Applied Mathematics and Data Analysis

May 19, 2024

Lecture Recap

Course Title

Lecture on Applied Mathematics

Main Topics of the Lecture

Importance of Applied Mathematics

  • The lecture begins with a brief description of the importance and nature of applied mathematics.
  • The objectives and methods of 20th-century applied mathematics include engineering and scientific applications using various tools such as sines, cosines, and functions.

21st Century Applied Mathematics

  • In the 21st century, applied mathematics has undergone significant changes:
    • Can be applied in all fields of mathematics.
    • Situations where numbers are multiplied and divided relate to data encryption (Visa card data encryption accepted by the UN is mainly defended in mathematics doctoral dissertations).
    • Probabilities and predictive analysis.
      • For example, the coin leads to the basic methods of business forecast analysis.
      • For handling large data volumes, the availability of approximate densities with 90-95% confidence.
    • Patterns and structures.
      • For example, the structure of a Rubik's cube is fundamental in quantum mechanics.
    • Number theory.

Topological Data Analysis

  • Topological shape from the perspective of a six.
  • For example, recognizing the structure of data by looking at the world approximately.
  • Professor Gunnar Carlsson's work on founding topological data analysis:
    • Recognizing the general structure by approximating the data.
    • Useful for noisy data.
    • Examples:
      • Rough estimate of data from Netflix, Amazon, or Apple.
      • Quick identification of types of diabetes using a topological approach.