Prerequisites for the textbook "Linear Algebra" (2nd Edition)?

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Discussion Overview

The discussion revolves around the prerequisites needed to effectively learn from the textbook "Linear Algebra (2nd Edition)" by Kenneth M. Hoffman and Ray Kunze. Participants explore the necessary background knowledge in mathematics, particularly in relation to proofs and abstract concepts, as well as alternative resources that may be beneficial.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant expresses concern about missing foundational knowledge before starting the textbook.
  • Another participant suggests that the content appears basic and may not pose a problem, though notes a bias towards mathematics that may not be necessary for physics students.
  • A different participant indicates that the book is typically used for upper-division courses and requires comfort with proofs and abstract mathematics. They recommend an easier book if the learner is not yet comfortable with proofs.
  • One participant prefers an alternative book, "Linear Algebra Done Right," stating it has no prerequisites beyond familiarity with proofs and discusses the placement of determinants in the text.
  • This participant also mentions supplementary resources, such as Artin's "Algebra" and "Vector Calculus, Linear Algebra, Differential Forms" by Hubbard and Hubbard, suggesting they provide concrete examples and complement the study of linear algebra.

Areas of Agreement / Disagreement

Participants express differing views on the prerequisites for the textbook, with some suggesting it is accessible while others emphasize the need for a solid understanding of proofs and abstract mathematics. No consensus is reached regarding the necessity of prior knowledge.

Contextual Notes

Some participants note that the discussion is influenced by individual backgrounds in mathematics and the varying levels of comfort with abstract concepts and proofs.

DartomicTech
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Summary:: What pre-requisites are required in order to learn the textbook
"Linear Algebra (2nd Edition) 2nd Edition
by Kenneth M Hoffman (Author), Ray Kunze (Author)"

Sorry if this is the wrong section to ask what the title and subject state. I read some of chapter 1 already, and that all made sense to me. But I don't want to actually start studying it, only to get to a point where I realize that I am missing a lot of needed knowledge to proceed learning the rest of the book.
 
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It looks pretty basic to me, so there shouldn't be a problem. Some content seems to be a bit biased towards mathematics, which is o.k. if you study mathematics, but might not be necessary if you study physics.
 
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fresh_42 said:
It looks pretty basic to me, so there shouldn't be a problem. Some content seems to be a bit biased towards mathematics, which is o.k. if you study mathematics, but might not be necessary if you study physics.
Thanks!
 
In the US that book tends to be used for upper-division, second courses in linear algebra. It requires you are comfortable with constructing proofs and reading abstract mathematics. If this is your first time learning linear algebra and you aren't comfortable with proofs yet, then I would recommend an easier book.

jason
 
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I prefer the book Linear Algebra Done Right. No prerequisite, only familiarity with proofs.

Its only shortcoming(can be a strength) is that determinants are relegated to the back of the book. You can easy supplement this with a book such as Artin: Algebra. Chapter 1 talks about matrices and determinants. Chapter 3 Vector Spaces, and Chapter 4 Linear Transformations and its properties.

To get concrete examples in R^n, you can view Vector Calculus, Linear Algebra, Differential Forms by Hubbard and Hubbard.

These books complement each other well, and you can learn quite a bit of mathematics doing so.

Hubbard and Hubbard is an interesting math book. A must on any shelf. It made it obvious to me that any linear transformation from R^n to R^m can be represented as T(v)=[T]v, where v is the column vector which is an element of R^n, [T] is the mxn matrix associated to the linear transformation T.
 
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