Should I study Analysis before Linear Algebra?

In summary, you do not need to study analysis before linear algebra. If you have a good introductory book on linear algebra with proofs, it can serve as a "proofs book" as well. Linear algebra may be easier than analysis, but some analysis books may require background knowledge from linear algebra. However, there are also analysis books that are independent of linear algebra and focus on reviewing single-variable calculus. A highly recommended introductory analysis book is Understanding Analysis by Abbot, and a good linear algebra book is Linear Algebra Done Right by Axler. While it is not necessary, reading a proofs book can be beneficial, especially if you are not familiar with proofs. A good book for learning proof methods is by Hammok, which can be legally downloaded
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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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1. Should I study Analysis before Linear Algebra?

It is recommended to study Analysis before Linear Algebra, as Analysis provides the foundation for understanding the concepts and techniques used in Linear Algebra. Analysis also helps develop critical thinking skills and mathematical maturity, which are essential for studying Linear Algebra.

2. Can I study Linear Algebra without studying Analysis?

While it is possible to study Linear Algebra without studying Analysis, it may be more challenging to fully understand the concepts and techniques without the foundation provided by Analysis. It is recommended to at least have a basic understanding of Analysis before diving into Linear Algebra.

3. What are the benefits of studying Analysis before Linear Algebra?

Studying Analysis before Linear Algebra can help develop a deeper understanding of the underlying concepts and principles used in Linear Algebra. It also helps develop critical thinking skills and mathematical maturity, which are essential for advanced mathematical studies.

4. How long does it take to study Analysis before Linear Algebra?

The length of time it takes to study Analysis before Linear Algebra may vary depending on individual learning pace and the depth of understanding desired. It is recommended to spend at least one semester studying Analysis before moving on to Linear Algebra.

5. Can I study Linear Algebra first and then Analysis?

While it is possible to study Linear Algebra first and then Analysis, it may be more challenging to fully understand the concepts and techniques in Analysis without the foundation provided by Linear Algebra. It is recommended to follow the traditional sequence of studying Analysis before Linear Algebra.

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