Advanced Undergrad Linear Algebra classes

In summary: Self studying and taking a class might work for you, but I would recommend getting a professor to help you out if you can. It's better to have someone to guide you through the material and make sure you're understanding it.
  • #1
DrummingAtom
659
2
Last semester I took a combined course of Diffy Q and Linear Algebra. I feel I know the basics of LA and want to explore things a bit further. After talking to some professors at my school they told me that the next linear algebra class is a graduate class.. After looking at the course notes for that grad class it's definitely out of my range because it's all proofs. They suggested to take real analysis and abstract algebra to prepare for that grad class. I know I won't be taking those classes, probably ever, and now I'm kinda disappointed that a class that sounds interesting is most likely out of reach.

Does linear algebra usually have a big jump in class level similar to my school? Intro undergrad class then full blown grad class?

I know the other classes (real analysis, abstract algebra) would develop math maturity but are they really necessary specifically for linear algebra? Is this a normal sequence?

My options are: 1) self study like mad and develop proof skills on my own and convince an adviser to let me take the class 2) audit the class, which I don't know if I can do because it's a grad class or 3) do an independent study with a professor.

Any help/guidance is appreciated.
 
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  • #2
Linear Algebra does often take an awkward spot in curricula.

Are you a math major? If so, take analysis and algebra (only algebra will likely be required but analysis builds up a lot of maturity) then take the graduate course. If not, I would take a math professor about doing a reading with them to learn more linear.
 
  • #3
Thanks for the response. I wish I was a math major but I'm an EE major. :wink: I guess an independent study does seem to be my best option.

Another question, what class(es) cover the theory of vector spaces? My class last semester only skimmed the surface of vector spaces and I feel like there's a lot more to them.
 
  • #4
DrummingAtom said:
Thanks for the response. I wish I was a math major but I'm an EE major. :wink: I guess an independent study does seem to be my best option.

Another question, what class(es) cover the theory of vector spaces? My class last semester only skimmed the surface of vector spaces and I feel like there's a lot more to them.
There is. Finite dimensional vector spaces, what most schools cover in an applied undergraduate course I believe, are not immensely interesting or complicated. But what's more important and very cool is infinite dimensional vector spaces. So much to say about those.

The only place where you are likely to be taught vector spaces in a real rigorous manner is linear algebra. Anywhere else, it's likely presupposed you already know a fair amount about them.

A reading is a great idea, because it also never hurts to get to know a professor really well.
 
  • #5
Hey DrummingAtom.

There is a book published by Springer that is called: "The Linear Algebra a Beginning Graduate Student Ought to Know" 2nd Ed by Jonathan S. Golan.

It's a very comprehensive book that might be beneficial to you.
 
  • #6
Ok thanks. I'll check out those things.
 
  • #8
As far as prerequisites, more advanced linear algebra usually wouldn't require algebra and analysis. It's probably more for getting a comfort level with proofs. But in some cases, you might want to do linear algebra over an arbitrary field instead of real number or complex numbers or something like that, and then abstract algebra would be relevant.

And, I actually only understood linear algebra when I took 2nd semester analysis because you need linear transformations for taking "total derivatives". I just wasn't that good at math when I took linear algebra, and this time, the prof explained it in such a way that it finally made sense. I usually feel like I don't owe much to my profs in terms of what I have learned because I'm self-sufficient, but I shudder to think what might have happened if I had missed out on that.
 

Related to Advanced Undergrad Linear Algebra classes

1. What is the purpose of studying Advanced Undergrad Linear Algebra?

Advanced Undergrad Linear Algebra is an essential course for students pursuing degrees in mathematics, engineering, and other related fields. It provides a deeper understanding of linear algebra concepts and prepares students for more advanced courses in their respective fields.

2. What topics are typically covered in an Advanced Undergrad Linear Algebra class?

Advanced Undergrad Linear Algebra classes cover topics such as vector spaces, linear transformations, eigenvalues and eigenvectors, matrix factorizations, and applications of linear algebra in various fields such as computer science, physics, and economics.

3. How is Advanced Undergrad Linear Algebra different from introductory linear algebra courses?

Advanced Undergrad Linear Algebra delves deeper into linear algebra concepts and introduces more advanced topics. It also requires a strong foundation in basic linear algebra, including matrix operations, determinants, and solving systems of linear equations.

4. What skills are needed to succeed in Advanced Undergrad Linear Algebra?

To succeed in Advanced Undergrad Linear Algebra, students should have a solid understanding of basic linear algebra concepts and strong mathematical reasoning skills. It is also beneficial to have experience with proof-based mathematics and a familiarity with computer programming.

5. What are the benefits of taking an Advanced Undergrad Linear Algebra class?

An Advanced Undergrad Linear Algebra class can provide students with a deeper understanding of linear algebra, which is a fundamental mathematical tool used in various fields. It also helps to develop critical thinking and problem-solving skills, which are valuable in many careers. Additionally, taking this course can open up opportunities for more advanced courses and research in fields such as mathematics, engineering, and data science.

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