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Hardest Math Course

  1. Sep 10, 2013 #1
    What is the hardest math course or end of the line mathematics? the reason i ask is cause an PhD mechanical engineer told me he was doing it and i forgot its name but it sounded like Waisz or something like that weizs not sure.
  2. jcsd
  3. Sep 10, 2013 #2
    There is no such thing.
  4. Sep 10, 2013 #3
    Was? vas? vant? vaunt? what is the end of the line of mathematics?
  5. Sep 10, 2013 #4
    The hardest math course is the one you can't pass...
  6. Sep 10, 2013 #5
    There is no "end of the line" in mathematics, because mathematics is not a line, and because there is so much mathematics known that you can't learn it all in a lifetime. And more is being discovered every day.
  7. Sep 10, 2013 #6


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    Maybe something about Weyl, which is pronounced like the world "veil".

    At any rate it still is true that there is no such thing as an end of the line math course. He may be referring to the fact that he's taking a topics in research course, which would be end of the line in the sense that it discusses current research mathematics and therefore we don't know anything that comes "after", although as a mechanical engineer it would surprise me greatly if he was taking such a thing
  8. Sep 10, 2013 #7


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    The toughest part of mathematics is probably algebraic geometry.
  9. Sep 10, 2013 #8
    He may also have been mispronouncing a name, such as Riesz. In any case, you should ask him to clarify what he meant, as there is no end of the line for such a wide topic as mathematics. New research in every topic is published every day, many of them going on to found new areas of research: http://arxiv.org/archive/math .
  10. Sep 10, 2013 #9
    Well there is a line to be honest cause math is based on what you know previously know like a foundation. You cant do Lie Groups if you havent done single variable for instance.
    The list goes:

    1. Single Variable Analysis
    2. Linear Algebra
    3. Multivariable Analysis
    4. Signals
    *. Nummerical Analysis
    5. Vector Calculus
    6. Complex Analysis
    7. Partial Differential Equations

    What most Engineers study on Bachelor Level.
  11. Sep 10, 2013 #10
    Those courses are all fields that are relatively complete: there is little to no activity in research for those fields (excepting PDEs). If you follow the link in my previous post, you will find a list of areas of modern research activity. Each of these areas requires knowledge of everything an undergraduate curriculum would cover plus many graduate courses and personal research projects. The courses you list may be considered to be the trunk of a tree: real mathematics occurs in the branches far above. They interlink in non-trivial ways: many subtopics of those areas can be studied without recourse to other areas while other subtopics require knowledge from several parallel areas, due to many theorems being based on connecting previously unrelated topics.
  12. Sep 10, 2013 #11
    "Signals" is not an area of math, and is certainly not a prerequisite for vector calculus (which is not a prerequisite for complex analysis, which is not required for PDE's).

    A partial order is not a linear order. The fact that some subjects have prerequisites does not imply that mathematics can somehow be ordered into a linear sequence. There is no "terminal" mathematics; mathematics is a collection of diverse subfields that frequently interact in one way or another. You either misunderstood your friend, or your friend doesn't know what he's talking about (If there were a "hardest math", you certainly wouldn't find an engineer anywhere near it).
  13. Sep 10, 2013 #12
    Sounds like you're asking what is the math course that requires knowledge of all other previous math courses. There really is no such thing because all math courses depend on each other in some basic way... and they overlap each other. But since Algebra is the foundation to all mathematics and people make more math errors in their algebra... I'd say algebra is the hardest math course.
  14. Sep 11, 2013 #13
    Probably triple integrals.
  15. Sep 11, 2013 #14
    Signals and generalized functions. Fourier series. Fourier Transform of continuous-time signals. Sampling of continuous-time signals. LTI-system. Laplace transforms. Existence and unicity of solutions of ODEs and system of ODEs.

    Methods to solve linear and separable ODEs of order 1 and for systems with constant coefficients.
  16. Sep 11, 2013 #15


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    I would think of mathematics more as a branching tree than a line. Once you've learned calculus there are dozens of new areas you can now study, and each one of these leads to many more. The leaves at the end of the tree are the current areas of research, but the tree keeps growing as new fields of study are added. As someone else said, the tree is already so complex that nobody can learn it all.
  17. Sep 11, 2013 #16


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    So Fourier Analysis?
  18. Sep 11, 2013 #17
    I don't want to brag, but I absolutely sailed through my math courses until we got to long division.

    But seriously, if you look at the website of almost any major university, you will see that the math department has its majors take core courses, and then lets them specialize in an area of their choice. So as almost everyone else has said, there is no one path, and no consensus on the "hardest course."
    Last edited: Sep 11, 2013
  19. Sep 11, 2013 #18

    jim mcnamara

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    David Hilbert (1862-1943)was often cited by colleagues as the last mathematician to fully understand all of the branches of mathematics at the turn of century - 1900. Now it is considered impossible for one person to do that.

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