# Mathematics

**What is mathematics?**

Mathematics can be described as the study of structures, quantities, and the relationships between different objects.

It's often viewed as an abstract and challenging subject, meant only for the brightest minds.

But in truth, it’s much more than just a collection of numbers and formulas: it’s a universal language that explains the world around us, from the inner workings of our bodies to the movement of planets.

Mathematics also plays a crucial role in our everyday lives.

For example, every time you send a message on WhatsApp or upload a photo to social media, you're relying on math. Compression algorithms, which reduce file sizes without losing quality, are based on sophisticated mathematical concepts like Fourier transforms and information theory.

## The branches of mathematics

Mathematics is divided into various branches, each with its own area of focus. Some of the most important include:

**Arithmetic**: the most basic branch, dealing with operations like addition, subtraction, multiplication, and division.**Algebra**: involves using symbols and letters to represent numbers and the relationships between them.**Geometry**: focuses on shapes, sizes, and the properties of space.**Calculus**: studies change and motion, and forms the basis of much of modern physics and engineering.**Statistics and probability**: used to analyze data and make predictions about future events.

Each branch of mathematics provides unique tools for solving specific kinds of problems.

For example, geometry is essential for studying architecture, while calculus is at the core of both physics and engineering.

## Conquering the fear of mathematics

For many, math can seem like nothing more than a set of tedious rules, and let’s face it—it can still feel a bit boring or even intimidating at times.

But don’t worry, the point here is that it can also be incredibly useful—and who knows, maybe even fun.

The key to overcoming this fear is changing how you approach it. Instead of seeing math as a rigid set of rules, you can **start thinking of it as a game** of logic and creativity.

Try viewing math problems as puzzles to be solved rather than boring tasks to complete.

Another critical factor is **practice**. Just like any other skill, mathematics requires consistent practice. It's normal to feel stuck at first, but with patience and persistence, anyone can improve.

No matter where you are in your journey, there's always more to learn. And if you've fallen behind, you can always catch up.

Who knows—next time you see an equation, you might not feel the urge to throw it out the window. But I make no promises!

## Mathematics lessons and notes

**Mathematics**

**Algebra**

- Algebra
- The zero product law
- The identity principle of polynomials
- Division by Zero
- Undefined operations in mathematics
- Equations

**Sets**

**Geometry**

**Trigonometry**

**Matrices**

- Matrices
- Row-column multiplication
- Element-wise product (Hadamard product)
- Determinant
- Rank
- Trace
- Minors of a matrix
- Symmetric matrix
- Opposite matrix
- Identity matrix
- Zero matrix
- Transpose of a matrix
- Square matrices
- Cofactor Matrix
- Adjugate Matrices
- Inverse Matrices

**Vectors**

- Vectors
- Scalar and vector quantities
- Equal vectors
- Vector operations
- Vector addition
- Parallelogram method
- Head-to-tail method
- Opposite vector
- Vector subtraction
- Vector multiplication
- Scalar multiplication of a vector by a constant factor
- Dot product (scalar product or inner product)
- Cross product
- Outer product
- Element-wise product (Hadamard product)
- Cartesian decomposition of a vector
- Calculating the angle between two vectors
- Length of the vector (magnitude)

**Calculus**

**Complex numbers**

- Complex numbers
- Complex plane (or Gauss plane)
- Imaginary unit ("i" or "j")
- Magnitude (modulus) of a complex number
- Argument of a complex number
- Conjugate of a complex number
- Addition complex numbers
- Subtracting complex numbers
- Multiplication
- Division
- Complex numbers in trigonometric form
- Complex numbers in exponential form

**Numerical calculation**

- Numerical calculation