The Papyrus Rhind is the source of most of modern knowledge about mathematics in Ancient EgyptIntroduction
Mathematics (sometimes shortened to maths or math), is the study of numbers, shapes and patterns. Mathematicians are people who learn about and discover such things in mathematics. Mathematics is useful for solving problems that occur in the real world, so many people besides mathematicians study and use mathematics. Today, mathematics is needed in many jobs. Business, science, engineering, and construction need some knowledge of mathematics.
Mathematicians solveproblems by using logic. Mathematicians often use deduction. Deduction is a special way of thinking to discover and prove new truths using old truths. To a mathematician, the reason something is true is just as important as the fact that it is true. Using deduction is what makes mathematical thinking different from other kinds of thinking.
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A picture of airflow, modeled using a differential equation
A differential equation is a mathematicalequation that involves variables like x or y, as well as the rate at which those variables change. Differential equations are special because the solution of a differential equation is itself a function instead of a number.
If a differential equation only involves x and its derivative, the rate at which y changes, then it is called a first order differential equation. A higher-order differential equation has derivatives of other derivatives. If there are more variables than just x and y, then it is said to be a partial differential equation. Sometimes, something in the world will obey several differential equations at the same time. These are said to be modeled by coupled differential equations.
Some differential equations can be solved exactly, and some cannot. Sometimes one can only be estimated, and a computer program can do this very fast. Although they may seem overly-complicated to someone who has not studied differential equations before, the people who use differential equations tell us that they would not be able to figure important things out without them. Most scientists and engineers (as well as mathematicians) take at least one course in differential equations while in college. Some mathematicians devote their career to investigating differential equations that are difficult to solve.
Illustration of the Pythagorean theorem. The sum of two sqares whose sides are the two legs (blue and red) is equal to the area of the square whose side is the hypotenuse (purple).
