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Courses The math level of computer scientists and physicists

  1. Dec 7, 2017 #1
    I am wondering, what is the math level of your average CS or physics major? Like how much math do these two take beyond stuff like the Calculus sequence, differential equations and linear algebra?

    I was having a discussion with one of my old math professors from my community college (I'm in a four year university by the way) about my major in the STEM field. I asked her about how much math do computer scientists and physicists take compared to a mathematician. She told me that the only important math classes that those two majors need are differential equations and linear algebra, and discrete math for CS majors (which I understand). She tells me that all those math classes (Calculus, Diffy Q, Algebra) are all baby stuff and that real mathematicians take/use Analysis, Abstract Algebra, Topology, etc and you won't be seeing CS or physics majors using abstract algebra or any other high level math course (complex analysis may be of some importance to physics majors). Linear Algebra is probably closer to what pure mathematicians do since its not just about matrices and eigenvalues, but proving abstract theorems if they are true or exist, she told me and I have taken a linear algebra class before so I understand.

    But i'd imagine that some CS and physics majors take more higher level math courses. I think some CS majors who take advanced math courses take more purer math courses as they deal with logic and some physics majors take more applied math courses like probability or partial diffy-q, is that right?

    Also, how important would abstract algebra be to a CS major? I've always wondered if that would be more important than say discrete math, which most CS majors take, and discrete math is very logical and proof based, just like abstract algebra.
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  3. Dec 7, 2017 #2


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    She gave you the straight answer. Of course you can always find someone myself included who has taken some pure math courses. However while I enjoyed struggling through them, I’ve never had to use them to do my job.

    If you’re programming visual things or doing computer simulation work or even game programming then you might use vector algebra and rotational matrices or even real or complex analysis but again the pure math topics are not used.

    One exception might be number theory and elliptical functions ...in computer based cryptanalysis though.
  4. Dec 8, 2017 #3
    I know someone who is about to get their PHD in physics, and the person's area is Group Theory. This person can pass as a mathematician. I think it depends how theoretical you get into CS/Physics.
  5. Dec 8, 2017 #4
    Physicists typically know more math/understand the math more deeply than CS majors since they are more likely apply it to reality, but know less discrete math and algorithms, since their training does not typically include it.

    Goofy math like topology, real analysis, abstract algebra etc are basically just academic subjects that exist for fairly contrived, formal reasons. Occasionally academics looking to get their jollies off will "apply" them to problems in physics, but usually with inscrutable or irrelevant consequences.
  6. Dec 8, 2017 #5
    As I stated before, I'd imagine that computer scientists know more of the abstract kinds of math that deal with logic and algorithms while physicists know more of the applied math topics that apply to everyday phenomenon. Those pure math courses (real analysis, abstract algebra, topology) seem like they would be relevant to say, a theoretical computer scientist (I would also like to add number theory, and data structures). While for a theoretical physicists, the advanced math courses that would seem relevant to them are (complex analysis, partial differential equations, probability, fourier analysis, etc), and these courses fall into the more applied math (save for complex analysis). But I really don't know. All I know is that physicists use math to model physical and natural phenomenon, and computer scientists use math to understand and solve algorithms, make use of logic, computer graphics and all. So I think both are equally adept at using math.
  7. Dec 8, 2017 #6
    The number of computer scientists with familiarity in topology, real analysis, and abstract algebra is a minuscule minority. In fact, even though they are a minority, there are probably more physicists who know about such things.

    As far as mathematical aptitude, computer scientists in general are trained with significantly less 19th century math than physicists, and focus more on algorithms. I was once in an interdisciplinary computational biology program and the computer science students often hadn't even seen calculus since they took it as first years. Instead they were more interested in data structures and algorithms, which I guess you can call a different branch of math.

    Both groups are skilled in different mathematical disciplines.
  8. Dec 8, 2017 #7
    Just a note on your terminology, the title of computer scientist or physicist or mathematician almost always implies a PhD in the subject. When you say physics major or math major, that means someone with an undergraduate level of education. It's a bit confusing when you keep switching between the two because they don't usually refer to the same group. It will help just generate more consistent responses by making it clear.

    As far as I know, for physics majors (undergraduates) the calc sequence, diff eq, and matrix/linear algebra are usually what's required for the degree and so I imagine that's where the average is. You get some exposure to more specialized topics in the mathematical methods course (using Boas's book for example) and obviously as it comes up in your work, but that's the extent of the full on math courses.

    In my experience, however, a number of physics majors, including myself, also tacked on math minors, which only meant taking a few more courses. Of those, PDEs, ODE II, and probability were probably the most popular.
  9. Dec 8, 2017 #8
    Statistics is an important course from computer scientists. You need to be able to analyze and understand very large amounts of data, so you have to be good at modeling them.
  10. Dec 8, 2017 #9


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    CS and physics of the future are way too broad to give such specific answers. With quantum computers, theorem provers, code breakers, data mining, medical imaging, robotics, artificial intelligence, etc., there is a tremendous amount happening in the next several decades. To put a limit on the amount of math required would be wrong.
  11. Dec 8, 2017 #10


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    I also want to add that although in CS, Calculus, (some) Linear Algebra and Discrete Math is what is basically required, this does not tell the whole story about the complexity - especially in discrete math, that any CS major will have to deal with - particularly if he/she follows Theoretical CS. A quite demonstrative and important example is Analytic Combinatorics - (the link is to the reference book of 2009 by the leaders in the field, Philippe Flajolet and Robert Sedgewick, legally available for research purposes (non-commercial single-use)), which enables precise quantitative predictions of the properties of large combinatorial structures. Quoted from the preface of the book

    It is quite obvious that it is far more involved than the usual Calculus and discrete math that we use in Algorithms.

    As already mentioned by jedishrfu, there is also nothing to stop you from taking pure math courses (I personally took Topology and Functional Analysis and a more thorough treatment of Linear Algebra). Besides the obvious beauty of taking more abstract math, in the long run, it will pay off in various even non-obvious ways.
  12. Dec 8, 2017 #11
    What about for computer scientists? As far as I have seen in a few colleges with different requirements, it seems that discrete math is the only required math course. Some colleges I've looked at also require students to take Linear Algebra (especially those specializing in graphics) and two semesters of Calculus.

    I was just thinking, would an upper level math course like abstract algebra be any use to a CS major, that is if CS majors decided to take additional math courses? My old professor mentioned complex analysis being of important to Physicists, that is of course of some physics majors take additional math courses? I'd imagine that if CS and physics majors decided to take upper level math courses, CS majors would tend to take purer math courses while physicists would tend to take more applied math courses, though applied math courses like probability and statistics are also important to CS majors.
  13. Dec 8, 2017 #12


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    I can't imagine a person actively doing physics on a job who does not know complex analysis fairly well. Same with differential equations. And statistics is fundamental for any experimental work.
  14. Dec 8, 2017 #13
    I don't know why I think purer math is more important for CS majors while applied math is more important for Physics majors. Only because for CS, you need to be able to do logic and think logically and be able to do proofs (but then again, i'm not a CS major, nor have I taken discrete math, but I have taken a mathematical proof workshop class), while for physics majors, they have to apply the math they learned in order to describe and model some natural phenomenon, so proving stuff is something most physicists won't even bother doing.
  15. Dec 10, 2017 #14


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    For the more advanced math, you will generally learn it as you need it during physics courses. For example, if you take quantum you will learn some things about group theory (relevant for discussing things like spin or symmetries), if you take general relativity you will learn about different geometry, etc.

    Abstract algebra is relevant to many areas in physics. It is essential to understand groups when learning about symmetries in quantum mechanics (which are very profound), spin, crystal structures, molecules in chemistry, and many other things. It also has applications in computer science like cryptography (I’m sure there are many others). Number theory is of course very related to group theory.

    Topology is relevant when studying things like defects and vortices, I think this may apply to some areas of fluid mechanics (you probably wouldn’t see that in undergrad.
  16. Dec 11, 2017 #15
    I don't know most of the material taught in most undergrad courses in complex analysis, only the stuff picked up along the way in diff eq and quantum mechanics courses. And most of the experimentalists I've known in my career are in the same boat.
  17. Dec 11, 2017 #16
    There are people assuming that the typical physicist is a theorist, which is probably false. Experimentalists are the largest category, and their knowledge base is not the same.
  18. Dec 11, 2017 #17


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    @Crass_Oscillator , when you talk about computer scientists, are you referring only to those who complete a BS in the field, or are you taking into account those who are pursuing a PhD program? Because whether or not computer scientists are familiar with fields like topology, real analysis, and abstract algebra will vary greatly between these two answers.

    There are fields of research within computer science (e.g. theoretical computer science, machine learning, numerical analysis, etc.) that are very heavy users of mathematics and most people I know who are specializing in these areas have very advanced mathematical expertise, including strong familiarity in topology, real analysis, algebra, etc. (in fact, the majority of people who are pursuing grad studies in these fields often have a double major in computer science and math). There are other people who are more like the students you encountered, where the level of math background is less stringent.

    So we need to be careful on not lumping all computer science students in the same bucket.
  19. Dec 12, 2017 #18
    This is wrong. First of all, physicists need to be knowledgeable in complex analysis, differential equations, Fourier analysis, even stuff like topology or group theory. This is certainly not less pure than the stuff a CS focuses on, which is mainly discrete mathematics.
    Secondly, if you are a theorist, you need to be proficient in proving statements because otherwise you would not be able to derive new mathematical models of nature. At least you need to be able to see the validity of the statements in a model which can't be done if you can't even see at which point mathematically simplifying assumptions had been made.

    In my country, Germany, a major in physics contains more maths than CS on average.
  20. Dec 12, 2017 #19


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    I agree. So much of this mathematics was developed by physicists, for physicists. It's hard to imagine a physicist doing much without a working knowledge of it.

    That being said, @Dr. Courtney points out that it can be learned "as needed" and that a math class may include a great deal that is not as useful. I think it depends on how much a person can learn on his own, without a class. And if there are courses for physicists, that would be ideal.
  21. Dec 12, 2017 #20
    I was at a grad school with a fancy machine learning department and my experience was that the student's backgrounds varied widely, and I would not say that the majority of them had backgrounds in goofy bourgeois math ala topology or real analysis, although real analysis was probably the most ubiquitous form of mathematics sourced from the math department that wasn't applied. In fact, I was often the only one with such experience, and I was in applications (computational biology) not theory. I did not overlap much with the theoretical CS people so I can't judge them.

    In your defense however, there is a very strong trend for machine learning students to develop more mathematical rigor and delve into such topics, more than I've seen in physics departments. The difference is between rigor and novel mathematical expressivity. Theory students in physics still, thankfully, see little use for mathematical rigor, but are more obsessed with mathematical novelty ("How can I apply academic math to a problem whether the problem calls for it or not, since I like convoluted academic math?") whereas my impression of CS students is that it was more about rigor ("How can I foist mathematical rigor on the algorithm, the irrelevance of mathematical rigor to successful techniques such as Nelder-Mead optimization or convolutional neural networks notwithstanding?").

    Suffice it to say, whichever department you ask about, having experienced both, they spend too much time on the wrong math, but in different ways, so I became an engineer.*

    *At least that's what I tell myself regarding why I became an engineer.
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