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Math needed for physics

Anonymous Sun 19 Dec 23:14:34 2021 No.13984648 View Reply Original Report

Quoted By: >>13984791 >>13984917 >>13985559 >>13986947 >>13990312 >>13992056 >>13992293 >>13992794 >>13993161 >>13993260

Linear algebra
Single variable calculus
Multivariable calculus
Ordinary differential equations
Mathematical methods
Complex analysis
Partial differential equations
Real analysis
Differential geometry/manifold theory
Functional analysis

Is this really all the math that is really needed for a PhD in physics?

Anonymous

Anonymous Sun 19 Dec 2021 23:20:57 No.13984667 Report

Quoted By: >>13984680 >>13984692

Pretty much. I found the undergraduate to be the most difficult time of my life. But I'm not qualified to answer your question because my studies only lasted until about half way through masters.

Anonymous

Anonymous Sun 19 Dec 2021 23:24:30 No.13984680 Report

Quoted By: >>13984705 >>13992030

>>13984667
Question, if you had a textbook which covered all the topics I previously listed, in a shortened condensed form, and you went through all of it before you started college, do you think that would have made getting your degree much easier? And second question, do you think it would have helped you greatly in understanding and quickly assimilating the physics you were studying?

Anonymous

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Anonymous Sun 19 Dec 2021 23:25:49 No.13984690 Report

Quoted By: >>13993503 >>13993928

Math needed for CS:

intro to discrete math
a faint memory of high school calculus and linear algebra

Anonymous

Anonymous Sun 19 Dec 2021 23:26:37 No.13984692 Report

Quoted By: >>13984765

>>13984667
Also, how much group theory did you use in your studies, can you tell me in detail any particular mathematics you had trouble understanding? Any specific subjects or sub fields within subjects?

Anonymous

Anonymous Sun 19 Dec 2021 23:28:50 No.13984705 Report

Quoted By: >>13984738 >>13984749

>>13984680
It wouldn't hurt. I was in the AP program in high school so I had some Calculus background going into the university. I found undergrad to be difficult because of the tight schedule. I had to be enrolled as honours student, meaning I had to take few extra classes.

Anonymous

Anonymous Sun 19 Dec 2021 23:34:17 No.13984738 Report

Quoted By:

>>13984705
That sucks, I found undergrad to be hard as well because I couldn't study, the solution for me was studying as much as I could 1 day or 2 days before the exam, I tried once to study a week before the exam, it didn't end well.

Anonymous

Anonymous Sun 19 Dec 2021 23:36:49 No.13984749 Report

Quoted By: >>13984790

>>13984705
Also, do you think you would have been better prepared for university level mathematics as a whole if during your junior and senior years of highschool, instead of studying pure calculus, you instead studied from a mathematical methods textbook such as Boas?

Anonymous

Anonymous Sun 19 Dec 2021 23:39:46 No.13984765 Report

Quoted By:

>>13984692
Not too much. I took the class in my second year. It's often a pre-requisite course for algebraic topology classes. As to which subject I had trouble with, it was discrete mathematics. I don't know why.

Anonymous

Anonymous Sun 19 Dec 2021 23:44:45 No.13984790 Report

Quoted By: >>13984825 >>13984844

>>13984749
I don't know. I think I would have had trouble regardless. It was always the workload that gave me trouble. I wish I was better qualified to answer your questions. I was a bottom tier student in university who got lucky that my classmates didn't purse grad school.

Anonymous

Anonymous Sun 19 Dec 2021 23:44:55 No.13984791 Report

Quoted By:

>>13984648
lmao, thats basically all the boring math

Anonymous

Anonymous Sun 19 Dec 2021 23:51:41 No.13984825 Report

Quoted By:

>>13984790
So, if you had your entire senior year in highschool only studying mathematical methods with maybe two other courses which consist of university level mechanics and university level general chemistry, do you think only having 3 courses and a sports elective throughout the entire senior year of highschool, due to the less workload from not studying english/history/ any other shit, that you would have done better on these courses.

How many courses in highschool would you have preferred to take maximally if you had a choice, I'm assuming 4 courses for spending 7 to 8 hours in highschool with a big lunch break?

Anonymous

Anonymous Sun 19 Dec 2021 23:55:04 No.13984844 Report

Quoted By:

>>13984790
Let's say there was only a single grade level after 12th grade, taught by only stem majors, where the classes were less than 10 people each, do you think that would have helped you?

Anonymous

Anonymous Mon 20 Dec 2021 00:09:27 No.13984917 Report

Quoted By: >>13984943 >>13990319

>>13984648
> a PhD in physics?
Totally depends on what your field is going to be.
>Complex analysis
>Partial differential equations
>Real analysis
>Functional analysis
All of these might be useful, but you don't need them. Complex analysis would be useful, but when it comes to actually using it you'll be limited to doing contour integrals. There's absolutely no reason to have real analysis. Unless you're going deep into the formulation of QM you'll (probably) never use functional analysis.. PDE's again are mostly going to be limited to solution methods, literally no one is going to care if you can prove a solution exists, instead that you're arguments in derivations.

Shit, even differential geometry and manifolds aren't really needed, unless you're going into hep-th (and even then going into the really high level stuff).

Anonymous

Anonymous Mon 20 Dec 2021 00:13:56 No.13984943 Report

Quoted By:

>>13984917
Looks like I didn't finish a thought:
>instead that you're arguments in derivations.
Instead that your arguments in your derivations are sound and that your equation makes verifiable predictions. I highly doubt that you'll read a physics paper and see someone talk about Sobolev spaces. During my masters there was a lot made about Hopf algebras, but the actual use of them was "hey, this is a neat product we can form with a Hopf algebra that has properties we want", which means I spend like $100 on a book for the first 10 pages of it... not that I'm bitter.

Anonymous

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Anonymous Mon 20 Dec 2021 03:10:31 No.13985559 Report

Quoted By: >>13986887 >>13988986

>>13984648
good list for theoretical physics

Anonymous

Anonymous Mon 20 Dec 2021 11:53:44 No.13986887 Report

Quoted By:

>>13985559
No

Anonymous

Anonymous Mon 20 Dec 2021 12:16:04 No.13986947 Report

Quoted By: >>13989312 >>13989315

>>13984648
Please learn symplectic and contact geometry. This is the geometry of dynamics.

Anonymous

Anonymous Mon 20 Dec 2021 21:27:02 No.13988986 Report

Quoted By:

>>13985559
What a cute and innocent looking girl

Anonymous

Anonymous Mon 20 Dec 2021 22:58:55 No.13989312 Report

Quoted By:

>>13986947
Give me an example. Give me the name of a textbook which consists of that stuff. Please

Anonymous

Anonymous Mon 20 Dec 2021 22:59:56 No.13989315 Report

Quoted By:

>>13986947
You're talking about something like the book geometric mechanics by Arnold? Right?

Anonymous

Anonymous Mon 20 Dec 2021 23:48:11 No.13989474 Report

Quoted By:

Single variable calculus
Multivariable calculus
Vector calculus
Tensor calculus
Calculus of variations
Ordinary differential equations
Partial differential equations
Linear algebra
Statistics and probability
Complex numbers

Anonymous

Anonymous Tue 21 Dec 2021 03:55:27 No.13990155 Report

Quoted By:

Part 1
Linear algebra
Multilinear algebra like chapters 1 and 2 of Renteln
Group representation theory

Part 2
Single variable calculus
Multivariable calculus
Ordinary differential equations and approximation

Part 3
Mathematical physics and special functions
Complex analysis, focus on using contour integrals for physics
Partial differential equations and approximation

Part 4
Real analysis
Differential geometry/manifold theory
Functional analysis

Anonymous

Anonymous Tue 21 Dec 2021 05:06:45 No.13990312 Report

Quoted By: >>13990651 >>13992059

>>13984648
You completely missed anything about topology which is a huge part of modern physics. If you studying high energy theory or are a good condensed matter theorist you will study topics like de rham cohomology, morse theory, characteristic classes, algebraic topology, and so on.

Anonymous

Anonymous Tue 21 Dec 2021 05:09:06 No.13990319 Report

Quoted By: >>13990321 >>13990651 >>13990983 >>13990991

>>13984917
You are way off. Differential geometry is used in every field of physics, and certainly it is used at a surface level of hep-th, since it underlies things like gauge theories and differential geometry. It is practically undergraduate physics

Anonymous

Anonymous Tue 21 Dec 2021 05:10:08 No.13990321 Report

Quoted By:

>>13990319
>since it underlies things like gauge theories and differential geometry.
gauge theories and general relativity I mean

Anonymous

Anonymous Tue 21 Dec 2021 07:33:45 No.13990651 Report

Quoted By: >>13990945 >>13990950

>>13990312
>>13990319
Is this better and more comprehensive? Or should I add more to it, the guy that spoke about geometric mechanics, that's way too much, like holy fuck, pure sympletic geometry

Part 1
Linear algebra
Multilinear algebra (Like in chapters 1 and 2 of Renteln)
Group representation theory

Part 2
Single variable calculus
Multivariable calculus
Ordinary differential equations and perturbation theory

Part 3
Mathematical physics [fourier analysis(series & transforms), calculus of variations, mathematics for quantum mechanics/statistical mechanics, special functions]
Complex analysis, focus on using contour integrals for physics
Partial differential equations and perturbation theory

Part 4
Real analysis
Differential geometry/manifold theory
Functional analysis

Part 4 should be similiar to Analysis by Lieb, a little graduate level real analysis, condensed functional analysis by Reed and simon for their first book and second book, and the manifold theory from Manifolds by Renteln focused on chapters 3 through 8 condensing it.

Anonymous

Anonymous Tue 21 Dec 2021 10:03:17 No.13990945 Report

Quoted By: >>13992026

>>13990651
It's not sufficient. That was my whole point. Look at Nakahara's geometry topology and physics for a rough outline of some of the math every high energy theorist is expected to know. Also homotopy groups from algebraic topology are common in both high energy and condensed matter.

Also your list is in a very strange order. Part 1 is not learned first. Linear algebra is learned in conjunction with Fourier series. Group representation theory (specifically Lie group representation theory, discrete group representations are not widely studied) is learned somewhere at the same level as differential geometry.

Anonymous

Anonymous Tue 21 Dec 2021 10:06:51 No.13990950 Report

Quoted By:

>>13990651
I'm guessing you are a math undergraduate and listed off a bunch of topics you know that you know are connected to physics. And you think there's no way a physics phd would know something you don't about math. Am I right?

Anonymous

Anonymous Tue 21 Dec 2021 10:26:11 No.13990983 Report

Quoted By: >>13990986 >>13990990

>>13990319
No. If your PhD is in photonics (for example) you will never see anyone talk about fiber bundles.

Anonymous

Anonymous Tue 21 Dec 2021 10:28:02 No.13990986 Report

Quoted By: >>13991005

>>13990983
Well I'm not counting you

Anonymous

Anonymous Tue 21 Dec 2021 10:29:11 No.13990990 Report

Quoted By: >>13991005

>>13990983
And also you guys do stuff with the Bloch sphere don't you? That is the canonical example of a fiber bundle

Anonymous

Anonymous Tue 21 Dec 2021 10:29:51 No.13990991 Report

Quoted By: >>13990996

>>13990319
?is it used in solid state physics, biophysics and molecular dynamics ?

Anonymous

Anonymous Tue 21 Dec 2021 10:30:24 No.13990996 Report

Quoted By:

>>13990991
>solid state
yes

Anonymous

Anonymous Tue 21 Dec 2021 10:37:25 No.13991005 Report

Quoted By: >>13991012 >>13991020 >>13991024

>>13990986
Okay.
>>13990990
Serious question, have you ever sat in a physics lecture before? Just because you can analyse something from a very high level mathematical doesn't mean that your standard physicist will. We get introduced to tensors as "things that transform as tensors" and use infinite dimensional vector spaces without ever taking a single functional analysis class. I don't think you know what you're talking about.

Anonymous

Anonymous Tue 21 Dec 2021 10:42:45 No.13991012 Report

Quoted By: >>13991037

>>13991005
I literally have a phd in physics. I know what I'm talking about. Obviously I am only talking about theorists and excluding some peripheral subfields

Anonymous

Anonymous Tue 21 Dec 2021 10:45:46 No.13991020 Report

Quoted By: >>13991037

>>13991005
hey anon, what kind of math do i need for experimental condensed matter and this
https://chemistry.mit.edu/areas-of-research/computational-theoretical/

Anonymous

Anonymous Tue 21 Dec 2021 10:46:48 No.13991024 Report

Quoted By: >>13991037

>>13991005
and this
http://lamm.mit.edu/

Anonymous

Anonymous Tue 21 Dec 2021 10:58:31 No.13991037 Report

Quoted By:

>>13991012
>I literally have a phd in physics
Sure ting mang, and my dad works at Nintendo.

But seriously. The guys that sit next to me in work have phds in photonics and biophysics, both would describe their work as theoretical, and both have never used differential geometry. I'll admit that perhaps I'm being a bit too tight with my arguments, that it's not just hep-th (that's just the field I have most experience with). A better way of saying it might be "there's only a very small set of fields on physics that would make heavy use of differential geometry" and then only likely subfields of those fileds.
>>13991020
>>13991024
Can't help you sorry, closest I ever got to that was reading a book on lattice QCD.

Anonymous

Anonymous Tue 21 Dec 2021 17:28:38 No.13992012 Report

Quoted By:

Bump, do any other physicists use exotic math?

Anonymous

Anonymous Tue 21 Dec 2021 17:34:46 No.13992026 Report

Quoted By:

>>13990945
High energy theory is gay

Anonymous

Anonymous Tue 21 Dec 2021 17:35:18 No.13992030 Report

Quoted By:

>>13984680
GET YOUR ALGEBRA RIGHT, DISTRIBUTIVITY, EXPONENTIALS(NEGATIVE AND FRACTION-AL), LOGARITHMS, TRIGONOMETRY AND ALL IDENTITIES

BY HEART

Anonymous

Anonymous Tue 21 Dec 2021 17:43:29 No.13992056 Report

Quoted By:

>>13984648
>Mathematical methods
No, take real courses.

Take a real course in Mathematical Probability (prerequisites should be calc 3 and proofs), Numerical Analysis (prerequisites should be analysis), and some Algebra and Topology.

Anonymous

Anonymous Tue 21 Dec 2021 17:43:47 No.13992059 Report

Quoted By: >>13993457

>>13990312
dont fall for the meme OP.
IF you go into something that has a special kind of math, you'll learn it. But this is like studying vernacular chinese pronounciations for oractle bone scripts for your 2nd grade English Grammar. WAY TOO EXTENSIVE.
There is no way in hell you'll jsut randomly get to the studying of AlgTop if you are asking anout basic calc and LA. Just learn what you need to at the present moment. You will NOT benefit from hundreds of hours of rigourious proofs in physics. For fuck's sake.
If you want to study physics(bsc, because that is the thing you want to do), just study physics. Simple as that. And when you need to study something else you'll do that. But don't bore yourself and waste your time and money on trying to learn something that YOU DONT ACTUALLY NEED.
Basic algebraBasic algebraBasic algebraBasic algebraBasic algebraBasic algebraBasic algebraBasic algebraBasic algebraBasic algebraBasic algebraBasic algebra

I couldn't count the students on my ten fingers who struggled with basic shit not just in the first semester!

Anonymous

Anonymous Tue 21 Dec 2021 17:54:12 No.13992102 Report

Quoted By:

>no numerics
yikes

Anonymous

Anonymous Tue 21 Dec 2021 18:00:49 No.13992142 Report

Quoted By: >>13992259

That was all I took for a BS in applied math, minus the analysis class and a few stats classes.

Anonymous

Anonymous Tue 21 Dec 2021 18:22:41 No.13992259 Report

Quoted By:

>>13992142
Was it fun? Did you like the math you learned? I actually was interested in applied mathematics seeing as how you can do alot with it.

Anonymous

Anonymous Tue 21 Dec 2021 18:29:46 No.13992293 Report

Quoted By:

>>13984648
Besides all the math that is just taught in addition to all the physics in the physics courses? Yes, that's all the pure math courses required depending where you go

Anonymous

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Anonymous Tue 21 Dec 2021 20:47:30 No.13992786 Report

Quoted By: >>13992895

What math would I need to be king of EE?
Pic unrelated.

Anonymous

Anonymous Tue 21 Dec 2021 20:49:17 No.13992794 Report

Quoted By: >>13992898 >>13992939

>>13984648
is it true you can learn this all for free on khanacademy at home

Anonymous

Anonymous Tue 21 Dec 2021 21:18:17 No.13992895 Report

Quoted By:

>>13992786
none, unironically

Anonymous

Anonymous Tue 21 Dec 2021 21:19:19 No.13992898 Report

Quoted By:

>>13992794
just as much as building a house on your own accord

Anonymous

Anonymous Tue 21 Dec 2021 21:30:34 No.13992939 Report

Quoted By:

>>13992794
No, after ordinary differential equations you have to use textbooks.

Anonymous

Anonymous Tue 21 Dec 2021 22:23:39 No.13993161 Report

Quoted By: >>13993170 >>13993245

>>13984648
You only "need" the first six except complex analysis (altough it is helpfull). PDE's are of course important but you'll probably learn about it in math methods. Differential geometry is also good to know, both in relativity but also for symplectic manifolds, but unless you're going into heavy theory I would say a curves and surfaces class with a bit of manifold theory will give you enough intuition.
If you want to go into research in theoretical physics as much math as possible is prefered, I would personally add general and algebraic topology and symplectic manifolds.

Anonymous

Anonymous Tue 21 Dec 2021 22:25:40 No.13993170 Report

Quoted By: >>13993245

>>13993161
Oh and also distribution theory if you want to learn more about the delta distribution.

Anonymous

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Anonymous Tue 21 Dec 2021 22:53:38 No.13993241 Report

Quoted By: >>13993252 >>13993272

Do physics undergrads really not learn anymore math than the average engineering? Engineering programs nowadays teach multi variable calc, ODEs and some PDEs, linear algebra, numerical methods and stats, and I even have some friends in mechanical that took complex analysis as an elective. Did you guys really just learn a bit more geometry and the physics applications? You’re getting ripped off

Anonymous

Anonymous Tue 21 Dec 2021 22:54:26 No.13993245 Report

Quoted By: >>13993311

>>13993161
>>13993170
Can you list textbooks which these things and the specific which correspond to it?

Anonymous

Anonymous Tue 21 Dec 2021 22:56:30 No.13993252 Report

Quoted By:

>>13993241
The emphasis is more on deriving, integrating, modeling problems from first based principles, also a high level theorist physicist could easily be a mathematician, but that's like 1percent

Anonymous

Anonymous Tue 21 Dec 2021 22:59:45 No.13993260 Report

Quoted By:

>>13984648
I would add Abstract algebra, general topology and lie groups.
Other subjects I would reccomend if you're into heavy theory are measure theory, distribution theory, Geometry from a Kleinian perspective and algebraic topology.

Anonymous

Anonymous Tue 21 Dec 2021 23:02:11 No.13993272 Report

Quoted By:

>>13993241
in many (most?) european universities physics and math undergrads would share courses

Anonymous

Anonymous Tue 21 Dec 2021 23:10:21 No.13993311 Report

Quoted By: >>13993320

>>13993245
For general topology I read James munkres topology book. Algebraic topology isn't really necessary, but if you want to learn about it, I would go for Hatcher, since the book can be found online.
https://pi.math.cornell.edu/~hatcher/

Symplectic manifolds is a topic I haven't studied that much, what I know is from lectures like https://www.youtube.com/watch?v=pXGTevGJ01o&list=PLDfPUNusx1EoVnrQcCRishydtNBYU6A0c.

I would add abstract algebra and lie groups and their algebras.
There are many good Abstract algebra books. If you want a cheap book, go for pinter, if you want something, but if you're downloading them anyways Galian is arguably a bit better, and if you want something more advanced, Aluffi is the way to go.
For lie groups a classic is Chevally, but there are probably better alternatives out there.

Anonymous

Anonymous Tue 21 Dec 2021 23:12:48 No.13993320 Report

Quoted By: >>13993477

>>13993311
Show me exactly what sub fields in physics use what you just listed, otherwise I'm thinking it's a bullshit mathematician who's never done physics recommending what to study.

Anonymous

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Anonymous Tue 21 Dec 2021 23:41:47 No.13993425 Report

Quoted By:

Part 1
Linear algebra, including mathematics for QM
Tensors (chapter 2 of continuum mechanics by Lai)
Multilinear algebra (Like in chapters 1 and 2 of Renteln)
Group representation theory

Part 2
Single variable calculus
Multivariable calculus, including mathematics for statistical mechanics (Microstates by kok, statistical mechanics by khinchin)
Ordinary differential equations and perturbation theory

Part 3
Mathematical physics [fourier analysis(series & transforms), calculus of variations, special functions, lagrangians and hamiltonians]
Complex analysis, focus on using contour integrals for physics
Partial differential equations and perturbation theory

Part 4
Real analysis (Analysis by Lieb)
Differential geometry/manifold theory (Paul Rentlen, Bernard Schutz)
Functional analysis (Kreyszig, Simon)
Numerical analysis (Tsynkov, Kress)

I've concluded that this is the definite amount of mathematics needed to study physics at both undergrad and grad level. Does anyone have anything to say to this list?

Anonymous

Anonymous Tue 21 Dec 2021 23:54:24 No.13993456 Report

Quoted By:

I fixed the previous post

Part 1
Linear algebra, including mathematics for QM
Tensors (chapter 2 of continuum mechanics by Lai)
Multilinear algebra (Like in chapters 1 and 2 of Renteln)
Group representation theory

Part 2
Single variable calculus
Multivariable calculus [including mathematics for statistical mechanics (Microstates by kok, statistical mechanics by Khinchin)]
Ordinary differential equations and ode perturbation theory

Part 3
Mathematical physics [fourier analysis(series & transforms), calculus of variations, special functions, lagrangians and hamiltonians, feynman path integrals]
Complex analysis, focus on using contour integrals for physics
Partial differential equations and pde perturbation theory

Part 4
Real analysis
Differential geometry/manifold theory
Topology (tangent and cotangent spaces, fiber bundles, vector fields, connections and parallel transport)
Functional analysis
Numerical analysis (Tsynkov, Kress)

Does anyone think this isn't enough to cover the supermajority of physicists who go onto graduate and research?

Anonymous

Anonymous Tue 21 Dec 2021 23:54:29 No.13993457 Report

Quoted By:

>>13992059
OP asked "is this all the math that is needed for a PhD in physics," not "what should I learn as an undergrad freshman." Algebraic topology is not going down the rabbit hole. Physicists don't need to know all the details but if you graduate with a PhD in physics you probably have heard of the first fundamental group and higher homotopy groups. It is part of the language of physics. This is used just as much (maybe more) in condensed matter than high energy or cosmology.

Anonymous

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Anonymous Wed 22 Dec 2021 00:00:11 No.13993470 Report

Quoted By:

I really don't know what else to add to the list. Like I'm pretty sure that's all the math that is needed for a supermajority of phd physicists. If anyone can argue against me, or convince me to add something then that's cool.

Anonymous

Anonymous Wed 22 Dec 2021 00:02:45 No.13993477 Report

Quoted By: >>13993499

>>13993320
I'm not him but he is right. Symplectic manifolds are used by people studying dynamical systems, high energy/mathematical physicists, and perhaps people doing work in fluids if they're good. The more mathematical aspects are not as studied outside these groups but of course everyone has the rudiments in terms of phase space and poisson brackets since it is part of the standard syllabus.

Topology is used all the time everywhere. Algebraic topology specifically is used to classify topological defects which are found in condensed matter, fluids, and quantum fields.

Lie groups are used everywhere since they underlie symmetries which is one of the cornerstones of physics.

Anonymous

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Anonymous Wed 22 Dec 2021 00:11:45 No.13993499 Report

Quoted By: >>13993510

>>13993477
It changed slightly but is this better?

Part 1
Linear algebra, including mathematics for QM
Tensors (chapter 2 of continuum mechanics by Lai, Tensor calculus by Neuenschwander, Lovelock)
Multilinear algebra (Like in chapters 1 and 2 of Renteln)
Group theory & Lie groups (Lie groups by Gilmore, Tensors & group theory Jeevanjee)

Part 2
Single variable calculus
Multivariable calculus [including mathematics for statistical mechanics (Microstates by kok, statistical mechanics by Khinchin)]
Ordinary differential equations and ode perturbation theory

Part 3
Mathematical physics [fourier analysis(series & transforms), calculus of variations, special functions, lagrangians and hamiltonians, feynman path integrals]
Complex analysis, focus on using contour integrals for physics
Partial differential equations and pde perturbation theory

Part 4
Real analysis (Analysis by Lieb
Differential geometry/manifold theory (Manifolds by Renteln, Geometrical methods by Schutz)
Topology (tangent and cotangent spaces, fiber bundles, vector fields, connections and parallel transport)
Functional analysis (Kreyszig, Simon & Reed)
Numerical analysis (Tsynkov, Kress)

Anonymous

Anonymous Wed 22 Dec 2021 00:13:25 No.13993503 Report

Quoted By: >>13993878

>>13984690
>i'm a barinless monkey and proud that what i do requires no skill

Anonymous

Anonymous Wed 22 Dec 2021 00:15:04 No.13993510 Report

Quoted By: >>13993514

>>13993499
Your section on topology is really a section on differential geometry.

>Topology(homotopy groups, cohomology, fiber bundles, index theorems)

Anonymous

Anonymous Wed 22 Dec 2021 00:16:22 No.13993514 Report

Quoted By: >>13993524

>>13993510
I know not all of algebraic topology is used, but what specific subjects within it are widely used?

Anonymous

Anonymous Wed 22 Dec 2021 00:20:02 No.13993524 Report

Quoted By:

>>13993514
Homotopy groups. People talk about things like Z_2 vortices and non-Abelian topological defects, and when they do that they are referring to a homotopy group. It is more of a language and understanding thing than something that is really used for calculation. Like someone might look up what the homotopy groups of a certain topological space are in a table to see if it supports topological defects.

Anonymous

Anonymous Wed 22 Dec 2021 01:01:22 No.13993627 Report

Quoted By: >>13993641

Part 1
Linear algebra, including mathematics for QM
Tensors (chapter 2 of continuum mechanics by Lai, Tensor calculus by Neuenschwander, Lovelock, chapter 2 continuum mechanics Mase)
Multilinear algebra (Like in chapters 1 and 2 of Renteln)
Group theory & Lie groups (Lie groups by Gilmore, Tensors & group theory Jeevanjee)

Part 2
Single variable calculus
Multivariable calculus [including mathematics for statistical mechanics (Microstates by kok, statistical mechanics by Khinchin)]
Ordinary differential equations and ode perturbation theory

Part 3
Mathematical physics [fourier analysis(series & transforms), calculus of variations, special functions, lagrangians and hamiltonians, feynman path integrals]
Complex analysis, focus on using contour integrals for physics
Partial differential equations and pde perturbation theory

Part 4
Real analysis (Analysis by Lieb)
Differential geometry/manifold theory (Manifolds by Renteln, Geometrical methods by Schutz, Mathematical methods by Arnold)
Symplectic & contact geometry (Mechanics & symmetry by Marsden, Manifolds by Banyaga, Geometrical mechanics by Holm)
Topology(homotopy groups, cohomology, fiber bundles, index theorems), found in algebraic topology
Functional analysis (Kreyszig, Simon & Reed)
Numerical analysis (Tsynkov, Kress)

That's it, this has to be all that one needs, right?

Anonymous

Anonymous Wed 22 Dec 2021 01:07:16 No.13993641 Report

Quoted By: >>13993802

>>13993627
you want to learn about tensors and Lie groups before calculus?

Anonymous

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Anonymous Wed 22 Dec 2021 02:05:33 No.13993802 Report

Quoted By:

>>13993641
I'll arrange it in order another time

Anonymous

Anonymous Wed 22 Dec 2021 02:32:21 No.13993878 Report

Quoted By:

>>13993503
he makes more money and has a better life than you

Anonymous

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Anonymous Wed 22 Dec 2021 02:48:40 No.13993928 Report

Quoted By:

>>13984690
>no category theory

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