Branches of Mathematics

Study Notes

Arithmetic: study of numbers and their operations (addition, subtraction, multiplication, division)
Algebra: study of variables and their relationships, often expressed through the use of symbols and equations
Geometry: study of shapes, sizes, and positions of objects
Calculus: study of change and motion, 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
Topology: study of properties of shapes and spaces that are preserved under continuous transformations

Addition: combining two or more numbers to get a total or a sum
Subtraction: finding the difference between two numbers
Multiplication: repeated addition of a number, resulting in a product
Division: sharing a quantity into equal parts or groups
Exponents: raising a number to a power, indicating repeated multiplication
Roots: finding a value that, when multiplied by itself, gives a specified number

Variables: symbols used to represent unknown values or quantities
Constants: values that do not change
Equations: statements that express the equality of two mathematical expressions
Inequalities: statements that compare two mathematical expressions using greater than, less than, or equal to
Functions: relationships between variables, often expressed as equations or graphs

Arithmetic involves 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 the use of symbols and equations.
Geometry is concerned with the study of shapes, sizes, and positions of objects.
Calculus is the study of change and motion, including limits, derivatives, and integrals.
Number Theory involves the study of properties of integers and other whole numbers.
Combinatorics is the study of counting and arranging objects in different ways.
Topology is the study of properties of shapes and spaces that are preserved under continuous transformations.

Addition is the process of combining two or more numbers to get a total or a sum.
Subtraction involves finding the difference between two numbers.
Multiplication is the repeated addition of a number, resulting in a product.
Division is the process of sharing a quantity into equal parts or groups.
Exponents involve raising a number to a power, indicating repeated multiplication.
Roots involve finding a value that, when multiplied by itself, gives a specified number.

Variables are symbols used to represent unknown values or quantities.
Constants are values that do not change.
Equations are statements that express the equality of two mathematical expressions.
Inequalities are statements that compare two mathematical expressions using greater than, less than, or equal to.
Functions are relationships between variables, often expressed as equations or graphs.