Books on Analysis and Linear Algebra

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Discussion Overview

The discussion revolves around recommendations for books on analysis and linear algebra, specifically evaluating the quality of Richard Courant's "Introduction to Calculus & Analysis - Volume 1" and seeking suggestions for suitable linear algebra texts. The scope includes personal experiences with these books and considerations of their appropriateness for different levels of mathematical background.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant expresses interest in the quality of Courant's book, seeking confirmation of its value.
  • Another participant praises Courant's work but critiques its treatment of the fundamental theorem of calculus, suggesting it presents a weaker version due to the order of topics covered.
  • A suggestion is made to consider Shilov's book for linear algebra, although its suitability for beginners is questioned.
  • Concerns are raised about the accessibility of Shilov's book for those without prior knowledge of linear algebra, with one participant noting their experience with Friedberg's text as less favorable.
  • A participant identifies themselves as a recent high school graduate currently studying Courant's book.
  • It is suggested that Shilov's book may be too advanced for someone just starting out, although its affordability is noted as a positive aspect.

Areas of Agreement / Disagreement

Participants generally agree on the quality of Courant's book, but there is disagreement regarding the appropriateness of Shilov's book for beginners, with some suggesting it may be too advanced.

Contextual Notes

There are unresolved questions regarding the prerequisites for understanding Shilov's book and the varying levels of familiarity with linear algebra among participants.

Who May Find This Useful

Readers interested in foundational texts for analysis and linear algebra, particularly those evaluating their suitability for different educational backgrounds.

JG89
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I just bought "Introduction to Calculus & Analysis - Volume 1" by Richard Courant. I am also looking for a good book on Linear Algebra.

1) Is the Courant book (I ordered it from the internet so I didn't get it yet) good?

2) What good books on Linear Algebra are there?
 
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This should be moved to the Science Books Review sections. In any case, Courant is excellent. I have yet to find an introductory book at its level. I have one an only one complaint about Courant: he presents a "weak" version of the fundamental theorem of calculus, only considering continuous integrands. I think this is due to the unavailability of the mean value theorem of differential calculus at the time he presents the theorem (he develops the integral calculus before differentiation), which is usually used to prove the stronger version. For linear algebra, have a look at Shilov.
 
'Linear Algebra Done Right' by Sheldon Axler is a good book for a first course in abstract linear algebra.
 
Is the Linear Algebra book by Shilov meant for first year undergraduate? Or does it require prior knowledge of linear algebra?
 
It's hard for me to say. My class (Advanced Linear Algebra 1) uses Friedberg, which I find inferior to Shilov. It's difficult to jump head first into Shilov's book without any prior exposure to some concepts from algebra. Are you a HS student? Have you read through university math literature before?
 
I just finished HS. I'm currently working through Introduction to Calculus and Analysis by Courant.
 
Then I suppose Shilov is a bit too advanced. It's inexpensive though, so you, if you want to try it, go for it.
 

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