What are the major branches of math?

I am interested in gaining a complete knowledge of math. What are the major branches that I need to pursue?

5 Answers

  • 10 years ago
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  • 10 years ago

    Well they are all major,because they all have their main points and purpose in them so for example in a maths test it might be a mixed test sheet and for example the student doing the test only knows measurement, the student will do good in the measurement section but might be stuck with maybe fractions.But if you are interested in the main parts of maths then just do all of them you don't have to be a pro at the different sections in maths just know how to do the questions but if you want to have a complete knowledge of maths then you should have more then a rough idea of maths in your mind.

    Hope this helps and good luck as well =].

    Source(s): Friends and family and teachers.
  • 10 years ago

    At what level? In what discipline?

    At the advanced undergraduate/graduate level, they are (more or less):

    Pure Math (these are pretty solid - if you go to graduate school for pure math, these are the core topics that you MUST know):

    Analysis (Real and Complex)


    Algebra (as in Abstract Algebra)

    Maybe throw in Number Theory as well, though it's mostly a hodge-podge of algebra and analysis.

    Then there are hybrids of each, such as algebraic topology/geometry, analytic number theory, etc.

    Applied Math is a little sketchier - it's more difficult to define them all, but some of the staples are:

    Differential Equations (to include Dynamics/Fluids)

    Numerical Analysis

  • rager
    Lv 4
    4 years ago

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  • 10 years ago

    As a student of mathematics, I will tell you what I know.

    In the grade school levels, we teach what is described as arithmetic, that is, the process of addition, multiplication, and their inverses.

    By extension, students are taught algebra, the relation of arithmetic to algebraic expressions, functions, and variables.

    Then there is geometry, the study of which the Greeks were interested in, that is, the study of figures, forms, lines, areas, and spaces.

    Trigonometry is an extension of geometry, whereupon geometric functions such as the sines of triangles are related to algebra and studied in their application to what is known. Analytic geometry, perhaps taught as part of the geometry curriculum, ties the link between algebra, geometry, and trigonometry (I will note here that the Greeks dealt with geometry without notion of algebra or variables in the modern sense).

    Beyond this there is calculus, which deals further with functions and with limits of expressions and functions, derivatives, and integrals.

    Discrete mathematics furthermore consists the further study of functions, equivalence relations, graph theory, set theory, and other branches of mathematics.

    Beyond this there is modern algebra, which seeks to verify and extend our algebraic systems rigorously and logically, and analysis, which seeks to treat the properties of real and complex numbers rigorously and systematically in order to prove the theorems that are considered fundamental to other branches of mathematical study.

    There is also number theory, which deals largely with the properties of integers and prime numbers, linear algebra which deals with vectors and matrices, topology, statistics, probability, and presumably many graduate-level mathematics courses about which I know relatively nothing.

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