# Feynman Lectures - Anything similar for Mathematics?

1. Nov 10, 2012

### converting1

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,

2. Nov 10, 2012

### 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...

3. Nov 10, 2012

### espen180

Bourbaki. :rofl:

4. Nov 10, 2012

### converting1

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

5. Nov 10, 2012

### mindheavy

Last edited by a moderator: May 6, 2017
6. Nov 10, 2012

### espen180

Last edited by a moderator: May 6, 2017
7. Nov 10, 2012

### micromass

Last edited by a moderator: May 6, 2017
8. Nov 10, 2012

### converting1

why?

9. Nov 10, 2012

### DrummingAtom

lol!

10. Nov 10, 2012

### 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.

11. Nov 10, 2012

### mindheavy

12. Nov 10, 2012

### converting1

oh ok,

any other suggestions?

13. Nov 10, 2012

### micromass

Last edited by a moderator: May 6, 2017
14. Nov 10, 2012

### converting1

Last edited by a moderator: May 6, 2017
15. Nov 10, 2012

### 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!

16. Nov 10, 2012

### 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?

17. Nov 10, 2012

### micromass

If I'm not mistaken, Spivak gives some solutions (but not all) at the end of the text.

18. Nov 10, 2012

### converting1

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.

19. Nov 10, 2012

### micromass

It only covers calc I-II (and a bit of complex analysis). It doesn't do multivariable stuff.

20. Nov 10, 2012

### converting1

I see,

thanks to everyone for responding