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/sci/ - Science & Math

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9221807 No.9221807 [Reply] [Original]

hey sci anons, for over a year I've been growing my will of becoming a math guru, I think now is the right time to stop doing other things and focus just on math
are there any websites/books/anything that will explain any math subject to me like I'm 5? I tend to start from the harder things, so it would be helpfull. If not, then just any source which explains math well enough to not feel bored after first hour?
Is it even possible to learn the harder things first and then the easier ones, or are they just too tied up?

>> No.9221818

>>9221807
Serge Lang _Basic Mathematics_
or Art of Problem solving books. The original books (Volume 1: Basics, Volume 2: And beyond) are best.
or Algebra : Structure and Method

Then calculus from Thomas, or Spivak/Apostol if you want to learn it at the level taught at schools like Caltech. Stewart is a meme version of Thomas. Actually you can just use MIT 18.01 video lectures and just use any computational calculus textbook for the problems. Serge Lang also wrote a calculus textbook whose difficulty and level of rigour is intermediate between that of Thomas and Spivak / Apostol. You can also use the AOPS (Art of Problem Solving) Calculus book

You can also use videos like Khan Academy

>> No.9221833
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9221833

>>9221807
>I tend to start from the harder things
start with algebraic topology, you can pick up the necessary topology, analysis and algebra as you go

>> No.9221838

Kolmogorov Mathematics: Its content, methods and meaning
Velleman How to prove it
Tao Real Analysis
Munkres Topology
Kostrikin, Manin Linear algebra and geometry
Rudin Functional analysis
Lang Fundamentals of differential geometry
Dummit,Foote Abstract algebra
May A concise course in algebraic topology
Shafarevich Basic algebraic geometry

>> No.9221840

>>9221833

Spanier is basically unreadable if you do not have a firm understanding of point-set topology, analysis, and algebra. I suggest Bredon, Hatcher, or Massey.

>> No.9221846

>>9221840
>Spanier is basically unreadable
I know, I suggested it because he likes taking the hard way. I haven't read Massey though, is it any good ?

>> No.9221889

>>9221807
>t. will drop it in a week

>> No.9222290

>>9221838
>Rudin Functional analysis
Rudin is a meme

>> No.9222505

>>9222290
That's why there's Tao as an introductory book. Rudin's functional analysis though has a well-deserved meme status.

>> No.9223164

Begin with Serre: A Course in Arithmetic.

>> No.9223180
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9223180

>>9223164
far too advanced for beginners, it's better to start with Weil's Basic Number Theory

>> No.9223593

>>9221807
The Great Coures*, The secrets of Mental Math, By Professor Arthur T. Benjamin.. www.thegreatcourses.com

>> No.9223599

>>9223593
It also many more that helps with a lot of possibility you might have interest in

>> No.9223758

>>9221807
How much do you know already? Khan Academy is exactly what you're looking for as long as you stay below university level. Beyond that, I dunno.