What is required to read this article?

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Discussion Overview

The discussion revolves around the prerequisites needed to read and understand a specific research paper in mathematics, authored by a respected professor. Participants explore the necessary mathematical background, including various fields such as ordinary differential equations, complex analysis, and normed spaces, as well as the potential interdisciplinary knowledge required.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • Some participants suggest that at least a 2nd year college level understanding of mathematics is necessary to grasp the initial sections of the paper.
  • One participant lists specific mathematical topics required, including ordinary differential equations (ODE), complex analysis, and normed spaces, recommending advanced texts for each area.
  • Another participant emphasizes the need for both introductory and advanced courses in differential equations, as well as knowledge in complex variables and linear control theory.
  • Some participants mention that while topology is referenced, it may not be essential for understanding the paper.
  • There is a recognition that a strong mathematical foundation may not be sufficient alone, and interdisciplinary knowledge could be beneficial.

Areas of Agreement / Disagreement

Participants generally agree on the necessity of a solid mathematical background, but there are varying opinions on the specific courses and topics required, indicating multiple competing views on the prerequisites.

Contextual Notes

Some assumptions about the reader's prior knowledge and the depth of understanding desired are not explicitly stated, which may affect the applicability of the suggested prerequisites.

Who May Find This Useful

Students or individuals interested in reading advanced mathematical research papers, particularly those in mathematics, engineering, or related fields.

MidgetDwarf
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Out of curiosity, I was wondering what is required to read and understand this research paper. The person who wrote it was one of my favorite professors. Very demanding, but helpful at the same time. I was an awe watching him lecture. As a result, I chose to major in mathematics. It is more for sentimental and educational milestone purposes.

http://ejde.math.txstate.edu/Volumes/2005/84/alwash.pdf
 
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Presumably you want to be able to understand it ... but to what depth?

I think it would take at least 2nd year college level math to understand the first paragraph from "We consider..." through, "...an open set." But that would be understood at 2nd year college level.
 
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MidgetDwarf said:
Out of curiosity, I was wondering what is required to read and understand this research paper. The person who wrote it was one of my favorite professors. Very demanding, but helpful at the same time. I was an awe watching him lecture. As a result, I chose to major in mathematics. It is more for sentimental and educational milestone purposes.

http://ejde.math.txstate.edu/Volumes/2005/84/alwash.pdf

Here's a list of things I see in the paper:
- Of course ODE. But Ross' ODE book likely won't cut it, you'll need something more advanced such as Teschl http://www.mat.univie.ac.at/~gerald/ftp/book-ode/
- Complex analysis language is used freely in the paper, including Rouche's theorem. A book like Freitag-Busam should cover enough: http://www.springer.com/us/book/9783540939825
- Normed spaces would be analysis. Carothers covers this well. https://www.amazon.com/dp/0521497566/?tag=pfamazon01-20
- He uses language from topology, but I'm sure you can actually get away with not knowing topology for this.
 
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micromass said:
Here's a list of things I see in the paper:
- Of course ODE. But Ross' ODE book likely won't cut it, you'll need something more advanced such as Teschl http://www.mat.univie.ac.at/~gerald/ftp/book-ode/
- Complex analysis language is used freely in the paper, including Rouche's theorem. A book like Freitag-Busam should cover enough: http://www.springer.com/us/book/9783540939825
- Normed spaces would be analysis. Carothers covers this well. https://www.amazon.com/dp/0521497566/?tag=pfamazon01-20
- He uses language from topology, but I'm sure you can actually get away with not knowing topology for this.

Great, thanks Micromass. Looks like if I work hard enough, I can get an understanding of these topics in 1 year, maybe 2 years. Thank you for taking your time responding with a well structured list of topics and resources.
 
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I think you would need an introductory course in differential equations at approximately the sophomore/ junior level, an advanced course in differential equations at about the jr/sr level. Complex variablles would also ne helpful and perhaps necessary. I also had a graduate course in advanced control systems (Electrical or Aerospace Engineering) that treated this material best. To prepare for this advanced course, you should have linear control theory at the sr or graduate level. You seem just the math may not give you the sufficient background. You may need to be interdisciplinary to treat this material best
 

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