So I've just finished reading a book about proofs. Next on my radar are calculus and linear algebra. Which one should I start with?
Also what do you think about doing an online course instead of learning with a book? I'd really prefer to do both but I don't have that much time. What would you choose? I'm thinking about the books listed below or MIT Opencourseware / edX courses. Calculus: - Introduction to Calculus and Analysis vol. 1, Courant - Elementary Calculus: An Infinitesimal Approach, Keisler Algebra: - Introduction to Linear Algebra, Strang - Linear Algebra Done Right, Axler.
Linear Algebra done right isn't good for a first course since it doesn't teach anything about matrices. Either go for Lay if you want applications or Linear Algebra Done Wrong. Hofman & Kunze is good too. Both calculus books are good, Apostol and Spivak are also highly-regarded. Read and most importantly work through books, not simply OCW materials. OCW is for when you don't understand what's in your books.
Jaxson Lee
I read Stewarts calculus when I was fourteen and honestly it was the easiest book to read with practically no pre-requirements. And I can easily say it was perhaps the most important step in my math career. Although other books I read afterwards weren't as easy as that one was, perhaps because they were more rigorous, it definitely game me the intuition needed for studying math.
Also what proof book did you read?
Easton Flores
What's the point of doing Stewart if the guy already worked through a proof book? If he know how to write proofs he'll gain a lot more working through Apostol, Courant or whatever than Stewart.
Elijah Nelson
If you want to do proofs then do linear algebra.
Calculus proofs are simply not calculus, even the simplest shit like the intermediate value theorem need topology, analysis, and top tier deduction.
Calculus existed before we were smart enough to comprehend it so even though computations are trivial, proofs are beyond the scope of any book.
On the other hand, linear algebra started trivial and only becomes complex later and that is why every book will have you do proofs from square one.
Nolan Foster
That's not necessarily true. You need topology to formalize analysis but you can do still do proofs, just take a look at Courant's book or Spivak. Just because it's not analysis doesn't mean that everything is trivial. In Bloch's intro to analysis, he gives a proof that the IVT is follows naturally from the least upper bound property. Have you actually read a good calc book?
Kevin Sanchez
All of those books have some problems.
>Courant this is a very good book, but somewhat outdated. It was written in the WWII-era, and while it's rigorous and has good exposition it shows it's age in the way things are done. >Keisler Interesting book, but doing things via infinitesimals isn't a good first approach because it's not standard practice and will handicap you later. Do epsilon-delta first.
>Strang One of the worst math texts I've ever read. Rambling, unfocused explanations, shallow examples, things are defined pages after they're used. >Axler A lot of people swear by this book for pure linear algebra, but I don't like it that much. Axler has a pathological hatred of matrices, determinants, and anything concrete; while those sorts of things can be abused, they're just as much a part of linear algebra as anything else. Axler is very much a "muh PURE math" sort of writer.
If you've finished a proof book you're probably mature enough to read Spivak or Apostol for Calc. Spivak if you like chattiness, Apostol if you want no-nonsense but dry.
For linear algebra Apostol's calc books have a good exposition of the useful theory, and Hoffman/Kunze has been the canonical theoretical text since the 70s. It's a tough read but after a proof book and a rigorous calc book you should be able to handle it.
Logan Nguyen
Provided you supplement Keisler with another book, it's pretty damn good. Also yeah don't fall for the Strang meme op. As for Axler, I think it's best read as a second course or when you know a little about abstract algebra. Hoffman/Kunze is definitely a good book. Also, Spivak was written in part to replace Courant which was getting old at the time.
Gavin Fisher
How to prove it - users.metu.edu.tr/serge/courses/111-2011/textbook-math111.pdf I'll consider Stewarts but wouldn't it be too basic? I'd rather not have to read another one afterwards. I found somewhere an exactly opposite opinion - to start with Done Right, not Done Wrong. Are they in any way complementary? I'll definitely get to applications, but I'd like to get a solid understanding and intuition of LA first, so is it reasonable to discard books concentrating on applications first?
Ayden Ortiz
Don't read Stewarts, go straight to spivak/apostol or whatever you like more. No that's the exact opposite, LA done right is for a second course, LADW is for people going into their first proof-based course (it's said in the preface). Between Hofman/Kunze and LADW, I personally like the latter more. It's more fun to work through and it's free, so that's cool too. It also covers more subjects (tensors for instance).
Jaxon King
rudin for calc. supplement where you lack with as much alternative texts as you want, but use rudin as your main text.
don't read axler unless you like being spoken to like a child.
Alexander Taylor
>this is a very good book, but somewhat outdated. It was written in the WWII-era, and while it's rigorous and has good exposition it shows it's age in the way things are done.
That's his Differential and Integral Calculus books. Fritz John updated Courants book into "Introduction to Calculus and Analysis"
>Interesting book, but doing things via infinitesimals isn't a good first approach because it's not standard practice and will handicap you later. Do epsilon-delta first
Seeing a different approach hardly is handicapping and it's still better than 99% that don't have proofs at all.
Josiah Foster
All right. I've decided to stick to: - "Introduction to Calculus and Analysis" by Courant and John - "Linear Algebra Done Wrong" by Treil Wish me luck or even better motivation.
Thanks anons.
Michael Price
is the sticky a good resource for starting down the math path? or is there a better more concise list of books?
Lincoln Wood
The wikia
Nicholas Taylor
Great images
Leo Wright
introduction to linear algebra by strang is not recommended.
John Murphy
Rudin and Hoffman-Kunze for the smart boys.
Spivak's Calc and some generic LinAlg book for the average boys.
