Mastering Binomial Theorem for Understanding Rudin's Analysis Proofs

In summary, the conversation discusses the difficulty the individual is having with understanding proofs in chapter three of Baby Rudin, which use the binomial theorem and its derived identities. They are struggling with theorem 3.20 in particular and are looking for additional resources to help them understand these concepts better. They also mention the possibility of switching to a different textbook, such as Spivak's calculus, which may be easier to understand. Overall, the main issue is understanding the proofs and finding additional resources to aid in this understanding.
  • #1
jecharla
24
0
I have been teaching myself analysis with baby rudin. I have just started chapter three in the past week or so and one thing I am having trouble with is the proofs which use the binomial theorem and various identities derived from it. Rudin pretty much assumes this material as prerequisite and his proofs use it so concisely that it is hard for me to follow since I pretty much learned the binomial theorem while studying rudin.

A good example of where I have trouble is 3.20. This theorem uses a few different identities derived from the binomial theorem which I am not familiar with and and it is hard for me to just learn in the context of these proofs.

A good example of where I have no trouble is theorem 3.31. This theorem requires just a straightforward use of the binomial theorem itself which I am fine with.

Is there a good textbook or website to get me up to date on these identities involving the binomial theorem?
 
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  • #2
What exactly is the problem? Can you understand the proofs (after staring at it for a while)?? Is the problem that you're unable to find such results yourself? I think that would be very reasonable. The most important thing here is understanding the proof in question. Finding such thing yourself will probably not be something you'll be able now.

Of course, Rudin is pretty concise and hard. Spivak's calculus is much more easy-going, but still covers a lot of analysis.

Or is the problem that you don't understand the proof? That is more serious.
 
  • #3
As of yet I have not been able to get through theorem 3.20. But I am just going to stare at it for longer :)

Can't expect them all to be easy.
 

FAQ: Mastering Binomial Theorem for Understanding Rudin's Analysis Proofs

What is the Binomial Theorem in Rudin?

The Binomial Theorem in Rudin is a mathematical formula that provides a way to expand an expression raised to a power, specifically binomial expressions. It is named after the mathematician Walter Rudin.

What is the general form of the Binomial Theorem in Rudin?

The general form of the Binomial Theorem in Rudin is (a+b)^n = a^n + n*a^(n-1)*b + (n*(n-1)/2!)*a^(n-2)*b^2 + ... + b^n, where n is a positive integer and a and b are real numbers.

What is the significance of the Binomial Theorem in Rudin?

The Binomial Theorem in Rudin is used to expand binomial expressions in a more efficient way, especially when the power is large. It also has applications in various fields such as probability, statistics, and physics.

How is the Binomial Theorem in Rudin related to the Pascal's Triangle?

The coefficients in the expansion of (a+b)^n correspond to the entries in the nth row of Pascal's Triangle. This relationship can be seen by looking at the coefficients in the expansion of (a+b)^n and the corresponding entries in Pascal's Triangle.

Can the Binomial Theorem in Rudin be extended to non-integer powers?

Yes, the Binomial Theorem in Rudin can be extended to non-integer powers using the Binomial Series. This involves using the concept of a binomial coefficient with negative, fractional, or even complex numbers as the power.

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