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Course Description

For higher-level courses in Data Science, it is convenient to review basic mathematical concepts. The objective of this learning block is to build an intuitive understanding of the underlying mathematics of Data Science. The zero module covers a basic introduction to R language. The first module shows the mathematics of optimization. It introduces calculus techniques and the use of matrices. Matrices are discussed in detail in the linear algebra modules. The second module introduces linear algebra and how it relates to data analytics. The mathematics of vectors and matrices are discussed. The third module introduces the mathematics of probability theory and how it relates to data analytics. The fundamental concept of probability distribution is discussed. The fourth module demonstrates how calculus, matrix algebra and probability are used in typical Data Science applications

Learner Outcomes

  1. Recognize data types: scalars, integers, numerical. (Module 0)
  2. Use basic data structures: matrix and vector. (Module 0)
  3. Use control structures: FOR loops. (Module 0)
  4. Use general operators: addition, subtraction, multiplication, division and exponentiation. (Module 0)
  5. Recognize a computer programming function and its syntax. (Module 0)
  6. Be able to install and invoke computer packages. (Module 0)
  7. Use software to take derivatives of polynomial, radical, exponential, and logarithmic functions. (Module 1)
  8. Describe the meaning of a derivative (Module 1)
  9. Evaluate definite integrals to find the net area between a curve and the x-axis using the Fundamental Theorem of Calculus (Module 1).
  10. Interpret Jacobians and Hessians within the context of gradient descent. (Module 1)
  11. Use gradient descent to optimize parameter values. (Module 1)
  12. Use mathematically correct language and notation for Linear Algebra. (Module 2)
  13. Perform common vector operations such as addition, subtraction, and multiplication. (Module 2)
  14. Perform common matrix operations such as addition, subtraction, and multiplication. (Module 2)
  15. Define the transpose, inverse, trace, and determinant of a matrix. (Module 2)
  16. Use software to diagonalize matrices. (Module 2)
  17. Use software to find the eigenvalues and eigenvectors of matrices. (Module 2)
  18. Explain the significance of eigenvalues and eigenvectors. (Module 2)
  19. Apply Linear Algebra to solve systems of equations. (Module 2)
  20. Articulate Axioms of probability (Module 3)
  21. Recognize the basic Theorems of Probability (Module 3)
  22. Define conditional probability (Module 3)
  23. Define and identify some basic probability distributions/random variables (Module 3)
  24. Articulate the need for an interpretation of probability theory (Module 3)
  25. Define the relative frequency interpretations (Module 3)
  26. Define the subjective interpretation (Module 3)
  27. Evaluate whether a given bet is fair. (Module 3)
  28. State the Dutch book theorem (Module 3)
  29. Describe how the thesis of probabilism is related to the subjective interpretation of probability (Module 3)
  30. Use Gradient Descent to minimize MSE to estimate parameter values. (Module 4)
  31. Compute a confusion matrix (Module 4)
  32. Estimate slope parameter values using Matrix Algebra (Module 4) 
  33. Find the linear transformation of a normal distribution (Module 4)
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Section Title
Mathematics for Data Analytics
Type
Online
Dates
Oct 31, 2022 to Dec 12, 2022
Delivery Options
Course Fee(s)
FREE Continuing Education Credit $0.00
Instructors
  • Francis Mendez
  • Alex White