# Applications of modern algebra

1. Mar 23, 2006

### Nothing000

Would an intro course to modern algebra be useful in any way to an electrical engineer? Here is a description of the class:
Introduction to set theory and logic; elementary properties of rings, integral domains, fields and groups.

By the way, I would like to eventually get into integrated circuit design. So is there any use of these topics to that specific field? I read somewhere that modern algebra is useful for circuit design. Is it?

2. Mar 23, 2006

### stunner5000pt

i am in physics and i too would like to see the benefits, if any, of taking a modern algebra course.
However, does abstract algebra have any applications to theoretical physics, or engineering?? Groups, rings, homomorphisms, and such??

3. Mar 23, 2006

### Nothing000

I thought that abstract algebra was the same thing as "modern" algebra.

4. Mar 23, 2006

### Nothing000

Are you currently taking modern algebra stunner? And if so have you not been told how it can be applied?

5. Mar 23, 2006

### Staff: Mentor

From the course description, I don't see anything directly useful in real EE work. A Linear Algebra course (matrices) would be more useful, since you use matrix math some to solve large simultaneous equation problems in EE, and since SPICE is based on matrix math a fair amount.

For IC design, be sure to get lots of classes in analog & digital circuit design, semiconductor physics, etc.

6. Mar 23, 2006

### George Jones

Staff Emeritus
It is used, but I think only for very specialized applications. About 10 years ago, I knew a grad student who had http://www.schulich.ucalgary.ca/resrch_electrical/Elect_Jullien.htm" [Broken] as an advisor, and he used this stuff for chip design.

Regards,
George

Last edited by a moderator: May 2, 2017
7. Mar 23, 2006

### George Jones

Staff Emeritus
Groups and algebras are used extensively in elementary particle physics and quantum field theory. A one-course introductory math course does get nearly far enough in these fields to be particularlu useful. Either several math courses are needed, or the math can be picked in the relevant physics courses, where rigor is relaxed and math can thus be covered (sometimes too) quickly.

Regards,
George

8. Mar 23, 2006

### mathwonk

basic rule: it is hard to apply ideas you do not know about.

or as my 12 year old son put it: the problems on the contest do not really need algebra, but if you know algebra it can be helpful.

as taught to us back in 11th grade in high school, an electrical circuit is nothing but a sequence of yes / no choices, hence can be modeled using boolean logic, the simplest form of abstract algebra.

boolean calculus can thus be used to make computations about the circuit.

this is just the little i recall from 47 years ago as a child.

as george jones points out, groups are nothjing but the mathematical study of symmetry hence are used wherever one studies that phenomenon. this includes fourier series, harmonics, heat transfer and propagation, and certainly electrical fields.

verbum sapienti:
a wise person is never sorry for having learned something, only for having not learned something.

Last edited: Mar 23, 2006
9. Mar 23, 2006

### matt grime

Short answer, yes. Electrical engineering (of a certain persuasion at least) is pretty much applying the theory of vector spaces over the field F_2, and computing discrete Fourier Transforms on groups.

10. Mar 23, 2006

### Nothing000

Do you guys think this class would be helpful to an electrical engineer:
Intro to Modern Analysis: An introduction to the proofs and theorums of one dimensional calclulus. Properties of the real numbers, sequences and series of constants and functions, limits, continuity, differentiation and integration.

11. Mar 25, 2006

### Maxwell

I think there are other mathematics classes that would serve you better as an EE. However, if you want to take it for fun, then by all means - do it.

12. Mar 25, 2006

### Nothing000

If I take those two classes (Intro to modern Algebra, and Intro to Modern Analysis) then I will earn a double major. That is the reason that I am asking. I think the algebra class looks very interesting, but I would be much more sure that I want to take these two extra classes if I knew that I would actually use the material in them.

13. Mar 25, 2006

### Nothing000

By the way, I asked the head of the math department if I could substitute two applied math classes for these two pure classes, and he said there is no possible way.

14. Mar 25, 2006

### heman

yeah i have seen my electrical mates doing lot of fourier stuff but whatd do you mean by first..

15. Mar 25, 2006

### matt grime

'First' what?

I'll assume you mean F_2 and vector spaces. You know what a vector space is, I assume, well, F_2 is the field with two elements, which is horribly obscurantist of me. It is just the numbers 0 and 1 with the obvious (to an electrical engineer!) properties that 0*0=0=0*1, 1*1=1 and 1+1=0. Well, this has to be clearly useful to an engineer since it is just bit manipulation.

16. Mar 25, 2006

### Nothing000

That went right over my head matt. I guess I do need to take this class!! But seriously, I am just in Calc 2 right now, so I don't know anything about vector spaces yet. Won't I learn the stuff you just mentioned in linear algebra though?
When I talked to the head of the math department I asked him if he thought I would use any modern algebra as an electrical engineer, and he said that most classes like that would just look good on an application, and he really downplayed the whole idea of how advanced math really can be handy to engineers. I found that kind of odd. It seems like even if I wouldn't use this stuff directly he would at least say that understanding this stuff will help me understand other abstract concepts, or just tell me that this class would be useful is some way. But all he said is that it would look good to an employer because it lets them know that I am willing to put in effort to complete a difficult task.

17. Mar 25, 2006

### mathwonk

well i am stretching to justify the foundations of analysis class, but even there if you are going to apply calculus, it helps to know the limitations of calculus.

i.e. the better you understand how a mathematical tool works, the more likely you are to apply it correctly, and the less likely you are to over estimate its accuracy for your purposes.

18. Mar 25, 2006

### Nothing000

If I take these classes that is what I mainly plan on gaining (especially for the intro to analysis class). I just don't want to take a class where all we do is learn about proofs. I would feel much better taking a class where it is at least somewhat applicable to a real world situation.

19. Mar 25, 2006

### mattmns

Then Modern (Abstract) Algebra and Analysis are the last classes you want to take.

20. Mar 26, 2006

### Nothing000

Why do you say that mattm? Because there are so many proofs, or because nothing in these classes has any real world applications? (or both?)

21. Mar 26, 2006

### mattmns

At my school both classes are nothing but proofs.

Matt has already pointed out some applications so they obviously exist, I just doubt that the classes at your school will go over any applications, which seems to be your interest. I would just ask your advisor whether or not the classes go over applications, because your school could be different.

22. Mar 26, 2006

### Nothing000

I think that engineering departments should teach all of the applied math classes, because I don't understand why engineering students would take the same calculus class, or any math class, as someone going into pure mathematics. Is that done anywhere?

23. Mar 26, 2006

### tmc

here, the engineers have special math classes.

calculus for engineers, diff.eq. for engineers, etc.

24. Mar 26, 2006

### leright

At my school, engineers take the same calculus classes, diff EQ, linear alg, etc as the math majors. But I feel like calculus and diff EQ it is such an important subject that the depth an engineer gets should be equal to that of a math major. As mathwonk said, a persons ability to correctly apply concepts is directly related to how well you understand the concepts. Plus, the math classes (calculus, DE, etc) should not be to learn applications....that is what the engineering classes are for!

When I was in HS taking algebra based physics, and more basic chemistry, I had trouble applying the concepts because they were introduced at a much more superficial level. However, in college all of the formulas are derived and the chemistry concepts are explored more deeply and I feel more capable of applying the concepts.

25. Mar 26, 2006

### Tom Mattson

Staff Emeritus
I think that there are far better ways for an EE major to spend his time than by taking a course in modern algebra. I would recommend any of the following over that course.

* A second course in linear algebra.

Someone already suggested linear algebra, but not for the reason that I would have. An intro course in linear algebra will give you all the conceptual tools you need for solving systems of equations. Besides, in practice you'll get Maple (or some equivalent) to do that for you. No, you'll want to get from linear algebra the idea of a vector space. For instance it's useful for an EE to know that the functions $\{\sin(x),\cos(x)}$ span the same vector space as the functions $\{exp(ix),exp(-ix)\}$.

* A second course in ODE's, including nonlinear ODE's.

Because real circuits aren't linear.

* A course in PDE's.

This will benefit you when you study EM field theory, as all EE's do.

* A course in advanced calculus, including vector calculus.

Ditto for this.

* A course in complex variables.

This course will give you a very powerful toolbox with which you can quickly cut through problems in EM field theory, inverting Laplace transforms, and much more.

* A course in discrete mathematics.

The standard course that goes by this name covers logic, mathematical induction, algorithm analysis, topology, graph theory, and boolean logic circuits. All of these are of great use to an EE.

* Any number of courses in "applied mathematics".

Look for one that covers ODE's with perturbation methods.

* A course in numerical methods.

Most problems in real life have to be solved numerically.