## Main Question or Discussion Point

Hi everyone. I am a second year maths major. I just wrote my first test in linear algebra. I am quite sure I did not do well. I'm pretty sure I did not get more than 70%. The problem was the proofs. I had trouble proving things, and I am uncertain if my proofs were valid. I knew the theorems and definitions pretty well, and that part I probably did pretty ok in. Time was an important factor. Given enough time I can work out proofs, but sometimes I still get them totaly wrong still. Is this something I need to be worried about, or is your first linear algebra test usually difficult, or what?

Vid
Yes, you should be worried.

Thanks, er, but can you give me a little more please?

No you shouldn't be worried.
Is this your first class with proofs? generally Calc 1,2 and even 3 don' focus much on proofs unless you are in the advanced course or honors or something. Thus many times a course in linear algebra or discrete maths will be a students first introduction to proof oriented maths.

Talk to your professor, ask her/him for extra help on how o study or prepare for proof portions of the test. Let them know i is your first class in proofs and its harder than you thought.

When I took Real Analysis, it was possibly the hardest math class i've done unless you count E&M. The tests were almost entirely proofs. The way I got through it was taking good noes on the proof in class. Then comparing the proofs from class to the ones in the book. Then I'd just try to pick the easier of the two and go through it over and over. You have to just memorize the theorems and their proofs. I don't know if theres any other way. Rather I don't mean you necessarily need to memorize the entire proof bu you need to know which theorems are needed to invoke to proof some given theorem and a general outline of the proof.

Study with a partner or group and exchange ideas on how to best prove theorems, but that being said you need to find the way you best understand not really the way that is quickest or easiest. If your proof is longer but you understand it all and it makes logical sense in your mind that is ok if you can explain it well.

Happy St. Patrick's Day!

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A good rule of thumb for doing proofs on tests (or for others to read) is to never write down anything that you don't know is true. That will force you to think "correctly". Also, experience helps a lot: experience doing proofs in general and specifically for linear algebra will give you the intuition you will need. Also, it is best to not spend too much time on one problem. There is such a mental difference in having 2 questions left and being stuck on those two problems then immediately getting stuck on problem 1 with 9 more to go. If you get stuck move on and go back to it. Finally, there is always an element of luck: we all have good and bad days.

symbolipoint
Homework Helper
Gold Member
How can one prepare for Linear Algebra and its proofs before actually studying Linear Algebra for credit? Linear Algebra seems much more complicated than most of Calculus 1, 2, and 3.

For ones first proof based course, "Euclidean" Geometry is usually the first course with rigorous proofs. Often students do not need the similar course in college (or do they really). I found a book by Howard Anton and another by Gilbert Strang on Linear Algebra, but I found them become difficult very quickly. This makes Linear Algebra seem very scary.

Vid
Howard Anton's Linear Algebra book is really bad. It's really easy and non of the theory has any motivation. It's just a list of facts to memorize.

Staff Emeritus
Gee, I liked Anton. He presents things in a way that will be useful once you take Abstract, but doesn't assume the reader knows any Abstract.

where are you going to school? that changes the advice a lot

We used Strang's book for my first course in Linear Algebra ( I plan to take an advanced course)
I have not checked in a while but when I took the course you could also find MIT's OpenCourseWare online for Strang's Lectures from his LinAlg. class at MIT.

Our course was not incredibly proof oriented in the sense that Real Analysis or Number Theory is proof oriented. So having taken LA before Number Theory and Real Analysis did not do much for me.

As far as preparing for LA before actually taking the class? Get a book from the library and start chugging away. Even if you can't follow proofs before taking the class, reading a book before hand and being familiar with Matrices and Vectors is a plus. Understanding the concepts behind "spaces" in math may be hard at first as LA may be your first "abstract" course in math. (the term abstract is used loosely there as I think LA is more abstract than calc 1 or 2, and general college algebra courses.... but far from a course in Analysis or Abstract Algebra"

Thanks a lot guys. I think I might schedule a meeting with my prof. I also did a Calc. II test, but I think I did pretty well there. Linear Algebra is definitely much harder.

How can one prepare for Linear Algebra and its proofs before actually studying Linear Algebra for credit? Linear Algebra seems much more complicated than most of Calculus 1, 2, and 3.

For ones first proof based course, "Euclidean" Geometry is usually the first course with rigorous proofs. Often students do not need the similar course in college (or do they really). I found a book by Howard Anton and another by Gilbert Strang on Linear Algebra, but I found them become difficult very quickly. This makes Linear Algebra seem very scary.
I believe there's a video lecture course from MIT OCW with Gilbert Strang on Linear Algebra which uses that book, you might want to watch that, maybe it will help.