Learning Real Analysis at My Own Pace

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Discussion Overview

The discussion revolves around the challenges and strategies of self-studying real analysis and other areas of mathematics. Participants share their experiences with various textbooks and seek recommendations for resources that balance rigor with intuitive understanding.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant expresses a feeling of overwhelm while studying real analysis and seeks books that provide a balance between rigor and intuition.
  • Another participant suggests several titles, including "Naive Set Theory" by Halmos and "What is Mathematics" by Courant, but questions their relevance to the original request.
  • A participant mentions familiarity with the Whittaker text on rigid bodies, noting it is more applied math rather than abstract math, and contrasts it with other texts like Bartle's measure theory.
  • Some participants note that the original poster's selection of books appears scattered and suggest focusing on a more structured learning path.
  • There is a discussion about prerequisites for studying elliptic and hyper-elliptic functions, with one participant mistakenly believing they could be found in complex analysis texts.
  • Several participants mention the importance of having access to a university library for a broader range of resources, while one participant notes limited access to a college library.
  • Another participant highlights the online availability of information regarding elliptic functions and suggests that the original poster is looking for books at various levels.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best approach to learning or the specific resources to use. There are multiple competing views on the appropriateness of the suggested texts and the order in which topics should be learned.

Contextual Notes

Some participants express uncertainty about the level of mathematics required for certain topics, indicating a potential mismatch between the original poster's current knowledge and the complexity of the materials they wish to study.

  • #31
Mr.Husky said:
Can anyone answer my question? I have knowledge roughly of a freshman.
How far have you read into Klein/Sommerfeld?
 
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  • #32
caz said:
How far have you read into Klein/Sommerfeld?
Nothing. Stopped after hearing elliptic functions.
 
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  • #33
Mr.Husky said:
Nothing. Stopped after hearing elliptic functions.
Exactly. You stopped at Chapter 0. You are not ready for it.

You have a freshman’s knowledge, but do not want to pursue intermediate classical, qm or em, although you might look at Susskind’s theoetical minimum books and lectures.
For classical, I would suggest looking at thermodynamics, waves, optics, fluid dynamics or relativity. If you are set on rigid bodies, pick up an engineering book on the subject.
For quantum, I would suggest starting with a “modern physics” book.
There is always Feynman.
Theoretical Concepts in Physics by Longair.
Dimensional Analysis by Bridgman
Gravity by Schutz
Nonlinear dynamics and chaos by Strogatz
Physics of the Earth by Stacey
An astronomy book
An Introduction to Error Analysis by Taylor
 
Last edited:
  • #34
You show extremely good taste in books. However the ones you have listed already would require years of study for most people. So instead of suggesting more, I recommend that you actually dive into some of the ones you already have, e.g. Spivak, and Hilbert-Cohn Vossen. You will be well repaid for the time spent reading them in depth and working as many exercises as possible.
 
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  • #35
Thanks @caz and @mathwonk for your suggestions. I will keep them in mind. Thanks everyone here for helping me.
 
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