Linear Algebra before Calculus?


by zodiacbrave
Tags: algebra, calculus, linear
zodiacbrave
zodiacbrave is offline
#1
Jun18-08, 02:00 AM
P: 11
Hello,

This might sound like a dumb question but can one learn Linear Algebra before Calculus?

Thank you.
Phys.Org News Partner Mathematics news on Phys.org
Researchers help Boston Marathon organizers plan for 2014 race
'Math detective' analyzes odds for suspicious lottery wins
Pseudo-mathematics and financial charlatanism
Mute
Mute is offline
#2
Jun18-08, 02:09 AM
HW Helper
P: 1,391
Yes. My first course in linear algebra required no calculus.
Defennder
Defennder is offline
#3
Jun18-08, 02:30 AM
HW Helper
P: 2,618
Definitely. I did a course on it without any background in calculus as well. What's interesting is that some results in linear algebra would also be used in a course on differential equations.

Llama77
Llama77 is offline
#4
Jun20-08, 12:08 PM
P: 113

Linear Algebra before Calculus?


My LA class had a few integrals and derivatives, but that as just for proofs, which we didnt need to know.
LukeD
LukeD is offline
#5
Jun20-08, 12:31 PM
P: 355
The only time I ever used integrals and derivatives in my Linear Algebra course was to prove some things about Differential Equations. These were just examples though; they were only applications of Linear Algebra.

None of the proofs of Linear Algebra theory require any knowledge of Calculus, so except for some examples of applications, you will not need to know how to do derivatives or integrals at all (though some stuff that you might do later in the course may require some knowledge of the properties of the real and complex numbers)
Fredrik
Fredrik is online now
#6
Jun20-08, 12:35 PM
Emeritus
Sci Advisor
PF Gold
Fredrik's Avatar
P: 9,000
I'm quoting myself from the linear algebra forum:
Quote Quote by Fredrik View Post
You don't need calculus. You need to understand what functions are and have some idea what sets are to understand the definition of a vector space, and you need know how to add and multiply real numbers (e.g. rules like (a+b)(c+d)=ac+ad+bc+bd). But that's it.
Howers
Howers is offline
#7
Jun20-08, 06:37 PM
P: 444
As already stated, linear algebra is completely independent of calculus. Algebra deals with discrete quantities, not continous ones.

You can successfully learn linear algebra without any knowledge of calculus. The only problem may arise in applications of linear algebra, such as viewing the integral as a linear map or differential equations. In any case, these are tiny fractions of the whole subject.
mathwonk
mathwonk is offline
#8
Jun20-08, 08:34 PM
Sci Advisor
HW Helper
mathwonk's Avatar
P: 9,424
yes linear algebra is actually prerequisite for calculus done right. but as courses go in the us, we usually teach calculus as a collection of computational techniques, and then teach linear algebra more abstractly. so we teach linear algebra second because it si thought more difficult to understand "abstract ideas" than computational ones.

in an ideal world linear algebra is taught first, then calculus is taught as an application of linear algebra.

i.e. correctly done, calculus is the art of using linear algebra to deduce things about non linear functions.

e.g. the inverse function theorem in calculus says: if the derivative of a smooth function f at a is an invertible linear map, then locally near a, f is an invertible smooth map.
LukeD
LukeD is offline
#9
Jun20-08, 10:35 PM
P: 355
Quote Quote by mathwonk View Post
e.g. the inverse function theorem in calculus says: if the derivative of a smooth function f at a is an invertible linear map, then locally near a, f is an invertible smooth map.
The problem with that is that "f is an invertible linear map" doesn't give me any geometric intuition. On the other hand, consider the more "calculus" explanation: that the tangent "plane" at a does not contain any of the axes, so in some area around near a, the function must be a bijection. I can actually visualize this, intuitively understand it, and think of how potentially do a proof.

Edit: Certainly, I could try picture every linear map as a geometric object, but I don't yet have that mathematical intuition, and it currently inhibits my ability to intuitively understand the abstract idea.
maze
maze is offline
#10
Jun20-08, 10:47 PM
P: 655
Quote Quote by mathwonk View Post
i.e. correctly done, calculus is the art of using linear algebra to deduce things about non linear functions.
This.


Register to reply

Related Discussions
[SOLVED] linear algebra - inner product and linear transformation question Calculus & Beyond Homework 0
linear algebra - solve linear system with complex constants Calculus & Beyond Homework 2
Linear Algebra: Linear Transformation and Linear Independence Calculus & Beyond Homework 8
LINEAR ALGEBRA - Describe the kernel of a linear transformation GEOMETRICALLY Calculus & Beyond Homework 6
How much calculus in linear algebra? Linear & Abstract Algebra 5