Mathematics Branches

Study Notes

Arithmetic: Study of numbers and their operations (e.g. addition, subtraction, multiplication, division)
Algebra: Study of variables and their relationships (e.g. equations, functions, graphing)
Geometry: Study of shapes, sizes, and positions of objects (e.g. points, lines, angles, solids)
Calculus: Study of change and motion (e.g. limits, derivatives, integrals)
Number Theory: Study of properties of integers and other whole numbers (e.g. prime numbers, congruences)
Combinatorics: Study of counting and arranging objects in different ways (e.g. permutations, combinations)
Topology: Study of properties of shapes and spaces that are preserved under continuous deformations (e.g. connectedness, compactness)

Sets: Collections of unique objects, used to define mathematical structures and operations
Functions: Relations between sets, where each input corresponds to exactly one output
Proofs: Logical arguments used to establish the truth of mathematical statements
Axioms: Self-evident truths used as the foundation for mathematical theories
Theorems: Mathematical statements proven to be true using axioms and previously proven theorems

Addition: Combining two or more numbers to get a total or sum
Subtraction: Finding the difference between two numbers
Multiplication: Repeating a number a certain number of times to get a product
Division: Splitting a number into equal parts or groups
Exponents: Raising a number to a power, indicating repeated multiplication
Roots: Finding the number that, when multiplied by itself, gives a specified value

Euclid: Ancient Greek mathematician who wrote the "Elements," one of the most influential works in the history of mathematics
Isaac Newton: English mathematician and physicist who developed calculus and laws of motion
Archimedes: Ancient Greek mathematician and engineer who made significant contributions to the field of geometry
Pierre-Simon Laplace: French mathematician who developed probability theory and celestial mechanics
Georg Cantor: German mathematician who developed set theory and introduced the concept of infinity

Arithmetic studies numbers and their operations, including addition, subtraction, multiplication, and division.
Algebra focuses on variables and their relationships, including equations, functions, and graphing.
Geometry examines shapes, sizes, and positions of objects, including points, lines, angles, and solids.
Calculus explores change and motion, including limits, derivatives, and integrals.
Number Theory investigates properties of integers and other whole numbers, including prime numbers and congruences.
Combinatorics deals with counting and arranging objects in different ways, including permutations and combinations.
Topology studies properties of shapes and spaces preserved under continuous deformations, including connectedness and compactness.

A set is a collection of unique objects used to define mathematical structures and operations.
A function is a relation between sets, where each input corresponds to exactly one output.
Proofs are logical arguments used to establish the truth of mathematical statements.
Axioms are self-evident truths used as the foundation for mathematical theories.
Theorems are mathematical statements proven to be true using axioms and previously proven theorems.

Addition combines two or more numbers to get a total or sum.
Subtraction finds the difference between two numbers.
Multiplication repeats a number a certain number of times to get a product.
Division splits a number into equal parts or groups.
Exponents raise a number to a power, indicating repeated multiplication.
Roots find the number that, when multiplied by itself, gives a specified value.

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