Catch Up as Math Major: Calc II, Linear Algebra, DiffEq & Analysis

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Discussion Overview

The discussion centers around the academic trajectory of a first-year university student majoring in computer science with an interest in mathematics. The participant seeks advice on course sequencing for Calculus II, Linear Algebra, Differential Equations, and Analysis, particularly in light of their self-study efforts and concerns about falling behind compared to peers with prior calculus experience.

Discussion Character

  • Exploratory
  • Homework-related
  • Debate/contested
  • Technical explanation

Main Points Raised

  • The original poster (OP) has self-studied Calculus I and performed well, expressing a desire to take Calculus II, Linear Algebra, and Discrete Structures in their second semester.
  • Some participants suggest that the OP should check the prerequisites for the Analysis course to determine if taking it without Multivariable Calculus is feasible.
  • One participant notes that the Analysis course emphasizes formal proofs and covers topics like limits and Riemann Integration, indicating that a solid foundation in prior mathematics is beneficial.
  • Another participant mentions that many universities offer a "Transition to Advanced Mathematics" course to bridge the gap between computational and proof-oriented courses, which the OP's university does not have.
  • Some participants recommend taking Calculus II and other foundational courses before attempting Analysis, while others believe the OP could handle Analysis after completing Calculus II.
  • There is a discussion about the potential challenges of transitioning from computation-heavy courses to proof-based courses, with some suggesting that Linear Algebra may help with this transition.
  • One participant advises that the OP should not rush into Analysis and should ensure they are comfortable with the material before proceeding.

Areas of Agreement / Disagreement

Participants express differing views on the appropriate sequence of courses for the OP. While some believe it is acceptable to take Analysis after Calculus II, others emphasize the importance of completing Multivariable Calculus and Differential Equations first. There is no consensus on the best approach, reflecting a variety of academic experiences and opinions.

Contextual Notes

The discussion highlights the lack of a standardized course sequence across universities, as well as the varying prerequisites for advanced mathematics courses. The OP's concerns about falling behind and the implications of course sequencing are also noted.

RandomPoster
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Hi, I saw there was another thread about becoming a mathematician, but as far as I know, this is somewhat different. Anyway, I am a first-year university student, and am going to start my 2nd semester next week. For various reasons I won't go into, I didn't really take any math in high school higher than precalc. However, I taught myself Calculus I before the start of the first semester with a textbook + practice problems online.

I did very well in the class, finishing with over 100%. This upcoming semester, I am registered for Calculus II, Introduction to Linear Algebra, and Discrete Structures. Technically, the last class is a Computer Science class (I am a CS major), but it seems to be a de facto math class, including the basics of proofs. I really enjoy math. I understand there will be less and less computation the further you go, but I am considering adding it as a second major. I have used the same strategy that I had with Calculus I to teach myself a good deal of Calculus II, including all of the methods of integration, and I have started with sequences and infinite series.

Technically speaking, this means I am able to register to take (in Fall 2017) the first Analysis class, but it's strongly recommended that you have Multivariable first. Assuming I cannot take any classes over the summer, what order should I go in? Of course, I'll talk to other math majors and advisers about it when I go back, but I am still very curious. Technically speaking, my school's four-year-plan has you taking Analysis I Fall 3rd year, but I would like to get it in earlier. The main reason is that I feel already behind math majors who have credit from high school for Calculus I and/or II, like my friend who took Multivariable last semester.

I suppose my main question is if I should worry about falling behind and not being able to take as many courses as are available. I don't know what I want to do after I graduate exactly; it's a toss-up between going to graduate school and just going to work, but it's obviously too early to say.

At the same time, I don't want to rush it. Also, should I try to take it Fall no matter what? I ask because it's part of a sequence with Analysis II, and I figured it would be better not to have a summer break in between. I also need to take Introduction to Differential Equations. My current plan, as far ahead as I can go, is to take DiffEq/Multivariable in the Fall and Analysis I in the Spring. I know one person who is going into Analysis I right after Calc II/Linear Algebra, so maybe I can ask them about it...
 
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Can you link the course here from your schools webpage so we can see what topics your intro Analysis course will cover? If it doesn't require Multivariate calculus as a prerequisite, or differential equations for that matter, then you'd be okay.

You're going to have to do those courses regardless, so I don't see the rush, and I would do those first.
 
"This course is a systematic study of basic analysis with an emphasis on formal proofs, examples and counter examples. Topics include properties of the real line, sequences, series, limits, continuity and differentiation of functions, and Riemann Integration. Note: Highly recommended is CMSC 203."

I could have sworn multivariable was recommended. I guess not. CMSC 203 is discrete structures, FYI.
 
RandomPoster said:
"This course is a systematic study of basic analysis with an emphasis on formal proofs, examples and counter examples. Topics include properties of the real line, sequences, series, limits, continuity and differentiation of functions, and Riemann Integration. Note: Highly recommended is CMSC 203."

I could have sworn multivariable was recommended. I guess not. CMSC 203 is discrete structures, FYI.

Then you're fine. You could do Analysis I with Multivariate and then Differentials. Analysis is going to cover a lot of topics you're already familiar with from Algebra and Calculus, more rigorously. I've never taken it myself, but the schools I'm familiar with have Multivariate and Differentials as prereqs to ensure some level of mathematical maturity rather than a firm need for the intro course itself.

Anyway, I think you're going to be okay whatever you choose to do. Just be ready to transition from computation and calculation to axioms and theorems. Linear Algebra (and your CS class for that matter) should help you some there, that's typically students first introduction to proofs. Good luck.
 
Does your university have a course called "Transition to Advanced Mathematics" or something like it? Many colleges and universities (in the US at least) have a course with a similar name that is intended to be a bridge between computation-oriented courses like intro calculus and proof-oriented courses like analysis. At the college where I work, it's a required course for all math majors.
 
Nope. For reference, if you're a math major, the suggested sequence (with no AP credit or anything) is Calc I -> Calc II -> Multivariable -> DiffEq + Linear Algebra + Supplementary Elective -> Analysis I + UL Elective + Supplementary Elective, which each arrow pointing to a new semester.
 
i would take calculus 2, intro physics (if it is required), and a general ed or two. Calculus 2 is time consuming, and many people still have trouble with algebra and trig. You may have to review a lot of previous material if you do not know it or are fluent. Maybe switch a general ed for a programming class.

You do not need calculus in order to study linear algebra. However, linear algebra can be extremely abstract if it is the first math class requiring to do mathematical proofs.

Second semester I would take linear algebra, differential equations, programming, maybe even another general ed.

Third semester, Analysis and what ever else you need.
 
I can't really change anything now, but I'm not too worried about this semester. It'll be very time-consuming, certainly, but I'm pretty confident. I took physics last semester and am taking it also this semester. But I'm pretty much fine with all algebra and trig. I think our intro linear algebra is mostly computational, too.
 
Yeah, you should be good to go for analysis after calc II. It's what I did too. Be sure to self-study it a bit.
 

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