Feynman Lectures - Anything similar for Mathematics?

AI Thread Summary
The discussion centers around finding suitable mathematics lecture books for a student with a solid background in various mathematical concepts, including calculus, algebra, and differential equations. Recommendations include Michael Spivak's books, which are noted for their rigor and focus on proofs, though they may present challenges due to their difficult exercises. The conversation also touches on the limitations of Bourbaki's works, which are deemed unsuitable for beginners. Other suggested titles include "Mathematics: Its Content, Methods and Meaning," Courant's "Differential and Integral Calculus," and Maclane's "Mathematics: Form and Function." The importance of having access to solutions for exercises is highlighted, with Spivak providing some solutions at the end of his text. The discussion concludes with a mention of "Visual Complex Analysis" for those seeking a less rigorous yet insightful approach to complex analysis, potentially paired with more rigorous texts like Ahlfors.
converting1
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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,
 
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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...
 
Bourbaki. :smile:
 
oli4 said:
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
 
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micromass said:
He was making a joke. Don't buy Bourbaki's books lol.

why?
 
espen180 said:
bourbaki. :smile:

lol!
 
  • #10
converting1 said:
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.
 
  • #12
micromass said:
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?
 
  • #15
converting1 said:
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!
 
  • #16
micromass said:
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?
 
  • #17
converting1 said:
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.
 
  • #18
micromass said:
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.
 
  • #19
converting1 said:
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.

It only covers calc I-II (and a bit of complex analysis). It doesn't do multivariable stuff.
 
  • #20
micromass said:
It only covers calc I-II (and a bit of complex analysis). It doesn't do multivariable stuff.

I see,

thanks to everyone for responding
 
  • #21
I would also like to add Courant's Differential and Integral Calculus vol I and II. I received this books as a gift when I was younger and the value I find reading it can easily be shown by how worn the pages have become.
 
  • #22
On a more serious note than earlier, I think that Maclane's "Mathematics: Form and Function" sounds like a very good book for your purpose.
 
  • #23
I have heard a lot of positive stuff about the Serge Lang books.
 
  • #24
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  • #25
In terms of style, if you want something "like" Feynman's Lectures, I would say Visual Complex Analysis. Not completely rigorous, but I think that can be an advantage at times. If you want more rigor, you can (1) look at another book later or (2) look at another book concurrently, whichever you please. For example, you could read Ahlfors alongside Visual Complex Analysis.
 

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