# Mathematical Foundation for Data Science (MFDS)

Data science requires a proper understanding of some basic mathematics. This module is designed to teach learners the basic math they will need in order to be successful in the later modules and is created for learners who have basic math skills but may not have taken algebra or pre-calculus. MFDS introduces the core math that data science is built upon, with no extra complexity, introducing unfamiliar ideas and math symbols one-at-a-time.  Learners who complete this course will master the vocabulary, notation, concepts, and algebra rules that all data scientists must know before moving on to more advanced modules. This includes a fundamental concepts of graph theory that are useful for social network analysis or path analysis in general.

Prerequisites                          : None

Objectives/Contents             :

1. The course will introduce students to the fundamental mathematical concepts required for a program in data science.
2. Basics of Data Science: Introduction; Typology of problems; Importance of linear algebra, and optimization from a data science perspective; Structured thinking for solving data science problems.
3. Linear Algebra: Matrices and their properties (determinants, traces, rank, nullity, etc.); Eigenvalues and eigenvectors; Matrix factorizations; Inner products; Distance measures; Projections; Notion of hyperplanes; half-planes.
4. Optimization: Unconstrained optimization; Necessary and sufficiency conditions for optima; Gradient descent methods; Constrained optimization, KKT conditions; Introduction to non-gradient techniques; Introduction to least squares optimization; Optimization view of machine learning.
5. Introduction to some basic Data Science Methods: Linear regression as an exemplar function approximation problem; Linear classification problems.
6. Upon the completion of the module, trainees should be able to answer most of the “why” and “what-if” questions in machine learning formulations. In other words, a good philosophical understanding of machine learning concept.

Reference:

1. Anton, H., & Rorres, C. (2013). Elementary Linear Algebra: Applications Version. John Wiley & Sons.
2. Thomas, G. (2018). Mathematics for Machine Learning. University of California, Berkeley.
3. Michaels, J. G., & Rosen, K. H. (Eds.). (1991). Applications of discrete mathematics(Vol. 267). New York: McGraw-Hill.
4. Solomon, J. (2015). Numerical algorithms: methods for computer vision, machine learning, and graphics. AK Peters/CRC Press.
5. Yang, X. S. (2019). Introduction to Algorithms for Data Mining and Machine Learning. Academic Press.
6. Simovici, D. (2018). Mathematical Analysis for Machine Learning and Data Mining. World Scientific Publishing Co., Inc.