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

10.5 Problems

Problem 1. Which sequences are convergent, ∞-divergent, or neither?

(a) a_n = 2^−n² (b) b_n = √2n-- (c) c_n = nn+1- (d) d_n = sin(1∕n) (e) e_n = e^n(−1)ⁿ

Problem 2. Calculate the following limits.

(a) lim -5n2+2- n→∞ 3n2−12

(b) ( 5n2+2-) limn →∞ ln 3n2− 12

(d) limn →∞ n1sin (n )

(e) lim_n→∞(1 + 2 n )ⁿ

Problem 3. Which series are absolute convergent, conditionally convergent, or divergent? (Use the direct comparison test, the root test, and the alternating series test.)

(a) ∑ ∞ 2 n=0e− n

(b) ∑ ( ) ∞n=0(− 1 )n sin 1n

(d) ∑ ∞ n+1- n=1 n2

(e) ∑ _n=0^∞ --1-- 2n+n

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