Should I study Analysis before Linear Algebra?

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SUMMARY

Studying Analysis before Linear Algebra is not necessary; a solid introductory book on Linear Algebra with proofs suffices. "Linear Algebra Done Right" by Axler serves as an effective resource for understanding Linear Algebra concepts. While some Analysis books may require a background in Linear Algebra, others can be independent, focusing on single-variable calculus theory. "Understanding Analysis" by Abbot is recommended for those venturing into Analysis, and reading a proofs book, such as Hammok's, can enhance understanding of mathematical proofs.

PREREQUISITES
  • Familiarity with basic Linear Algebra concepts, such as n-tuples and vector norms.
  • Understanding of single-variable calculus.
  • Knowledge of mathematical proofs and proof techniques.
  • Access to introductory texts like "Linear Algebra Done Right" and "Understanding Analysis".
NEXT STEPS
  • Read "Linear Algebra Done Right" by Axler to grasp Linear Algebra theory.
  • Study "Understanding Analysis" by Abbot for a comprehensive introduction to Analysis.
  • Explore proof techniques by reviewing Hammok's proofs book.
  • Investigate the relationship between Linear Algebra and Analysis to understand their interdependencies.
USEFUL FOR

Students and educators in mathematics, particularly those studying or teaching Linear Algebra and Analysis, as well as anyone seeking to strengthen their understanding of mathematical proofs.

terrytosh
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Or is reading a proofs book enough
 
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No, you don't need to study analysis before linear algebra.

And if you get a good introductory book on LA (with proofs!) then there is no need to first read a "proofs book", either. In fact, I think such a book on LA would make for a good "proofs book" by itself.
 
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terrytosh said:
Or is reading a proofs book enough
Linear Algebra, at least for me, was easier than analysis.

Depending on the analysis book you choose to study from. It may require a bit of background from linear algebra. Ie., what is an n-tuple , norm of a vector , and some other topics.

Or the analysis book can be independent of linear algebra. Ie., it is a review of single-variable calculus, but now you work through the theory of it.

A very good intro analysis book is Understanding Analysis by Abbot.
A good Linear Algebra (theory) is Linear Algebra Done Right by Axler.

You do not necessarily need to read a proofs book, but it does not hurt to read one. Especially if you are not familiar proofs.

A good proof method book is by Hammok. A pdf of the book can be legally downloaded.
 
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