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 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

Variables: symbols that represent unknown values or quantities
Constants: values that do not change
Equations: statements that express the equality of two mathematical expressions
Functions: relations between variables, often represented as f(x) = y
Graphs: visual representations of functions and relationships
Proofs: logical and systematic arguments to establish the truth of a mathematical statement

Addition: combining two or more numbers to get a total or sum
Subtraction: finding the difference between two numbers
Multiplication: repeated addition of a number
Division: finding the quotient of two numbers
Exponents: powers to which a number is raised (e.g. 2^3 = 8)
** Roots**: values that, when multiplied by themselves, give a specified number (e.g. √4 = 2)

** Numbers**: integers, fractions, decimals, and other numerical values
Operators: symbols used to perform mathematical operations (e.g. +, -, ×, ÷)
Parentheses: used to group expressions and clarify order of operations
Symbols: abbreviations and notation used to represent mathematical concepts (e.g. π, e, ∞)

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 and motion, 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.

Variables are symbols that represent unknown values or quantities.
Constants are values that do not change.
Equations are statements that express the equality of two mathematical expressions.
Functions are relations between variables, often represented as f(x) = y.
Graphs are visual representations of functions and relationships.
Proofs are logical and systematic arguments to establish the truth of a mathematical statement.

Addition is the process of combining two or more numbers to get a total or sum.
Subtraction is the process of finding the difference between two numbers.
Multiplication is the process of repeated addition of a number.
Division is the process of finding the quotient of two numbers.
Exponents are powers to which a number is raised (e.g. 2^3 = 8).
Roots are values that, when multiplied by themselves, give a specified number (e.g.√4 = 2).

Numbers include integers, fractions, decimals, and other numerical values.
Operators are symbols used to perform mathematical operations (e.g.+, -, ×, ÷).
Parentheses are used to group expressions and clarify order of operations.
Symbols are abbreviations and notation used to represent mathematical concepts (e.g.π, e, ∞).