# Feynman Lectures - Anything similar for Mathematics?

by converting1
Tags: feynman, lectures, mathematics, similar
 P: 65 Last year I got volume 1-3 of the Feynman lectures but as a soon mathematics major I think it'd be appropriate to read more mathematics lectures (and more enjoyable). Is there anything similar I could ask for for my upcoming birthday? Thanks,
 P: 218 Hi converting1, it's quite hard to match 'similar' it all depends on what you mean/expect. If you haven't heard about it by now, I'd recommend having a look at Michael Spivak books, I don't know if they will meet your specific expectations, but there is no way they will be any kind of a bad gift for your birthday :) cheers...
 P: 836 Bourbaki.
P: 65
Feynman Lectures - Anything similar for Mathematics?

 Quote by oli4 Hi converting1, it's quite hard to match 'similar' it all depends on what you mean/expect. If you haven't heard about it by now, I'd recommend having a look at Michael Spivak books, I don't know if they will meet your specific expectations, but there is no way they will be any kind of a bad gift for your birthday :) cheers...
I'm just looking for something which really underlies the foundations of mathematics, something rigorous with a lot of proofs, but still requires a proficiency in mathematics. Here is what I've studied so far:

Factor, remainder theorm
Algebraic Division
Definite intergration
Coordinate Geometry and Further Differenciation
Trigonometry
Geometric Series
More Differenciation: Product,Quotient,Chain rule
Trigonemetric manipulation: Double angles, Half angles, reciprocol functions
Mappings and Functions
Implicit Differenciation
Parametric equations
Further Integration: Substitution, Recognation, Integration by parts
Partial Fractions
Vectors
Matrices
Proof by induction
Series
Basic conics
Numerical Techniques, iteration etc
Complex Numbers
Further Complex numbers: Loci,De Movrie, Roots of Unity etc
1st Order Differencial Equations
2nd Order Differncial Equations
Polars
Further Series
Roots
Taylor expansions
Hyperbolic functions; inverses etc
Further coordinate systems: Equations for an ellipse, loci, parametric equations for a hyperbola & ellipse etc tangents normals etc,
Differentiating hyperbolic functions, inverses & trigonometric functions
Integration - standard integrals, integrating expressions with hyperbolic functions, integrating inverse trigonometric and hyperbolic functions
Further vectors- triple scalar product, writing the equation of a plane in the scalar, vector or Cartesian form.
Further Matrix algebra; determinant, inverse of 3x3 matrix, linear transformations etc

when working through the topics above I would really have to attempt the proofs myself, and if I couldn't do it it'd take a while to be able to find a proof online, so it'd be nice to have it all summarized in a book or so
P: 61
 Quote by espen180 Bourbaki.

Are you referring to this book?

http://www.amazon.com/Bourbaki-A-Sec.../dp/0821839675
P: 836
 Quote by mindheavy Are you referring to this book? http://www.amazon.com/Bourbaki-A-Sec.../dp/0821839675
No, to their collection of 9 series of books, each cosisting of about 3 books on a given area of mathematics.
Mentor
P: 18,323
 Quote by mindheavy Are you referring to this book? http://www.amazon.com/Bourbaki-A-Sec.../dp/0821839675
He was making a joke. Don't buy Bourbaki's books lol.
P: 65
 Quote by micromass He was making a joke. Don't buy Bourbaki's books lol.
why?
P: 661
 Quote by espen180 bourbaki.
lol!
Mentor
P: 18,323
 Quote by converting1 why?
They're not very suitable for beginners. And they're quite difficult to read through. It's more like an encyclopedia than a textbook.
 P: 61 does anyone have an opinion on this dover book? Mathematics: It's Content, Methods and Meaning
P: 65
 Quote by micromass They're not very suitable for beginners. And they're quite difficult to read through. It's more like an encyclopedia than a textbook.
oh ok,

any other suggestions?
Mentor
P: 18,323
 Quote by mindheavy does anyone have an opinion on this dover book? Mathematics: It's Content, Methods and Meaning
That's a very good book. The OP might want to look at this one.

Other nice books are:

http://www.amazon.com/s/ref=nb_sb_ss...mp%2Caps%2C281

and of course

http://www.amazon.com/Calculus-4th-M...eywords=Spivak
P: 65
 Quote by micromass That's a very good book. The OP might want to look at this one. Other nice books are: http://www.amazon.com/s/ref=nb_sb_ss...mp%2Caps%2C281 and of course http://www.amazon.com/Calculus-4th-M...eywords=Spivak
I've heard a lot of Spivak, do you think it would be suitable given my previous background? (second post)
Mentor
P: 18,323
 Quote by converting1 I've heard a lot of Spivak, do you think it would be suitable given my previous background? (second post)
I think it might be worth to try it. You already know a lot of calculus (derivatives, series, integrals, etc.), so that won't be the problem. The hard part of Spivak is going to be the rigor and the proofs. The first two or three chapters are going to be very easy things you know already, but you should make the exercises to get used to the proofs involved. If you can't get used to proofs, then you might want to look at a proof book.

That said: Spivak has a reputation for having very hard exercises. Don't be discouraged by this.

But yes, I should try the book if I were you!
P: 65
 Quote by micromass I think it might be worth to try it. You already know a lot of calculus (derivatives, series, integrals, etc.), so that won't be the problem. The hard part of Spivak is going to be the rigor and the proofs. The first two or three chapters are going to be very easy things you know already, but you should make the exercises to get used to the proofs involved. If you can't get used to proofs, then you might want to look at a proof book. That said: Spivak has a reputation for having very hard exercises. Don't be discouraged by this. But yes, I should try the book if I were you!
thanks, I'll be sure to get it.

Also, I hear most undergraduate textbooks don't have any answers attached, wouldn't this be a problem if it has very hard exercises?
Mentor
P: 18,323
 Quote by converting1 thanks, I'll be sure to get it. Also, I hear most undergraduate textbooks don't have any answers attached, wouldn't this be a problem if it has very hard exercises?
If I'm not mistaken, Spivak gives some solutions (but not all) at the end of the text.
P: 65
 Quote by micromass If I'm not mistaken, Spivak gives some solutions (but not all) at the end of the text.
I see, thanks

out of curiosity does this book cover calc I-III in the US education system? I'm from the UK and we don't have that sort of system afaik.

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