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Mathematics (Foundations (Theoretical Computer Science (Computability…
Mathematics
Foundations
Category Theory
deals in an abstract way with mathematical structures and relationships between them :
Theoretical Computer Science
Computability Theory
examines the limitations of various theoretical models of the computer, including the most well-known model – the Turing machine
Complexity Theory
study of tractability by computer; some problems, although theoretically solvable by a computer, are so expensive in terms of time or space that solving them is likely to remain practically unfeasible, even with the rapid advancement of computer hardware
Information Theory
concerned with the amount of data that can be stored on a given medium, and hence deals with concepts such as compression and entropy.
Mathematical Logic
includes the mathematical study of logic and the applications of formal logic to other areas of mathematics
Set Theory
studies sets or collections of objects
Pure Mathematics
Space
Trigonometry
deals with the study of relationships of lengths and angles of triangles.
Geometry
is the study of figures such as shapes and how they interact with each other
Differential Geometry
deals with the study of curves, surfaces, and manifolds.
Topology
refers to the properties of space through deforming.
Fractal Geometry
deals with the study of fractals.
Fractals
are objects that are used to describe naturally occurring events
Measure Theory
deals with the study of measure.
Measure
is a systematic way to assign a number to each suitable subset of that set
Structure
Combinatorics
deals with combinations of objects belonging to a finite set in accordance with certain constraints
Number Theory
deals with the study of positive integers.
Algebra
is the study of mathematical symbols and letters as variables for numbers
Group Theory
deals with the study of groups.
Groups
consist of a set of elements equipped with an operation that combines any two elements to form a third element and must satisfy the following axioms.
Associative Property
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Identity Property
Closure Property
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Inverse Property
Graph Theory
deals with the study of graphs.
Graphs
are mathematical structures used to describe relations between objects
Order Theory
investigates the intuitive notion of order using binary relations
Quantity
Arithmetic
is the study of numbers, and its operations.
Numbers
are objects that make most of mathematics and related topics.
Whole Numbers
0,1,2,3
Integers
-2, -1, 0, 1, 2
Irrational Numbers
sqrt(3), pi, 0.10010001...
Rational Numbers
-3, 1/3, 1.23
Real Numbers
-4(3.14), sqrt(2), e
Imaginary Numbers
sqrt(-1)
Complex Numbers
a+bi
Natural Numbers
1, 2, 3, 4, 5
Operations
are calculations from input values that result into an output value.
Addition
Subtraction
Multiplication
Division
Applied Mathematics
