*Here, you find my short advent calender about mathematical symbols. Each video introduces a symbol that one uses in mathematics. You can also download the pdf versions of the videos here.*

#### Part 1 - Kronecker Delta

The first video is about the **Kronecker Delta**:

#### Part 2 - Levi-Civita Symbol

Let’s continue with the related **Levi-Civita Symbol**, which can be used to describe the cross product in $ \mathbb{R}^3 $.

#### Part 3 - Nabla-symbol

The next symbol is called **Nabla** and used for partial derivatives. We find the notation is the my video series about multivariable calculus again where we talk about gradients and directional derivatives.

#### Part 4 - Factorial

In the following video, we explain the common **Factorial** notation. It is used in a lot of mathematical contexts.

#### Part 5 - Gamma Function

The **Gamma Function** is a generalisation of the last video:

#### Part 6 - Composition

For denoting the **composition** for functions, we use a special symbol:

#### Part 7 - Sum Symbol

The capital sigma we use to denote the **sum symbol**:

#### Part 8 - Product Symbol

Moreover, the Greek capital Pi is used for the **product symbol**:

#### Part 9 - Restriction

Do you know the symbol for the **restriction** of a function?

#### Part 10 - Pauli matrices

Some matrices you see in physics a lot: **Pauli matrices**.

#### Part 11 - Set Brackets

Naturally a fundamental notation: **set brackets**.

#### Part 12 - Big O

The **Big O** notation is used in a lot of formulas.

#### Part 13 - Binomial Coefficient

Next, we look at the **binomial coefficient**

#### Part 14 - Modulo

The **modulo** notation is important when you work with numbers.

#### Part 15 - Beta Function

The next video is about the **Beta function**.

#### Part 16 - Map Arrows

Also a fundamental notation is given by the **map arrows**. This is a notation that is used throughout mathematics. Please note that different arrows are used for the different levels.

#### Part 17 - Little o

For some formulas the **Little o** notation is helpful.

#### Part 18 - Outer Product

Next, let’s discuss the **outer product**. This is a special symbol, which is also used in other contexts. However, the outer product is the simplest one of the usages.

#### Part 19 - Euler’s Phi Function

Are you interested in **Euler’s Phi Function**

#### Part 20 - Laplace Operator

The **Laplace operator** a very important object in differential equations. It is given by second-order partial differential operators.

#### Part 21 - Convolution

Next symbol ist about the **convolution**

#### Part 22 - Heaviside Function

Do you know the **Heaviside function**? It is a function that has one heavy side but the name comes from the famous mathematician **Heaviside**.

#### Part 23 - Quaternions

Let us talk about **quaternions**.

#### Part 24 - Infinity

And finally the last video in this series is about **infinity**. A symbol that is used for a lot of different contexts. However, one can also calculate with it, in some sense.

#### Part 25 - Element Symbol

This is one of the most often used symbols in mathematics. It originated from a lowercase epsilon and it simply describes the set-element relation.

#### Part 26 - Empty Set

Talking about sets: there is a very special set that just describes nothingness.

#### Part 27 - Subset Symbol

In mathematics, we imagine that sets are collections of objects and such collections can be compared. The usual and natural way is to do that with the **subset** notation.

#### Part 28 - Partial d

The next symbol is very special one. It does not use a character from an alphabet but is somehow a deformed d or lowercase delta. It’s always used to denote partial derivatives such one common name is **partial d** but a lot of people call it and pronouce it **del**.

#### Part 29 - D’Alembert Operator

This symbol looks like a box and it’s often used in physics and in mathematics for partial differential equations.

#### Part 30 - Inner Product

This is an important construction for giving a geometry to different spaces. Especially in Quantum Mechanics, this notation got popular.

#### Part 31 - Integral Symbol

Ah, the integral symbol. One of the symbols that really calls for a mathematician. However, essentially, it’s just a stylized **S** but now with a lot of meaning in different fields of mathematics.

#### Part 32 - Closed Line Integral

This is a special notion for an integral that is often used in **complex analysis** and **vector analysis**.

#### Part 33 - Natural Numbers

If you start learning mathematics, you immediately learn about sets and the set of natural numbers is the first **infinite** set in this introduction.

#### Part 34 - Integers

Let’s finish this series with integers, a set that shows that even an infinite set as the natural numbers can be extended in a natural way.

#### Summary of the course Advent of Mathematical Symbols

- You can download the whole PDF here.
- You can download the whole printable PDF here.