You're reading from Mathematics of Machine Learning Master linear algebra, calculus, and probability for machine learning

Product type Paperback

Published in May 2025

Publisher Packt

ISBN-13 9781837027873

Length 730 pages

Edition 1st Edition

Concepts

Machine Learning

Author (1):

Tivadar Danka

View More author details

Table of Contents (36) Chapters

Introduction

Part 1: Linear Algebra FREE CHAPTER

1 Vectors and Vector Spaces

2 The Geometric Structure of Vector Spaces

3 Linear Algebra in Practice

4 Linear Transformations

5 Matrices and Equations

6 Eigenvalues and Eigenvectors

7 Matrix Factorizations

8 Matrices and Graphs

References

Part 2: Calculus

9 Functions

10 Numbers, Sequences, and Series

11 Topology, Limits, and Continuity

12 Differentiation

13 Optimization

14 Integration

References

Part 3: Multivariable Calculus

15 Multivariable Functions

16 Derivatives and Gradients

17 Optimization in Multiple Variables

References

Part 4: Probability Theory

18 What is Probability?

19 Random Variables and Distributions

20 The Expected Value

References

Part 5: Appendix

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Index

Appendix A It’s Just Logic

1. Appendix B The Structure of Mathematics

2. Appendix C Basics of Set Theory

3. Appendix D Complex Numbers

9.2 Functions in practice

In our study of functions, we started from arrows between sets and ended up with mental models such as formulas and graphs. For pure mathematical purposes, these models are perfectly enough to conduct thorough investigations. However, once we leave the realm of theory and start putting things into practice, we must think about how functions are represented in programming languages.

In Python, functions are defined using a straightforward syntax. For instance, this is how the square(x) = x² function can be implemented.

def square(x): 
    return x**2

The result is an object of type function. (In Python, everything is an object.)

type(square)

function

Functions are called using the () operator.

square(12)

Python is well-known for its simplicity, and functions are no exception. However, this doesn’t mean that they are limited in features – quite the contrary: you can achieve a lot with the clever use of functions.