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I hope to apply graduate math department for MS/PhD in math. My area of interest are discrete math, combinatorics, graph theory... etc.Now I have few questions :

  1. Which are the prerequisites for these courses ? and Which grade of my undergraduate are more important ?
  2. I am also a bit confused that whether I will apply for a pure or applied dept ?
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    What country are you in? What country do you want to do your PhD in?
    – astronat
    Dec 28 '20 at 11:32
  • 1. Usually the prequisites are listed in the syllabus. 2. You should find out the exact degree on the university website.
    – stephanmg
    Dec 28 '20 at 11:37
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  • Can you talk with a local prof about that?
    – user111388
    Dec 28 '20 at 13:11
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    Combinatorics is an area where there are both very applied programs (in particular look at programs in "Combinatorics and Optimization" or "Algorithms, Combinatorics, and Optimization") and programs where combinatorics is studied as pure mathematics. Dec 29 '20 at 0:22
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This is a US centric answer. If you are applying to a mathematics doctoral program in the US and have a mathematics undergraduate degree then the specialty you want to pursue isn't especially important. First, a broad based undergraduate degree has what you need to get started in a US doctoral program. If your undergraduate degree is other than math, you have a more complicated situation, but admission is still possible if you have, in general, "enough" math.

But one reason that this is the case is that such programs start out heavy in coursework, so if you need more combinatorics, for example, you will be able to get it before starting research.

The prerequisites you need for research are probably at the discretion of the advisor you will (later) choose to guide you. They may have some specific suggestions.

The one thing you might need to consider, however, is whether the pure and applied math specialties are contained within a single department or split between departments. Some splitting is common, as having statistics (different example, I know) separate from math. If pure an applied are in a single department, then you don't need to make a selection before applying, and you may be able to delay that decision for a year or two while you take some courses and learn more about possible advisors.

In other countries the situation might be drastically different, of course, with more expected on entry but a shorter time-frame for getting the degree.

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Be aware that in some universities, discrete mathematics might happen in the computer science departments, e g at ETH Zürich.

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