Need some advice for linear algebra

[scsig805]

Alright so Calculus seemed to come relatively easy to me. I was able to get good grades without much struggle. However now my linear algebra class is killing me. I feel like I am understand the text and lectures fairly thoroulghy and even feel like I am able to understand most homework problems. However when a test comes along I have no Idea how to solve half of the questions. The text I am using is Strang 6th ed and I am also watching his lectures online. Did anyone else have similar struggles in this class in particular? What could you recommend to perhaps get a different perspective on this class. Or is their any problem solving skills you could recomend? I am spending about twice as much time on this class as I am on all my other classes combined. And I am constantly in with the proffessor. So any help would be greatly appreciated.

 

[chuy]

I think you should take a look in other text of linear algebra also, as a complement. I know the MIT professor is very good, but seeing some things from different points of view also helps. Also you should practice solving problems.
I've been working with Linear Algebra Done Right by Sheldon Axler and Linear Algebra of Hoffman. I'm pretty sure there are other texts that will help you.

Good Luck.

 

[Defennder]

Are you doing an upper level Linear Algebra course or an introductory one?

 

[HallsofIvy]

Several years ago, I had an experience that I think is relevant here.

I was teaching a Linear Algebra course and typically started the class by asking if there were any questions about the homework. One day, everyone in the class had absolutely no idea how to do one of the problems- asking for a proof of something, exactly what I have forgotten.

I looked at the problem, wrote one of the key words on the blackboard and asked "what is the definition of that word?". I got no answer.

So I sat down, placed my hands on the desk in front of me and looked at the class. Everyone sat there staring at me until a few students started leafing through their textbooks. Finally, a student looked up the word in the index and found the definition (in the same section the homework was from)! Once they had the definition in hand, the problem was easy.

The point is: learn the definitions. Learn the precise words, not just the "general idea". Definitions in mathematics are "working definitions". You use the precise words of the definitions in proofs and solving problems. The most important thing to do in Linear Algebra (or any higher mathematics) is make sure you know the precise definitions of all terms.

 

[lifengma_1983]

Understand doesn't mean you can solve every problem. You should practise more.

 

[mathwonk]

i second halls' advice. on the calc test i just graded most students could not define an integral, even though we had given the definition many times, used it to approximate and to compute integrals,, and even handed out old tests on which that was a question beforehand.

apparently many students do not realize they need to understand the words used in discussing math concepts, having only been asked to compute the results from plugging numbers into formulas, at least up through calc and beginning linear algebra.

 

[scsig805]

okay thanks for the advice I purchased a few problem books online. And Il try spending more time with the details of the definitions. I had my first test on monday which I actually felt pretty good about. This seems to actually be getting a little easier as the course goes on. Once again thanks a lot for the help.

 

[matqkks]

It is important in linear algebra that you learn and understand the definitions thoroughly. You need to know the precise meaning and an image might be helpful to understand these definitions.

 

[maze]

I recommend you always have a visual picture in your head of what is going on, in terms of vectors, planes, projections, subspaces, etc. Then you may quickly see what the heck the problem means in your mind, which makes it much easier to see the strategy for a solution.

Luckily linear algebra is an area of math where such visualizations work well.

 

[JasonRox]

i second halls' advice. on the calc test i just graded most students could not define an integral, even though we had given the definition many times, used it to approximate and to compute integrals,, and even handed out old tests on which that was a question beforehand.

apparently many students do not realize they need to understand the words used in discussing math concepts, having only been asked to compute the results from plugging numbers into formulas, at least up through calc and beginning linear algebra.

Me three.

The first few years in mathematics is mainly learning definitions and applying them to prove results or solve problems.

You can't prove results or solve problems without knowing what the definition is.