Table of Contents
What is the Definition of Mathematics
Mathematics is a field of study that deals with the quantitative analysis of shapes, patterns and relationships in space and time. It is the oldest and most fundamental science.
History of Mathematics
Mathematics is one of the oldest academic disciplines. It evolved from counting, measurement, and the systematic study of shapes and their properties. The earliest use of mathematics might have been in trading where simple arithmetic was used to calculate goods.
The Egyptians were probably the first to develop a system of mathematics. They used a decimal system with symbols for 10, 100, 1,000, and 10,000. They also used a symbol for zero which allowed them to perform complex calculations. The Babylonians were also early developers of mathematics. They used a sexagesimal (base 60) system and were the first to develop algebra and geometry.
Greek mathematicians were some of the earliest to develop mathematical theories. Euclid developed the principles of geometry, while Archimedes developed the principles of mathematics. Other Greek mathematicians developed the concepts of calculus and trigonometry.
The Arabs were the next major developers of mathematics. They translated Greek texts into Arabic, and added their own discoveries to the field. They developed the concepts of zero, algebra, and algorithms.
Mathematics reached its height of development in the Renaissance period. Mathematicians such as Fibonacci and Leonardo da Vinci developed new theories and concepts.
Since the Renaissance, mathematics has continued to evolve. New theories and concepts have been developed, and new applications have been found for mathematics.
Branches of Mathematics
There are many branches of mathematics, some of which are listed below:
1. Algebra: Algebra is the study of mathematical relationships between variables. It is a branch of mathematics that is used in many different fields, including physics and engineering.
2. Calculus: Calculus is the study of change. It is used in many different fields, including physics, engineering, and economics.
3. Statistics: Statistics is the study of data. It is used in many different fields, including business, economics, and political science.
4. Geometry: Geometry is the study of shapes and their properties. It is used in many different fields, including mathematics, physics, and engineering.
5. Trigonometry: Trigonometry is the study of triangles and the relationships between their angles and sides. It is used in many different fields, including mathematics, physics, and engineering.
Rules In Mathematics
In mathematics, there are a few basic rules that are followed. These are called the axioms of mathematics.
The first axiom is that mathematics is consistent. This means that any two statements that are mathematically true are also logically true. In other words, there is no contradiction in mathematics.
The second axiom is that mathematics is complete. This means that every statement that is logically true is also a mathematical statement.
The third axiom is that mathematics is independent. This means that the truths of mathematics are not based on any other truths outside of mathematics.
Class Wise Important Topics in Mathematics for Class XII
1. Algebra: Quadratic equations, inequalities, complex numbers, matrices and determinants.
2. Calculus: Limits, continuity, differentiation, integration, sequences and series.
3. Vectors: Algebra of vectors, magnitude and direction of a vector, addition and subtraction of vectors, scalar and vector products, unit vectors.
4. Probability: Probability distribution, conditional probability, Bayes’ theorem.
5. Trigonometry: Trigonometric functions, inverse trigonometric functions, properties of trigonometric functions, solutions of triangles, heights and distances.
6. geometry: Points, lines, angles, triangles, parallelograms, squares, rectangles, circles, basic geometric constructions, surface areas and volumes.
7. Statistics: Sampling distributions, estimation, hypothesis testing, regression.
