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🧮 Mathematics

Tip

$μὴ$ $εἶναι$ $βασιλικὴν$ $ἀτραπὸν$ $ἐπί$ $γεωμετρίαν$
"There’s no royal road to mathematics."

• 𓁞 Euclides, to the pharao Ptolemy I of Egypt 𓁛

🦋 The study of emergent properties, such as $\color{#52BFDD}patterns$ and $\color{#43BFDD} relationships $.

🌪 Mathematics answers questions with definite answers.

🔭 We don’t decide if it’s true, we decide to ask the question.

🔩 Axioms are built, and the rest is discovered.

0. Fundamentals of Math

Here you will learn the basic tools of mathematics:

• How the process of problem solving is used.

• The core fundamentals of how to think mathematically

• We present NUMBERS and the basic notions of Arithmetics, this is the manipulation of numbers and quantities.

  • How we use notation and number bases to represent quantities.
  • Advanced arithmetic such as exponents and logarithms in a comprehensive way.

• Sets, the stars of Mathematics

• Pre-Algebra, the introduction of variables and algebraic principles with universal applications.

1. 🔎Mathematical Language & Logic

   🏛 The foundation of mathematics. Strongly related to philosophy. It deals with the principles of reasoning and inference. In mathematics, logic helps us ensure the soundness of arguments, proofs, and mathematical reasoning, enabling mathematicians to establish the validity of statements and proofs.

   🧠 Logical thinking allows mathematicians to create and follow precise steps to arrive at valid conclusions.

   In mathematics, the art of asking questions is more valuable than solving problems.

   • Georg Cantor

2. 🫘 Arithmetics

   

   Arithmetics, from the greek $\color{#42BFDD}Arithmos$ (number), is the study of $\color{#BBE6E4}numbers$.

   🐏 It was, probably, the first field to appear in mathematics. It relates to numbers, their meaning, properties, and operations that can be applied to numbers: Addition, subtraction, multiplication, division...

   💫 Some numbers, such as π or ℯ, have caused a lot of obsessions. People have died over these numbers. why? Well, π (pi) is irrational and transcendental, and ℯ (Euler's number) is the base of the natural logarithm and has many important properties in mathematics.

3. 📏 Geometry

   

   Concerns with Space and relationships of objects in spaces.

   🧩 Studies Shape, size, position, figures...

   📐 Trigonometry

   • The specific field concerned with triangles.

4. ⚖️ Algebra

   The study of structure. How mathematical models are organised. From the Arabic $\color{#4ECDC4}Al‒Jabr$ ("reallocation")

   🪬 It uses symbols to represent values, that may be variable.

   👁 It explores the rules of mathematics.

   🎯 It also helps to discover the behaviour of equations.

5. Functions

6. 📊Calculus

   Discovered by Gottfried Leibniz and Isaac Newton.

   🎢 Concerned with change, rates, and accumulation.

   ⛰️ The two main concepts are differentiation (rates of change) and integration (accumulation).

7. 🍩 Topology

   The study of spaces.

8. Probability and Statistics

9. Algorithms

10. Geometric Algebra

11. Abstract Algebra

12. Linear Systems

13. Chaos Theory

14. Applied Maths

15. Programming and Optimization

16. Physics

17. Discrete Mathematics

18. Number Theory

19. Induction

20. Information Theory

21. Proofs

22. Financial Mathematics

23. Fuzzy Mathematics

24. History of Mathematics

⚛️ Applied Maths

⚙️🔭🧬🔬⚗️💻 Mathematics is the engine that runs the industrial civilization the language of science and technology the code of the information age

Math is everywhere

🎹 Music is the pleasure the human soul experiences from counting without being aware that it is counting.

Phones (signal processing)
Airplanes 
Face recognition 
Disease spread
Elections
Casinos
Universe
Movement
Atoms
Galaxies
Science
Economics

♻️ Mathematics exists before its applications. It’s essential.