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overview-of-mathematics.md

Mathematical symbols and equations arranged in a complex pattern Overview of Mathematics

Tapestry of Mathematics

Mathematical symbols and equations arranged in a complex pattern

Introduction

Mathematics is the abstract study of topics encompassing quantity, structure, change, and space. Far from being solely a collection of numbers and equations, mathematics serves as the foundation for nearly all scientific and technological endeavors.

The Language of the Universe

Some have described mathematics as the "language of the universe," capturing the underlying patterns and relationships that govern natural phenomena. For a deeper look into this concept, read mathematics-as-universal-language.md.

Arithmetic and Number Theory

Arithmetic is often our first exposure to mathematics, focusing on basic operations like addition and subtraction. Number theory extends these concepts, exploring the properties and relationships of numbers, especially integers. Learn more in arithmetic-and-number-theory.md.

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A displacement graph tracking the erratic movement of a squirrel in a dog's field of vision. Squirrel kinematics!

Algebra

Algebra provides the means to generalize arithmetic, allowing us to manipulate mathematical symbols rather than specific numbers. This extends to solving equations and understanding mathematical structures. For a detailed view, consult overview-of-algebra.md.

Geometry

Geometry involves the study of shapes, sizes, and the properties of space. The subject can range from elementary topics, such as the study of circles, to more complex fields like topology. Read more at overview-of-geometry.md.

Calculus

Calculus is the mathematical study of continuous change. It is divided into differential calculus, which concerns rates of change and slopes, and integral calculus, concerned with areas and accumulation. To explore further, see overview-of-calculus.md.

Elements of Calculus

Graphs and equations representing calculus concepts

Statistics and Probability

Statistics is the study of data: how to collect, summarize, and interpret it. Probability theory provides the theoretical foundation for statistics, allowing us to understand and quantify uncertainty. For more details, refer to statistics-and-probability.md.

Discrete Mathematics

Discrete mathematics deals with mathematical structures that are fundamentally discrete, as opposed to continuous. This includes subjects like graph theory, combinatorics, and number theory. Learn more by visiting overview-of-discrete-mathematics.md.

Applied Mathematics

Applied mathematics concerns the application of mathematics to solve problems in other fields like physics, engineering, economics, and biology. For a deeper understanding, consult overview-of-applied-mathematics.md.

The Future of Mathematics

As we make advancements in technology and our understanding of the world, new areas of mathematics continue to emerge. Whether it's in data science, cryptography, or machine learning, the role of mathematics is ever-expanding. For a glimpse into the future, see future-of-mathematics.md.

Conclusion

Mathematics is a rich and diverse field that provides the tools necessary for understanding and shaping the world around us. Its utility spans multiple disciplines, offering endless avenues for exploration and discovery.

Intricacies of Mathematics

A maze composed of mathematical symbols, representing the complexities and intricacies of the subject