Should Electrical Engineers Learn Modern Algebra for Integrated Circuit Design?

[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?

 

[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??

 

[Nothing000]

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

 

[Nothing000]

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

 

[berkeman]

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?

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.

 

[George Jones]

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?

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" as an advisor, and he used this stuff for chip design.

Regards,
George

 

[George Jones]

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??

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

 

[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.

 

[matt grime]

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.

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.

 

[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.

 

[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.

 

[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.

 

[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.

 

[heman]

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.

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

 

[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.

 

[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 let's them know that I am willing to put in effort to complete a difficult task.

 

[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.

 

[Nothing000]

...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...

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.

 

[mattmns]

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.

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

 

[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?)

 

[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.

 

[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?

 

[tmc]

here, the engineers have special math classes.

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

 

[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.

 

[quantumdude]

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.

 

[quantumdude]

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.

Don't just settle for a "yes/no" answer either. I took a course called "Abstract Algebra" because I wanted to learn groups for QM/QFT. It was a good course, and I'm glad I took it, but I did learn an important lesson: mathematicians and physicists mean two completely different things when they use the word "application". I walked into class one day and the professor said, "We're going to look at some applications of our theory today". I thought, "Oh boy, oh boy! What ever could it be? Angular momentum addition? Rotations? Translations? Lorentz transformations?"

I was mistaken. He "applied" the theory to purely mathematical problems. Well, you learn something new every day!

 

[Nothing000]

* 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.

I thought that discrete math was basically the same thing as modern algebra. (?)

Here is the discription of the two classes at my school:

Intro to Modern Albegra:
Introduction to set theory and logic; elementary properties of rings, integral domains, fileds and groups.

Discrete Math 1:
Logic, set theory proof techniques, probability and combinatorics, relations and functions, matrix algebra graphs, Boolean algebra ad lattices.


I thought both of these classes emphasise formal logic and set theory.

 

[quantumdude]

I thought that discrete math was basically the same thing as modern algebra. (?)

No, they're very different. Neither course really emphasizes set theory or logic, but they both introduce them. One big difference between the two courses is that modern algebra builds vertically while discrete math builds horizontally.

In the algebra course you would find that you need to master the material as you go because subsequent lessons build on previous ones. But it is neither desirable nor possible to connect the ideas later in the course with the basics of logic and set theory that you would learn early in the course. That's why I say that it wouldn't emphasize those things.

On the other hand, you would find that the discrete math course is a survey of topics that don't explicitly depend on each other. Once set theory and logic are over, then they're over and you move on to something else.

Intro to Modern Albegra:
Introduction to set theory and logic; elementary properties of rings, integral domains, fileds and groups.

Discrete Math 1:
Logic, set theory proof techniques, probability and combinatorics, relations and functions, matrix algebra graphs, Boolean algebra ad lattices.

These look the same to you? There are no rings, integral domains, fields, or groups in discrete math. And there is not probability, combinatorics, boolean algebra, or lattices in modern algebra. The modern algebra coruse would cover functions, although it may not call them that ("mapping" is another term), and they might consider matrix algebra or graph theory as an application. IMO the stuff that's covered in the discrete math course is far more useful to an EE major.

 

[Nothing000]

IMO the stuff that's covered in the discrete math course is far more useful to an EE major.

I would have to think so too, since my school lists discrete math as an applied math course. That is why I asked the head of the math department if I could substitute modern algebra and modern analsis with two applied courses, and he said no way.
But do you think it would be worth it to take those two classes that I probably would not use just to double major? If I don't take those two classes then I only minor in math.
Here are the math classes that I am going to take, or have already taken:
Calc 1
Calc 2 (I am currently taking this class)
Ordinary Diff E (I am currently taking this class)
Linear Algebra (I am curently taking this class)
Calc 3
Multi-Variable Calc
Complex Variables
Linear Programming
Numerical Methods

All of are either required for the EE degree, or count toward electives for the EE degree. Do if I just take those two extra classes on top of these classes then I actually double major.

 

[Nothing000]

I would like to subsitute those two classes with ODE 2, and Partial Differential Equations, which are both higher level courses than the algebra and analysis classes, but the guy in charge of the math department said that even higher level courses can not be subsituted for these required classes. That sure would be sweet if I could take all of those math classes I am already going to be taking and also take ODE 2 and PDE.

 

[George Jones]

As a number of posters have said, other courses are more useful for EE, but I can understand why the head of math is sticking to his guns with respect to the requirements. It's hard to imagine that someone could major it math without taking some "foundational" courses.

It comes down to how badly you want a math major on your degree.

I took both of the courses - it didn't kill me, and I didn't get a math major. I enjoyed both the courses, but one of the reasons I took math courses was because I wanted to learn about mathematics as mathematics, not just as mathematics applied to science and engineering.

Everyone is different - some people lose interest in a math course if they can't see how it is applied in the real world - or at least how it's applied in their chosen discipline .

In the end, you're the person that has to make the decision.

Regards,
George

 

[quantumdude]

I think that engineering departments should teach all of the applied math classes,

I think that would be a big mistake. Applied mathematics is a discipline that requires as much expertise as engineering. You pay the big bucks for university so that you can be taught by people who are experts in their respective fields. An expert engineer is at best an amateur when it comes to applied mathematics.

Besides, it is against the ABET code of ethics for an engineer to render any service outside his area of competence.

 

[matt grime]

It is quite clear from all this that no one course will suffice and that all courses will teach material you don't strictly need. Ultimately you have to talk to the people who teach you about this and not us. (And looking at a syllabus is no replacement for this).

I presumed you already knew linear algebra (what else do they teach in high school?), and if you don't then there's little point in trying to learn about discrete Fourier series on finite abelian groups (I recommend Terras's book on the subject to the cogniscenti here). You should probably do enough calculus to be comfortable with Fourier series, by the way, which is why analysis is recommended.

 

[Maxwell]

I presumed you already knew linear algebra (what else do they teach in high school?)

I'm pretty sure this has been discussed numerous times on this board (and perhaps mathematics boards everywhere?), but what Americans call Linear Algebra and what people in the UK call it seem to differ. Based on the American definition, Linear Algebra is not taught in high schools.

 

[Nothing000]

I am taking linear algebra right now, and I am in college. It certainly was not offered in my high school