Abstract:

Learning the theoretical background required for machine learning can be intimidating as per the multiple fields involved. These requirements must be designed such as to insure a good basic knowledge and advanced understanding of various branches of Mathematics. The optimization of the learning content is extremely important to provide the instruction in time with affordable cost.

In mathematics, it could be achieved by incorporating uninterrupted links between the components of algebra, linear algebra, calculus, and statistics, as required to understand the math fundament of the data science. Following such principle, this work suggests a topics-sequence to build the mathematical background necessary to get up and running in data science work. These suggestions are derived from the author own experience in physics and mathematics, following up with the latest published references about data science, and recommendations from the Data Analytics Program at the School of Cybersecurity and Information Technology in the University of Maryland Global Campus.

Listing the most significant topics, the following sequence condenses the idea of the work; grouped in one book, each topic is introduced follow previous related content required to build the new one, always considering how to facilitate learning:
- Linear Algebra including Eigenvalues and Vectors with application to Data Problems, Basis, Transformation of Matrix and Mappings.
- Multivariable Calculus, including functions with thousands of inputs. Vector Calculus, Gradient Descent, and Optimization. Special attention to Multivariate Chain Rule and its application to calculate the influence of each parameter of the networks. Linear Regression, Taylor series and linearization, Jacobian and Hessian, and Dimensionality Reduction.
- Statistics with Calculus and Python Programming background will be include as required to develop mathematical intuition and ability to solve and derive the result.

While an intimate study of mathematics will be referred on the book, it’s deeply pure mathematical study is not required. However, a very well instrumented mathematical tool is necessary, which in most cases relies on computer programs to solve problems related to data science. Thus, in this work is offered an intuitive mathematical training for Data Science professionals’ preparation.

Keywords:

Machine Learning, Data Science, Mathematics, Prieto-Valdes, Elena Gortcheva, algebra, linear algebra, calculus, statistics, Artificial Intelligence.