Introduction to Mathematics

• Mathematics is the study of numbers, quantity, space, patterns, structure, and change.
• It is an abstract science which uses logical reasoning to draw conclusions.
• Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, finance, and social sciences.

Core Areas of Mathematics

• Arithmetic involves basic operations on numbers like addition, subtraction, multiplication, and division.
• Algebra generalizes arithmetic by using variables to represent numbers, allowing for the formulation of equations and relationships.
• Geometry deals with the study of shapes, sizes, properties of space, and dimensions.
• Calculus studies continuous change and motion, and includes topics such as limits, derivatives, integrals, and functions.
• Trigonometry focuses on relationships between angles and sides of triangles.
• Statistics concerns the collection, analysis, interpretation, presentation, and organization of data.
• Probability is the measure of the likelihood that an event will occur.
• Logic encompasses the principles of valid reasoning and inference.
• Number Theory deals with properties and relationships of numbers, especially integers.
• Topology studies properties of geometric objects that are preserved under continuous deformations.
• Discrete Mathematics involves the study of mathematical structures that are fundamentally discrete rather than continuous.

Key Mathematical Concepts

• Axioms are fundamental assumptions that are taken to be true without proof, serving as the starting point for deducing other truths.
• Theorems are proven statements based on axioms and previously established theorems.
• Proofs are logical arguments that demonstrate the truth of a statement.
• Sets are well-defined collections of distinct objects, considered as an object in its own right.
• Functions are relationships between sets that assign to each element of one set exactly one element of another set.
• Algorithms are step-by-step procedures for solving problems.
• Models are mathematical representations of real-world phenomena.

Branches of Mathematics

• Pure Mathematics focuses on the study of mathematical concepts for their own sake.
• Applied Mathematics concerns the use of mathematical methods to solve real-world problems.

Explore the core areas of mathematics, including arithmetic, algebra, geometry, and calculus. Learn how math is an abstract science using logical reasoning to draw conclusions. Discover its application in various fields like natural science, engineering and finance.