Table of Contents
What are the Branches of Mathematics?
The branches of mathematics can be classified into three categories: pure mathematics, applied mathematics, and statistics.
- Pure mathematics is the study of mathematics for its own sake. It includes the study of abstract concepts such as number theory, geometry, and algebra.
- Applied mathematics is the application of mathematics to solve real-world problems. It includes the study of mathematical models and techniques that can be used to solve practical problems in science and engineering.
- Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. It is used to make informed decisions in business, government, and other fields.
Algebra: Branch of Mathematics
Algebra is a branch of mathematics that uses symbols to represent numbers and operations. Algebra is used to solve problems and to model real-world situations. Algebra is a critical tool for solving mathematical problems in many different areas of mathematics.
Formulas of Algebra
There are a variety of formulas in algebra that help to solve equations or systems of equations. Some of the most common formulas are the following:
- The Quadratic Formula: This formula helps to solve quadratic equations.
- The Formula for Determining the Square Root of a Number: This formula helps to find the square root of a number.
- The Formula for the Sum of a Series: This formula helps to find the sum of a series of numbers.
- The Formula for the Product of a Series: This formula helps to find the product of a series of numbers.
Arithmetic: Branch of Mathematics
that deals with the properties and operations of numbers.
- Algebra: Branch of Mathematics that deals with the properties and operations of algebraic expressions and equations.
- Geometry: Branch of Mathematics that deals with the properties and relations of points, lines, angles, surfaces, and solids.
Addition of Numbers with Properties
We can add numbers with mathematical properties using the order of operations. This is also called the “PEMDAS” or “Please Excuse My Dear Aunt Sally” method.
The order of operations is:
P: Parentheses first
E: Exponents (ie Powers and Square Roots, etc.)
MD: Multiplication and Division (left-to-right)
AS: Addition and Subtraction (left-to-right)
Successor and Predecessor
Functions
The successor function finds the next largest number in a sequence of numbers, while the predecessor function finds the previous smallest number in a sequence.
The code for the successor function is:
def successor(n):
if n > 0:
return n + 1
else:
return 0
The code for the predecessor function is:
def predecessor(n):
if n > 0:
return n – 1
else:
return 0
Subtraction with its Properties
The inverse of addition is subtraction. Subtraction is the process of removing a quantity from another quantity. In symbols,
x – y = z
where x is the quantity to be subtracted from y. The symbol “-” is called the subtraction operator.
Subtraction is commutative, meaning that the order of the operands does not affect the result:
x – y = y – x
Subtraction is associative, meaning that the order of the operands within parentheses does not affect the result:
(x – y) – z = x – (y – z)
There is a unique identity element for subtraction, which is the number 0. For any other number a,
a – 0 = a
Subtraction is distributive. For any numbers a, b, and c,
a – (b + c) = a – b – c
Non – Associativity
Non – Associativity is a term used in mathematics to describe a situation in which the order of operations matters. For example, in the expression 3 + 5 * 2, the order of operations is 3 + 5 = 8 and then 8 * 2 = 16. However, in the expression 5 + 3 * 2, the order of operations is 5 + 3 = 8 and then 8 * 2 = 16. This is because the multiplication operator (*) is associative, which means that the order of operations does not matter.
Multiplication with its Properties
Multiplication is a mathematical operation that is used to calculate the result of two or more numbers being multiplied together. The symbol for multiplication is an asterisk (*).
Multiplication is associative, meaning that the order of the multiplication does not affect the result. For example, 3 * 4 * 5 = 15, and 5 * 4 * 3 = 20.
Multiplication is commutative, meaning that the order of the numbers being multiplied does not affect the result. For example, 3 * 5 = 15, and 5 * 3 = 15.
Multiplication is distributive. This means that when one number is multiplied by a group of numbers, the result is the same as if the number was multiplied by each individual number in the group. For example, 6 * (2 + 4) = 6 * 6 = 36, and (2 + 4) * 6 = (2 + 4) * (3 + 2) = (2 + 4) * 10 = 32.
Rules of Multiplication
1. Multiply the first number by the second number.
2. Write the answer below the first number.
3. Repeat the process for the rest of the numbers.
4. Write a multiplication sign between each number.
5. Write the answer at the bottom.
For example:
3 × 4 = 12
3
4
12
Division with its Properties
A division is a mathematical operation that is used to find the quotient (or result) of two numbers. The dividend (or top number) is divided by the divisor (or bottom number) to produce the quotient. The divisor cannot be zero, or the division will result in an error.
The division symbol is ÷, and it is read “divided by.” For example, 5 ÷ 2 would be read “five divided by two,” and would result in a quotient of 2.5.
The properties of division are:
- The division of two positive numbers always produces a positive result.
- The division of two negative numbers always produces a negative result.
- The division of a positive number by a negative number always produces a negative result.
- The division of a negative number by a positive number always produces a positive result.
Geometry as a Branch of Mathematics
Geometry is the study of the shapes and properties of objects. It is a branch of mathematics that deals with points, lines, angles, surfaces, and solids.
Different Types of the Polygon:
- Triangle: A three-sided polygon.
- Quadrilateral: A four-sided polygon.
- Pentagon: A five-sided polygon.
- Hexagon: A six-sided polygon.
- Heptagon: A seven-sided polygon.
- Octagon: A eight-sided polygon.
- Nonagon: A nine-sided polygon.
- Decagon: A ten-sided polygon.
Trigonometry as a Branch of Mathematics
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used in a variety of applications, including physics, engineering, and surveying.
Why do Students Need to know About the Branches of Mathematics?
The branches of mathematics are important for students to know because they provide a foundation for more advanced mathematics courses. The branches of mathematics are also important for students to know because they provide a foundation for other subjects such as physics and engineering.
