WWYD? I'm considering taking Multivariable Calc this Fall

[luuknam]

Thing is, I haven't taken any math classes in about a decade. My wife took Multivariable Calc at UTD (a decade ago), and says it'd be good to take Linear Algebra first (something I've heard from other people too), but it's not a prereq, and the CC won't offer Lin Alg until the Spring. I could take Lin Alg during the Summer I semester at U of Buffalo, but that would cost twice as much as taking it at the CC would (which is a big deal at our income), and I'm not sure I'd want to take it in a 5.5 week session while still having to deal with the second half of Q4 for homeschooling my kids (the university thinks summer starts early May, but the elementary schools here all go till late June, so that's what I put on the IHIP for my kids too). 

 

The obvious answer is to just wait until Spring and take Lin Alg at the CC then, and then take Multi Calc the Fall after that, but I'm not sure I want to do that... I've looked up the course offerings a couple of times in the past few years and come to the same conclusion and then of course it doesn't happen. On the one hand, it doesn't really matter since I have no plans of getting a job until my 1st grader is in high school at least (or maybe not until after he graduates high school). OTOH, it'd be nice to have my undergrad completed in case something happens and I need to get a job (because life happens).

 

Anyway, long story short... should I just bite the bullet and take Multi Calc at the CC this Fall without taking Lin Alg first? Feeling like I'm overthinking this.

[regentrude]

I don't see any reason to take Linear Algebra before multivariable calculus. At my university, only two semesters of single variable calculus are prerequisite; some vector stuff is included in mutlivariable calc.

Most of the majors that require multivariable calc for their students do not require linear algebra.

[luuknam]

I don't see any reason to take Linear Algebra before multivariable calculus. At my university, only two semesters of single variable calculus are prerequisite; some vector stuff is included in mutlivariable calc.

Most of the majors that require multivariable calc for their students do not require linear algebra.

 

 

Thanks. See, when my wife took it it wasn't a prereq at UTD, but now it *is* a prereq at UTD (even though they haven't changed the course description), but it's not a prereq at the CC here nor at U of Buffalo, so I just didn't know:

 

https://catalog.utdallas.edu/2012/undergraduate/courses/math2451

 

http://www.genesee.edu/academics/catalog/dspCourseDetails/?SubjCode=MAT&CourseNo=245&Term=201709

Edited April 17, 2017 by luuknam

[kiana]

If it were a prereq where you were going, you should obv. take it, but since it's not they'll teach the stuff that you would need to know in the class.

 

But what I would heavily recommend is that you review single-variable calc, especially differentiation and integration. 

Edited April 17, 2017 by kiana

[luuknam]

The other thing I was wondering about is the level of the courses (see links in my previous post). I know Regentrude posted in some recent thread that classes at the CC tend to be less rigorous than at the university. 

 

The U of Buffalo description is:

 

"Geometry and vectors of n-dimensional space; Green's theorem, Gauss theorem, Stokes theorem; multidimensional differentiation and integration; application to 2- and 3-D space."

 

Not that I'd have a clue as to how to glean the rigor of a course from the course description - seems like that would be too little info. Ugh. Decisions, decisions.

 

ETA: one of the things that bothers me about the CC's description is that it doesn't mention Green, Stokes, nor Gauss, even though it's long and both unis do mention them.

 

ETA2: Genesee does have a transfer agreement with Buffalo, so I'd imagine they do teach that but just for some reason don't mention those theorems by name in their description, but it's just weird.

Edited April 17, 2017 by luuknam

[luuknam]

I added a couple more comments to my previous post. In case it matters, this is probably for a Math for Dummies major (degree requirements listed near bottom of page):

 

https://catalog.buffalo.edu/academicprograms/mathematics_ba_-_general_study_math.html

 

On the one hand, maybe I should just take everything at UB right away, even though it costs more, since I'd basically need to meet the degree requirements and the 30 hours they'll want for transfer students to take at UB, and I should be able to absorb these lower-division courses into those 30 hours. My main hesitation about that is that we may very well move, so I'd rather just take these at a lower cost at a CC rather than at UB and then move before completing a degree, since every university will require you take 30 hours there to completely your degree. Plus, it wouldn't hurt to take more upper division math courses to hit those 30 hours rather than the bare minimum. Then and again, I just want that piece of paper that says I've graduated - I'll probably go back at some point to get a masters, maybe in biostatistics? - depends on what I want to be when I grow up. 

[regentrude]

What does the CC course description say? Does it mention vector calculus at all?

[luuknam]

What does the CC course description say? Does it mention vector calculus at all?

 

 

It does mention vectors:

 

http://www.genesee.e...245&Term=201709

 

Catalog Description: Covers infinite series, curves in parametric and polar forms, vectors, partial differentiation, and multiple integrals. Applications of these topics focus on analysis of functions and surfaces in 3 dimensional space. 

Course Student Learning Outcomes (CSLOs):

Upon completion of Calculus III, students will be able to do the following, either by hand on an exam (using a graphing calculator for computations) or, where possible, using a computer algebra system software for a collected assignment:

 

1. Given a function in parametric or polar form, sketch the graph of the resulting curve.

2. Given a set of vectors in space, algebraically define magnitudes, dot-products, cross-products, unit vectors, and triple scalar products of these vectors.*

3. Find the equation and give a (rough) sketch of any of the following surfaces in 3-space: sphere, plane, cylinder, quadric.

4. Evaluate a function of two variables at a specific point, and/or determine and sketch its domain.

5. Given a function of two or more variables, find and evaluate any partial derivatives, directional derivatives and/or gradient vectors.*

6. Find the minimum and maximum value of a function of two variables over a defined interval.

7. Use a double integral in either rectangular or polar form to find the volume of the solid defined by a function of two variables.*

8. Given an infinite series, determine the convergence or divergence of the series using any of the following tests (as appropriate): divergence, ratio, root, comparison, limit comparison, geometric, harmonic, integral, p-series.

9. Given a power series, find the interval of convergence.

10. Given a function of a single variable, find and evaluate a Taylor polynomial or Taylor series for the function at a given point.

 

* This course objective has been identified as a student learning outcome that must be formally assessed as part of the Comprehensive Assessment Plan of the college. All faculty teaching this course must collect the required data and submit the required analysis and documentation at the conclusion of the semester to the Office of Institutional Research and Assessment.

 

Content Outline: 

I. Infinite Series

1. Introduction: Taylor polynomials and approximations

2. Sequences

3. Series and convergence

4. The Integral Test and p-Series

5. Comparisons of series

6. Alternating series

7. The Ratio and Root Tests

8. Power series

 

II. Plane curves, parametric equations, and polar coordinates

1. Plane curves and parametric equations

2. Parametric equations and calculus

3. Polar coordinates and polar graphs

 

III. Vectors and the geometry of space

1. Vectors in the plane

2. Space coordinates and vectors in space

3. The dot product of two vectors  

4. The cross product of two vectors in space

5. Lines and planes in space

6. Surfaces in space

7. Cylindrical and spherical coordinates

 

IV. Vector-valued functions

1. Vector-valued functions

2. Differentiation and integration of vector-valued functions

3. Velocity and acceleration

4. Tangent vectors and normal vectors

 

V. Functions of several variables

1. Introduction to functions and several variables

2. Limits and continuity

3. Partial derivatives

4. Differentials

5. The Chain Rule

6. Directional derivatives and gradients

7. Tangent planes and normal lines

8. Extrema of functions of two variables

9. Applications of extrema of functions of two variables

10. Lagrange multipliers

 

VI. Multiple integration

1. Iterated integrals and area in the plane

2. Double integrals and volume

3. Change of variables: Polar coordinates

4. Center of mass and moments of inertia

5. Surface area

6. Triple integrals and applications

 

VII. Vector analysis (Optional)

1. Vector fields

2. Line integrals

3. Surface integrals

Edited April 17, 2017 by luuknam

[regentrude]

Vector analysis, line integrals and surface "optional"? That does not seem not equivalent to the other course that included Green's, Stokes' and Gauss' theorems.

 

Maybe Kiana can chime in?

 

 

[luuknam]

Vector analysis, line integrals and surface "optional"? That does not seem not equivalent to the other course that included Green's, Stokes' and Gauss' theorems.

 

Maybe Kiana can chime in?

 

 

Yeah, I didn't notice it said optional until I went through it and highlighted it, even though I'd read through it before (there's a reason I highlighted the word optional in a different color). 

 

I think I maybe should talk to the instructor at the CC and get his take on it. FWIW, there are other CCs in the area too, but they offer it (and Lin Alg, and Diff Eq) at impossible schedules - I cannot go to class 4 days a week in the middle of the day for 16 weeks in a row - at this CC it'd be only 2 days a week in the morning, which I could convince my wife to work from home 2 mornings/week. I think my wife would rather that I'd spend 2x as much money at UB (which has better hours too), than make her work from home 4 full days a week, so it's either this CC or UB (or maybe Buffalo State - haven't looked into that).

 

ETA: N/m Buffalo State - they cost almost as much as UB, so there wouldn't be any point in that.

 

ETA2: I just sent an email to the prof teaching Calc 3 at Genesee this Fall, so I'll let you know what he says when he gets back to me.

Edited April 17, 2017 by luuknam

[kiana]

Talk to Buffalo as well but the optional section is where green's/gauss's/stokes theorems (the first two are special cases of the third) are hiding out, which strongly suggests that they consider optional something Buffalo considers essential.

 

Another option, though, is to talk to the professor at the CC and ask if they'll mark homework for correction only (frankly this is much easier for me than assigning points) for you to go through the optional sections independently, or set assignments on the computer if they're using that. After all, what matters is that you have all the knowledge and the transferrable course, not that the knowledge was acquired IN the course. 

[luuknam]

Talk to Buffalo as well but the optional section is where green's/gauss's/stokes theorems (the first two are special cases of the third) are hiding out, which strongly suggests that they consider optional something Buffalo considers essential.

 

Another option, though, is to talk to the professor at the CC and ask if they'll mark homework for correction only (frankly this is much easier for me than assigning points) for you to go through the optional sections independently, or set assignments on the computer if they're using that. After all, what matters is that you have all the knowledge and the transferrable course, not that the knowledge was acquired IN the course. 

 

 

Right. However, IF we were to move, then the university I'd end up transferring to likely would NOT have a transfer agreement with the CC, so then the question becomes whether they'd let me transfer a substandard multi calc course in, even if I did the extra work. 

 

Sigh.

 

Why does college have to be such a headache???

 

(obviously, the safest option would be to just take it at UB - I'm 99.999% sure I wouldn't transfer to any university that would look down on UB's classes - my background is inconsistent enough that I don't think any university that's substantially better would let me in, and if there were such a unicorn, I wouldn't be able to afford it)

[kiana]

If they don't have a transfer agreement and you want to challenge it, you will very often get a single chance to take a comprehensive final and prove that you do know the material. But calc 3 does tend to transfer okay because a lot of people do take it at CC's. 

[luuknam]

Thank you so very much Regentrude & Kiana, I really appreciate it. 

[luuknam]

Okay, so this is what prof wrote back to me:

 

We cover Green’s Theorem but that is as far as we go in Vector Analysis, which is fairly typical of most other colleges --- almost all local two year colleges go about as far as we do, and some four year colleges, too. For example , Brockport used to offer their Calculus sequence as 3 credit hour classes, so they didn’t cover any of those concepts until their Advanced Calculus course (and I think now it depends on the specific instructor as to whether those are covered in Calc III). So yes, there is about another 2-3 sections of content that UB covers in their course that we do not cover. Typically students transferring to UB are advised to either cover those omitted sections on their own to fill in the gap.

 

I will tell you, however, that as someone who went on to earn my Master’s Degree in Mathematics (60 additional credit hours after Calculus III), I never once used Gauss’s or Stokes theorem in another course other than when they were covered in my Advanced Calculus course during my final semester of graduate work. Unless you are going on to your PhD in analysis, or decide to become an engineer specializing in magnetic/gravitational fields or fluid dynamics, you very likely do not need even a basic level understanding of the concepts. Reading those sections on your own after you complete the course is probably sufficient for your understanding of the concepts.

 

ETA: I didn't even realize Brockport had a university. Apparently only 2% of their students have SAT reading scores between 700-800, and only 1% have math scores between 700-800, whereas UB has 5% reading between 700-800, and 11% math between 700-800.

Edited April 18, 2017 by luuknam

[kiana]

Pretty much what I expected. I haven't looked at this stuff myself since the last person I tutored almost 10 years ago (I don't teach this class because all the other profs seem to want to and I don't like it enough to try and get a turn in). I did see it show up in complex variables as well as advanced calculus (buffalo calls this class real analysis) but I honestly don't think it's worth worrying about. 

 

BTW, buffalo's is not a "math for dummies" major but a very standard math major. Possibly you're comparing it to European standards where (since there is no gen ed) a lot more math would be completed. A student who was targeting really elite colleges for grad school would of course go beyond the basic requirements but it would be adequate class coverage for at least 90% of master's programs and probably more. 

[luuknam]

BTW, buffalo's is not a "math for dummies" major but a very standard math major. Possibly you're comparing it to European standards where (since there is no gen ed) a lot more math would be completed. A student who was targeting really elite colleges for grad school would of course go beyond the basic requirements but it would be adequate class coverage for at least 90% of master's programs and probably more. 

 

 

I wasn't so much comparing it to European standards, as much as that UB itself has several versions of its math major, and this is the one with the least math. It also is relatively weak compared to UTD's math major, iirc (which is more in line with the other versions of UB's math major). But, glad to know that you think it's okay. :)

[luuknam]

Oh, and this is of course not just a potential problem with Multi Calc - I also still have Lin Alg and Diff Eq to take, so there might be similar issues with those. Anyway, at least I'll know now that I'll have to keep my eyes open and very well might have to put in extra work to match the rigor of UB, if I choose to go with the CC. 

[regentrude]

 

I will tell you, however, that as someone who went on to earn my Master’s Degree in Mathematics (60 additional credit hours after Calculus III), I never once used Gauss’s or Stokes theorem in another course other than when they were covered in my Advanced Calculus course during my final semester of graduate work. Unless you are going on to your PhD in analysis, or decide to become an engineer specializing in magnetic/gravitational fields or fluid dynamics, you very likely do not need even a basic level understanding of the concepts. Reading those sections on your own after you complete the course is probably sufficient for your understanding of the concepts.

 

He obviously never took any physics beyond the basic intro requirement.

These theorems are crucial in electrodynamics and physics majors definitely need them at an undergraduate level.

Edited April 18, 2017 by regentrude

[kiana]

He obviously never took any physics beyond the basic intro requirement.

These theorems are crucial in electrodynamics and physics majors definitely need them at an undergraduate level.

 

Yeah, I wrote (but for some reason cut it out) that I would be a lot more worried if luuknam were doing applied mathematics or physics or electrical engineering. But they really don't pop up in pure mathematics so much. 

[luuknam]

Yeah, I wrote (but for some reason cut it out) that I would be a lot more worried if luuknam were doing applied mathematics or physics or electrical engineering. But they really don't pop up in pure mathematics so much. 

 

 

I have hardly committed to pure mathematics (more like, not at all). The current plan is to get that math degree (partially because any degree is better than no degree), and then possibly grad school, *maybe* in biostatistics... But, my background is pretty much all over the place - back in NL, I did a year in biomedical science & engineering with some extra classes in AI before moving to the US, where I started out in EE and then switched to neuroscience before dropping out, then did a bit of business administration before settling on library science (thought there was maybe science/engineering reference librarian), before being forced to move to WNY with only 13 hours left. IOW, uh, nothing is set in stone. 

Edited April 18, 2017 by luuknam

[kiana]

I have hardly committed to pure mathematics (more like, not at all). The current plan is to get that math degree (partially because any degree is better than no degree), and then possibly grad school, *maybe* in biostatistics... But, my background is pretty much all over the place - back in NL, I did a year in biomedical science & engineering with some extra classes in AI before moving to the US, where I started out in EE and then switched to neuroscience before dropping out, then did a bit of business administration before settling on library science (thought there was maybe science/engineering reference librarian), before being forced to move to WNY with only 13 hours left. IOW, uh, nothing is set in stone. 

 

Ya. 

 

If you change your mind, I estimate that it would take a couple of weeks max to learn these well and thoroughly enough to be able to do problems with them as well as anyone who went through Buffalo's course. 

 

It's different if, just, the whole class is taught at a less rigorous level (for example, if all of the problems are easier/include more steps/whatever). I'm going to give an example from a lower-level class (algebra). 

 

There is a big difference between asking a question such as "Solve the following equations for all real solutions: a-h" and "Solve this equation by factoring with the difference of squares. Solve this equation with the quadratic formula. Solve this equation by squaring both sides. Solve this equation by ..." you get my drift. The first student is going to be okay in a precalculus class. A student who's only been exposed to exams of the second type has no idea whether they're ready or not, but probably isn't.

 

But I don't think that's the case for the MVC -- I have a pretty good opinion of SUNY CC's based on the people I've known who've gone there. And frankly I'd much rather see the syllabus abbreviated than to see them try to somehow cover the entire syllabus and give the students easier questions. 

[luuknam]

And... our landlord wants to fix up the house (she's been neglecting it for years) and sell it, so we've got to move out by the end of May. Which means that my wife is more motivated to try to ask for a promotion/raise or find a job elsewhere, so, who knows where I'll be this fall. On the bright side, if she gets a promotion then we should stay here long enough for me to finish my degree at UB, and if not, we'll be elsewhere... regardless, it'll likely take care of the "we're probably not going to be here long enough to finish my degree" issue (of course, if we move out of state I'd have to deal with the time it takes to establish in-state residency).