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Logic vs Proofs for Physics

  1. Jan 2, 2015 #1
    I know that I have already posted a couple of threads like this one (albeit dealing with different courses), but I have had excellent responses here, and I was hoping I could get a couple more. I know that it is best to speak to academic advisors and professors, but there are only a couple that I can speak to at my school, and I have done so. Their advice has been useful, but I would still love to hear fro people who have taken physics at an upper-year level to solidify the decision.

    Last semester I was enrolled in computer science and took a discrete mathematics course that included basic proofs and logic. In the course, I was introduced simple proofs, proofs by induction, things like the pigeonhole principle and structural induction, basic propositional logic and predicate logic. The course, as a computer science course, was more focused on solving problems than proofs, but the professor comes from a mathematics background and she proved everything, in full, during class. As a result of having such an excellent professor, I feel very comfortable with all of these things, although more so with the logic than the proofs.

    I have to choose this semester between a proofs course taught via the mathematics department that will cover similar things to the ones above, albeit in more depth, or a computer science logic course that will go in to logic in much greater depth. Behind the decision lies the fact that I am hoping to complete a degree in physics (probably with a comp. sci. minor), where the computer science course can be used toward the minor, but is not a requirement for the minor. Additionally, it is taught by a superb professor (the same one who taught the other proofs/logic course I took). The proofs course is taught by a professor with a good reputation, although I haven't had one of his courses.

    What I am really unsure of, and what is of the most importance to me, is whether one of the topics is going to be more useful in a physics degree than the other. I recognize that proofs are less central to physics than they are to mathematics, but obviously if I am going to be taking some upper year applied mathematics courses, the proofs will be useful, particularly for more advanced linear algebra (intro. linear algebra is a prerequisite for the proofs course). I don't know how important logic at this level is for a physics degree. Is it more important to have the basic propositional/predicate stuff, or should I delve more deeply into things like predicate calculus?

    Here is the description of the proofs course:

    "Primarily for students interested in pursuing a degree in one of the mathematical sciences. Logic, set theory, relations, functions and operations, careful study of the integers, discussion of the real and complex numbers, polynomials, and infinite sets."

    Here is the logic course description:

    "Propositional and predicate logic; representing static and dynamic properties of real-world systems; logic as a tool for representation, reasoning and calculation; logic and programming."

    I was hoping that some of the excellent advisors out there with experience at the upper levels of physics will have a feeling as to which one is of more direct use. Any advice you can offer, as always, is greatly appreciated.
     
  2. jcsd
  3. Jan 2, 2015 #2

    micromass

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    To be honest, it doesn't matter at all. Both courses won't be essential at all for a physics degree.
    Furthermore, you already had a proof course (although at a CS level), so what's the use of doing another one? Can't you do some course that'll be actually useful for physics, such as linear algebra?

    If you have to choose between the two, then I recommend the proofs course, since it contains relatively more useful stuff than the logic things.
     
  4. Jan 2, 2015 #3
    Thanks, micromass. I have taken a first-year linear algebra course, and I would definitely take the second linear algebra instead if possible, but I don't have one of the prerequisites for the linear algebra course offered via the Applied Mathematics Department that was recommended above a pure math variant of linear algebra in another thread. I could take the pure math second course in linear algebra, but it would still leave me with the same problem, as I would have to replace one of my current courses and the time slot where the proofs and logic courses fit would still need filling.

    I am with you on finding a course that is actually useful, but the way my prerequisites and the timetable work out, it is a problem. I am sort of straddling both the first and second years (with some areas in third year) because of a previous degree, which has created all sorts of headaches in timetabling. Unfortunately, the straddling of first- and second-year also causes problems because some of the courses I would be able to take are in the same time slot because most students would be unable to take both. My physics advisor tried to help me find classes and we couldn't come up with much that would work. In the end his recommendation was to take classes with good professors if you can't find courses that are specific to the degree. It seems like good advice to me.

    Are there any other areas you would recommend to look in? I have tried searching in chemistry, biology and a few humanities departments, like the philosophy of science. It may be a case of just taking a class to fill out the timetable as opposed to one that will work.

    I appreciate your advice, and I will plan on taking the proofs course unless I somehow manage to find something that works better. Although, as detailed in another thread on scientific writing, I have been combing the academic calendar for a couple of weeks now without a whole lot of success.
     
    Last edited: Jan 2, 2015
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