What is Linear Algebra?

Discus: College Confidential Café: What is Linear Algebra?
 By Cherrybarry (Cherrybarry) on Friday, October 01, 2004 - 01:44 pm: Edit

???

 By Justice (Justice) on Friday, October 01, 2004 - 05:25 pm: Edit

its a math class generally taken after bc calc that consists of matrix study and eigenvectors. it's pretty easy

 By Haithman (Haithman) on Friday, October 01, 2004 - 08:00 pm: Edit

I'm taking it after Multi. Variable and Diffy E (which im taking next year, my senior year). It's not that easy..its all about proofs so you better be on your toes.

 By Ubercollegeman (Ubercollegeman) on Friday, October 01, 2004 - 11:56 pm: Edit

To call Linear Algebra easy is like calling basic algebra easy. Sure, it kind of is. But anybody who's ever taken a look at the USAMO or other olympiad questions can tell you that problems requiring nothing more than basic algebra and logic can be EXTREMELY hard.

Your experience with linear algebra depends on what class you're in and/or what book you use. It can be either very easy or one of the hardest math classes you'll ever take.

 By Tongos (Tongos) on Friday, October 01, 2004 - 11:57 pm: Edit

requires a thorough understanding of calculus, well multivariate does anyway
linear algebra goes through
matrices
vectors, space paths
Its like multi dimensional algebra

multivariate calculus-
partial differentiation
functions of several variables
surface integrals and line integrals
stokes and greens theories
fourier series
triple integrals
gamma function
- and a lot more fun stuff!

 By Welshie (Welshie) on Saturday, October 02, 2004 - 03:10 am: Edit

Yeah, I think I'm going to take Multivariate Calculus and Linear Algebra next semester (I'm currently a first semester student at BYU).

 By Bballerd7 (Bballerd7) on Sunday, October 03, 2004 - 03:42 am: Edit

---> the most useful math course you can take is statistics. you analyze a lot of data and draw conclusions from every day situations. i absolutely love it. calc etc are for those in "engineering, electricity" etc, but can be for business majors as well.

statistics is the most fun math too. god, every time i was looking at sins/cosins and graphs, and matricies, i thought 'when on god's green earth am i going to use this gibberish language'.

i HATED that cosine graph with a PASSION. so TEDIOUS and so BORING.

stats is from everything in every day life, finding the probablity of copius events in copious situations, it can just go on. a lot of reading though, and it is more conceptual math whereas every other one is mechanical.

unless your major requires those courses, i love stats! lol gamma function/fourier series = fun?

i don't think so...unless you love a buncha dots, digits, and senseless patterns repeated in a numerical value..grrr....

 By Cherrybarry (Cherrybarry) on Sunday, October 03, 2004 - 11:30 am: Edit

I thought stats was so contrived. All we did was cookbook math with made-up recipes. Even the book said the procedures were prescribed recipes. It was so boring. I wish we touched more upon theory in stats instead of simply using recipes to find p or whatever.

Like why can you only use sampling distribution for an SRS? Or why the equation for the normal distribution is the way it is? And how the hell do you derive all those recipes to find p? How the hell can you prove the Students T distribution? It was like they give you a recipe and you are supposed to follow it blindly without any sense of the mechanics you are working with. I felt like a robot in that class.

 By Welshie (Welshie) on Sunday, October 03, 2004 - 11:44 am: Edit

I agree with Cherrybarry-- the handfed formulas were basic and led to little learning. However, I will say that in college-level Statistics you can/will prove/derive those formulas so that's kind of interesting I guess. Also, Calculus is just as applied to the real world as Statistics. Engineers use it in all the world they do, NASA scientists use it non-stop, it has it's application in the corporate world (including Economic analysis). Just because there are x's, y's, and z's instead of N's, p's, and t's doesn't make Calculus any less applicable to the real world.

 By Cherrybarry (Cherrybarry) on Sunday, October 03, 2004 - 12:08 pm: Edit

Yeah. One of the things that frustrates me the most is when some kids in math or science class question the usefulness of the things we are studying. They ask....when are we ever going to use this?

It's so ignorant. I mean, the whole reason the world runs the way it does it because of science and math. Without it, there would be no airplanes, cars, electricity, chemicals, computers, houses, streets, buildings, civilization.

You don't hear any math geeks complaining about the usefulness of writing Petrarchan sonnets, so what right do English freaks have to question the useful of math and science?

In fact, calculus has more practical applications than Petrarchan sonnets.

 By Haithman (Haithman) on Sunday, October 03, 2004 - 01:03 pm: Edit

Eww statistics? I am in stats right now and find it soo boring. Perhaps because I am the number crunching type of person who finds Calculus, Differential Equations, Number Theory beautiful. Wait until you need to do stats with continuous variables in college..yup calc will be there.

 By Bballerd7 (Bballerd7) on Sunday, October 03, 2004 - 01:37 pm: Edit

boring? how? stats is the most useful. go look it up. yea true cal can be useful but "everyday situations", stats is very helpful.

anyway i totally blew my first test...lol...at least i could make that up. grr!

 By Feuler (Feuler) on Sunday, October 03, 2004 - 04:01 pm: Edit

Calculus is extremely applicable to everyday situations, but only with respect to theory. The problem is that in the US we don't teach theory and understanding, we teach formulas and other garbage which help you pass the AP test, but that's about IT.

However, that is not to say taking Calculus is not worthwhile. To my experience, the people that complain about advanced math/sci not being necessary for daily life are the people who are not doing very well in the class, and don't put forth the effort to actually understand stuff.

So the problem is two-fold: schools are too concerned with test scores to show kids the meaning behind subjects, and kids are too damn lazy to find it for themselves, preferring to just whine incessantly about the system.

ANY subject, whether Calculus, Statistics, or Literature, can be meaningful if you make the effort to look deeper and figure out the reasoning behind it. If you don't make this effort, and only try to ace the tests, of course it will be meaningless, and a waste of your youth.

 By Tigeruppercut (Tigeruppercut) on Sunday, October 03, 2004 - 04:40 pm: Edit

linear algebra is HARD

 By Avoidingwork (Avoidingwork) on Sunday, October 03, 2004 - 07:31 pm: Edit

mathematics is beautiful and fun. it needs no justification regarding its application to the 'real' world.

For those who do care about such matters, I suggest taking physics where mathematics is considered to be just a tool

 By Justice (Justice) on Sunday, October 03, 2004 - 09:26 pm: Edit

lol how is it hard...it's just really intuitive proofs and a few key concepts, like row echelon form and reduced echelon form. i'm not saying it's super primitive/easy, but compared to calc or even stats, there's just not as much breadth and depth in linear algebra.

 By Tongos (Tongos) on Sunday, October 03, 2004 - 10:25 pm: Edit

mathematics in school should teach understanding rather than just memorizing the formulas, does it?, not really. Well, im doing it on my own then. that's the whole beauty of mathematics.

I remember one experience of mine, when i was first acquinted with calculus back when i was fifteen or so. And i remember looking at this rate question while flipping through the book, and that's when i saw the difference between higher math and lower math. Because i saw that the rate was changing, and then i became very interested in the subject.

 By Irock1ce (Irock1ce) on Sunday, October 03, 2004 - 11:34 pm: Edit

well. ill be taking Math 54M (Linear Algebra with computers) at UC Berkeley in the spring. I know someone who took this class and they said it was the HARDEST class they have ever taken in their life.

 By Ubercollegeman (Ubercollegeman) on Monday, October 04, 2004 - 02:20 am: Edit

Irock, 54M isn't the super-hardcore one at Berkeley. H54 is the one that's scary.

My sister was a math major at Berkeley. H54 was the class that single-handedly convinced her to change to business :D. She realized there was very little chance that she would get even a B in H54 even with hours of work every day, so she dropped it for regular 54 (maybe 54M...I think they're similar in difficulty) and easily got an A.

BIG difference between honors and regular math at Berkeley...

 By Fabrizio (Fabrizio) on Monday, October 04, 2004 - 07:29 pm: Edit

OK. I haven't taken linear algebra yet. Let that be known.

I asked one of my then-senior now collegiate-sophomore friends last year this same question. His answer was "Linear Algebra studies the easiest way to solve the equation Ax + B = C."

OK...

When I told my dad that, he laughed. I guess my friend's explanation is not the whole story. I'll formally find out two years from now.

Yeah, linear algebra is usually taken after some formal calculus training, but I don't think you n eed calculus for linear algebra.

Just because a class is usually taken after another in a standard sequence does not mean that the earlier classes taught are necessary prerequisites for later classes.

I took AP Calculus without formal Euclidean Geometry training and I beat everyone in the class and made a five on the test.

For a more general case, you don't need geometry for trigonometry even though the former class is usually taught before the latter class.

 By Originaloog (Originaloog) on Tuesday, October 05, 2004 - 09:30 am: Edit

and it an easy way to solve simultaneous eq's!

 By Takiusproteus (Takiusproteus) on Wednesday, October 06, 2004 - 09:43 pm: Edit

Feeling the subway car jerk makes me think about the third derivative of position.