Deep Learning for Finance

Chapter 4. Linear Algebra and Calculus for Deep Learning

Algebra and calculus are integral parts of data science. Machine learning and deep learning algorithms are mostly based on algebra and calculus techniques. This chapter introduces some key topics in a way that everyone can understand.

Algebra is the study of operations and relational rules, as well as the constructions and ideas that result from them. Algebra covers topics such as linear equations and matrices. You can consider algebra as the first step toward calculus.

Calculus is the study of curve slopes and rates of change. Calculus covers topics such as derivatives and integrals. It is heavily used in many fields such as economics and engineering. Many learning algorithms rely on the concepts of calculus to perform their complex operations.

The distinction between the two is that while calculus works with ideas of change, motion, and accumulation, algebra deals with mathematical symbols and the rules for manipulating those symbols. Calculus focuses on the characteristics and behavior of changing functions, while algebra offers the foundation for solving equations and comprehending functions.

Linear Algebra

Algebra encompasses various mathematical structures, including numbers, variables, and operations like addition, subtraction, multiplication, and division. Linear algebra is a fundamental branch of algebra that deals with vector spaces and linear transformations. It is heavily used in machine learning and deep learning ...