Well Veeky Forums, what are you reading over winter break?

Books from the library I'm studying for next semester
Dummit and Foote algebra
Lang complex analysis
Ash complex variables

Books I own that I'll look through and leave here at my family's house
Hoffman and Kunze linear algebra
Axler linear algebra
Lang linear algebra
Jordan linear operators for quantum mechanics
Bamberg and Sternberg mathematics for physics 1
Marsden basic complex analysis
Bartle elements of real analysis
Rudin principles of mathematical analysis
Rosenlicht introduction to analysis
Townsend quantum mechanics
Liboff quantum mechanics
Shankar quantum mechanics
Lawrie unified grand tour of theoretical physics (read everything except the statistical mechanics at the end)

These papers

arxiv.org/pdf/1401.1044.pdf
math.harvard.edu/~lurie/papers/moduli.pdf
math.harvard.edu/~lurie/papers/survey.pdf

Something about Kähler geometry, particularly 3d and 4d Calabi-Yau stuff. Will start with relevant chapters of pic related and then try to find more specialised articles.

Popsci books about viruses and antibiotic resistant bacteria that my moms are buying me for Christmas.

Other organic synthesis methods beyond the ones in pic related, this is way too comfy

That doesn't indicate any knowledge of what he/she doing. OP literally has a stack of standard references.

Probably going to read pic related to learn MATLAB and how to use it for optics. May read through a linear algebra book and a lasers book to prepare for spring semester classes as well if I am bored.

I'll be reading portions of Stein's Singular Integrals and Differentiability Properties of Functions and Chemin's Perfect Incompressible Fluids.

Still trying to decide which probability book to read that's good for self-study. Recommendations welcome

>Introduction to Econometrics
>no book yet but planning on getting into differential equations

standard references in and around -algebra- (master race). I just really like all those books (except stewart no idea how good that one is)

>Programming: Principles and Practice using C++
>Project Euler exercises
>Maybe Introduction to Algorithms
Being a Brainlet is hard, man.

project euler is super fun, but it's not as good for learning algorithms as say competitive programming 3 + uva. especially since you're doing C++, check those out.

Speaking of which, does anyone have a good recommendation for diff eq books that aren't terribly written?

It's a literal meme collection.

Ah ok. Thanks for the advice, man.

for mathematicians? hirsch & smale

If you nees to whole break to learn that you are doomes my man. It's much better to actually learn calc 2.

Not him.
Any specific theorems should I look into before Calc 2?

fundamental theorem of calculus

pythagoras

thats it

I'm working on something instead of studying something. A derivation of some interesting physics and mathematics. Can't say what though, you know you would steal it if you're in the field.

Protip: Eisenbud contains way more information than you actually need to do Hartshorne.

What do I need for Hartshorne then, give or take? Note I will be going through Shafarevich first too

Know calc 1, I'm assuming that for everyone, calc 1 is differential calculus in 1 variable and calc 2 is integral calculus. Depending on how heavy your course is on the theory, you should modulate your study. Maybe just take a crash course about integrals and FTC, and then just grind with integration methods so you can dedicate your time to more formal approaches (Riemann sums, Jordan measure and even a bit of Lebegue measure if you are interested enough).

The division I had was:

Calc 1 - integral and differential calculus, focusing on key topics like chain rule and integral solutions for various functions

Calc 2 - Introduction of full theory of exponential and logarithmic functions, infinite series, Taylor series and related results

Calc 3 - multivariate and vector calculus, Green-Kelvin-Stokes theorem, divergence and Gauss' theorems, etc.

meant for

Most people don't really "read" Eisenbud as far as I'm aware.
Hartshorne will draw on a shitload of commutative algebra without explaining or proving it. When this happens you open up your copy of Eisenbud, read the relevant portion, and then go back to Hartshorne.
If you're really interested in ring theory you could probably read more substantial portions but Eisenbud is first and foremost a tool for making Hartshorne's book usable.

But how exactly am
I going to understand something in, say, chapter 5 of Eisenbud without having first read most of the previous chapters?

K, if you are confident with your calc 1 skills, then just go right into the theory of series.

Well, for this break I decided I would break down my reading into two sections.
1) A review of what I learned this year that is useful for general problem solving (as in Putnam style)
2) Topics I care about

For the first one, I am using a textbook that reviews all of undergrad math. My main goals are to memorize key techniques I feel are important for general problem-solving. When it comes to general problem solving the classes I took this year are linear algebra, calc 3, probability and differential equations so I am going over those topics carefully to memorize the main concepts.

For example, in Calc 3 I am memorizing all the types of integrals, how to compute the Jacobian and what it means (i.e, linear approximation of a function), how to compute curvature and how to compute the Hessian.

I especially care about integration because in general problem solving you always see integrals with no antiderivatives but one of the techniques to solve those is to somehow rewrite the integral as a double integral, so I really wanna be fresh with my integration.

2) I will go as far as I can with Introduction to Analytic Number Theory. Gonna start from chapter 3 and push through with full force to see how far I get. Last time I read from chapter 1 to chapter 5 and in chapter 1,2 and 3 I was really strong, solving almost all the problems on my own. But starting chapter 4 and 5 I was literally solving one in 10 problems and googling the rest. I did not like that so I stopped and decided I'd come back to it when I had more maturity. Hopefully, now I have enough fuel to destroy all those chapters' problems and maybe go beyond.

>not using mits free data structure course

I'm reading the hunger games xD.

Been meaning to catch up.

Gonna read some beginner maths and computer graphics principles or something

Bump

Im going to be reading up on bachelardian philosphy of science and maybe check out some more recent stuff possibly by Anderson on emrrgent bebaviour.

Other then that, I have to finish an essay by Althusser about the structuring of theoretical practice and thr theory of theoretical practice and how this relates to the general social practice and historical materialism.

If i get bored ill read up on what all the buzz related to quantum topological computation is about.

jesus christ

This

muh refrigerators

This man knows what he's doing

I'm trying to figure out what the fuck i'm studying.
Yes, i fell for "compsci is not a science" and SICP memes, took them seriously, it's been fun

For the languagelets out there, from top to bottom:
What Is This Thing Called Science? Chalmers
Introduction to Mathematical Philosophy, Russell
Mathematics, Science and Epistemology, Imre Lakatos
SICP, the meme

what are you doing nigga

>hartshorne
more like shartstorm lmao

For comparison, Atiyah-Macdonald contains probably 90% of what you need for Hartshorne and is only 126 pages.

seconding , I learned commutative algebra from the concise, clear Atiyah-Macdonald and that will allow you to use eisenbud and other heavier commutative algebra texts as references when doing AG

I also have Reid's undergraduate commutative algebra in my possession, and in the preface he mentions he has everything AM has but more concise

you do all of that in only 2 weeks?

that's just my book stack, im only doing galois and eisenbud. Also my break is 4 weeks

have to learn java for second semester. is o'reilly any good, shop.oreilly.com/product/0636920023463.do or picture

I'm reading Calculus, physics and diferential geometry. :v

You need classical algebraic geometry and some knowledge of where to find commutative algebra references. Knowing some complex manifold theory would also be tremendously useful.

what's classical algebraic geometry? point me to some books so i can get the gist of it

...

Ch.1 of Hartshorne, but not Ch.1 Hartshorne because it's bad

So Shafarevich?

...

Who said I needed a whole break to learn that? I just said I was going to learn it over the break. That doesn't imply that it'll take the entire break.

>Dieso
absorutely disgusting

>memorizing
Kys

>From Calculus to Cohomology
What is that? Is it just some algebraic Topology kind of book?

For my impending algebra comp.
>Dummit and Foote Abstract Algebra
>Hoffman Linear Algebra

For my own pleasure and future endeavours
>Banach Algebras
>Maybe some quantum group stuff
>Maybe some Commutative Algebra / Algebraic Geometry

Also gonna try to read more papers. I think I'm trying to be too ambitious with this list.

>What is that? Is it just some algebraic Topology kind of book?
amazon.com/Calculus-Cohomology-Rham-Characteristic-Classes/dp/0521589568

>De Rham cohomology is the cohomology of differential forms. This book offers a self-contained exposition to this subject and to the theory of characteristic classes from the curvature point of view. It requires no prior knowledge of the concepts of algebraic topology or cohomology. The first ten chapters study cohomology of open sets in Euclidean space, treat smooth manifolds and their cohomology and end with integration on manifolds. The last eleven chapters cover Morse theory, index of vector fields, Poincaré duality, vector bundles, connections and curvature, Chern and Euler classes, Thom isomorphism, and the general Gauss-Bonnet theorem. The text includes over 150 exercises, and gives the background necessary for the modern developments in gauge theory and geometry in four dimensions, but it also serves as an introductory course in algebraic topology. It will be invaluable to anyone who wishes to know about cohomology, curvature, and their applications.

12 week summer break.
Currently working through Signals and Systems (6.003 MIT OCW). I'm only focusing on one unit at a time, so I wanted to go though it quickly, 2.5 weeks of work per week.
Unfortunately I have been slacking off, and have only completed the first two weeks in a two week period.

Over time I hope to get as many MIT OCW courses on control engineering as possible.
For context, I'm formally studying mechanical engineering, and I take all the control engineering units it can, which is only 3.

stfu, you absolute indle

Everything Flows
Analysis by Apostol

Just as a note, from the beginning, it basically assumes all knowledge from (multivariable) calculus

>languagelets
>lee libros en español

ayyy

Mathematical Statistics and Probability

Mathematics for Computer

Neural Networks and Deep

All of these texts are just random pdf's I found online, I'm not home currently and I don't remember the author's names. Pretty good books so far though.

What major are you in user?

*mathematics for computer science

I accidentally a word.

This and Recursive Aspects of DST by Weinkampt for reference.

Can anyone tell me if this list is legit? I've worked my way through a third of "the book of proof" by Hammack and I like it so far. I want to know if going through this list will give me a solid understanding of basic mathematics or if it's brainlet stuff that won't work. I plan on finishing Hammack either way.

That'll do. Hell, even supplement with an undergrad book like Reid.

They are good initial books but they are filled with redundancy. Two or three books from there are more than enough. Your proof book, one calculus and one basic math book.

What does invariant refer to here?

kill urself my man

what are some other good logic books out there? can't find the laws of truth on internet

You seriously think you should read 7 books before learning basic analysis? I think the two proofs books are fine if you need them. Then you can start learning analysis from Rudin, Rosenlicht, Spivak, Pugh, Tao, etc....
The placement of basic mathematics by Lang makes no sense because all it covers is high school math. Foundations of analysis has no reason to be a necessary book, literally no one I know, analysts even, has bothered to read it. If you don't know what it is, it's literally just all the theorems and proofs necessary to construct the number systems, not especially useful to study from. Similarly set theory and logic are not a required tool for mathematicians to know. If you don't believe me please take a look at the preface to Halmos's book on set theory, where he recommends students to be interested in it, learn it, then forget it.
The list is too slow. By the time you've finished, you could have read a book on analysis, a book on linear algebra, and a book on real analysis or abstract algebra. Don't spend your time with a bunch of undergraduate books when you could push to grad level material where it actually gets interesting.

>set theory and logic are not a required tool for mathematicians to know

what the fuck

Rate them.

And feel free to recommend decent books on these subjects as well as Modern Physics (about 3000 level).

0

that was quick. sorry i meant
>the material covered in books solely on set theory and logic are not a required tool for mathematicians to know

Doesn't count without explanation.

The preservation of equivalence classes under borel functions. Look up Borel Complexity theory.

it's on libgen, I really recommend laws of truth, amazing book to understand and get interested in logic

yeah it's true, but some mathematicians like to put a lot of emphasis in their foundations, which I think can be a good thing, still, one good intro book should be enough.

although its for work, im out of school

Good taste, you might want to also check out math.uh.edu/~shanyuji/Complex/Complexgeometry.pdf
books.google.com/books?id=6bqvDAAAQBAJ&source=gbs_book_other_versions
press.princeton.edu/titles/4632.html
bookstore.ams.org/fourman/
I would suggest reading vakil's notes instead, or at the very least supplementing hartshone with some other books. Some books that cover classical AG are Beltrametti's lectures con curves, surfaces, and varieties, Holme's royal road to AG, and shafarevich BAG I & II.
I'm finally getting around to reading some of Milnor's more advanced texts, specifically the ones on characteristic classes and K-theory. After that reading Tao's book on nonlinear dispersive equations and this book I found on geometric measure theory. Also gonna look into some stuff on representations of compact and discrete groups, there's actually a lot of cool stuff that connects it number theory and dynamical systems.

I am in electrical engineering + physics minor. I just began focusing on an optics/photonics route and the only related class Ive had was an upper level EM theory class, but I plan to take about 4 to 6 optics/photonics related courses over my last 3 semesters