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Miloslav Číž 2021-12-26 16:09:09 +01:00
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@ -12,11 +12,11 @@ Following are some areas of math one, as a programmer, should be familiar with:
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- **basics** (high-school level math): arithmetic, expression simplification, equations, geometry, trigonometry, systems of linear equations, quadratic equations, [complex numbers](complex_number.md), logarithms, ... - **basics** (high-school level math): arithmetic, expression simplification, equations, geometry, trigonometry, systems of linear equations, quadratic equations, [complex numbers](complex_number.md), logarithms, analythical geomtery (many problems generalize to intersecions of N-dimensional shapes), [polynomials](polynomial.md) (used in many areas, e.g. error correction codes in networking), ...
- **advanced notation**: ability to understand the notation that's often used in papers etc. (the big sigma for sum etc.) - **advanced notation**: ability to understand the notation that's often used in papers etc. (the big sigma for sum etc.)
- **formal [logic](logic.md)**: computers are based on Boolean logic, knowing basic formulas and theorems here is crucial (e.g. the completeness of [NAND](nand.md)), formal logic is also just generally used in formal texts, one should know about predicate vs propositional logic, the notation symbols, etc. - **formal [logic](logic.md)**: computers are based on Boolean logic, knowing basic formulas and theorems here is crucial (e.g. the completeness of [NAND](nand.md)), formal logic is also just generally used in formal texts, one should know about predicate vs propositional logic, the notation symbols, etc.
- **[linear algebra](linear_algebra.md)**: aka "vectors and matrices", essential in many fields such as [graphics](graphics.md) and [machine learning](machine_learning.md). - **[linear algebra](linear_algebra.md)**: aka "vectors and matrices", essential in many fields such as [graphics](graphics.md) and [machine learning](machine_learning.md).
- **[calculus](calculus.md) and differential equations**: just essential for advanced math and many fields (graphics, physics, machine learning, electricity, physics, any optimization, ...). - **[calculus](calculus.md) and differential equations**: just essential for advanced math and many fields (graphics, machine learning, electricity, physics, any optimization, ...).
- **theoretical [computer science](compsci.md)**: [computational complexity](computational_complexity.md) (very important), [computability](computability.md), [formal languages](formal_language.md), computational models ([automata](automaton.md), [Turing machines](turing_machine.md), ...), ... - **theoretical [computer science](compsci.md)**: [computational complexity](computational_complexity.md) (very important), [computability](computability.md), [formal languages](formal_language.md), computational models ([automata](automaton.md), [Turing machines](turing_machine.md), ...), ...
- **number and set theory**: sets of numbers (natural, rational, real, imaginary, ...), [prime numbers](prime.md) (important e.g. for [cryptography](cryptography.md)), ... - **number and set theory**: sets of numbers (natural, rational, real, imaginary, ...), [prime numbers](prime.md) (important e.g. for [cryptography](cryptography.md)), ...
- **discrete math**: basic structures such as [groups](group.md) and [fields](field.md) and their properties. - **discrete math**: basic structures such as [groups](group.md) and [fields](field.md) and their properties.