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

In summary: I don't want to call myself an expert, but I've had a lot of experience with Calculus I and II, and I'm sure I'll be able to handle it. I'm more worried about the transition to advanced math, but I'm hoping Linear Algebra and my CS class will help with that."In summary, the conversation revolves around the speaker's academic plan as a first-year university student. They have taught themselves Calculus I and are registered for Calculus II, Introduction to Linear Algebra, and Discrete Structures. They are considering adding a second major in math and are wondering about the recommended order for taking courses. The conversation also touches on the need for a course to bridge the gap between computation-oriented courses and proof-oriented
  • #1
RandomPoster
5
0
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...
 
Physics news on Phys.org
  • #2
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.
 
  • #3
"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.
 
  • #4
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.
 
  • #5
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.
 
  • #6
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.
 
  • #7
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.
 
  • #8
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.
 
  • #9
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.
 

1. What are the main topics covered in "Catch Up as Math Major: Calc II, Linear Algebra, DiffEq & Analysis"?

The main topics covered in this course include Calculus II, Linear Algebra, Differential Equations, and Analysis. These are fundamental concepts in mathematics that are essential for any math major.

2. Who is this course designed for?

This course is designed for students who are majoring in mathematics or a related field and need to catch up on these specific topics. It is also beneficial for students who are struggling with these subjects and need additional help to improve their understanding.

3. How will this course help me as a math major?

This course will provide you with a comprehensive review of key concepts in Calculus II, Linear Algebra, Differential Equations, and Analysis. It will help strengthen your understanding of these subjects and prepare you for more advanced courses in your math major.

4. Are there any prerequisites for this course?

It is recommended to have a basic understanding of Calculus I before taking this course. However, the course does include a brief review of Calculus I concepts to help students who may need a refresher.

5. How is the course structured?

The course is divided into four sections, one for each topic: Calculus II, Linear Algebra, Differential Equations, and Analysis. Each section includes video lectures, practice problems, and quizzes to test your understanding. There is also a final exam at the end of the course to assess your overall knowledge.

Similar threads

  • STEM Academic Advising
Replies
6
Views
1K
  • STEM Academic Advising
Replies
8
Views
1K
  • STEM Academic Advising
Replies
6
Views
1K
  • STEM Academic Advising
Replies
3
Views
1K
  • STEM Academic Advising
Replies
8
Views
1K
  • STEM Academic Advising
Replies
11
Views
2K
  • STEM Academic Advising
Replies
6
Views
935
  • STEM Academic Advising
Replies
9
Views
2K
  • STEM Academic Advising
Replies
22
Views
4K
  • STEM Academic Advising
Replies
17
Views
3K
Back
Top