Mathematics is a science field of study.
General mathematics concepts
A closed-form expression is a mathematical expression that can be evaluated in a finite number of standard operations, such as addition, subtraction, multiplication, division, roots, exponents, logarithms, and trigonometric functions. It is an exact, compact representation of a value or solution, avoiding the need for infinite series or recursive steps.
Mathematics main branches
Mathematics main branches:
- Pure
- Applied
Pure
- Algebra
- Geometry
- Analysis
- Number theory
- Topology
Algebra
You can read this post about algebra.
Mathematical analysis
Mathematical analysis is divided into:
- Calculus
- Real analysis
- Complex
- Functional
- Measure theory
Calculus
Calculus is a subfield of the mathematical analysis.
It is the entry point of analysis. Real analysis would be the real calculus.
It is divided into:
- Differential calculus
- Integral calculus
Taylor’s theorem
The Taylor’s theorem gives an approximation of a k-times differentiable function around a given point by a polynomial of degree k, called the k-th-order Taylor polynomial.
Reference:
- Taylor’s theorem. Wikipedia. Available at: https://en.wikipedia.org/wiki/Taylor%27s_theorem
Applied
- Mathematical optimization
- Probably theory
- Statistics
Mathematical optimization
You can read this post about gradient descent.
Probability theory
You can read this post about probability theory.
Statistics
You can read this post about statistics.
Learning Resources
- Math [online]. Khan Academy. Available at: https://www.khanacademy.org/math/