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"Thereโs no royal road to mathematics."
- ๐ Euclides, to the pharao Ptolemy I of Egypt ๐
๐ฆ The study of emergent properties, such as
๐ช Mathematics answers questions with definite answers.
๐ญ We donโt decide if itโs true, we decide to ask the question.
๐ฉ Axioms are built, and the rest is discovered.
Here you will learn the basic tools of mathematics:
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How the process of problem solving is used.
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The core fundamentals of how to think mathematically
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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.
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Pre-Algebra, the introduction of variables and algebraic principles with universal applications.
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๐Mathematical Language & Logic
๐ 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.
๐ง 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
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๐ซ Arithmetics
Arithmetics, from the greek
$\color{#42BFDD}Arithmos$ (number), is the study of$\color{#BBE6E4}numbers$ .๐ 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...
๐ซ Some numbers, such as ฯ or โฏ, have caused a lot of obsessions. People have died over these numbers. why? Well, ฯ (pi) is irrational and transcendental, and โฏ (Euler's number) is the base of the natural logarithm and has many important properties in mathematics.
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๐ Geometry
Concerns with Space and relationships of objects in spaces.
๐งฉ Studies Shape, size, position, figures...
๐ Trigonometry
- The specific field concerned with triangles.
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โ๏ธ Algebra
The study of structure. How mathematical models are organised. From the Arabic
$\color{#4ECDC4}AlโJabr$ ("reallocation")๐ชฌ It uses symbols to represent values, that may be variable.
๐ It explores the rules of mathematics.
๐ฏ It also helps to discover the behaviour of equations.
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Functions
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๐Calculus
Discovered by Gottfried Leibniz and Isaac Newton.
๐ข Concerned with change, rates, and accumulation.
โฐ๏ธ The two main concepts are differentiation (rates of change) and integration (accumulation).
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๐ฉ Topology
The study of spaces.
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Probability and Statistics
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Algorithms
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Geometric Algebra
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Abstract Algebra
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Linear Systems
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Chaos Theory
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Applied Maths
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Programming and Optimization
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Physics
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Discrete Mathematics
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Number Theory
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Induction
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Information Theory
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Proofs
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Financial Mathematics
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Fuzzy Mathematics
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History of Mathematics
โ๏ธ๐ญ๐งฌ๐ฌโ๏ธ๐ป Mathematics is the engine that runs the industrial civilization the language of science and technology the code of the information age
Math is everywhere
๐น 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
โป๏ธ Mathematics exists before its applications. Itโs essential.