Textbook or online website with Epsilon-Delta Proofs?

In summary: I'm trying to internalize the proofs, but I get stuck after a few steps and need help.In summary, the person wants help practicing epsilon delta proofs and is looking for a place to find a lot of questions. They suggest Spivak, Erdman, and Ross texts. They also mention that they are average intelligence and that thinking about proofs is important.
  • #1
kramer733
323
0
I don't do well by just reading a proof and internalizing it. I need problems to solve and would LOVE to internalize epsilon delta proofs by practicing 100s of them. It's how I got decent at integrals. It's how anybody gets good at math and music and in general your craft right?
I Don't know a place where i can find a ton of epsilon delta proof questions to do though. Can anybody help me?
And I've read paul notes. I don't want links about the idea of epsilon delta proofs. Just the exercise questions and the answers to them.
Please and thank you.
I'm willing to buy a textbook if it has a lot of them in it.

PLEASE HELP! I Just want to practice like mad. I want practice! It getrs boring practicing the same 2 questions my prof provided.
 
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  • #2


Get W. Rudin's Principles of Mathemtical Analysis. The exercises are hard but still doable. Solutions are scattered on the web (Except for some problems).
A very good supplement to Rudin would be G.M. Bergman excercises packet, which can be found here:

http://math.berkeley.edu/~gbergman/ug.hndts/
 
  • #3


I'm looking for somethijng a bit easier. well a lot easier.. But i'll definitely check it out. Something that first year math majors are expected to do. I also have average intelligence.
 
  • #4
Spivak's Calculus uses epsilon-delta proofs throughout, and is just generally awesome.
 
  • #5
Schaum's Advanced Calculus has some worked problems:
https://www.amazon.com/dp/0071623663/?tag=pfamazon01-20

There is also the Kaczor & Nowak series, but I haven't used them personally:
https://www.amazon.com/dp/0821820508/?tag=pfamazon01-20

You can find a free problem text by John Erdman here:
http://www.mth.pdx.edu/~erdman/PTAC/PTAClicensepage.html

In addition to the Spivak suggestion, if you want to start basic, try Ross' Elementary Analysis. It starts off about as slow as any text can.
There are solutions on some university websites.
https://www.amazon.com/dp/038790459X/?tag=pfamazon01-20
 
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  • #6
Any introductory real analysis text and I don't suggest Rudin which is not introductory.

Also just throwing yourself at problems doesn't really work, you have to think about them for a while except in trivial cases.
 

1. What is an Epsilon-Delta Proof?

An Epsilon-Delta Proof is a mathematical method used to formally prove the convergence or continuity of a function. It involves choosing a small value of epsilon and finding a corresponding value of delta that ensures the function stays within a certain distance of a given point.

2. What is the importance of Epsilon-Delta Proofs?

Epsilon-Delta Proofs are important because they provide a rigorous and precise way to prove mathematical concepts in analysis. They are commonly used in calculus, real analysis, and other advanced math courses. They also help to build a strong foundation for understanding and applying more complex mathematical concepts.

3. How is an Epsilon-Delta Proof different from a traditional proof?

An Epsilon-Delta Proof is different from a traditional proof because it involves the use of specific values of epsilon and delta to prove a statement about a function. It requires a more systematic and logical approach, rather than relying on intuitive reasoning or algebraic manipulation.

4. Can Epsilon-Delta Proofs be used for any type of function?

Yes, Epsilon-Delta Proofs can be used for any type of function, as long as the function is defined and continuous at a given point. However, some functions may be more difficult to prove using this method, and alternative approaches may be necessary.

5. Are there any tips for mastering Epsilon-Delta Proofs?

Some tips for mastering Epsilon-Delta Proofs include practicing with different types of functions, understanding the definitions and principles behind the method, and breaking down the proof into smaller steps. It is also important to seek help and guidance from teachers or peers if needed.

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