Should I take linear algebra over the summer?

In summary, it is suggested to take linear algebra over the summer instead of an elective due to its importance as a basis for many sciences and its potential to make future courses easier. The course will cover basic properties of systems of linear equations, matrices and matrix algebra, determinants, vector spaces, subspaces, linear independence of vectors, basis and dimension of subspaces, linear transformations, eigenvalues and eigenvectors of a matrix, orthogonality of vectors, inner product and length of vectors. The book used is Linear Algebra and its applications by David C. Lay (fourth edition) and the course will involve a mixture of tedious hand computations and proofs. It is suggested to take the course in the spring if one struggles with proofs
  • #1

member 545369

Current schedule:

Summer: Elective
Fall: -not important, but it can't be changed in any way-
Spring: Differential Eqs., Classical Mechanics & Mathematical Methods 1 (Physics), Linear Algebra, Chemistry Lab, Elective

I'm thinking that since the spring schedule looks kinda heavy I can switch up the summer elective with Linear Alg instead? The summer semester is one month long, but I heard that Linear Alg is fairly easy. Is it a integral part of Classical Mechanics 1? What do you guys think?

I haven't taken Calc 3 yet (but I've taken Calc 2., which is the requirement of Lin Alg).
 
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  • #2
The answer is yes. Regardless what will come, linear algebra is the basis for almost every science that has a minimum of math.
 
  • #3
fresh_42 said:
The answer is yes. Regardless what will come, linear algebra is the basis for almost every science that has a minimum of math.

Your justification kinda confused me. I'm not asking whether or not I should take the course, I'm asking whether I should take it over the summer or just do it in the spring.
 
  • #4
In my opinion, it definitely wouldn't hurt. However, it depends on your school and what type of linear algebra they tend to throw at you. Some colleges use linear algebra as the first introduction to a proof based class. If that's the case for you then, it might be hard for a novice to learn how to do proofs and learn the math at the same time at an accelerated pace. However, if your school focuses more on computational aspects (i.e. find row reduced form, calculate determinate, find an eigenvalue, or do the g-s process by hand) then it shouldn't be that bad, just tedious.

With all that said, I encourage people to take LA early because I find it gives a good background to the math one does in some portions of Calc III or differential equations. Knowing how to calculate a determinant made Calc III easier on me and finding eigenvalues and basis made differential equations easier. (In fact, I vaguely recall being really happy for 2 weeks because I didn't have to study much since I knew the material already).
 
  • #5
Linear algebra has no prerequisites on the Spring classes but some of the Spring classes may depend greatly on linear algebra. I wouldn't say that linear algerbra is necessarily easy. It depends on how much is covered.
 
  • #6
It would help a lot if you could provide the contents of the course and the book used.
 
  • #7
micromass said:
It would help a lot if you could provide the contents of the course and the book used.

Of course!

Textbook: Linear Algebra and its applications by David C. Lay (fourth edition)
Course contents: Basic properties of systems of linear equations, matrices and matrix algebra, determinants, vector spaces, subspaces, linear independence of vectors, basis and dimension of subspaces, linear transformations, eigenvalues and eigenvectors of a matrix, orthogonality of vectors, inner product and length of vectors.

As quoted from the syllabus:

The first midterm might be something like https://math.colorado.edu/~rmg/3130/u3130a.pdf [Broken].
The second midterm might be something like https://math.colorado.edu/~rmg/3130/u3130b.pdf [Broken].
The final might be something like https://math.colorado.edu/~rmg/3130/u3130f.pdf [Broken].

How do they look? Thing is, from my experience with math, I've noticed that just giving time for the material to sink in really helped me understand concepts I was confused about - with the summer this won't really be an option for me since we'll be taking a lot of material really quickly. i just think that the Classical Mechanics course I'm taking over the spring is going to be really dense so a) having Linear Algebra under my belt would help and b) lightning the load by substituting it with an elective might help.
 
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  • #8
MarneMath said:
In my opinion, it definitely wouldn't hurt. However, it depends on your school and what type of linear algebra they tend to throw at you. Some colleges use linear algebra as the first introduction to a proof based class. If that's the case for you then, it might be hard for a novice to learn how to do proofs and learn the math at the same time at an accelerated pace. However, if your school focuses more on computational aspects (i.e. find row reduced form, calculate determinate, find an eigenvalue, or do the g-s process by hand) then it shouldn't be that bad, just tedious.

With all that said, I encourage people to take LA early because I find it gives a good background to the math one does in some portions of Calc III or differential equations. Knowing how to calculate a determinant made Calc III easier on me and finding eigenvalues and basis made differential equations easier. (In fact, I vaguely recall being really happy for 2 weeks because I didn't have to study much since I knew the material already).

We have a discrete mathematics course provided in our university that is definitely considered the "introduction" to a proof based class, so I don't think we're going to be an intro to a proof based class. Nevertheless, I have provided the course contents above if you'd like to take a look.
 
  • #9
I'm fairly familiar with David Lay's book. There's generally an even mixture of tedious hand computations and proofs. I think what it comes down to is how confident are you with your proof ability? From my days as a tutor, I didn't really feel any proofs were extremely difficult in his book. A lot of it were simply apply a definition do a calculation and the end. However, if you struggle with proofs still or don't feel like you have a good flow for how proofs work, then the course may be unnecessarily difficult in the summer.
 
  • #10
Having already had linear algebra will help you a lot in differential equations. It will probably help with your math methods class as well, especially if they cover Fourier series.

I like David C. Lay's linear algebra textbook. I keep an extra copy of the third edition around in case I need to give it to someone.
 
  • #11
Hey telrefae.

If you take linear algebra it would help to put it in context with multi-variable calculus which makes heavy use of it.

Linear algebra - like most other mathematics subjects, can be easy or hard depending on the lecturer, content, and nature of assessment so don't write it off as easy.

If you take it then I'd recommend thinking about it in terms of both algebraic and geometric terms. Linear algebra is dealt with in both and both perspectives help re-enforce the other one and give clarity to the ideas being expressed.

Most of geometry is in some way covered with linear algebra (in some form or another) and understanding the notion of linearity with respect to derivatives helps put a lot of this in context with the multi-variable and vector calculus techniques and identities.

Just remember not to rely too much on geometric intuition since linear algebra encompasses results that span arbitrary dimensional spaces (your course will look at a finite number of dimensions - there are extensions to an infinite number but they are dealt with in graduate coursework most of the time).
 

1. What are the benefits of taking linear algebra over the summer?

Taking linear algebra over the summer allows you to focus solely on one subject, rather than balancing multiple classes during a regular semester. It also allows you to complete the course at a faster pace, potentially freeing up your schedule for the following semester.

2. Will taking linear algebra over the summer be more challenging or easier than taking it during the regular semester?

This depends on your personal learning style and work ethic. Taking it over the summer requires a more condensed and intensive study schedule, but some students may find this more manageable. However, if you struggle with time management or prefer a slower pace, taking it during the regular semester may be a better option.

3. Are there any disadvantages to taking linear algebra over the summer?

One potential disadvantage is that the course material may be more challenging to grasp in a shorter amount of time. Additionally, if you plan on taking other classes or working during the summer, balancing your schedule may be more difficult.

4. How does taking linear algebra over the summer affect my GPA?

As with any course, your grade in linear algebra over the summer will affect your GPA. However, since the course is completed in a shorter time frame, there is less room for error and it may be more difficult to recover from a low grade.

5. Is it recommended to take linear algebra over the summer if I am not a strong math student?

It ultimately depends on your personal abilities and determination. If you are willing to put in the extra effort and time to study, taking linear algebra over the summer may be a good option for you. However, if you struggle with math or have not had success in previous math courses, it may be better to take it during a regular semester when you have more time and resources available.

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