Lists of mathematics topics facts for kids
This page is like a big map of all the different topics in mathematics! It helps you explore the amazing world of numbers, shapes, and patterns. Some parts of this map lead to hundreds of articles, while others might only have a few. Think of it as a guide to help you find your way around math.
These lists cover everything from basic math you learn in school to more advanced ideas. They include different ways to solve problems, important math rules, and even famous mathematicians. You'll find topics about numbers, shapes, and how math is used in the real world.
Contents
Basic Math Skills
This section covers the math you usually learn in middle school or early high school. It's the foundation for everything else!
- Arithmetic: This is about adding, subtracting, multiplying, and dividing numbers.
- Discrete Mathematics: This deals with things that can be counted, like whole numbers or specific items in a list.
- Calculus: This is a powerful tool for understanding how things change, like speed or growth.
- Geometry: This is the study of shapes, sizes, positions, and properties of space.
- Geometry Basics: A simple overview of geometry.
- Trigonometry: This part of geometry focuses on triangles and angles.
- Trigonometry Basics: An overview of trigonometry.
- Trigonometric Rules: Important formulas for trigonometry.
- Logarithms: These are like the opposite of exponents, helping us solve for powers.
- Logarithm Integrals: Advanced rules for logarithms.
- Sets: This is about groups of objects or numbers.
- Logic: This helps us understand how to reason and prove things in math.
Exploring Advanced Math Areas
Math gets even more exciting when you dive into advanced topics! We can divide these into "pure" math (focused on ideas) and "applied" math (focused on real-world uses), but they often mix together.
Pure Mathematics
Pure mathematics is about understanding math for its own sake. It's like exploring new ideas and discovering hidden patterns.
What is Algebra?
Algebra is a part of math where you use letters (like x or y) to stand for numbers. It helps you solve puzzles and understand how different things relate to each other. It also studies special structures made of sets and operations.
- Algebra Basics: A simple guide to algebra.
- Abstract Algebra: This explores more complex algebraic structures.
- Algebraic Structures: Different types of math systems with rules.
- Boolean Algebra: Used in computer science and logic.
- Linear Algebra: Deals with lines, planes, and spaces, often used in computer graphics.
Geometry and Topology Fun
Geometry starts with studying shapes like circles and cubes. But it gets much bigger! Topology is like a super-flexible geometry. It looks at properties of shapes that don't change even if you stretch, bend, or twist them (but not tear them!). For example, a donut and a coffee cup are the same in topology!
- Algebraic Geometry: Combines algebra and geometry.
- Algebraic Topology: Uses algebra to study shapes.
- Circle Facts: Everything about circles.
- All About Pi: The famous number related to circles.
- Cool Curves: Different types of lines and curves.
- Differential Geometry: Studies smooth shapes and spaces.
- General Topology: The basic ideas of topology.
- Geometric Shapes: A list of different shapes.
- Knot Theory: The math of knots and how they can be untangled (or not!).
- Topology Topics: More about how shapes can be deformed.
- Types of Topologies: Different ways to define "closeness" in spaces.
- Triangle Facts: Everything about triangles.
Combinatorics: The Art of Counting
Combinatorics is all about counting and arranging things, especially when there are many possibilities. It helps us figure out how many ways something can happen or how to organize things efficiently.
- Combinatorics Basics: An overview of counting and arranging.
- Graph Theory: Studies networks of points and lines, like social networks or road maps.
Logic: The Rules of Thinking
Logic is the foundation of all mathematics. It's about figuring out what makes an argument valid and what a mathematical proof really is. It helps us think clearly and solve problems step-by-step.
- Boolean Logic: Used in computers and true/false statements.
- Mathematical Logic: The study of reasoning in math.
- Set Theory: The study of collections of objects.
Number Theory: The Queen of Math
Number theory is a special part of math that focuses on whole numbers, especially prime numbers. Primes are numbers that can only be divided by 1 and themselves (like 2, 3, 5, 7). There are many mysteries about prime numbers that mathematicians are still trying to solve!
- Algebraic Number Theory: Combines number theory with algebra.
- Number Theory Topics: More about numbers and their properties.
- Prime Numbers: A list of different kinds of prime numbers.
Applied Mathematics
Applied mathematics uses math to solve problems in the real world. It's how math helps us understand science, engineering, and even games!
Dynamical Systems and Equations
A differential equation is a math problem that involves a function and how it changes. Think of it like a rule that describes how something moves or grows over time.
A dynamical system uses a rule to describe how something changes over time in a space. For example, the way a clock pendulum swings or how water flows in a pipe can be described using dynamical systems.
- Dynamical Systems and Equations: More about how things change over time.
- Partial Differential Equations: More complex equations used in physics and engineering.
Math in Physics
Mathematical physics is all about using math to understand how the universe works. It helps scientists describe things like gravity, light, and tiny particles.
- Math in Mechanics: How math describes motion and forces.
- Math in Quantum Theory: How math helps us understand the super-small world of atoms.
- Math in Relativity: How math explains space, time, and gravity (like Einstein's theories).
Computers and Math
Math and computers are super connected! Computer science uses math to create algorithms (step-by-step instructions) and organize data. Scientific computing uses math to solve problems in science and engineering with computers.
- Algorithms: Step-by-step instructions for solving problems.
- Computability and Complexity: How hard it is for computers to solve problems.
- Computer Graphics: How math creates images on screens.
- Numerical Analysis: Using math to find approximate solutions with computers.
Information and Signals
Information theory is about measuring and understanding information. It helps us figure out how to send messages efficiently and reliably, like how your phone sends texts.
Signal processing is about analyzing and changing signals, like sounds, images, or even brain waves. It helps us filter out noise, compress files, and understand what signals mean.
- Information Theory: More about how information works.
- Cryptography: The math behind secret codes and keeping information safe.
Probability and Statistics
Image:Normal approximation to binomial.svg Probability theory is the math of chance and uncertainty. It helps us predict how likely something is to happen. Statistics is about collecting, analyzing, and understanding data. It helps us make sense of information from surveys, experiments, and observations.
- Probability Topics: More about chance and likelihood.
- Probability Distributions: Different ways to show how likely outcomes are.
- Statistics Topics: More about collecting and analyzing data.
Game Theory: Math of Decisions
Game theory is a branch of mathematics that uses models to study how people (or even animals or computers) make decisions when they interact with each other. It's used in economics, politics, and even military strategy to understand choices and outcomes.
- Games in Game Theory: Examples of situations studied in game theory.
Operations Research: Smart Decisions
Operations research uses math, statistics, and computer methods to help people make better decisions, especially in complex situations. It aims to make systems work as well as possible, like planning the best delivery routes or scheduling factory production.
- Network Theory: How math helps understand connections, like roads or social networks.
Math Methods and Tools
- Graphical Methods: Ways to show math ideas using pictures and graphs.
- Math-Based Methods: Different approaches to solving problems using math.
- Rules of Logic: How to make valid conclusions in logic.
Important Math Statements
Mathematical statements are like facts, formulas, or ideas in math. They can be axioms (basic truths), theorems (things that can be proven), or conjectures (ideas that haven't been proven yet).
- Algorithms: Step-by-step instructions for solving problems.
- Axioms: Basic truths that are accepted without proof.
- Conjectures: Ideas that mathematicians think are true but haven't proven yet.
- Equations: Math sentences with an equals sign.
- Formulas with Pi: Important equations that use the number pi.
- Inequalities: Math sentences that show one thing is greater or less than another.
- Mathematical Identities: Equations that are always true.
- Theorems: Important math statements that have been proven to be true.
Cool Math Concepts
- Convexity: About shapes that "bulge out" and don't have dents.
- Fractals: Amazing shapes that look the same no matter how much you zoom in.
- Logarithm Topics: More about logarithms.
- Number Systems: Different ways to write numbers (like Roman numerals or binary).
- Partitions: Ways to break numbers into smaller parts.
- Permutations: Different ways to arrange things in order.
- Polynomials: Math expressions with variables and exponents.
Mathematical Objects: What Math Studies
Math studies all sorts of "objects" like numbers, functions, sets, and different kinds of "spaces."
- Math Examples: Real-world examples of math concepts.
- Curves: Different types of lines that bend.
- Math Constants: Special numbers that never change (like pi or e).
- Math Functions: Rules that turn one number into another.
- Math Shapes: A variety of shapes studied in math.
- Math Spaces: Different kinds of environments where math happens.
- Matrices: Rectangular grids of numbers used in many areas of math and computing.
- Numbers: Different types of numbers (whole numbers, fractions, decimals, etc.).
- Polygons and Polyhedra: Flat shapes with straight sides and 3D shapes with flat faces.
Equations Named After People
- Famous Equations: A list of important equations named after the scientists who discovered them.
All About Mathematicians
Mathematicians are people who study and discover new things in math. They publish their new ideas in special journals. There are so many new math discoveries happening all the time!
- Movies About Mathematicians: Films that tell the stories of famous mathematicians.
- Famous Mathematicians: A list of important people who have contributed to math.
Work of Particular Mathematicians
Many math ideas, theorems, and concepts are named after the brilliant mathematicians who discovered them. Here are just a few examples:
- Things named after Archimedes
- Things named after Augustin-Louis Cauchy
- Things named after Carl Friedrich Gauss
- Things named after Leonhard Euler
- Things named after Isaac Newton
- Things named after Pythagoras
- Things named after Alan Turing
Images for kids
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Venn diagrams are illustrations of set theoretical, mathematical or logical relationships.
