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

16.4 Problems

Problem 1. Compute the partial derivatives and the Hessian matrix of the following functions.

(a) f(x₁,x₂) = x₁^3x₂² + 2x₁x₂ + x₂³ (b) f(x₁,x₂) = e^{x₁²−x₂} + sin(x₁x₂) (c) f(x₁,x₂) = ln(x₁² + x₂²) + x₁e^x₂ (d) f(x₁,x₂) = cos(x₁x₂) + x₁² sin(x₂) (e) f(x₁,x₂) = f(x₁,x₂) = x2+x2 x11−x22

Problem 2. Compute the Jacobian matrix of the following functions.

(a)

⌊ ⌋ x21x2 + ex2 f(x1,x2) = ⌈ x2⌉ sin(x1x2)+ x1e

(b)

⌊ ⌋ ln(x21 + x22) + x1x2 f(x1,x2) = ⌈ 2 x1 ⌉ cos(x1)+ x 2e

(c)

⌊ ⌋ x3 − x2 f(x1,x2) = ⌈ 1 2 ⌉ ex1x2 + x1 cos(x2 )

(d)

⌊ ⌋ ⌈ tan (x1x2 )+ x32 ⌉ f(x1,x2 ) = ∘x2-+-x2-+ sin(x ) 1 2 1

(e)

⌊ ⌋ x ex2 − ln(1 + x2) f(x1,x2) = ⌈ 1 1 ⌉ x22cos(x1)+ x1x2

Problem 3. Let f(x₁,x₂) = x₁ ∘ |x2|- . Show that f is partially differentiable but not totally differentiable at (0,0).

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