posted
College Algebra, Vectors and Matrices, and Calculus II.
Whats the scope and rough material of each course generally? Ill be taking this next semester and could use some anectdotal opinions before researching the material as I intend to over my christmas break to get started.
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posted
I'm guessing College algebra is the highest level of the courses, based on when my Math major roommate took it.
I followed my University's general path for engineers, and took Calculus II (I took basic Calculus in High School), Calculus III, Linear Algebra (which is probably what your Vectors and Matrices class is), and basic Differential Equations. I also took Discrete Math, which is more of a parallel path, but you still needed Calculus I to be comfortable with it.
posted
Okay, really, I'll make some assumptions about these classes and their mapping to the classes at my undergraduate school.
If you've had Calculus I, you shouldn't take College Algebra.
If you haven't had Calculus I you shouldn't take Calculus II (and probably not Vectors and Matrices, although a motivated student could probably do alright).
Making an almost completely arbitrary rating of the difficulty of the material (again with the caveat that I have no idea of the actual content of these courses as taught at your school): College Algebra = 1, Calculus II = 5, Vectors and Matrices = 4. Also, FWIW, Calculus I = 3 and DiffEq = Multi-variate Calc = 6.
Here are the course descriptions of the classes I'm familiar with:
quote:College Algebra
Functions, polynomials, theory of equations, exponential and logarithmic functions, matrices, determinants, systems of linear equations, permutations, combinations, binomial theorem.
Calculus 1
Differential and integral calculus: limits; continuity; the derivative and applications; extrema; the definite integral; fundamental theorem of calculus; L’Hôpital's rule.
Calculus 2
Techniques and applications of integration; sequences, series, convergence tests, power series; parametric equations; polar coordinates.
Elementary Linear Algebra
Linear systems, matrices, vectors and vector spaces, linear transformations, determinants, inner product spaces, eigenvalues, and eigenvectors.
I don't think he means Abstract Algebra (which is the highest undergraduate Algebra at my school), but I could be wrong.
If you're thinking of taking a high level Algebra course, Blayne, I would recommend against it. Certainly until you've taken Linear Algebra, and even then I'm not sure whether you would enjoy such a class.
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posted
Lemme just reiterate the idea that if you're asking about College Algebra, you definitely shouldn't be considering Calculus 2. Unless by some very strange series of educational events, you took Calc 1 both without taking Calc 1 and being certain you wouldn't have to worry about College Algebra.
Posts: 17164 | Registered: Jun 2001
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posted
College Algebra is pretty much the Algebra 2 you took in high school, though it may be more akin to the non-trigonometry stuff in a highschool/college class called "precalculus."
They're all -- including calc 2 -- plug and chug courses. Though it is weird that you're asking about College Algebra if you've taken Calc 1.
Math is pretty much plug and chug all the way through the four standard calculus classes that they make engineers take (i.e, calc 1 and 2 plus Multivariable Calc and Differential Equations.)
Math courses probably remain plug and chug simple so long as you avoid upper-division proof based courses.
Posts: 532 | Registered: Feb 2009
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posted
Are you talking about College Algebra or are you about Linear Algebra (which I assume would be the same as Vectors and Matrices) or are you talking about Abstract Algebra, which should not be taken before Linear Algebra.
As for difficulty, it really depends on the type of person you are. For instance, given those three classes, the one I'd probably make the lowest grade in would be an actual College Algebra course - even though it is "technically" the easiest.
Posts: 1321 | Registered: Jun 2006
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quote:Originally posted by SenojRetep: Okay, really, I'll make some assumptions about these classes and their mapping to the classes at my undergraduate school.
If you've had Calculus I, you shouldn't take College Algebra.
If you haven't had Calculus I you shouldn't take Calculus II (and probably not Vectors and Matrices, although a motivated student could probably do alright).
Making an almost completely arbitrary rating of the difficulty of the material (again with the caveat that I have no idea of the actual content of these courses as taught at your school): College Algebra = 1, Calculus II = 5, Vectors and Matrices = 4. Also, FWIW, Calculus I = 3 and DiffEq = Multi-variate Calc = 6.
Here are the course descriptions of the classes I'm familiar with:
quote:College Algebra
Functions, polynomials, theory of equations, exponential and logarithmic functions, matrices, determinants, systems of linear equations, permutations, combinations, binomial theorem.
Calculus 1
Differential and integral calculus: limits; continuity; the derivative and applications; extrema; the definite integral; fundamental theorem of calculus; L’Hôpital's rule.
Calculus 2
Techniques and applications of integration; sequences, series, convergence tests, power series; parametric equations; polar coordinates.
Elementary Linear Algebra
Linear systems, matrices, vectors and vector spaces, linear transformations, determinants, inner product spaces, eigenvalues, and eigenvectors.
Warning: I have nothing useful to contribute to this thread.
I am just reflecting that I took Calc I as a junior in High School, and that's the last math class I ever took. It's too bad, too. I remember a lot of the stuff Senoj mentioned (Derivatives, limits, FTC, etc.) but probably couldn't apply it right now without some significant review. I enjoyed math, too, since it made sense to me and came pretty easily. But, well, it wasn't a passion of mine and since I received college credit for the class I took in HS, I didn't have to take math to get my college degrees.
Posts: 1099 | Registered: Apr 2005
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posted
If you have the pre-reqs for Calculus II, then don't bother with College Algebra. There's literally nothing in College Algebra that you don't know from high school, anyway. It's for people who will never take any other math classes. If you've forgotten some concepts/formulas from high school, you'll remember them all within the first couple of Calc classes anyway.
Or maybe College Algebra means something entirely different at your school, but I doubt it.
What previous classes have you taken?
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posted
Calling a class "college algebra" is fairly non-informative. I have seen classes with that name that were as SR mentioned above, ones that were essentially the same thing as what is more often called Linear Algebra (or sometimes Finite Math) and several in between.
Blayne, don't you have course descriptions? TEXTBOOKS?
Posts: 32919 | Registered: Mar 2003
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Blayne Bradley
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posted
Okay time to clarify somethings:
1- I HAVE to take all THREE regardless, I just wanted to know the experiences of other people regards to them, they are all prerequsites for taking an Undergraduate major in Computer Sciences.
I have already taken and passed Cal-1.
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In Calculus II you'll mostly focus on integration techniques.
Towards the final third or quarter of the class you'll get into the summation of series, like adding every value of (1/2^n) from 1 to infinity. Is the answer infinite or is the result a real number? You have to use integration to find out. The substance of the class should be integration techniques though. Integration by parts...integration by partial fractions...etc.
Maybe your class though will have a significant "applied" component in which case it should be more challenging.
The class called Vectors and Matrices can deal with some fairly abstract material, but really, the problems, much like with differentiation and integration in calc, can be mastered through practice. It's possible that your teacher will focus on the simple side of the material. However, even the non-plug and chug problems -- the ones where when you look at them you don't know what to do immediately -- should be mostly doable.
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posted
First off, it really isn't possible to tell much from the information you've given us. Course titles mean different things at different Universities. Material covered in Calculus II at one University, might be covered in Calculus I at another University or perhaps in an advanced Calculus class at yet another. Your University almost certainly has a course catalog that will give you more detail about the topics covered in each class and the degree of difficulty of the courses. You can likely also get a detailed syllabus and list of required texts for these classes which will give you an even better idea of what the courses actually cover.
Math programs usually assume that you have taken courses in a particular order and the instructor will likely assume you have that background before you start the course. The class catalog will tell you what courses are required or recommended before taking a given class. Even if the department doesn't strictly enforce prerequisites, its foolish to take a math class without having taken and passed all the prerequisites. You may be able to get by, but there is no reason to put yourself at that kind of disadvantage.
If you haven't already done so, I highly recommend you talk to an academic advisor from computer science. Science and Engineering programs tend to be highly structured. It is generally required that you take courses in a particular sequence. Most departments have put together a recommended course of study that will ensure you have all the prerequisites for every class. If you don't pay attention to that, you can get stuck. You don't want to find that you can't register for any junior level classes because they all require some class you were supposed to take in your sophomore year but decided to put off. It is not uncommon for classes in science and engineering programs to be offered only once a year rather than every semester. Pay attention to this. I've known students who have ended up being delayed an entire year because they missed one important prerequisite course.
An academic advisor should be able to alert you to all these potential pit falls. They may also be able to give you a more accurate idea of what you really have to take. For example, at many universities, "college algebra" is a prerequisite for Calculus I and many students will have learned this material in high school. Even though it's listed as a requirement, you might find that the requirement will be waved if you can pass a placement test or have a passing grade in Calc I.
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quote:Originally posted by The Rabbit: If you haven't already done so, I highly recommend you talk to an academic advisor from computer science.
I was assuming he had done so. But even if he had, it's probably a good idea to discuss it further with his advisor if he still has questions.
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posted
Eh, they're courses that smelly undergrads are allowed to take, how hard can they be? Apart from that, vectors and matrices you absolutely need if you're going to do any games development, so pay attention. Calc II could be either memorisation of techniques for integration, in which case you'll scrape a pass, or else complex analysis, and then you'll also scrape a pass. College Algebra could be anything; do you have a course description?
Anyway, though, since you apparently must take these courses whatever the difficulty, what's the use of asking?
[ November 25, 2009, 01:09 PM: Message edited by: King of Men ]
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quote:Anyway, though, since you apparently must take these courses whatever the difficulty, what's the use of asking?
I think it would be worthwhile knowing what you are up against under any circumstance. If you are anticipating a class will be very challenging, you approach it differently. You put more effort into it from the start. You may choose not to take too many other classes, to work less, commit to fewer projects and clubs or a variety of things along those lines.
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quote:Originally posted by The Rabbit: If you haven't already done so, I highly recommend you talk to an academic advisor from computer science.
I was assuming he had done so. But even if he had, it's probably a good idea to discuss it further with his advisor if he still has questions.
I guess I've been a professor for too long to take that for granted. I've known way too many students who have really messed up because they planned their schedules based on what they learned through the rumor mill or advice from friends rather than asking their official academic advisor.
I also know many Universities have general advisors for incoming freshman rather than advisors from with in the major and that these freshman advisors frequently give students the wrong information. I have been involved with some serious disputes between engineering departments and "freshman advising" because the general advice given to freshman is so often completely wrong for engineering majors.
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Blayne Bradley
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posted
I already asked my academic advisor and yes these are the courses I need to take and can take all at once before I can submit a degree change for next fall. My impression that 'College Algebra' is this description already mentioned.
"Functions, polynomials, theory of equations, exponential and logarithmic functions, matrices, determinants, systems of linear equations, permutations, combinations, binomial theorem."
And vector maths is probably Linear Algebra.
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I've seen both of those problems in a variety of contexts. He should definitely be talking to a CS advisor (even if he hasn't been assigned one yet, since he isn't in the program).
Posts: 15770 | Registered: Dec 2001
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That's a very strange requirement, as it would be a pitiful Calculus 1-2 series and linear algebra course that between them didn't cover all of that most thoroughly.
Not to mention that almost everything on that list should be covered for everyone in high school.
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posted
Well, 'functions' could in principle hide something like, say, a convolution of a sum of four Dalitz-dependent hyperbolic trig terms with a triple Gaussian, in which case you would spend an extra year on your dissertation and have your hair grow below shoulder length. But it seems more likely they'll have you learning definitions of ranges and domains and analyticity and suchlike grade-school stuff. And the rest of the list can be done counting on your fingers. Protip: Take your shoes off and you can count all the way to 22!
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quote:Originally posted by King of Men: Protip: Take your shoes off and you can count all the way to 22!
If you learn to count on your knuckles, you can count to 12 on one hand and still have a free thumb for texting.
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quote:I already asked my academic advisor and yes these are the courses I need to take and can take all at once before I can submit a degree change for next fall.
This is really unusual. I would normally expect at least some of those courses to be prerequisites for the others. If I were you, I'd triple check to make sure you can't test out of the College Algebra requirement. If you have taken and passed calculus, you have almost certainly learned the material in this class.
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quote:Originally posted by King of Men: Protip: Take your shoes off and you can count all the way to 22!
If you learn to count on your knuckles, you can count to 12 on one hand and still have a free thumb for texting.
Well yes, and if you use your teeth correctly you can count to 2^32 and have both hands for typing. But you have to tailor the advice to the audience.
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posted
Actually, I would say that College Algebra is harder than Calculus. But that's probably because for me College Algebra means things like linear algebra and so on.
Posts: 3060 | Registered: Nov 2003
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posted
Yes, but he's a computer science student. They don't usually make them take linear or abstract algebra without having them take one of those "intro to higher math" courses first. At least at most universities.
I'm 90% certain college algebra means high-school esque algebra 2.
posted
For me, though, the distinction "College" means that it's a heck of a lot harder than what you'd encounter in High school. Otherwise, why bother calling it College Algebra, and not just Algebra II?
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quote:Originally posted by Phanto: For me, though, the distinction "College" means that it's a heck of a lot harder than what you'd encounter in High school. Otherwise, why bother calling it College Algebra, and not just Algebra II?
Because Algebra II might mean the second semester of the two semester abstract algebra sequence.
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Blayne Bradley
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posted
quote:Originally posted by Clive Candy: Yes, but he's a computer science student. They don't usually make them take linear or abstract algebra without having them take one of those "intro to higher math" courses first. At least at most universities.
I'm 90% certain college algebra means high-school esque algebra 2.
I already did various math courses in CEGEP (Thats College for you yanks) which give me exceptions to having to do the prereqs to the prereqs.
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Oh, you're in Canada. You might be signing up for an abstract/linear algebra course then. In fact, all your classes might be really hard. Good luck.
Posts: 532 | Registered: Feb 2009
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posted
What he selected as similar to the description is not an intro to higher math-type courses. It is math for all the people who don't really remember how to do the math they taught in high school.
It would be very strange for it to be a linear algebra course, since another of the courses is definitely a linear algebra course.
And there's no reason at all for a CS undergrad to be required to take an abstract algebra course, so I'm pretty sure it isn't that.
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quote:Originally posted by fugu13: What he selected as similar to the description is not an intro to higher math-type courses. It is math for all the people who don't really remember how to do the math they taught in high school.
It would be very strange for it to be a linear algebra course, since another of the courses is definitely a linear algebra course.
And there's no reason at all for a CS undergrad to be required to take an abstract algebra course, so I'm pretty sure it isn't that.
this post contains much truth and should be heeded.
Posts: 532 | Registered: Feb 2009
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quote:Originally posted by Blayne Bradley: "Functions, polynomials, theory of equations, exponential and logarithmic functions, matrices, determinants, systems of linear equations, permutations, combinations, binomial theorem."
And vector maths is probably Linear Algebra.
Blayne, at my university they have a free standardized math aptitude test. It generates several problem sets per mathematical concept, and then shows which classes you're prepared for, which classes you're unprepared for, and which classes would be entirely redundant.
Rabbit has warned of the dangers of not taking a prereq class you need, so let me warn of the mind numbing drudgery of sitting through classes teaching concepts you mastered in 9th grade. I highly recommend you take your school's equivalent of said test if it exists, and if not, go to the library, browse the textbook for the class, and if you feel there's nothing new, test out of it.
However, the fact it's a mandatory prerequisite suggests to me either A) there's more to it than there seems or B) I have no idea how Canadian college works.
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posted
Blayne, Is the academic advisor you spoke with some one who advises all majors or only people in the CS program?
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