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

12.4 Problems

Problem 1. Calculate the derivative of the tanh(x) function defined by

ex − e− x tanh(x) = -x---−-x. e + e

Problem 2. Define the function

( |{ 0 if x <0, f(x) = |( x2 otherwise.

Find the derivative of f(x). Is f^′(x) differentiable everywhere?

Problem 3. Define the function

( | { x2 if x ∈ ℚ, f (x ) = |( 2 − x otherwise.

Show that

(a) f is differentiable at 0, and f^′(0) = 0, (b) and f is nowhere else differentiable.

Problem 4. Calculate the derivatives of the following functions.

(a) f(x) = e⁻ (b) f(x) = x²e^{sin x} (c) f(x) = sin(cosx²) (d) f(x) = x2+1 x2−-1

Problem 5. Find the Taylor expansion of the following functions around 0.

(a) f(x) = sinx (b) f(x) = cosx (c) f(x) = log x (d) f(x) = e^{-x2}

Problem 6. Find the Taylor expansion of the function

( |{ − 12 f(x) = e x if x ⁄= 0, |( 0 if x = 0.

around 0. Is the Taylor expansion of f equal to f?

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