Mathematics

Mathematics includes the study of such topics as quantity (number theory), structure (algebra), space (geometry), and change (mathematical analysis). It has no generally accepted definition. https://en.wikipedia.org/wiki/Mathematics#cite_note-Mura-7

• Number theory (or arithmetic) https://en.wikipedia.org/wiki/Number_theory

• Algebra https://en.wikipedia.org/wiki/Algebra

• Geometry https://en.wikipedia.org/wiki/Geometry

• Mathematical analysis (Math of change) https://en.wikipedia.org/wiki/Mathematical_analysis

• Analytic geometry https://en.wikipedia.org/wiki/Analytic_geometry

• Infinitesimal calculus (Math of change) https://en.wikipedia.org/wiki/Calculus

https://www.youtube.com/watch?v=w3GV9pumczQ

• Differential calculus (Derivative) https://en.wikipedia.org/wiki/Differential_calculus

• Integral calculus https://en.wikipedia.org/wiki/Integral

• Fundamental theorem of calculus https://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus

• One of the applications of Mathematical analysis (Calculus in particular) is for Signal processing

• Applied mathematics: Some disciplines are considered to be applied mathematics. Sin embargo, no me queda claro si las área que estoy enumerando aquí realmente forman parte de lo que se conoce como Applied mathematics. En particular, Statistics can be considered to be a distinct mathematical science rather than a branch of mathematics. https://en.wikipedia.org/wiki/Statistics

• Discrete mathematics https://en.wikipedia.org/wiki/Discrete_mathematics

• Numerical analysis https://en.wikipedia.org/wiki/Numerical_analysis

• Computer algebra https://en.wikipedia.org/wiki/Computer_algebra

• Statistics https://en.wikipedia.org/wiki/Statistics

• Applications of mathematics:

• Signal processing:

One of the applications of Mathematical analysis (Calculus in particular) is for Signal processing.

When processing signals, such as audio, radio waves, light waves, seismic waves, and even images, Fourier analysis can isolate individual components of a compound waveform, concentrating them for easier detection or removal. A large family of signal processing techniques consists of Fourier-transforming a signal, manipulating the Fourier-transformed data in a simple way, and reversing the transformation. https://en.wikipedia.org/wiki/Mathematical_analysis#Signal_processing

• Time-frequency analysis https://en.wikipedia.org/wiki/Time%E2%80%93frequency_analysis

• Fourier transform https://en.wikipedia.org/wiki/Fourier_transform

• Seismic processing

• Time-frequency analysis in Seismic processing:

A set of mathematical formulas used to convert a time function, such as a seismic trace, to a function in the frequency domain (Fourier analysis) and back (Fourier synthesis). The Fourier transform is used extensively in signal processing to design filters and remove coherent noise. Many filtering operations are performed in the frequency domain. The Fourier transform has applications in image analysis and in pattern recognition in geological systems. https://www.glossary.oilfield.slb.com/en/Terms/f/fourier_transform.aspx#:~:text=A%20set%20of%20mathematical%20formulas,and%20back%20(Fourier%20synthesis).&text=The%20Fourier%20transform%20is%20used,filters%20and%20remove%20coherent%20noise.