Textbook or online website with Epsilon-Delta Proofs?

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Discussion Overview

The discussion centers around finding resources for practicing epsilon-delta proofs in mathematics. Participants are seeking textbooks or online materials that provide numerous exercises and solutions, emphasizing the importance of practice in mastering the concept.

Discussion Character

  • Homework-related
  • Debate/contested

Main Points Raised

  • One participant expresses a strong desire for practice problems specifically focused on epsilon-delta proofs, indicating that they learn best through solving numerous exercises.
  • Another participant recommends W. Rudin's "Principles of Mathematical Analysis," noting that while the exercises are challenging, they are still manageable, and solutions can be found online.
  • A different participant seeks easier resources, suggesting that they are looking for materials suitable for first-year math majors.
  • Spivak's "Calculus" is mentioned as a resource that incorporates epsilon-delta proofs throughout and is described as generally excellent.
  • Another suggestion includes "Schaum's Advanced Calculus," which contains worked problems, along with other texts like Kaczor & Nowak's series and Ross' "Elementary Analysis," which is noted for its gradual approach.
  • One participant advises against Rudin for beginners and emphasizes the importance of thoughtful engagement with problems rather than just attempting to solve them without understanding.

Areas of Agreement / Disagreement

Participants express varying opinions on the appropriateness of different textbooks, with some advocating for more advanced texts while others prefer easier introductory materials. There is no consensus on a single recommended resource.

Contextual Notes

Some participants highlight the difficulty level of certain recommended texts, indicating that the suitability of resources may depend on individual backgrounds and learning preferences.

kramer733
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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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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/
 


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.
 
Spivak's Calculus uses epsilon-delta proofs throughout, and is just generally awesome.
 
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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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.
 

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