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Applications of modern algebra

  1. Mar 23, 2006 #1
    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?
     
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  3. Mar 23, 2006 #2
    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??
     
  4. Mar 23, 2006 #3
    I thought that abstract algebra was the same thing as "modern" algebra.
     
  5. Mar 23, 2006 #4
    Are you currently taking modern algebra stunner? And if so have you not been told how it can be applied?
     
  6. Mar 23, 2006 #5

    berkeman

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    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.
     
  7. Mar 23, 2006 #6

    George Jones

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    It is used, but I think only for very specialized applications. About 10 years ago, I knew a grad student who had this guy as an advisor, and he used this stuff for chip design.

    Regards,
    George
     
  8. Mar 23, 2006 #7

    George Jones

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    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
     
  9. Mar 23, 2006 #8

    mathwonk

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    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.:smile:
     
    Last edited: Mar 23, 2006
  10. Mar 23, 2006 #9

    matt grime

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    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.
     
  11. Mar 23, 2006 #10
    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.
     
  12. Mar 25, 2006 #11
    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.
     
  13. Mar 25, 2006 #12
    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.
     
  14. Mar 25, 2006 #13
    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.
     
  15. Mar 25, 2006 #14
    yeah i have seen my electrical mates doing lot of fourier stuff but whatd do you mean by first..:confused:
     
  16. Mar 25, 2006 #15

    matt grime

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    '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.
     
  17. Mar 25, 2006 #16
    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.
     
  18. Mar 25, 2006 #17

    mathwonk

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    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.
     
  19. Mar 25, 2006 #18
    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.
     
  20. Mar 25, 2006 #19
    Then Modern (Abstract) Algebra and Analysis are the last classes you want to take.
     
  21. Mar 26, 2006 #20
    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?)
     
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