Intro book for Mathematical Analysis

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Discussion Overview

The discussion revolves around recommendations for introductory books on mathematical analysis for self-study. Participants compare various texts, discussing their suitability and approach for learners new to the subject.

Discussion Character

  • Exploratory, Debate/contested, Homework-related

Main Points Raised

  • Some participants inquire about the comparison between "Real Mathematical Analysis" by Pugh and "Baby Rudin," suggesting a preference for Pugh for self-study.
  • Others express skepticism about Rudin as a self-study resource, proposing alternative texts like Strichartz's "The Way of Analysis," which presents concepts in a narrative style, and Ross's "Elementary Analysis," which is likened to Spivak's calculus but aimed at a lower level of analysis.
  • One participant recommends "Introduction to Real Analysis" by Bartle and Sherbert as a good introductory book for self-study, noting it is not as thorough as others.
  • Serge Lang's "Undergraduate Analysis" is mentioned as another good option for learners.
  • Concerns are raised about the difficulty of self-learning analysis, with some suggesting that Rudin may be challenging even in a classroom setting.
  • One participant asks about prerequisite courses for self-studying analysis.
  • Another participant supports Bartle's book for those hesitant about Rudin, while also affirming Rudin's quality as a resource.
  • A suggestion is made to explore Dover Publishing for affordable quality books, with a specific link provided to a recommended title.
  • A participant references a previous thread related to the topic, indicating ongoing discussions about analysis resources.

Areas of Agreement / Disagreement

Participants express varying opinions on the best resources for self-studying mathematical analysis, with no consensus on a single recommended text. Some support Pugh and Bartle, while others advocate for different books or express concerns about Rudin.

Contextual Notes

Participants mention different levels of difficulty and approaches in the recommended texts, indicating that the suitability of a book may depend on the learner's background and preferences. There are also references to the narrative style of some books versus more rigorous texts.

Who May Find This Useful

Individuals interested in self-studying mathematical analysis, particularly those seeking introductory resources or comparing different textbooks.

kmgh
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I am looking to learn analysis on my own - would like to know how does the book "real mathematical analysis" by Pugh compare to baby Rudin.
 
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i don't know anything about pugh, but I don't think rudin is the best book for self studying.

strichartz's the way of analysis isn't the best reference book but it describes things in a "story-like" manner which might help for someone self studying. ross's elementary analsyis is kinda comparable to a spivak calculus type deal, but more geared towarfds lower end analsyis.

ive also heard great things about rosenlicht's intro to analysis (its a cheap dover)
 
I really liked Introduction to Real Analysis by Bartle and Sherbert. It is a good intro book and it can be used for self study. Pretty good INTRO book. Not as thorough as other books however.
 
Serge Lang, Undergraduate analysis is a good book.
 
analysis self-learning is tough - rudin would be hard as it is if you were in a class. go with pugh.
 
what courses should you have b4 trying to self-study analysis?
 
Ditto Bartle if you are afraid of baby Rudin. Not that anyone should be afraid of baby Rudin--- it's a wonderful book!
 

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