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.