What math textbook are you studying over the summer?

Lang's graduate algebra (the intro and as much as I can cover really) and a short pdf intro to homotopy theory

Diestel Graph Theory.

Conceptual Math + Haskell Road

William F. French, "Elementary Differential Equations with Boundary Value Problems"

Yay math! :)

Elementary Analysis: The Theory of Calculus by Kenneth Ross and Calculus by Spivak

Also add Simon Singh's the code book to this list.

I just finished a linear algebra course and somehow ended with a B. I'll probably read Linear Algebra done right over summer. Trying to teach myself some code as well so its not an absolute priority

did you guys go into diagonalization, traces etc. or just vector spaces and matrix stuff?

>Elementary Analysis: The Theory of Calculus by Kenneth Ross

Why are you reading brainlet books?

>textbook
What is this 1895?

Thanks For mentioning Haskell road. I'm going to get it now. I like conceptional math.

Anyways to answer thread, I'm going through category theory for scientist, discrete mathematics (Rosen), Haskell programming from first principles.

Been reading a book about engineering thermodynamics.

Jus' remember dat Carnot cycle lesson, nigga.

How to Prove It
Matrices and Linear Transformations
CLRS

Oof. Everyone assigns that one, but it can be pretty frustrating when you want an explanation of how a mechanism actually works. You might want to pick up a couple more if you have access to a good library. I found the books by Ruoff and Askeland very good supplements.

For me, I've got:
Modern Control Engineering by Ogata,
Digital Control of Dynamic Systems by Gene Franklin and J David Powel
Computer Organization and Design by Hennessy and Patterson

Because I've never done analysis before and Ross' book is apparently good for beginners?

I want to get my algebra up to Graduate level standard before I start my masters next year (since I will be taking alg geom, alg topology and elliptic functions)
I tried reading Lang's graduate algebra but was a bit too much.

Should I try Artin, or Lang undergraduate then try graduate, or Ruffi's chapter 0? I also want to pick up on some Galois theory on the way if possible.

some basic calc 1 textbook, it's in the other room so I don't know the title

I haven't done calc in like a decade so I need to brush up, all I remember is how to do, like, basic U substitution of the simplest integrals

>Should I try Artin, or Lang undergraduate then try graduate, or Ruffi's chapter 0? I also want to pick up on some Galois theory on the way if possible.

It really depends on how much background you have.

For Artin, how much background do you have in serious linear algebra?

>Ruffi's chapter 0

How much serious background do you have in the very basics like discrete math, relations, and so on? While he starts off super basic he doesn't throw punches.

If you are really weak in Algebra pick up Pinter. Go through the entire book, even the boring parts. Then graduate up to one of the other books.

If you are stronger in Algebra and strong in linear algebra then any of the books you mentioned are fine.

I like what Chapter 0 does by introducing category theory.

Lang's Basic Mathematics

Below my level academically but really want to ensure I have a proper foundation before entering into serious engineering studies

Well, I'm finishing my third year now at uni and have done some linear algebra (first year, not very deep tho, but with proofs, up to Jordan normal form/eigenvectors, etc), some algebra at the level of Pinter (I actually have that book, but didn't glance at the Field/galois theory section), including ring theory/group theory and some algebraic number theory. I'm somewhat mathematically mature if that means anything, after going through also some intro real analysis, complex analysis and topology.

Does any of those require you to know linear algebra, or would you be able to pick it up from reading their (I suppose not so easy) treatments? I read the first chapter of Aluffi and found it quite good.

Honestly just pickup any of the books that interest you, that you mentioned. Work through them and if you get stuck then review background material as needed and move forward. I think you'll be okay given your background to start any of the books.

I'm also thinking about relearning some linear algebra, in a hopefully not very computational manner, but more abstract instead, any recs? Also thanks btw

Ayyy me too. Except I'm reading it now, not over the summer.

Linear Algebra Done Right is the classic.

Precalculus by Carl-Stitz is better, especially for engineering.

Spivak just arrived in the mail.

Matching Theory by Lovasz and Plummer. It's fairly entertaining.

>Maths C3&4 revision guide

Linear algebra done right - Axler
Understanding analysis - Abbott
Standford mathematics problem book - Polya

Yes, I'm a noob.

Munkres' Topology, some random Python book, and some random cryptology book.

Good luck, I have C12 exam tomorrow, myself.

>noble duel
>not loading his pistol, getting shot and abonded by his second and friends to be found by some peasent and die the next day
>all over some whore

multivariate calculus
classical mechanics: electricity, magnetism, and thermodynamics.

Reading Reed/Simon (all four volumes) and Simons new five volume analysis text. Already familiar with a good chunk of the material in both but I've heard very good things about Simon's style of writing and want stronger/more diverse analysis background, I've actually almost finished reading the first volume of each series and have thoroughly enjoyed both. Also plan on perusing a few physics/geometry texts, namely Naber's two volume set, Jost, Nakahara, Frankel, Choquet, and fomenko, not really a proper read, just seeing which ones I like. The things I'm most exciting about reading though are Milnor's text, I've finally got all of them and want to read them all> For the most part I set my expectations way to high to complete all of it, but at the very least I want to finish Simon's book by summers end and the rest before the year ends.

Try Dummit and Foote then, it's a very easy to read book, hell at times I wish it was more terse, but it's loaded with examples and tons of problems to work through, plus the later chapters cover some basics of algebraic geometry, representation theory, and homological algebra. Normally I would recommend Lang as a grad algebra (or maybe even bourbaki) but since you had trouble with it DM is probably what you want to go with, then use Lang as a second course in grad algebra, it'll help you transition into more abstract subjects. Another good set of books is knapps basic algebra and advanced algebra, longer than DM but covers more advanced material, also free online.

Elementary Calculus: An Infinitesimal Approach

I'm already past halfway through the book, I just require more concentration to finish it.

Eisenbud - Commutative Algebra with a View Towards Algebraic Geometry
Liu - Algebraic Geometry and Arithmetic Curves
But I'm not planning on reading all that. I'll be spending a month in a country with no internet so I'll try to use that time to also do some non-mathematical reading and a lot of writing, maybe take a computer and do some programming.

All luck, math is a beautiful odyssey

What is a good graduate level textbook on differential geometry?

>Using ugly girl photos instead of glorious shutterstock.

Fomenko has a 3 volume text on differential geometry (also a short intro covering all the basics), Kuhnels book is also good so is Spivaks 5 volume series. Other texts like Lee's manifolds and differential geometry and Nicolaescu's Geometry of Manifolds cover more modern topics. Bergers books are also good for this, he has one that is for differential geometry and one for riemannian geometry, though both don't require too much overhead in terms of background.

Introduction to Analytic Number Theory by Apostol

Jost's "Riemannian Geometry and Geometric Analysis" is my favorite.

The girls you posted have got more makeup caked on. That's all.

Also a great book, though it may not be suitable for a grad course in differential geometry specifically since there's a lot about "general" differential geometry not covered, only the bits necessary for riemannian geometry, things like curves, surfaces, "classical" geometries and spaces, differences between local and global theories, cartan's method, and more generally building experience doing these sorts or problems and using these tools. Also many of the concepts in the book shouldn't be your first intro to said concept, as such it'd be an amazing riemannian geometry textbook, though, only after you have had a good differential geometry book.

I assumed since he specified graduate book, he would have already had some undergrad differential geometry (classical curves/surfaces stuff, smooth manifolds, etc.)

Introduction to Analysis by Maxwell Rosenlicht
Introduction to Graph Theory by Douglas B West

Former because I didn't really grasp Real Analysis that well this semester and figure a different (and shorter) book could help.

Latter for funsies.

How can you teach linear algebra without diagonalization/eigenvalues?
What's the point.

Ayy another ece guy. I almost went into control theory for my ee concentration but went for DSP instead, still want to take some classes in it though

My processor arch class used CO&D, we used it to write a MIPS processor in vhdl. Great book and learned a lot but never again

A=B

Generatingfunctionology

the fuck are traces?

sum of the diagonal entries of a matrix.

Ashcroft-Mermin
Not math though

Personally I hated Artin and Dummit and Foote. Artin was too focused on things I found uninteresting like linear algebra and his proofs often used the same stuff. His organization is very strange as well. Dummit and Foote is gigantic and would only be useful if I ended up stranded on an island. It wastes too much space for my taste by going into too much detail and putting key definitions in examples.

Since you'll be doing some serious abstract algebra work I recommend Herstein and both of Lang's algebra books. You should also pick up some commutative algebra from Atiyah and MacDonald as well.

Jordan Schultz

>reading that shitty meme book
get Veeky Forums senpai

thinking of taking a complex analysis or combinatorics class in the fall. looking into Complex Analysis by Stein and Shakarchi

and maybe an algebra because I flunked that class so hard and feel so much shame

>named William F. French
not a french

Get Aluffi for the category theoretic perspective, especially useful for alg. geometry and topology.

Bought that book last summer but never cracked it. Used Khan Academy instead and it was wholly sufficient for preparing me for calc 1 (I'm assuming that's about where you are). I'd just do that instead

That's a GOAT tier book, I remember reading that shit my senior year of high school. Good times.

>topos theory by johnstone
>higher topos theory by lurie
And if I have time, something about homotopy in a topos.

I am become study, destroyer of curves.

Shelah. Wish me luck. Hope i won't end up in psych ward

A book on information theory

I don't bother cause i now despite what my plans were i won't probably gonna do shit. I have a lot of summers like this behind.

apostol calculus

very good book. only part i didn't like was the geometry

also the fact that the author was a socialist, but at least he was tactful enough to leave politics out of math

he was 18, 18 year olds have hubris

Tao Analysis I & II, Pugh's Real Mathematical Analysis; Hoffman and Kunze, and Linear Algebra Done Right. Thinking of picking up Gamelin's complex analysis. Any thoughts?

clrs struggles

are you doing 6.006 ocw too?

Aluffi's Chapter 0 is the absolute best. Stick to it and get as far as you can and you'll have a solid foundation for any future algebraic work

I'm reading Euler's and Leibniz' books on calculus, it's comfy as fuck

I'm doing pre-CLRS studying. Going through the entirety of Rosen's text (minus some Boolean algebra/circuit drawing stuff).

Royden's Real Analysis
Lehman's Elements of Large Sample Theory

youtube.com/watch?v=kgQfoXIJiWI

(yes i bought the book)

Baby Rudin

Just took on a masters degree in applied math from a batchelors in engineering. Gotta get my skills up to scratch

Is Thomas' Calculus (ISBN: 978-0-321-88407-7) a decent Calc book? It's what we used in Calc I. I thought it was decent, certainly much better than any of the texts we used in high school, but my experience is pretty limited. This summer I was going to review and supplement it with Apostol, Courant, or Spivak, as I've seen those recommended as very rigorous for this level. Is there anything else someone could recommend to get ready for Calc II?

I read some of it and remember liking it

You have bachelor's and haven't yet read Rudin? How is this allowed?

Mathematics for Australia 12 Mathematical Methods

Doing it for school, it's pretty easy atm.

Maybe not American

My master's project involves differential topology with required texts milnor topology from a differential viewpoint and Hirsch. What are some prereqs for these that I should at least be quite confident in? I have some (algebraic) topology and differential geometry (do carmo curved and surfaces), and the description says we could venture into some algebraic number theory (of which I know some of too), so anything on that?

I will just watch anime and porn this summer.

>studying in summer while chad is banging hot bitches

fucking nerds :^)

are there people that have read the whole EGA+SGA series ?

Mochizuki.

my man