Should I start my undergrad with Calc 3?

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Discussion Overview

The discussion revolves around whether a new undergraduate physics major should start with Multivariable Calculus (Calc 3) or Linear Algebra, considering their recent high school calculus experience and placement exam results. Participants explore the implications of starting at a higher level in mathematics, the potential challenges, and the relevance of these courses to a physics curriculum.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant expresses a desire to take Multivariable Calculus or Linear Algebra to potentially graduate early, despite concerns about the difficulty of these courses.
  • Some participants suggest that starting with honors calculus could provide a more challenging experience, while others recommend jumping directly into Multivariable Calculus if the participant has already taken Calculus 1 and 2.
  • There is a discussion about the relevance of honors calculus for a physics major, with some arguing that it may not be necessary unless the student is interested in proofs and rigorous analysis.
  • Several participants emphasize the importance of reviewing foundational calculus concepts before taking Multivariable Calculus, as high school courses may not cover all necessary material adequately.
  • One participant shares their experience of starting from scratch in calculus despite placing into higher-level courses, suggesting that this approach led to a better understanding of the material.
  • Concerns are raised about the prerequisites for Multivariable Calculus and whether taking Linear Algebra first is necessary, especially since one professor indicated that Linear Algebra concepts apply to Multivariable Calculus.
  • Another participant notes that while Multivariable Calculus may not be strictly necessary for a physics major, it is often directly applicable in physics courses.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the original poster should take Multivariable Calculus or Linear Algebra first. There are multiple competing views regarding the necessity of honors calculus and the importance of reviewing prior material.

Contextual Notes

Some participants mention that the placement exam was not as challenging as expected, which may affect the confidence in starting higher-level courses. Additionally, there is uncertainty about the prerequisites for the courses the original poster intends to take, particularly regarding the relationship between Linear Algebra and Multivariable Calculus.

Who May Find This Useful

This discussion may be useful for incoming physics majors or students considering advanced mathematics courses, particularly those evaluating their readiness for higher-level calculus and linear algebra based on prior coursework and placement exam results.

mckmetal
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Hi everyone. I just graduated from high school this month and I will be attending Stony Brook University as a Physics Major in the fall. Even though I took AP Calculus BC, I was forced to take the mathematics placement exam because my AP scores won't be back in time for orientation, which happens to be tomorrow.

I was able to score a 9 on the placement exam when I took it this morning. The confirmation email I received from the school stated that I should strongly consider registering for a 200-level course in Linear Algebra or Multivariable Calculus. I would love to take the 8 credits, especially since I would like the opportunity to possibly graduate early, or maybe even double major. However, I realize that starting off with one of these classes could be very difficult.

Math was never my strongest subject in high school, but I do well when I take the time to study, not to mention that I tend to be a quick learner. Also, I feel that retaking these courses might bore me a little; I'm usually more motivated when faced with a difficult challenge. I was wondering if any of you think that it would be a good idea for a freshman to jump right into Calculus 3 or linear algebra, and how difficult it would be to possibly double major or minor in mathematics. I would greatly appreciate any advice.
 
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You could take honors calc if your school offers it. That will almost assuredly not bore you. Infact, at most schools, honors calc is really very challenging.

Otherwise... I personally would just start in multivariable calc if I didn't do honors.
 
Hmm... yes Stony offers Honors Calc I and II. I'll look into it. I was sort of surprised by the brevity and ease of the placement exam... it was nothing like the practice questions and was not very different from the AP course I took. One would think that they would make it very challenging, so students could not easily skip over difficult Calc courses at the college. Btw I meant that Calc 1 and 2 might bore me b/c I have taken them already, not because I would find them easy... I didn't mean to come off snobby; I'm sure that any college level Calc course is harder than its AP counterpart that I have taken. Well, I'm sure I will know more tomorrow when I go over it with my academic advisor. Thank you Jorriss :)
 
From my experience so far with placement tests and prerequisites, if you are being strongly encouraged to start out at a certain level based on their administered tests... I would say you should absolutely do it. The only reason I would not is if you really wanted to take honors calculus. If you did, you could probably take them while you take other classes if you just space it out a bit.
 
You're a physics major not a math major you don't need honors calculus. Now if you are interested in proofs and everything you should take honors calc because usually it's quite rigorous. When I started college as a physics major I took multi and did very well. A lot what you learn in multi will have direct applications in physics. I use the stuff I learned in multi all of the time.
 
I was in a similar situation as you, passed out of calculus and physics. I chose to just start from scratch because I didn't feel I was prepared enough even though I placed into those classes. I don't regret it because even though it was a little boring learning the material over again, I really learned the material better and impressed those professors.

It would definitely be nice to start out ahead though. If you choose to take multivariate or linear algebra, I'd definitely recommend reviewing over the summer before the classes actually start. That way, you'll be prepared and be ahead. I think that would be the best thing to do.
 
mckmetal said:
Btw I meant that Calc 1 and 2 might bore me b/c I have taken them already

If you have already taken Calc 1 and Calc 2, you should definitely register for multivariate calc. How were your marks in those classes?
 
xdrgnh said:
You're a physics major not a math major you don't need honors calculus. Now if you are interested in proofs and everything you should take honors calc because usually it's quite rigorous. When I started college as a physics major I took multi and did very well. A lot what you learn in multi will have direct applications in physics. I use the stuff I learned in multi all of the time.
Yeah, the material won't be needed but I don't think anything improves problem solving/thinking more than a solid class on analysis. Those proofs take a lot of thought.
 
Jorriss said:
Yeah, the material won't be needed but I don't think anything improves problem solving/thinking more than a solid class on analysis. Those proofs take a lot of thought.

I agree with you and that is why I plan on taking Analysis. But I feel for a physics major it's more important to learn the math that will be needed in your physics class first before undertaking extra stuff.
 
  • #10
xdrgnh said:
I agree with you and that is why I plan on taking Analysis. But I feel for a physics major it's more important to learn the math that will be needed in your physics class first before undertaking extra stuff.
Yeah, I personally would take multivariable calc but starting so far ahead gives him some wiggle room. Just throwin' options around.
 
  • #11
How comfortable are you with taylor series?
calculus with parametric equations and change of variable?
basic differential equations?

Going straight to multivariable calc. could be a great idea, but make sure you've covered everything in I and II. A lot of HS don't really do calculus justice. If you did well on the placement, yours probably did, but take a look at what is covered in the first two classes to be sure.
 
  • #12
ecneicS said:
If you have already taken Calc 1 and Calc 2, you should definitely register for multivariate calc. How were your marks in those classes?

Well I took AP Calc BC my senior year of HS. Even though I slacked a little, I managed to pull off a 91 for the class. I don't know how I did on the AP exam yet, but I think I did fairly well.
 
  • #13
Stengah said:
It would definitely be nice to start out ahead though. If you choose to take multivariate or linear algebra, I'd definitely recommend reviewing over the summer before the classes actually start. That way, you'll be prepared and be ahead. I think that would be the best thing to do.

DrewD said:
Going straight to multivariable calc. could be a great idea, but make sure you've covered everything in I and II. A lot of HS don't really do calculus justice. If you did well on the placement, yours probably did, but take a look at what is covered in the first two classes to be sure.

Yes I agree with both of you. I'm very comfortable with calculus 1 material, but some of my knowledge of series and ODE's needs a little polishing. However, I figured that instead of just enrolling in Calc II again it might be more advantageous for me to review over the summer, then jump into Multi in the fall. Thanks :)
 
  • #14
Thank you all for your input; fortunately I was able to register for "Calc III with applications" today at Stony- let's hope it was the right choice! UNFORTUNATELY, I was unable to register for the Classical Mechanics I Honors course, because it was full, so I'm stuck in regular Classical Mechanics I. Will I be at a disadvantage because of this?

Also, I was a little confused by one of the professors who I talked to: he told me that Multivariable applies the theory learned in linear algebra. If that is the case, then shouldn't I learn linear first? Since I have already registered for Multi, should I even bother taking linear algebra my second semester?
 
  • #15
Have you looked at the course catalog? If not, it's available here. If you're taking MAT 203, Calculus III with Applications, then the prerequisite is Calculus II. Linear Algebra is not listed as a prereq. (However, MAT 205, the "normal" Calculus III course, does list MAT 211, Introduction to Linear Algebra, as a prerequisite/corequisite.)
 
  • #16
eumyang said:
Have you looked at the course catalog? If not, it's available here. If you're taking MAT 203, Calculus III with Applications, then the prerequisite is Calculus II. Linear Algebra is not listed as a prereq. (However, MAT 205, the "normal" Calculus III course, does list MAT 211, Introduction to Linear Algebra, as a prerequisite/corequisite.)

Yes I have seen the course catalog, but thanks. The descriptions of the courses weren't available to me when I chose them at orientation. In fact, MAT 203(Calc with Applications) was suggested for me. This must have been the case because "normal" Calc III (MAT 205) wasn't open for whatever reason. It wasn't listed as an option.

MAT 203: Calculus III with Applications

Vector algebra in two and three dimensions, multivariate differential and integral calculus, optimization, vector calculus including the theorems of Green, Gauss, and Stokes. Applications to economics, engineering, and all sciences, with emphasis on numerical and graphical solutions; use of graphing calculators or computers. May not be taken for credit in addition to AMS 261 or MAT 205.

The only difference in "normal" Calc III is that it's more theoretical, is only geared towards applications of the physical sciences, and I'll learn about divergence and curl if I take it. Even though I'm majoring in physics, I'm not sure if it will really matter which class I take, as long as I'm learning the math... right?
 
  • #17
Make sure you go through your calculus I and II material this summer and you'll be fine. Up until Green's theorem etc. calc III is pretty much the same stuff you already learned but harder to draw:smile:
Green's, Gauss's, and Stokes's theorems can be difficult to grasp intuitively, but that won't come until the end of the class.
 
  • #18
DrewD said:
Make sure you go through your calculus I and II material this summer and you'll be fine. Up until Green's theorem etc. calc III is pretty much the same stuff you already learned but harder to draw:smile:
Green's, Gauss's, and Stokes's theorems can be difficult to grasp intuitively, but that won't come until the end of the class.

Yea you're probably right. If anything it sounds like this class will be fun and challenging, so I'm looking forward to it :smile:
 
  • #19
mckmetal said:
The only difference in "normal" Calc III is that it's more theoretical, is only geared towards applications of the physical sciences, and I'll learn about divergence and curl if I take it. Even though I'm majoring in physics, I'm not sure if it will really matter which class I take, as long as I'm learning the math... right?

According to the catalog, MAT203 is okay for a physics major:
B. Courses in Mathematics

1. One of the following sequences: MAT 125, 126, 127 Calculus A, B, Cor MAT 131, 132 Calculus I, II or MAT 141, 142 Honors Calculus I, II or MAT 171 Accelerated Single Variable Calculus or AMS 151, 161 Applied Calculus I, II
2. One of the following: MAT 205 Calculus III or MAT 203 Calculus III with Applications or AMS 261 Applied Calculus III
3. One of the following: MAT 305 Calculus IV or MAT 303 Calculus IV with Applications or AMS 361 Applied Calculus IV: Differential Equations
Note: Equivalency for MAT courses achieved on the Mathematics Place*ment Examination is accepted as fulfillment of the corresponding requirements, as indicated in the Course Descriptions section of this Bulletin.
 
  • #20
eumyang said:
According to the catalog, MAT203 is okay for a physics major:

Yes I know that it's an option under the math requirements for the major, but I wasn't sure if it would be as beneficial to me as MAT 205. Well, I'm sure it will be fine; I'll be learning the same math and learning how to apply it in different disciplines :)
 

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