Algebra

Algebra is a branch of mathematics that substitutes letters for numbers, and an algebraic equation represents a scale where what is done on one side of the scale is also done to the other side of the scale and the numbers act as constants.

source:
thoughtco.com

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math-drills.com

Combinatorics

Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics, from evolutionary biology to computer science, etc.

source:
en.wikipedia.org

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math.stackexchange.com

Geometry and Topology

Basically, topology is the modern version of geometry, the study of all different sorts of spaces. The thing that distinguishes different kinds of geometry from each other (including topology here as a kind of geometry) is in the kinds of transformations that are allowed before you really consider something changed.

source:
math.wayne.edu

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yumpu.com

Infinitesimal Calculus

In order to grasp the importance of this method, it must be pointed out that it was not the infinitesimal calculus itself which was of practical importance, but only the cases in which its use resulted in finite quantities. Three kinds of such problems were particularly important in the history of mathematics.

source:
encyclopediaofmath.org

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mhpbooks.com

Logic

Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics. It bears close connections to metamathematics, the foundations of mathematics, and theoretical computer science.

source:
en.wikipedia.org

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math.toronto.edu

Mathematical Analysis

Mathematical analysis. Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions. These theories are usually studied in the context of real and complex numbers and functions.

source:
en.wikipedia.org

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keywordsuggest.org

Mathematical Physics

Mathematical physics refers to the development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories".

source:
en.wikipedia.org

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4-designer.com

Number Theory

Number theory is the study of the set of positive whole numbers. 1;2;3;4;5;6;7;:::; which are often called the set of natural numbers.

source:
math.brown.edu

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math.stackexchange.com