A glossary of mathematical terms and definitions is a valuable resource that provides concise explanations of various mathematical concepts and terminology. Below is an extensive glossary covering a wide range of mathematical terms:

1. Absolute Value: The magnitude of a real number without considering its sign. It is denoted by |x|.

2. Algorithm: A step-by-step procedure or set of rules for solving a specific mathematical problem or performing a computation.

3. Area: The measure of the amount of space inside a two-dimensional shape, usually expressed in square units.

4. Average: The mean of a set of numbers obtained by adding all the values and dividing by the total number of values.

5. Binomial: An algebraic expression consisting of two terms connected by either addition or subtraction.

6. Circle: A closed curve in which all points are equidistant from the center, and the distance is called the radius.

7. Coefficient: The numerical factor of a term in an algebraic expression or equation.

8. Congruent: Two geometric figures that have the same shape and size.

9. Deductive Reasoning: A method of logical thinking that involves drawing conclusions from given premises or facts.

10. Derivative: The rate of change of a function at a specific point, representing its slope or tangent at that point.

11. Equation: A statement that two expressions are equal, typically containing an equal sign (=).

12. Exponent: A small number written above and to the right of a base, indicating how many times to multiply the base by itself.

13. Factorial: The product of all positive integers from 1 to a given number (n), denoted by n!.

14. Geometry: The branch of mathematics that deals with the study of shapes, sizes, and properties of space.

15. Hypotenuse: In a right-angled triangle, the side opposite the right angle.

16. Inequality: A mathematical expression indicating that one quantity is less than, greater than, or not equal to another.

17. Integer: A whole number (positive, negative, or zero) without a fractional or decimal part.

18. Irrational Number: A real number that cannot be expressed as a simple fraction, usually having an infinite decimal expansion.

19. Logarithm: The exponent to which a specified base must be raised to produce a given number.

20. Matrix: A rectangular arrangement of numbers or symbols in rows and columns used for various mathematical operations.

21. Numerator: The top part of a fraction, representing the number of equal parts considered.

22. Obtuse Angle: An angle greater than 90 degrees but less than 180 degrees.

23. Parabola: A U-shaped curve formed by the graph of a quadratic function.

24. Quadratic Equation: An equation of the form ax^2 + bx + c = 0, where a, b, and c are constants, and x represents the variable.

25. Ratio: A comparison of two quantities by division, usually represented as a/b or a:b.

26. Set: A collection of distinct objects or elements grouped together for analysis or study.

27. Theorem: A statement or proposition that can be proven to be true based on accepted mathematical axioms and principles.

28. Trigonometry: The branch of mathematics dealing with the relationships between angles and sides of triangles.

29. Variable: A symbol used to represent an unknown quantity or a changing value in an equation or expression.

30. Volume: The measure of the space occupied by a three-dimensional object, typically expressed in cubic units.

This glossary provides a foundation for understanding common mathematical terms encountered in various mathematical disciplines. It is a valuable resource for students, educators, and enthusiasts to enhance their mathematical knowledge and communication.