Difference between revisions of "Mathematics"

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: Formally, a function f from a set X to a set Y is defined by a set G of ordered pairs (x, y) such that x ∈ X, y ∈ Y.
 
: Formally, a function f from a set X to a set Y is defined by a set G of ordered pairs (x, y) such that x ∈ X, y ∈ Y.
  
−
: In mathematically we usually write <maty>y = f(x)</math>
+
: In mathematically we usually write <math>y = f(x)</math>
 
: We say <math>y</math> is a function of <math>x</math>
 
: We say <math>y</math> is a function of <math>x</math>
 
: Which means that mathematically <math>y</math> depends on <math>x</math>.
 
: Which means that mathematically <math>y</math> depends on <math>x</math>.

Revision as of 15:28, 5 September 2020

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


Linear algebra is the branch of mathematics concerning linear equations, linear maps, and their representations in vector spaces and through matrices.
https://www.youtube.com/watch?v=w3GV9pumczQ
  • 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





  • 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
  • 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.



  • What is a function:
In mathematics, a function is a binary relation over two sets that associates every element of the first set, to exactly one element of the second set.
Intuitively, a function is a process that associates each element of a set X, to a single element of a set Y.
Formally, a function f from a set X to a set Y is defined by a set G of ordered pairs (x, y) such that x ∈ X, y ∈ Y.
In mathematically we usually write
We say is a function of
Which means that mathematically depends on .
So, as in this case, the independent variable is often designated by . The dependent variable is often designated by .



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