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# Algebra

Algebra is a branch of Mathematics which deals with structures utilizing letters and symbols to represent specific values and their relations to each other. Basic Algebra deals with natural numbers, which are generally positive integers, and their arithmetical operation, while the more complex rules and properties of these mathematical structures are explored in Number Theory. Thus, it can be seen that Algebra is essentially a study of arithmetic computations with non-numerical mathematical objects.

Consider the following equation:

3x+4 = 9

where,

x is the unknown

3, 4 and 9 are the known natural numbers

Through the use of algebra, the unknown value in the above equation can be solved. One important rule to remember is that an algebraic equation represents a scale, so an operation done to one side must be done to the other. Thus, for the above equation, we can isolate x by subtracting 4 from both sides, then divide both sides by 3:

3x+4(-4) = 9(-4)

3x = 5

x = 5/3

Thus, it can be seen that by understanding algebra and its operations is extremely important for all facets of mathematics.

## Categories within Algebra

### Basic Algebra

Solutions: 7,149

Basic Algebra, also known as Elementary Algebra, deals with the arithmetic operations of unknown variables and natural numbers.

### Number Theory

Solutions: 425

Number Theory is the examination of integers.

### Graphs and Functions

Solutions: 2,524

A function is a relationship between inputs and outputs with a specific property that one input is related to only one output.

### Linear Algebra

Solutions: 2,116

Linear Algebra is the study of systems of linear equations, with applications in vector spaces and linear mapping.

### Group Theory

Solutions: 234

Group Theory refers to the study of algebraic structures known as groups.

### Boolean Algebra

Solutions: 90

Boolean Algebra is a sub-discipline of algebra which deals with the truth values of specific variables.

### Combinatorics

Solutions: 427

Combinatorics is a sub-discipline of Algebra which is concerned with the study of combination, enumeration and permutation of sets of elements.

### Ring Theory

Solutions: 239

Ring Theory is the study of abstract algebraic structures in which addition/multiplication operations are well defined.

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