Can you recommend some excellent mathematics books for expanding my knowledge? I have heard from different sources that authors such as Stewart have some of the best books, but I honestly don't know where to start and am lost. I have very little experience with trigonometry and little to none with calculus and absolutely none in further fields, and I want to fix this.
Any help and recommendations are greatly welcomed and appreciated!
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How much do you know?
I said it in my original post. I don't know anything past a little trigonometry due to bad schooling when I was younger and I want to be self taught.
Algebra by Gelfand and Shen
Trigonometry by Gelfand and Saul
Basic Mathematics by Lang
Depends on how serious you are about learning math rigorously, but Spivak's Calculus is a rigorous introduction. But learning proper math is really hard without a good community of people around you.
followed by the stuff here
Veeky Forums-science.wikia.com/wiki/Mathematics#Calculus
define proper math
Doing Spivak on your own will be very annoying.
Real and complex analysis by Walter Rudin
Functional analysis with applications by Philippe Ciarlet
Is this picture of compiled books good?
>New Jerusalem Bible
did you even open the image
or did i just get rused epicly
Too scattered in level and aim. Rudin is a reference textbook. Also most people will never actually take a course in set theory because typically it is just a tool.
It would be less frustrating and more productive to look at course notes for real analysis and foundations of mathematics and stuff online rather than at most of these books.
Excluding the Biblem most of these are referebce books that PhD mathematicians cite because whenever they were an undergraduate they had the equivalent of what nowadays would be considered a "graduate level" background. If OP doesn't knows math, he certainly won't learn it reading any of that.
I took an undergraduate mathematics course in set theory, it was a senior/graduate level course.
Binmore and Steward really are excellent books, especially for non mathematicians
There's nothing wrong with the NJB
Math that's important enough to get you hired.
>I have heard from different sources that authors such as Stewart have some of the best books
kekeroni
what do you want to learn? just grab a random freshman calc book desu, later do analysis or something for clarity
Important enough to get hired? What are you, 12 years old?
If you know any mathematics worth to speak of almost no one put in charge to make decisions about your future job will be able to judge your skills.
Try the Book of Proof if you want to get serious with mathematics. It is free, you can just look for it in a search engine.
Except it's a shit book.
> but muh history
Start with the Greeks
Yyep, most will be women and most will judge you based on how much (and where ) you've been employed before.
A good starting point is knowing everything in these.
Hoffman and Kunze - Linear Algebra
Rudin - Principles of Mathematical Analysis
Spivak - Calculus on Manifolds
Artin - Algebra
From here you can branch out to just about anything.
Quick question senpai, when you study a textbook, are you able to prove every theorem in the book by the end of your studies?
not him, but yeah.
How can you move on in the book if you can't prove the key theorems?
You should be able to prove the important theorems. But you won't know what theorems are important until you really understand it. For example I don't really care about most theorems involving matrices and wouldn't know there proofs, but I know that they aren't hard and I'd be able to work it out easily.
Addendum. Hoffman and Kunze can be replaced with Axler if you don't like algebra. You can safely ignore the last two chapters of Rudin.
spivak's manifolds is graduate level, OP struggles with trigonometry are you insane user
this - good if you lack some high school math, and acts as a great bridge into undergraduate stuff
another book - it isn't very rigorous but explains concepts simply with pictures - get james stewart's calculus: early transcendentals
what the fuck is big rudin doing in there - real and complex analysis by rudin is graduate level shit, look at OP's background
>You can safely ignore the last two chapters of Rudin
why come?
where can I get a supplement?
This list isn't something to be done quickly even though there are only four books in it. It should take around two years. Half a year for each book. It should also be done in order. Hoffman and Kunze is the gentlest of the books and is good preparation for real mathematics. Also I recommend using other sources as necessary. Well prepared students could just read all four easily but OP will probably need to supplement his learning and research what he is unfamiliar with. After working hard through even two chapters of Hoffman and Kunze all of the basic math in high school will be easy.
His chapter on calculus on manifolds makes no sense and doesn't fit with his style at all, that's why Spivak is on the list. His last chapter on Lebesgue theory isn't necessary to know but you can read it if you want some motivation for measure theory. The first half of Rudin's Real and Complex Analysis is on that essentially that.
the art of problem solving - intermediate algebra
It's a joke version of this
You're better off reading Munkres Analysis on Manifolds for Chapter 9&10 fleshed out. And any graduate textbook on analysis will do Lebesgue Theory better.
But the bible is Greek :^)
bump
ive been out of highschool for about 5 years, and attended my first year of college but had to drop out due to money and and getting my own place to live. now i'm going back, and i have to take college precalculus. i desperately need a refresher, what's a good book i should read prior to starting this next semester to help me get back on track/not be super behind?
Algebra by Gelfand and Shen
Functions and Graphs by Gelfand, Glagoleva, and Shnol
The Method of Coordinates by Gelfand, Glagoleva, and Kirillov
Trigonometry by Gelfand and Saul
They're hard but work through them and you'll have nothing to fear.
Too hard for OP, but all the math books there are good and readable. Completely disagree that rudin is only a rference. It is very clearly written and easy to learn from. I like folland better though--it covers more that I actually use as an analyst in my opinion. It gave me more of a feel for what analysis was lik than rudin did.
When I started my career, Paul Dawkins was my hero.