Approaching Analysis: Unlocking the Basics of Rudin's Text

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In summary, the conversation is about the best way to approach analysis for someone with a basic understanding of proof mechanics. The book "Rudin" is recommended but the author finds it too concise and difficult to understand. It is suggested to try practicing symbolic logic and using a different book, "Mathematical Analysis" by Zorich, which has a gentler introduction to abstract concepts and uses examples from physics and topology. The book "Rudin" is described as being packed with generality and not suitable for beginners.
  • #1
mathmuncher
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This isn't so much a query for books as a query for the best way by which one should approach analysis. For someone who has a basic familiarity with the mechanics of proof, I have found the treatment in Rudin to be sorely concise. A few concepts which the author deemed trivial and subsequently chose to omit, seem unobtainable with first sight. The text celebrates terseness in the cost of clarity, and I am very much deluded as to why the book is recommended so tastefully. This leads me to believe that it has something to do with how I'm approching the subject, or the book.

Perhaps it's a lack of visualizing abstract concepts, or plainly the fact that I'm not too familiar with the subject matter, but if I'm not able to obtain the basics from Rudin, how can I ever be able to?
 
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  • #2
Practice symbolic logic, and you will dominate introductory analysis.
 
  • #3
Rudin reperesents Bourbaki-style maths, i.e. it is packed with generality. It is NOT an introductory text. I advise you to work with Zorich, "Mathematical Analysis" instead. It has a gentle introduction to abstract concepts and makes things clearer and visual by using examples from physics and topology/modern geometry.
 
  • #4
Rudin reperesents Bourbaki-style maths, i.e. it is packed with generality. It is NOT an introductory text. I advise you to work with Zorich, "Mathematical Analysis" instead. It has a gentle introduction to abstract concepts and makes things clearer and visual by using examples from physics and topology/modern geometry.
 
  • #5
oh sorry for two posts...didn't mean to do that!
 

1. What is Rudin/Analysis?

Rudin/Analysis refers to the textbook "Principles of Mathematical Analysis" written by Walter Rudin. It is a standard text used in introductory courses on real analysis, a branch of mathematics that deals with the properties of real numbers, sequences, and functions.

2. Is Rudin/Analysis difficult to understand?

The level of difficulty of Rudin/Analysis depends on the individual's mathematical background and ability. It is considered to be a challenging text, but it provides a rigorous and comprehensive introduction to real analysis.

3. How is Rudin/Analysis different from other analysis textbooks?

Rudin/Analysis is known for its concise and elegant writing style, as well as its emphasis on mathematical rigor and proof-based thinking. It also covers a wide range of topics in real analysis, making it a comprehensive resource for students.

4. Do I need a strong foundation in mathematics to read Rudin/Analysis?

A basic knowledge of calculus and set theory is recommended before reading Rudin/Analysis. However, the book does provide a brief review of these topics in the beginning, making it accessible to students with varying levels of mathematical background.

5. How can I use Rudin/Analysis in my studies or research?

Rudin/Analysis is a valuable resource for students and researchers in mathematics and related fields. It provides a strong foundation in real analysis, which is essential for advanced studies in many areas of mathematics, including differential equations, topology, and functional analysis.

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