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Julio Toboso edited this page Sep 18, 2024 · 69 revisions

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$ฮผแฝด$ $ฮตแผถฮฝฮฑฮน$ $ฮฒฮฑฯƒฮนฮปฮนฮบแฝดฮฝ$ $แผ€ฯ„ฯฮฑฯ€แฝธฮฝ$ $แผฯ€ฮฏ$ $ฮณฮตฯ‰ฮผฮตฯ„ฯฮฏฮฑฮฝ$
"Thereโ€™s no royal road to mathematics."

  • ๐“ž Euclides, to the pharao Ptolemy I of Egypt ๐“›

๐Ÿฆ‹ The study of emergent properties, such as $\color{#52BFDD}patterns$ and $\color{#43BFDD} relationships $.

๐ŸŒช Mathematics answers questions with definite answers.

๐Ÿ”ญ We donโ€™t decide if itโ€™s true, we decide to ask the question.

๐Ÿ”ฉ Axioms are built, and the rest is discovered.

Here you will learn the basic tools of mathematics:

  1. ๐Ÿ”ŽMathematical Language & Logic

    ๐Ÿ› 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.

    ๐Ÿง  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. ๐Ÿซ˜ Arithmetics

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

    ๐Ÿ 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...

    ๐Ÿ’ซ Some numbers, such as ฯ€ or โ„ฏ, have caused a lot of obsessions. People have died over these numbers. why? Well, ฯ€ (pi) is irrational and transcendental, and โ„ฏ (Euler's number) is the base of the natural logarithm and has many important properties in mathematics.

  3. ๐Ÿ“ Geometry

    Concerns with Space and relationships of objects in spaces.

    ๐Ÿงฉ Studies Shape, size, position, figures...

    ๐Ÿ“ Trigonometry

    • The specific field concerned with triangles.
  4. โš–๏ธ Algebra

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

    ๐Ÿชฌ It uses symbols to represent values, that may be variable.

    ๐Ÿ‘ It explores the rules of mathematics.

    ๐ŸŽฏ It also helps to discover the behaviour of equations.

  5. Functions

  6. ๐Ÿ“ŠCalculus

    Discovered by Gottfried Leibniz and Isaac Newton.

    ๐ŸŽข Concerned with change, rates, and accumulation.

    โ›ฐ๏ธ The two main concepts are differentiation (rates of change) and integration (accumulation).

  7. ๐Ÿฉ 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

โš›๏ธ Applied Maths

โš™๏ธ๐Ÿ”ญ๐Ÿงฌ๐Ÿ”ฌโš—๏ธ๐Ÿ’ป Mathematics is the engine that runs the industrial civilization the language of science and technology the code of the information age

Math is everywhere

๐ŸŽน 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

โ™ป๏ธ Mathematics exists before its applications. Itโ€™s essential.

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