecdote about a professor, it wasn't worth reading anyways. I wonder if you're a jeet wasting his energy on elementary geometry problems and pretending these "reps" count for maturity.

Anonymous at Mon, 20 May 2024 01:54:24 UTC No. 16183703

>>16183694
> I wonder if you're a jeet wasting his energy on elementary geometry problems and pretending these "reps" count for maturity.

Not a pajeet. You'd be surprised how much you can learn by going through the more challenging problems in a textbook from a subject you've already taken a course on. It's not an accident that math professors really encourage things like problem books when students are trying to learn analysis/probability/algebra etc.

You could be literally Terry Tao and you'd still probably get something out of spending a few minutes going through problems you haven't seen before in something like measure/topology/algebra etc.

Anonymous at Mon, 20 May 2024 02:23:03 UTC No. 16183730

>>16183689
>schizo rambling
They could just do the same to Spivak or Apostol, re-order the questions, but they don't. For a reason.

>>16183689
>It's not used at top schools in the honours programs
If you were at a top school in the honors program you wouldn't be on /sci/ asking how to learn calculus, but you're not. You're a mentally disabled social anxiety ridden autist online, ergo read Stewart.

Anonymous at Mon, 20 May 2024 02:43:01 UTC No. 16183744

>>16183730
>asking how to learn calculus
Do you think everyone that posts is OP? Do you know how this site works?

You cannot push Stewart over Apostol or Spivak and call others retarded.

Anonymous at Mon, 20 May 2024 03:04:53 UTC No. 16183762

>>16182312
By starting with applications and analysis.
Don't even fucking bother with the """topic"""
Like who cares about some retarded methods when you'll learned their actual analysis only in analysis.
So I would start with PDEs and Real Analysis.

Anonymous at Mon, 20 May 2024 04:31:16 UTC No. 16183858

>>16182312
Mathematics for Physicists by Altland, buy it from Amazon and download the solutions manual from libgen.rs
It's teaches you linear algebra, single and multivariable calculus and complex integration with differential equations, you won't regret it.

Anonymous at Mon, 20 May 2024 04:47:08 UTC No. 16183878

Bump

Anonymous at Mon, 20 May 2024 05:02:49 UTC No. 16183906

>>16183858
I prefer Boas. Why Altland?

Anonymous at Mon, 20 May 2024 05:04:14 UTC No. 16183910

>>16183730
>schizo rambling
Son, one day you will realize the schizos have always been right.

Anonymous at Mon, 20 May 2024 05:19:13 UTC No. 16183938

>>16183744
>You cannot push Stewart over Apostol or Spivak and call others retarded.

You can when you have people specifically asking how to learn calculus for the first time. If someone is learning analysis for the first time or states that they have previous experience with rigorous math/proofs sure, but otherwise recommending rigorous calc books to people is moronic

Anonymous at Mon, 20 May 2024 05:48:41 UTC No. 16183986

>>16183906
>>16183906
I partially read Boas, her exposition sucks immensely compared to Altland. To compare it would be like Boas is just throwing to you notation and methods and forcing you to just accept it while Altland somehow ingeniously manages to explain to you it's origins in a succinct manner while showing geometric proofs and how it directly applies to physics. And the problems are more interesting than Boas, far more interesting, what takes Boas to explain in 20 pages Altland does it in 2 pages while showcasing its origins and how it directly applies to physics. It's kinda like reading Milan's book on Linear algebra, except more concise and more interesting. Altland write the de fwcto condensed matter theory textbook which every physicist uses, so it doesn't surprise me that a genius guy like him made a better and more compact math methods book than anybody else on the market. Despite how small his section on differential equations is you can immediately after finishing altland go through a book on PDE. Which is why I reccomend mathematical physics by tikhonov immediately after Altland. And he teaches you all you need about complex analysis and group theory set theory vector spaces. It's just a crazy good book, buy it and read the entire thing and do every problem and you'll appreciate his style of writing compared to Boas. The problems are simply better made and more interesting than Boas, that's what makes it easier to remember the concepts despite their not being that many problems. Altland has 331 multi step problems while Boas has over 5000 problems, you can finish all of Altland in 1 semester, you can't do that for Boas, and by all I mean complete every problem and read the entire textbook in one semester.

Anonymous at Mon, 20 May 2024 05:54:55 UTC No. 16183995

>>16183906
Also Altland teaches you some differential geometry, multilinear algebra, group theory and some other stuff that can't be found in any math methods textbooks. You could after finishing altland complete Prugovecki's Quantum Mechanics and an understanding and confidently solver every problem, you could also do Mathematical Physics by Tikhonov. Boas teaches you nothing about mathematical theory or the theoretical portions of linear algebra which you need for understanding graduate level quantum mechanics and graduate level mechanics and Boas is bloated.

Anonymous at Mon, 20 May 2024 08:28:52 UTC No. 16184142

>>16183670
Because this is /sci/, not /g/. Intro logic/proof books are also unnecessary (perhaps useful for codefa/g/s only) -- you'll learn that in Spivak's calculus, for example.

Anonymous at Mon, 20 May 2024 09:24:32 UTC No. 16184199

>>16183186
It’s legit, but if you’re starting from zero, you’ll probably get discouraged and stop. He repeats himself about how difficult it will be, so I don’t think he’s being dishonest. The other anon talking about it being a reference book is true, but it can work by itself if you really dedicate yourself to it.

Anonymous at Tue, 21 May 2024 01:35:32 UTC No. 16185422

Bump

Anonymous at Tue, 21 May 2024 01:58:00 UTC No. 16185448

>>16182312
Mathematics for Physicists by Altland, buy it from Amazon and download the solutions manual from libgen.rs

Anonymous at Tue, 21 May 2024 02:22:34 UTC No. 16185468

Bump

Anonymous at Tue, 21 May 2024 02:28:19 UTC No. 16185472

>>16185448
I wish there was a "physics for mathematicians" kind of book
An engineer once told me multiplying by a negative number is a rotation
I lose braincells every time I talk with one.

Anonymous at Tue, 21 May 2024 02:37:24 UTC No. 16185481

>>16185472
Mathematical Methods for Classical Mechanics by Arnold. I think Spivak also wrote a physics book.

Anonymous at Tue, 21 May 2024 02:39:05 UTC No. 16185483

>>16185481
*for -> of

Anonymous at Tue, 21 May 2024 02:45:23 UTC No. 16185492

>>16185472
He most likely was referring to a group table or a cylic group.

Anonymous at Tue, 21 May 2024 02:48:14 UTC No. 16185495

>>16185483
You're not going to learn any physics from that book, its all sympletic geometry. Buy Taylor classical mechanics used and download the solution manual on libgen.rs

Use the solutions to figure out how he solved the problems then do the problem without looking at the solutions manual from memory

Anonymous at Tue, 21 May 2024 02:58:52 UTC No. 16185499

>>16185472
It is. Multiplying by sqrt(-1) is rotation by π/2 radians. Multiplying by (-1) is rotation by π radians. That's not even a physics thing, it's a complex functions thing.

Anonymous at Tue, 21 May 2024 03:03:59 UTC No. 16185502

>>16185492
Nah, you're absolutely over thinking it.

Let's say you have a collection of complex points (a_n + b_n i) for n in some Index set. What happens to those points when you multiply them all by (-1)? The collection of points rotates in the plane by π radians.

Anonymous at Tue, 21 May 2024 03:07:15 UTC No. 16185506

>>16185502
Ty i understand, I never thought of it that way.

Anonymous at Tue, 21 May 2024 03:19:47 UTC No. 16185518

>>16185499
No it's not.
You haven't even defined a rotation
multiplication and imaginary numbers are not dependent ideas on angular rotations.
In fact rotations of uninteresting and meaningless without fixed information about the transform.
A complex function is literally nothing more or less than that: a complex function e.g. a mapping defined as a function of X to C
Rotations can be defined differently especially in different spaces.

Anonymous at Tue, 21 May 2024 03:24:04 UTC No. 16185524

>>16185502
are you a fucking retard?

Anonymous at Tue, 21 May 2024 04:12:54 UTC No. 16185564

>>16185524
No, you obviously are.
>>16185518
Okay, so let me get this straight. You've been so poisoned by Bourbaki bullshit that you have forgotten that homomorphic transformations of complex numbers are reducable to unique scaling and rotation operations? Go back to undergrad you retard.

Anonymous at Tue, 21 May 2024 04:14:12 UTC No. 16185567

>>16185564
Holomorphic* oops.

Anonymous at Tue, 21 May 2024 04:21:24 UTC No. 16185575

>>16185564
ADDITIVE INVERSE AND ORTHOGONALITY PROPERTIES
You're just another child molesting physcuck obsessed with rotations because of your monkey brain
rotating and stretching your tiny pp will never make it bigger you fucking delusional physgooner.

Anonymous at Tue, 21 May 2024 04:31:33 UTC No. 16185581

>>16185575
I'm not a physicist. I'm an engineer. Physicists are retarded and can't see the forest for the trees. You seem to take after them in that way.

You can deny the reality that multiplication of a complex number by some exp(i theta) is a rotation operation if you'd like. You'll be wrong, but you can deny that reality.

Anonymous at Tue, 21 May 2024 04:38:46 UTC No. 16185590

>>16185581
>OH MY SCIENCE!!! I DID A MULTIPLICATION IN A LINEAR SPACE AND CALLED IT A SCALE AND ROTATION I AM LITERALLY GOONING RIGHT NOW!!!
ALSO LEARN WHAT A HOMOMORPHISM YOU FUCKING VERKEKSIUM WATCHING KEKGINEER
DID I EVER SAY AN ENGINEER SUBHUMAN WAS ALLOWED TO TALK TO ME?

Anonymous at Tue, 21 May 2024 04:39:30 UTC No. 16185592

>>16185590
Nigger, a linear operation (multiplication by a scalar is a linear operation) is homomorphic.

Anonymous at Tue, 21 May 2024 05:11:07 UTC No. 16185628

>>16185564
>Bourbaki bullshit
Rent free

Anonymous at Tue, 21 May 2024 05:21:35 UTC No. 16185642

>>16183451
>non-trivial

Anonymous at Tue, 21 May 2024 05:25:38 UTC No. 16185644

>>16185592
engineer moment

Anonymous at Tue, 21 May 2024 05:36:54 UTC No. 16185665

>>16185644
Lmk when you get your head out of your own ass and actually do something with all of the math education you have. And by do something I mean more than scribble some algebraic garbage on your arxiv for nobody to read.

Anonymous at Tue, 21 May 2024 13:40:12 UTC No. 16186185

Bump

Anonymous at Tue, 21 May 2024 14:52:22 UTC No. 16186239

>>16186185
If you are the OP, just ignore people who are saying you need some heavily rigorous approach to calculus to begin with. If you want to study deeper mathematics, having a rigorous proof-based approach to calculus will help you, but what really matters is that you actually stick to it and develop the habit of challenging yourself.

It really doesn't matter what book you start with, what level of rigor it offers or any of this other stuff. What matters is that you put in time, do exercises and understand the examples, and get in the habit of slowly developing your mathematical maturity.

Stewart is fairly easy, offers an accessible approach to a lot of calculus topics, and is very cheap to get a used copy of. If that satisfies what you are looking for, it isn't a bad choice. Kline's calculus book is also good and comprehensive. Ultimately, the best self study book is the one that you actually spend time reading and engaging with, whatever that book ends up being.

Anonymous at Tue, 21 May 2024 18:31:22 UTC No. 16186519

>>16182312
Mathematics for Physicists by Altland, buy it from Amazon and download the solutions manual from libgen.rs
Afterwards you try Partial Differential Equations by Arrigo since he has detailed solutions to all his problems. Then you move onto whatever you want.

Anonymous at Tue, 21 May 2024 21:45:31 UTC No. 16186821

>>16185472
>I wish there was a "physics for mathematicians" kind of book
There is, dumbass, it's called Classical Mechanics by Taylor, or Electrodynamics by Griffiths, or Quantum Mechanics by Griffiths, or Statistical Mechanics by Reif. What no physicist will tell you is that there are unique cases in physics, which is why you have to have access to the solutions manual in order to understand how a problem is solved, which makes sense because the exposition in physics text doesn't contain enough examples for a good reason, size. Classical mechanics by taylor has over 800 problems, each are unique cases to an extent or some are very similar, you can't put 800 similar examples in a book that book just so you can solve every problem which is why you use the solutions manual for it online to learn by reversing the problem solving process

Anonymous at Tue, 21 May 2024 22:08:49 UTC No. 16186861

>>16186821
>To solve the problems you look up the answers
I am calling for total physicist death.

Anonymous at Tue, 21 May 2024 22:29:30 UTC No. 16186888

>>16186861
Based. Soon you'll understand that mathematicians fit in there too and engineering is the true path forward.

Anonymous at Tue, 21 May 2024 22:53:03 UTC No. 16186923

>>16182312
find any old russian higher math problem book and do the problems

Anonymous at Wed, 22 May 2024 00:39:27 UTC No. 16187079

>>16186888
No, I want the physicists to stop larping as faggots and be replaced by applied mathematicians. The engineers will benefit by sitting at the feet of these better teachers.

Anonymous at Wed, 22 May 2024 01:22:12 UTC No. 16187137

>>16187079
Bro half of the "applied mathematicians" you find out there are engineers.

Anonymous at Wed, 22 May 2024 01:24:04 UTC No. 16187140

>>16187137
Engineers think the end of mathematics is their Calc 3 course.

Anonymous at Wed, 22 May 2024 01:52:13 UTC No. 16187165

>>16187140
You don't know anything about what engineers do, do you? My undergrad EE degree required us to do Fourier analysis, numerical analysis, Lebesgue integration and complex integration, more linear algebra than you could even imagine etc.

Sure, we didn't do topology, but we did more in depth Analysis than typical math majors get until grad school.

Anonymous at Wed, 22 May 2024 02:05:29 UTC No. 16187184

>>16183938
>You can when you have people specifically asking how to learn calculus for the first time. If someone is learning analysis for the first time or states that they have previous experience with rigorous math/proofs sure, but otherwise recommending rigorous calc books to people is moronic

Spivak presents everything from the ground up though and gives sufficient intuition for what he introduces. I would agree suggesting Rudin to someone without any calc knowledge is often moronic because such analysis books presume basic intuition from calculus, but suggesting something like Spivak doesn't have this problem. Low IQ to think so desu

Anonymous at Wed, 22 May 2024 02:22:24 UTC No. 16187214

>>16182312
>Heidelberg
pick the less jewish one

Anonymous at Wed, 22 May 2024 02:33:59 UTC No. 16187229

>>16187165
>more linear algebra than you could even imagine
Oh wow, he took a determinant of a 3x3 matrix. Those topics were probably just chapters in the "survey" book you were asked to read. You're a formula monkey, and everyone knows it.

Of course it's a different story if you did EE at a top school.

Anonymous at Wed, 22 May 2024 02:35:37 UTC No. 16187232

>>16187165
>Sure, we didn't do topology, but we did more in depth Analysis than typical math majors get until grad school.

Kek no you fucking didn't, you just learnt the end tools and theorems of "grad school analysis" without ever knowing how or why they are true to any level of rigor. You are simply a monkey trained to follow the instructions of your superiors (mathematicians).

Anonymous at Wed, 22 May 2024 02:37:50 UTC No. 16187233

>>16187229
>Of course it's a different story if you did EE at a top school.

It's no better. You can look at the courses and syllabi for EE at these top schools, its simply formula monkeying with slightly higher level math.

Anonymous at Wed, 22 May 2024 02:40:22 UTC No. 16187237

>>16186888
>Based. Soon you'll understand that mathematicians fit in there too and engineering is the true path forward.
Engineers are far worse than mathematicians or physicists. Entirely full of ego-inflated NPCs

Anonymous at Wed, 22 May 2024 02:40:51 UTC No. 16187240

>>16187229
I did EE at a school that's competitive with MIT if that changes your perception at all. Also, linear systems theory and control theory is literally just a mix of the basics of the linear operator theory part of functional analysis (though generally a finite dimensional vector space rather than a general hillbert space) and abstract linear algebra. Take a look at modern control theory by Brogan if you want a look at our senior undergrad linear control course. Not exactly proof oriented but far less simple than you're pretending.

>>16187232
The end tools being literally the entirety of signal processing (which is just a subset of Fourier analysis) and control theory (which is a subset of linear operator functional analysis and "abstract linear algebra").

Anonymous at Wed, 22 May 2024 02:44:37 UTC No. 16187243

>>16187237
At some point it's hard not to develop a chip on your shoulder when you're the only one actually doing any real work with mathematics while mathematicians pretend their zero citation arxiv papers about "polytopic xenomorphisms on a Sheckleberg space" are to be taken seriously.

Anonymous at Wed, 22 May 2024 02:56:13 UTC No. 16187254

>>16187240
>I did EE at a school that's competitive with MIT
Well if true, then good for you, but realize that you're an atypical engineer, and you should not perceive the general indictment to your profession as a personal slight. I do hope you're paid more than the formula monkeys sitting next to you.

Anonymous at Wed, 22 May 2024 03:01:47 UTC No. 16187257

>>16187254
I don't perceive it as a personal slight. I did a grad elective in measure theory recently with math grad students. Their background in the proof oriented side of mathematics is far stronger than mine, but they have absolutely no experience with computational mathematics and actual problem solving.

As soon as an integral actually involved some amount of computation and wasn't just "find the right sequence of functions to apply dominated convergence theorem to" they basically blew over. These are different skills for different emphasis.

Anonymous at Wed, 22 May 2024 03:34:52 UTC No. 16187295

>>16187257
>As soon as an integral actually involved some amount of computation
We reach for Mathematica / Matlab / whatever package... yes.

Anonymous at Wed, 22 May 2024 03:43:57 UTC No. 16187308

>>16187295
This approach is fine if you are only doing numerical solutions. If you need analytical forms this approach is really doing you a disservice.

An easy example of this is within estimation theory the concept of the CRLB. You can always numerically approximate using Matlab/mathematica/python/R, but if you actually want to determine the conditions for observability of your parameter you need to stop being a lazy fuck and actually do the math.

Unfortunately, most mathematicians don't actually have any experience doing proper analytical solutions for complicated problems and as a result large subsections of probability theory, control theory, optimization theory and convex analysis and information theory are left entirely to engineers.

Anonymous at Wed, 22 May 2024 05:13:57 UTC No. 16187362

Textbook wars are for pseuds who clearly don't have any upper education. Even recommending a single textbook or a path of textbooks is stupid.

Literally, you should be reading 3-5 textbooks per math subject. 1 should be your core and highly rigorous, 1 should be an alternate to the core and very simple in build up and approach, the rest should be PURELY application focused ideally with one that teaches you the concepts with a modern programming language.

You flip between them as you learn. When you get stuck, you switch to the other texts to understand things more deeply. You can master any math textbook this way. No author is perfect and many of the math texts are actually quite lacking in many locations and omit critical explanations or the author literally sets problems up stupidly that are much more easily shared through other lenses.

If you're looking for a single textbook on a subject to learn from, you are a mathlet.

Anonymous at Wed, 22 May 2024 05:18:42 UTC No. 16187367

>>16187308
In my experience, the engineers actually omit large pieces of the math and make very simple assumptions and approximations in their core texts.

This was my experience at least in the one time I actually stepped into engineering math for control systems. Very immature texts compared to the even core stochastic differential equations that simply touch on control such as Oksendal and Kallianpur.

Again, just my experience.

Anonymous at Wed, 22 May 2024 05:30:59 UTC No. 16187374

>>16187367
> In my experience, the engineers actually omit large pieces of the math and make very simple assumptions and approximations in their core texts.

This can certainly be the case, though I don't know where exactly the line is between a textbook approaching things from a simplified perspective as a pedagogical choice (i.e., placing emphasis in a different area) vs. out of a lack of rigor.

I wouldn't, as an example, consider Royden inferior as a measure book to Cohn's measure theory textbook just because Royden constructs the Lebesgue measure solely on the real line and doesn't leave abstract measure spaces/measurable spaces until later.

In terms of control theory texts tending to make simplifying assumptions, I agree but I think you are somewhat missing the point (especially when it comes to optimal control for potentially non-linear systems). Any system that is locally controllable can be arbitrarily well approximated by a control strategy which minimizes some strongly convex function in the same state space. The whole motto of control theory is "keep it simple stupid." If you can avoid Runga-Kutta approximation of the dynamics and get a stable and computationally tractable approximation out of a local second order expansion, that's probably a better bet even if it's simpler.

Control Theory as a discipline encourages specifically keeping things as simple as possible as it is very rare that a single controller is operating in a vacuum without being in some network. Predicting and controlling the dynamics of a system with 48 integrators and 9 separate controllers will be far more tractable if those individual blocks are quadratic approximations and those controllers are as simple as can be managed.

Anonymous at Wed, 22 May 2024 05:32:20 UTC No. 16187379

>>16187374
Doesn't approach abstract measure spaces/measurable spaces until later* sorry it's late and my brain is broken (not that it ever worked well anyways).

Anonymous at Wed, 22 May 2024 06:11:51 UTC No. 16187405

>>16182312
Mathematics for Physicists by Altland, download the solutions manual from libgen.rs -> Partial Differential Equations by Arrigo because it includes all solutions.

Anonymous at Wed, 22 May 2024 10:00:39 UTC No. 16187586

>>16187165
>Fourier analysis, numerical analysis, Lebesgue integration and complex integration, more linear algebra than you could even imagine etc.
Your typical undergraduate physicist does all of that

Anonymous at Wed, 22 May 2024 13:56:05 UTC No. 16187876

>>16182312
>>16182373
you might like Inside Calculus by Exner

Anonymous at Wed, 22 May 2024 19:35:44 UTC No. 16188369

Mathematics for Physicists by Altland, download the solutions manual from libgen.rs

Anonymous at Wed, 22 May 2024 21:35:44 UTC No. 16188561

>>16187165
>You don't know anything about what engineers do, do you?
Can you design a circuit board Mr EE? It's often surprising to people that engineers actually spend very little time working on electronics, and it's almost a certainty nowadays that they're not taught soldering (that's too beneath them, that's for "technicians").

Anonymous at Wed, 22 May 2024 21:43:59 UTC No. 16188569

>>16188561
I did an undergrad course in digital integrated circuits, but no, my job is not designing circuit boards. I do statistical signal processing and information theoretic statistics.

Just like mathematicians don't spend all day writing out log-tables anymore, not every EE designs circuitboards. I knew soldering before I went to school for EE anyways, but that's most because I liked working on audio equipment as a hobby and would terminate my own cables.

Anonymous at Thu, 23 May 2024 01:04:20 UTC No. 16188794

Mathematics for Physicists by Altland, download the solutions manual from libgen.rs

Anonymous at Thu, 23 May 2024 02:18:58 UTC No. 16188859

>>16188794
Why are you spamming this book so much in so many threads? Do you feel some weird personal attachment to it or something?

Anonymous at Thu, 23 May 2024 02:34:42 UTC No. 16188874

>>16182312
If you're learning it from the first time just buy the popular textbook high schools use. Don't try to jump into some super complicated shit because /sci/ recommends it.

Anonymous at Thu, 23 May 2024 03:40:43 UTC No. 16188931

You haven't read a single page have you op?

Anonymous at Thu, 23 May 2024 04:57:44 UTC No. 16188980

>>16188931
Hey man, it's me, your OP. Nah I just collect pdfs, and then make textbook threads to talk about books and debate the ideal dependencies for the perfect path through mathematics.

Anonymous at Thu, 23 May 2024 07:59:09 UTC No. 16189149

>>16188859
It's the best
>>16188980
Mathematics for Physicists by Altland, buy it and download the solutions manual from libgen.rs then you can do Taylor classical mechanics.

Anonymous at Thu, 23 May 2024 20:22:32 UTC No. 16190044

>>16188980
Cheers. I just hoard pdfs and charts. Never cared much for discussion

Anonymous at Fri, 24 May 2024 06:18:02 UTC No. 16190723

>>16182312
What kind of practical applications are you interested in?

Anonymous at Fri, 24 May 2024 11:13:04 UTC No. 16190948

Mathematics for Physicists by Altland

Anonymous at Fri, 24 May 2024 12:11:38 UTC No. 16190983

Pertinent: >>16190490

Anonymous at Sat, 25 May 2024 07:17:32 UTC No. 16192243

Bump

Anonymous at Sat, 25 May 2024 11:20:29 UTC No. 16192460

>>16182312
>No one has yet to mention prof leonard
This board has fallen
https://www.youtube.com/watch?v=fYyARMqiaag&list=PLF797E961509B4EB5

Anonymous at Sun, 26 May 2024 06:21:51 UTC No. 16193654

Read Newton's Principia Mathematica

Anonymous at Sun, 26 May 2024 09:20:12 UTC No. 16193807

>>16187405
This is a good book, I can recommend

Anonymous at Sun, 26 May 2024 12:05:46 UTC No. 16194036

>>16182312
This is all you need OP, download the solutions manual for the physics textbook and use it to help you understand problem solving.

Anonymous at Sun, 26 May 2024 13:34:49 UTC No. 16194133

Is this thread a fucking joke? Just pick up a calculus book and be done with it. I recommend Stewart.

Anonymous at Sun, 26 May 2024 14:08:06 UTC No. 16194175

>>16194133
Naw bruh, mathematics for Physicists by Altland

Anonymous at Sun, 26 May 2024 19:20:49 UTC No. 16194577

>>16194175
How much are you paid per post?

Anonymous at Sun, 26 May 2024 22:23:33 UTC No. 16194864

>>16194577
>altland
wew we have unironicall shill on /sci/

Anonymous at Sun, 26 May 2024 22:29:16 UTC No. 16194874

>>16194864
Yeah it's really strange. I'm sure it's a decent book but it's weird to see it literally shilled. It's not like it's new or anything.

Anonymous at Sun, 26 May 2024 22:45:49 UTC No. 16194891

>>16194874
Maybe the shilling works, because now I'm at least going to look at it.
>Hit up ligbgen
>DL the pdf
>Ahh, now time to file it away. Which folder should it go in...? Math or physics.. hmm.. "help me out chat!" [Don't].

Anonymous at Sun, 26 May 2024 23:17:29 UTC No. 16194936

>>16194891
Upon a very brief review of the subjects covered, this looks like a very useful book to a beginning Engineer or Physicist. I was impressed to see that right away they start talking about group theory.

By the amount it was shilled, I expected to see some flashy American style text, but the two authors teach in German universities, so that gives me some confidence that my positive first impression will be correct.

Anonymous at Sun, 26 May 2024 23:23:49 UTC No. 16194946

Also, why does the Altland shill keep telling us to download the solutions manual, the book contains solutions...?

Anonymous at Sun, 26 May 2024 23:29:55 UTC No. 16194955

>>16194936
Just when I was saying nice things, I decided to read the preface... Oh no.

Anonymous at Sun, 26 May 2024 23:53:51 UTC No. 16195001

>>16194036
>Griffiths qm and Reif
Revolting
Use Townsend and Stowe instead

Anonymous at Mon, 27 May 2024 00:57:59 UTC No. 16195061

>>16195001
>Townsend
No point, sakurai teaches everything Townsend does except with better exposition/clarity/rigor.
>Stowe
That's a book for engineers, over 75% of the book is basic thermodynamics, the math is non rigorous and doesn't prepare you for grad school or research in statistical mechanics.

Anonymous at Mon, 27 May 2024 00:59:35 UTC No. 16195062

>>16194955
Just ignore that, it never refers to the reader as a she in any of the chapters, that got to me too.

Anonymous at Mon, 27 May 2024 01:00:36 UTC No. 16195064

>>16194946
The book contains half the solutions, while the manual contains the other half

Anonymous at Mon, 27 May 2024 01:07:36 UTC No. 16195071

>>16195062
Hah yeah soon after posting I confirmed it.
>>16195064
Right, and also something I'd have noticed if I'd finished the preface before posting.

Anonymous at Mon, 27 May 2024 18:08:59 UTC No. 16196207

>>16194036
Meme book list

Anonymous at Tue, 28 May 2024 07:58:15 UTC No. 16197351

Bump

Anonymous at Wed, 29 May 2024 01:18:53 UTC No. 16198480

>>16195064
One downside I've noticed is that he book contains an astonishing number of typos. Are proof readers not a thing these days?
https://homepages.physik.uni-muenchen.de/~vondelft/ADBook/typos.pdf

Anonymous at Wed, 29 May 2024 03:13:37 UTC No. 16198597

>>16182312
Just do Simmons and Apostol

Anonymous at Wed, 29 May 2024 04:22:31 UTC No. 16198650

>>16198597
Apostol is a nice choice. Another alternative is Zorich Analysis I, II especially as it contains applications for physics (common in Russian texts). Analysis is being used here in the sense of Advanced calculus, and it starts from the ground up.

Two faults with Zorich are: The exercises are at a difficulty level higher than the text itself which is bad for self study even though the exposition is very clear. Secondly, unlike Apostol it doesn't contain any material on linear algebra or Analytic Geometry (which Russians obviously learn during pre-school).

Both Apostol (Calculus) and Zorich are two volume books so it will take some time to cover these.

Anonymous at Wed, 29 May 2024 08:25:03 UTC No. 16198867

>>16198597
>>16198650
Way too fucking long, that would take OP 4 years to do, while altlabd would take 1 year to do instead.

Anonymous at Wed, 29 May 2024 09:13:35 UTC No. 16198911

>>16198867
Altand is assuming a highschool level of calculus, and since OP is going to self-study, he may need something else first. I have no idea what a highschool calculus book even is, but the Dover book "Mathematical Methods its Content and Meaning" does give a very readable introduction to Calculus (They'll call it Analysis), this is huge tomb though, which tries to cover everything.

As for Atland, I like the book, I've been reading it throughout the day, but it goes faaaast through many topics that I wonder if a beginner would understand if it were the first time (I have a background in Analysis, so it's hard to guess).

A four year math degree and then reading Altland/Delft actually seems like a great way to go. Gain the understanding, and then reduce it to what you really need at the end.

Anonymous at Wed, 29 May 2024 09:14:54 UTC No. 16198912

>>16198911
*tome, but it's probably filled with dead mathematicians.

Anonymous at Wed, 29 May 2024 13:02:40 UTC No. 16199057

>>16198911
Nobody spends 4 years of school just to read Altland, at the school where it's used they go through it in one semester, and the physicists there still get phds and work in academia and industry.

Anonymous at Wed, 29 May 2024 14:18:58 UTC No. 16199125

>>16198911
4 years of doing proofs in mathematics then reading a math methods books, that's pretty fucking stupid. The supermsjority of physicists never use anything in real analysis.

Anonymous at Wed, 29 May 2024 18:13:56 UTC No. 16199391

>>16198650
I did Zorich 1 and it was the best thing ever. I'm guessing op is talking about single variable calculus, so Zorich 1 would certainly be a good alternative if he doesn't mind a slight more advanced approach.
I'd choose Simmons + Zorcih 1 anytime for sure. It's just that I tend to overestimate how much I could have actually followed these book had I encountered them in high-school.

Anonymous at Wed, 29 May 2024 18:24:11 UTC No. 16199407

>>16199057
>>16199125
The 4 years part was a joke you sperg(s). Yet even without it being analysis, a student should at least see a more thorough treatment of single variable calculus, otherwise things will be missed. For example, again from Altland/Delft

P1 in the derivative chapter is to take the derivative of a polynomial. Simple right? Well they haven't discussed the linearity of the derivative, or even more simply, the "sum rule". If a student is reading this without any background, how could 'she' expect that she has any right to just assume it?

Anonymous at Wed, 29 May 2024 18:27:24 UTC No. 16199410

>>16199391
>I tend to overestimate
At one point, I was convinced that I should have just read Amann/Escher at 13, and breezed through highschool. I probably would have ran into difficulties. I did work through Apostol during the summer after HS and it was easy enough, but it's very dry.

Anonymous at Wed, 29 May 2024 19:11:42 UTC No. 16199455

>>16199407
What the fuck, you never read chapter 1 for calculus, he talks about how the derivative is a linear approximation. The algebra for the sum rule is covered in the group theory chapter for linear algebra. You need to slow down when reading, otherwise you'll miss important concepts he talks about within the paragraphs.

Anonymous at Wed, 29 May 2024 19:40:06 UTC No. 16199487

>>16182312
How is it going, op? Have you picked a book yet?

Anonymous at Wed, 29 May 2024 19:56:31 UTC No. 16199513

>>16199455
Linear approximation != linearity property... physicists man, I'll tell you what.

In the linear algebra section yes, there is a discussion of linearity and differential operators. That section L9 depends on later sections of the calculus part C6 (which implicitly implies C1). So no, it hasn't been covered prior to our student's reading of her calculus 1 chapter. All they needed was a simple
d(f+g)=df+dg, d cf = c [or combine them, applicability to polynomials follow by induction]

This is omitted, because it's assumed she has studied calculus in high school. There's explicit mentions to this, I'm not even sure what there is to dispute.

Anonymous at Wed, 29 May 2024 19:57:57 UTC No. 16199516

>>16199513
>d cf = c
*The typo here has been left as an exercise to the reader.

Anonymous at Wed, 29 May 2024 20:39:23 UTC No. 16199609

>>16199513
>d(f+g)=df+dg
how could this not make sense, it's just algebra, i don't see what the big deal is you're making it out to be, a person doesn't need a proof to understand that d(f+g)=df+dg.

This is why the physicist can learn in one semester what the mathematician takes 4 years to learn, and they still get paid more than mathematicians. Not everything needs a proof, I don't understand why you would need a proof for that honestly, it's pretty obvious to me.

Anonymous at Wed, 29 May 2024 21:02:17 UTC No. 16199662

>>16199609
I didn't even say it needed a proof (even though it could be done in a few lines), it's literally just not even mentioned.

Despite sneaky notation, it's not algebra in the elementary sense. d is of course a function (operator if you will), and being able to write that requires the property of linearity. For example, sine obviously doesn't have that property.
[math]sin(\pi+\pi/2) \neq sin(\pi)+sin(\pi/2)[/math]

It should have been stated, it's a fact used all the time. It's not like I'm arguing he needs to define a polynomial as an element of a formal power series over some arbitrary ring. If you're one of his students, let him know.

Anonymous at Wed, 29 May 2024 22:46:19 UTC No. 16199822

>>16199662
If you say so

Anonymous at Wed, 29 May 2024 23:44:52 UTC No. 16199928

I just grinded through khan academy watching the lectures at 2x speed and taking notes, and then breezed through my colleges Calc courses with ease

Glad I didn't waste my time bumbling through some struggle just to feel special

Anonymous at Wed, 29 May 2024 23:56:06 UTC No. 16199949

>>16183670
>Why do so many of you autists reject the Stewart Canon?
Because I have OCD that makes me do every single exercise in a book, and Stewart provides too many easy/computational exercises.
Also, I remember once doing a broad comparison of big-book calculus (Stewart, Larson, Anton, and Thomas), comparing the explanations for Rolle's & MVT, for the FTC, for indeterminate forms, and some other shit, and imo Anton is the superior, more pedagogically sound writer.

Anonymous at Thu, 30 May 2024 03:06:40 UTC No. 16200150

>>16199822
At least your shilling resulted in a book sale (hardcopy naturally). I've been looking for something like this for some time to give to software "engineers" whose math skills (whatever they were) have atrophied since university and something like this can serve as a good refresher. There's an Amazon review from some other mathfag who liked it for similar reasons. So far so good, minor gripes notwithstanding.

This part made me laugh though, because occasionally you see a level of rigour you don't expect to see. The inner German always comes out I guess.

Anonymous at Thu, 30 May 2024 05:27:26 UTC No. 16200269

>>16182312
>Samuel Burstein
Anything written by a Jewish or Israeli author should be taken with a grain of salt. I would suggest you find real Calculus books.

Anonymous at Thu, 30 May 2024 05:40:42 UTC No. 16200286

>>16200269
For your consideration, Shalom goy.

Anonymous at Thu, 30 May 2024 06:12:19 UTC No. 16200336

Bump

Anonymous at Thu, 30 May 2024 21:01:59 UTC No. 16201378

>>16200336
Stewart and just grind through exercises

Anonymous at Thu, 30 May 2024 21:36:47 UTC No. 16201461

>>16201378
>Burger math slop
Stewart is for cattle and future formula monkeys.

Anonymous at Fri, 31 May 2024 05:05:29 UTC No. 16202040

>>16201461
What book is not slop and not a meme?

Anonymous at Fri, 31 May 2024 05:35:03 UTC No. 16202071

>>16202040
I'll just include books which either start from zero or have very primitive requirements, and those which cover the topics an American calls Calculus even though some of these are called Analysis.

Unironically, the book by Altand/Delft the other anon has been shilling in this thread is very good. Zorich is another nice choice if you want something more rigorous (as in proof based), and Amann/Escher is an option for well prepared students who want to study math for its own sake (more abstract than Zorich).

Other notable classics are:
Spivak
Apostol
Courant/John
Piskunov

Anonymous at Sat, 1 Jun 2024 05:33:58 UTC No. 16203667

>>16202071
>posts the meme list

Anonymous at Sat, 1 Jun 2024 05:37:21 UTC No. 16203668

>>16203667
Just read the nine volume series Éléments d'analyse by Jean Dieudonné in the original French, or you're never going to make it.

Anonymous at Sat, 1 Jun 2024 20:41:56 UTC No. 16205141

>>16182312
Get off 4chan, read the content and do the questions

Anonymous at Sun, 2 Jun 2024 20:56:01 UTC No. 16206703

>>16203667
Why do you consider that a meme list? What would you suggest then?
>>16202071
Do you know of a rigorous calculus/analysis book that doesn’t overwhelm the reader with too many exercises?

Anonymous at Sun, 2 Jun 2024 22:18:42 UTC No. 16206855

>>16206703
Zorich doesn't have too many exercises, I just think they go beyond the material in the book on occasion, almost as though they've been designed to challenge students in a room with a TA to work through them. You could always read Zorich, do any questions that interest you (there are some good ones) and then work through an analysis problem book with worked solutions (and not too many unsolved) like pic rel.

Anonymous at Sun, 2 Jun 2024 23:08:07 UTC No. 16206916

>>16206855
nice, i like it!

Anonymous at Mon, 3 Jun 2024 09:47:44 UTC No. 16207526

>>16183242
You mean Single Variable Calculus and Multivariable Calculus?

Anonymous at Mon, 3 Jun 2024 11:46:41 UTC No. 16207651

>>16182312
Just open a book and start reading you fucking nigger I swear faggots like you on this board keep posting which book to start jacking off to but never read

Boo-ker at Mon, 3 Jun 2024 11:47:42 UTC No. 16207653

>>16207651

Anonymous at Mon, 3 Jun 2024 20:52:42 UTC No. 16208362

>>16207526
On mit ocw I only did the single variable course
When I said both books I meant the both of the books op mentioned

Anonymous at Mon, 3 Jun 2024 21:19:30 UTC No. 16208394

>>16182312

Anonymous at Mon, 3 Jun 2024 22:57:10 UTC No. 16208596

>>16208394
You are never going to make it.

Anonymous at Mon, 3 Jun 2024 23:00:51 UTC No. 16208605

>>16182312
https://www.youtube.com/playlist?list=PLxYuYMkf8ir0fjeyQDFjBxQXbiZioZpkw

Anonymous at Mon, 3 Jun 2024 23:08:21 UTC No. 16208626

>>16208394
Rather overwhelming, all over the place and redundant, but serves as an outline with references to standard texts for most subjects

Anonymous at Mon, 3 Jun 2024 23:10:31 UTC No. 16208629

>>16208605
What was this guy's story? I know he drowned himself in the end and heard he was autistic/schizophrenic but fermenter seeing a couple of videos from him and he didn't seem to just be talking nonsense

Anonymous at Tue, 4 Jun 2024 07:04:32 UTC No. 16209342

Mathematics for physicists by Altland