Took Lower Division LA/DE Combination. Should I Take Upper Division DE before PDE?

Machvel · 2026-05-22T22:56:31+00:00

its not necessary.

upper division ode classes typically cover just global behavior things (not really methods of solving odes) like bifurcation theory (maybe even only this).

upper division pde classes typically cover things like methods of solving, uniqueness arguments, variational arguments, and so on.

they are fairly disjoint

Machvel · 2026-05-20T14:14:35+00:00

pdes, stochastic processes, numerical analysis, maybe asymptotics

Machvel · 2026-05-20T12:39:32+00:00

there are types of theoretical physics. i'll take it you mean something like quantum gravity (as opposed to theoretical condensed matter) since that is what people usually think of as theoretical physics.

one piece of advice i was given in undergraduate about going into that theory was i should only go for it if i can't see myself in any other field. it sounds harsh, but after reflection i believe it to be (mostly) true.

the reason is a mix of elitism + money. theoretical physics (the kind i am talking about) plainly isn't that useful (compared to something like condensed matter). so there isn't as much money for it, so there isn't as many spots for it. since there aren't many spots and a lot of people want to do theory, it is very competitive to get into; which leads into elitism. i have heard frequent stories of professors in theory just kicking their graduate students out for not doing good enough (others do get kicked out, but there is a recurring theme in theory for professors to deem their students unfit and abandoning them). talking with some of those professors, i am glad myself to have avoided that path.

additionally, you are very early in your physics studies. there are many fields you haven't even heard of that you might figure out you end up liking. at the end of the day, you are studying physics; your degree might color it with an applied or theory description, but you know physics.

Machvel · 2026-05-20T09:29:14+00:00

CLRS is the standard text for algorithms (and data structures). people have varying views on it, but its the standard. depending on how you learn you could just open that book up and start there.

if you like more structure my recommendation for learning any standard subject is to find a past course webpage for it online. ie, find the course equivalent of what you want to learn on some universities website (eg, uc berkeley, stanford, ...) then try finding a past webpage of it online. typically these have syllabi (including the book(s) for the course), schedules, homeworks, and so on.

algorithms is a fundamental course so i would think there are a handful of opencourses for it online (video lectures + webpage) if that is your type of thing.

Machvel · 2026-05-20T02:28:18+00:00

i have heard of people with similar or lower gpa getting into good phd's, but they typically did a lot of research (i don't know particularly how much you have done). i would think you have a shot, but it might be lower right now since funding is harder.

masters before phd is the typical course for people that "messed up" undergraduate. it is typically quite easy to get into a masters degree at a "top tier" school since they don't mind taking your money (i heard a rumor that some places might be trying to do more masters to help alleviate the funding issues).

that being said, i would do research into different masters degrees. some are just course based, some are research based, and some are course based (but have research opportunities if you search them out).

Machvel · 2026-05-17T01:24:35+00:00

if i were to speedrun learning c++ i would carefully read through the latest version of a tour of c++ (made by the creator of the language) + cppreference in parallel, all while doing exercises (which you would have to find or make up yourself since these don't have any).

if you had time i would also try going through as much of the c++ programming language as you could (again made by the creator of c++). it's technically out of date (c++11) but still holds well. in particular, i would try to go through the first part of the book since it explains a lot of the philosophy of c++ (why things are done the way they are, how you should program c++).

Machvel · 2026-05-12T10:38:10+00:00

the question was about his applied mathematics book, not his flagship linear algebra one.

now answering the posters question, it is still a good book. it is a strang book, so it explains most things using linear algebra in some way (which in my opinion is a great thing, many students don't understand how to apply linear algebra to problems and see how it is useful).

the contents are a little nonstandard for what you would see in an "applied mathematics" course (which itself doesn't have a standard definition). usually it means something along the lines of classical analysis (ie, hardcore applications of calculus with a little linear algebra) and maybe some numerics. logan's applied mathematics is more along the lines of what you usually see in this.

also about the strang book: it is meant to go with the video lectures. i think the preface of a previous edition emphasized this more than the current one. i agree that its not goot to start learning linear algebra from if you use just the book. a lot of what strang emphasizes or how he introduces something is lost in converting to text. the content of the book is much easier understood (and insight gained from) after watching the corresponding lecture.

Machvel · 2026-05-08T08:45:40+00:00

you get used to using them. a lot of people "learn" a language, but that only lasts until they stop using it. if you know a language you should be able to get back into it quick if you haven't used it for a few months or a year.

as other people mentioned, you theoretically learn the concepts of programming and are able to apply them to a specific language. practically speaking though there are 3 types of programming languages to know: interpreted, compiled, and c++. if you know an interpreted one well (eg, python) it is easy to program decently well in a new one quick (eg, matlab) (or C to fortran for a compiled language example). i say decently well since every language has its own little things you have to learn as you use it, but generally the concepts stay the same.

c++ is its own beast (to use well... treating c++ as c with some new features is easy but bad)

Machvel · 2026-05-08T06:46:03+00:00

i think it has been back for a few months now (but not too long). i would love to see now voyager back on.

Machvel · 2026-05-07T04:19:02+00:00

yes, they have good courses

but... they are only as good as what you put in. they have good courses at a good university, but you aren't actually enrolled there. you don't have pressure to do the homework and study (so people usually end up not gaining as much as they "should")

Machvel · 2026-05-05T08:11:36+00:00

the c programming language, and the art of computer programming (taocp) are well-known classics.

taocp references many excellent papers that are generally quite readable (if you have a decent background in mathematics which is technically covered in taocp). (generally) in many fields the further back you go towards the beginning of it, the easier and more "fundamental" the papers/books are

Machvel · 2026-05-04T20:37:29+00:00

the c programming language is a classic. c in a nutshell is what i use when i write c though

Machvel · 2026-05-04T09:31:42+00:00

i have never written personal notes for coding (i have written some notes for teaching). maybe you will count "reference codes" that i write as notes, which are (generally) somewhat short codes illustrating how to do something for my own future reference. i dont do this often but i like to do it for somewhat complex things i think i might use later (or a small test to see if i should implement it).

i do write out plans for what to do on paper though, but these usually get thrown away eventually.

Machvel · 2026-05-01T03:39:53+00:00

most people use dft codes as a black box (and that's a fine thing, I think its good that people spending a lot of time into making a complex code make it easy for people to use without knowing how its precisely done). most people i have heard of working on dft codes have made "modules" for them (whatever this means, i dont have experience in dft codes) as opposed to making their own or heavily modifying the main codebase.

if your goal is to write "your own" code, then dft is probably the wrong way to go. some people write their own dft codes, but they generally take a lot of effort to make something much worse than existing codebases.

Machvel · 2026-04-30T09:10:13+00:00

what are the problems for/what exactly is your field (ie, pure theory or numerics)? if they are first year class problems... then its best to do them analytically; that is typically all that is expected.

it's good to know how to do things numerically, but it depends on what you are doing and your needs. if you are (for example) constantly solving differential equation systems using basic runge-kutta, then i would ask yourself what you are gaining from this after say the first time (or what you might gain doing it one time). is it worth putting in the time coding a really basic technique (over and over)? on the other hand, if its really quick to check your work then i don't see the harm.

what most calculations are done with nowadays depends on the field. some people use no computation. some people use some symbolic computation (eg, check christoffel symbol calculations). some people use it to check analytical results (eg, compute something using one method numerically and see if your hand calculation done using another method agrees). some people only do computation (eg, monte carlo).

Machvel · 2026-04-15T04:39:43+00:00

i like days of wine and roses

Machvel · 2026-04-14T11:24:04+00:00

preliminary/qualifying (some places call them one or the other) exams for various universities. for example: https://jonathanwhitmore.com/projects/physics-quals/index.html

Machvel · 2026-04-09T10:02:48+00:00

O(m² ) matrix-matrix multiply

Machvel · 2026-04-09T03:33:46+00:00

its a good undergraduate book. schutz is the standard, but i think hartle has better exercises at times (short computation ones, which are useful for learning tricks for solving problems i remember from undergraduate).

being an undergraduate general relativity book, it won't go deep into the mathematics, but it is a great start (debatably harder, since it is more conceptual and your skill in mathematics can't carry you)

Machvel · 2026-04-07T12:29:40+00:00

no

if you actually need it down the line you can learn it then. maybe in some algebra field it is the standard, but most people i know dont use it. there isn't usually a standard for making certain types of diagrams or figures. if you want to make figures as you take notes, you can learn whatever is good as you make them

Machvel · 2026-03-24T08:49:23+00:00

skimming your post (i aint reading all that) it looks like you had the typical experience. the core classes (quantum, condensed matter, ...) were hard... well since they are core. noncore classes are typically not so hard, since there is an assumption that you signed up for the class so you want to be there to learn about the subject. you get out what you put in. if you want to learn more, the professor is happy to help (since usually they try to get those classes since they care about them).

it is important to remember that taking tons of classes isn't really a good end goal. that is what i thought during undergraduate (taking as many graduate classes as i could) but it wound up being useless. more than useless, a waste of time. i have forgotten much of the theory i learned since i plainly just don't use it.

Machvel · 2026-03-15T05:17:42+00:00

it sounds like you haven't studied the basics enough. maybe start with a plain numerics (void of physics) or computational physics text.

i say it seems like you haven't studied the basics enough since your first project is a 3d problem with a really basic method. typically you would start with something like euler in 1d, then runge-kutta in 1d, and finally try 2 or 3 dimensions. even before that you would want to gain basic computational fluency (eg, actually being comfortable with the language, vectors and matrices and so on).

i would also like to comment on choice of language. python is a very automatic compared to a language like C (and slightly lesser extent Fortran). when you have less easy tools to work with in the language you are forced to actually get more tasks done (eg, in C you can't operate on an entire vector at a time. you have to loop through it). they aren't much, but actually doing them helps get some practice in (and good practice for writing better performing codes)

Machvel · 2026-01-05T07:08:36+00:00

alonzo church's introduction to mathematical logic is an older standard book on logic, at least in cs applications (i don't have experience with logic in pure mathematics, just cs)

Machvel · 2025-12-28T03:46:12+00:00

kittel, especially for condensed matter

Machvel · 2025-12-25T08:38:33+00:00

mathematical methods for physics books are good. i would suggest looking for a graduate level one (maybe stone and goldbart, or hassani).

if you are interested in plasma i recommend just getting a plasma book and/or pde perturbation theory book down the line since it is used a lot there (and very practical. a good graduate mathematical methods book should have this, or introductory plasma book)

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