How Can I Best Prepare for a Proof-Based Linear Algebra Course?

[randomperson8]

Hi. I'm going to be taking my Linear Algebra course in about a month. We had a kind of intro to proof-based math course that was a prereq to it that I took a semester ago. Honestly I really struggled in that class because I got behind and lacked a lot of motivation to do well. And it was just very difficult.

So I'm worried this is going to hurt me when I take Linear. My motivation is back for sure, and I *really* want to do well in this course. What should I do in the next month to get ready?

I'm thinking of going through the KhanAcademy videos on Linear Algebra, but I'm worried they may be too basic. I've heard the class is very proof-based. What should I do to prepare?

 

[micromass]

I think going through the Khan academy videos is a good thing to do. Because that allows you to get a feeling for linear algebra and to understand it conceptually.
Once you knows what's going on, the proofs aren't really all that difficult. The proofs that you encountered in your proof class were probably much more difficult than the proofs you'll actually encounter in linear algebra, so don't worry to much!

If you're finished with khan academy and still feel uncertain, then you should pick up a proof-based linear algebra book and work through some of the first pages. You'll see that there's really not all that much to it.

 

[magicarpet512]

Another supplement that you might want to check into is the Opencourseware program at MIT. The link below takes you to the undergraduate MIT course on Linear Algebra taught by Gilbert Strang. There is a whole semester's worth of lecture videos, assignments, exams, solutions, etc. These lecture videos should give you a good idea of what to expect in class. Also get yourself a book on linear algebra and work through some of the exercises; Gilbert Strang authors his own book which is used for the classes on these video lectures. Stephen Leon authors another good introductory book on linear algebra.
From my experience, the proofs in an introductory linear algebra course really aren't that bad; i think a lot of the course will be getting you focused on how to use linear algebra to solve numerical problems.

 

[magicarpet512]

Oh, and here is the link...
http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/

 

[blue_raver22]

I understand your concerns about preparing for Linear Algebra. It is a complex and proof-based subject that requires a strong foundation in mathematics and critical thinking skills. However, it is important to not let past struggles discourage you from approaching this course with determination and a positive mindset.

To prepare for Linear Algebra, I suggest starting by reviewing and strengthening your understanding of fundamental mathematical concepts such as algebra, geometry, and trigonometry. This will help you build a solid foundation for the more advanced concepts in Linear Algebra. Additionally, you can review the material covered in your intro to proof-based math course to refresh your memory and fill in any gaps in your understanding.

In terms of resources, Khan Academy is a great starting point. However, as you mentioned, it may be too basic for the level of rigor expected in your Linear Algebra course. I recommend supplementing your studies with textbooks or online resources specifically geared towards proof-based Linear Algebra. You can also reach out to your professor or teaching assistant for recommended resources or additional practice problems.

It is also important to stay organized and on top of the material throughout the semester. Make a study schedule and stick to it, and don't be afraid to seek help from your professor or peers if you are struggling with a particular concept.

Remember, with determination and hard work, you can overcome any challenges and excel in your Linear Algebra course. I wish you the best of luck in your studies.