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 https://en.wikipedia.org/wiki/Mathematical_analysis

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

• Infinitesimal calculus https://en.wikipedia.org/wiki/Calculus

• 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

• 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

• Applications:

• 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

• 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.