# Linear Algebra or Calculus?

• tumkan
In summary, it is usually done in parallel in the first year of a study. Calculus, however, studying on your own, should be easier, and more intuitive. You can draw most of the things, whereas only two dimensions are available for linear algebra, which usually becomes more interesting in higher dimensions. Additionally, there are tons of free computer material for linear algebra that can draw things for you and compute stuff with matricies.f

#### tumkan

Summary: Hello! I'm an high school student and i want to study more math but I'm not sure where to start. Should i first study linear algebra or calculus?

Hello! I'm an high school student and i want to study more math but I'm not sure where to start. Should i first study linear algebra or calculus?

It is usually done in parallel in the first year of a study. Calculus, however, studying on your own, should be easier, and more intuitive. You can draw most of the things, whereas only two dimensions are available for linear algebra, which usually becomes more interesting in higher dimensions.

tumkan, vanhees71 and malawi_glenn
Kinda also depends on what math you already know and what you mean by study.
Self study? Enroll for a class?

Do you know how to differentiate and integrate functions with one variable? Do you know basic limits?
Do you know vectors and systems of linear equations?

While calculus could be more intuitive as mentioned, linear algebra is easier to do the proofs already at an introductory level. Furthermore, there are tons of free computer material for linear algebra that can draw things for you and compute stuff with matricies.

For some kind of inspiration, you could have look at these two playlists by 3blue1brown

If you want to study more math, but have limited background knowledge, you can give one of these free textbooks a try which are more focused on reading and writing mathematical statements, proofs and concepts more than computational nitty gritty stuff

“Mathematical reasoning”
https://scholarworks.gvsu.edu/cgi/viewcontent.cgi?article=1024&context=books
mer info https://www.tedsundstrom.com/mathematical-reasoning-3

“Book of proof”
https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf

“A gentle introduction to the art of mathematics”
https://github.com/osj1961/giam/blob/master/GIAM.pdf?raw=true

“An introduction to mathematical reasoning”
https://sites.math.washington.edu/~conroy/m300-general/ConroyTaggartIMR.pdf

“Proofs and concepts - the fundamentals of abstract mathematics”
https://batch.libretexts.org/print/Finished/math-23870/Full.pdf

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Hamiltonian, PeroK, tumkan and 3 others
Have you ever seen the movie "Sophie's Choice"? For a mathematician, answering your question is a lot like that. I think that you should learn the basic concepts of both and then you can pick one to study in more depth.
IMO, it is easier to understand the basic concepts of calculous, since so much that follows is learning tricks for individual types of integrals and derivatives. Linear algebra just keeps going and going and going. Also, calculus has immediate and clear applications in physics.

tumkan, hutchphd and DaveE
Have you ever seen the movie "Sophie's Choice"?
I think the shock comes with both, namely that school math has little to do with real math. I observed that it is usually harder for high school students to make the step into linear algebra than it is into calculus. It is simply closer to what they had experienced at school. Unfortunately, linear algebra is such a universal tool that it applies in all other areas, non-mathematical included.

tumkan, vanhees71 and FactChecker
Linear algebra just keeps going and going and going. Also, calculus has immediate and clear applications in physics.
Totally depends on the course outline. Linear algebra has many applications in physics, it is almost mandatory to know once you into physics stuff that happens in more than one spatial dimension. But sure, calculus you get into motion, work etc quicker

tumkan and vanhees71
If you do decide to go the linear algebra route. There is an amazing book by Paul Shields. Can be found very cheap online. It stick to R^2 and R^3 only, but it gives you the basics.

tumkan, vanhees71 and malawi_glenn
tumkan and vanhees71
There's a long thread where you are searching for a calculus textbook. Have you changed your mind?

I think your plan to whip through the material quickly rather than deeply
Thanks a lot for everyone who answered. The answers are very precious to me. No sir, that's not my plan. I was going to study calculus for national physics olympiads but i couldn't pass to the second stage -which means i have to enter first stage again, the problems in first stage are calculus non mandotary- so i decided not to study calculus. And i am planning to apply for a quantum programming course which is for high school students. And knowing basics of linear algebra is one of the requirements of course. I wasn't sure if i need to study calculus before taking linear algebra. That's why i asked this question.

Thanks a lot for everyone who answered. The answers are very precious to me. No sir, that's not my plan. I was going to study calculus for national physics olympiads but i couldn't pass to the second stage -which means i have to enter first stage again, the problems in first stage are calculus non mandotary- so i decided not to study calculus. And i am planning to apply for a quantum programming course which is for high school students. And knowing basics of linear algebra is one of the requirements of course. I wasn't sure if i need to study calculus before taking linear algebra. That's why i asked this question.
Hmm. look up what the description of the computing course is. Maybe Anton: Linear Algebra, may be at the appropriate level for the course. I do not know any about computing, since I majored in pure math...

malawi_glenn
Just in case, much of advanced Math ( ad thereforeot a chunk of Physics) comes down to Advanced Calculus ad Linear Algebra; sometimes in not so obvious ways. So if you do plan to do any of these at some point, it would not hurt you to brush up on these.

I wasn't sure if i need to study calculus before taking linear algebra. That's why i asked this question.
Typically students study Calculus or at least START it, before Linear Algebra. This does not mean that student cannot begin studying some level of Linear Algebra first. Many Intermediate Algebra and College Algebra students do study a limited part of Linear Algebra (depending on the institution's course content).

i am planning to apply for a quantum programming course which is for high school students. And knowing basics of linear algebra is one of the requirements of course. I wasn't sure if i need to study calculus before taking linear algebra.
Calculus is not a prerequisite for linear algebra. I don't think that it would help much in either linear algebra or quantum computing. (Quantum annealing might be an exception where it might help.)

malawi_glenn
If you treat the derivative as a linear operator, then you get a beautiful fusion of calculus and linear algebra!

hutchphd, Mark44, gleem and 3 others
I do not know any about computing, since I majored in pure math...
The "since" suggests an implication that is, in fact, not true.

The "since" suggests an implication that is, in fact, not true.
Besides semantics, the meaning of my post was clear...

Delta2
Anton: Linear Algebra
That book has additional sections "for students who knows calculus" so in that way it is kinda nice.

vanhees71 and Delta2
The "since" suggests an implication that is, in fact, not true.
That depends what was required. Maybe he only did the very minimum to earn his Pure Mathematics degree and so still feels he knows very little about computing(computer science or programming).

I do not know any about computing, since I majored in pure math...

The "since" suggests an implication that is, in fact, not true.

Besides semantics, the meaning of my post was clear...
It was clear to me. The meaning of "since" here is more like "because" rather than "since the time of." There was another thread in the GD forum about clear writing, part of which was devoted to a discussion of "since" vs. "because."

In any case, I believe that @MidgetDwarf meant that his major was pure mathematics, which at his university didn't require any courses in programming. Parsing his sentence any other way is a bit pedantic, IMO.

Mondayman, symbolipoint, malawi_glenn and 1 other person
https://dictionary.cambridge.org/grammar/british-grammar/since

## Since: reason​

We use since as a subordinating conjunction to introduce a subordinate clause. We use it to give a reason for something:

Sean had no reason to take a taxi since his flat was near enough to walk to.
Since her husband hated holidays so much, she decided to go on her own.
They couldn’t deliver the parcel since no one was there to answer the door.

We do the same in swedish. "Då" can mean both something temporal and something causal. My wife use it all the time to describe causality. It bugs me alot, why not use the word "eftersom" (because)?

https://dictionary.cambridge.org/grammar/british-grammar/since

## Since: reason​

We use since as a subordinating conjunction to introduce a subordinate clause. We use it to give a reason for something:

We do the same in swedish. "Då" can mean both something temporal and something causal. My wife use it all the time to describe causality. It bugs me alot, why not use the word "eftersom" (because)?
TWO DIFFERENT SENSES for since. Each is very well known and each is very often used for the fitting purpose. These senses are also very well documented in established high quality dictionaries.