Branches of Mathematics

Study Notes

Arithmetic: Study of numbers and their operations (e.g., addition, subtraction, multiplication, division)
Algebra: Study of variables and their relationships, often expressed through equations and functions
Geometry: Study of shapes, sizes, and positions of objects
Calculus: Study of change, including limits, derivatives, and integrals
Number Theory: Study of properties of integers and other whole numbers
Combinatorics: Study of counting and arranging objects in different ways
Graph Theory: Study of graphs, which are collections of nodes and edges

Addition: Combining two or more numbers to get a total or a sum
Subtraction: Finding the difference between two or more numbers
Multiplication: Repeated addition of a number
Division: Splitting a number into equal parts or groups
Exponents: Raising a number to a power to get a result
Roots: Finding the number that, when raised to a power, gives a specified value

Sets: Collections of unique objects, known as elements or members
Functions: Relations between a set of inputs (domain) and a set of possible outputs (range)
Equations: Statements that express the equality of two mathematical expressions
Inequalities: Statements that express a relationship between two mathematical expressions, such as "greater than" or "less than"
Graphs: Visual representations of relationships between variables

Euclid: Known as the "Father of Geometry" for his work in developing the field
Isaac Newton: Developed calculus and laws of motion
Archimedes: Made significant contributions to the field of mathematics, particularly in the discovery of pi
Pierre-Simon Laplace: Developed probability theory and made significant contributions to statistics

Arithmetic is the study of numbers and their operations, including addition, subtraction, multiplication, and division.
Algebra is the study of variables and their relationships, often expressed through equations and functions.
Geometry is the study of shapes, sizes, and positions of objects.
Calculus is the study of change, including limits, derivatives, and integrals.
Number Theory is the study of properties of integers and other whole numbers.
Combinatorics is the study of counting and arranging objects in different ways.
Graph Theory is the study of graphs, which are collections of nodes and edges.

Addition is the process of combining two or more numbers to get a total or a sum.
Subtraction is the process of finding the difference between two or more numbers.
Multiplication is the process of repeated addition of a number.
Division is the process of splitting a number into equal parts or groups.
Exponents involve raising a number to a power to get a result.
Roots involve finding the number that, when raised to a power, gives a specified value.

A set is a collection of unique objects, known as elements or members.
A function is a relation between a set of inputs (domain) and a set of possible outputs (range).
An equation is a statement that expresses the equality of two mathematical expressions.
An inequality is a statement that expresses a relationship between two mathematical expressions, such as "greater than" or "less than".
A graph is a visual representation of relationships between variables.

Euclid is known as the "Father of Geometry" for his work in developing the field.
Isaac Newton developed calculus and laws of motion.
Archimedes made significant contributions to the field of mathematics, particularly in the discovery of pi.
Pierre-Simon Laplace developed probability theory and made significant contributions to statistics.