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15 Math Concepts Every Data Scientist Should Know
15 Math Concepts Every Data Scientist Should Know

15 Math Concepts Every Data Scientist Should Know: Understand and learn how to apply the math behind data science algorithms

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15 Math Concepts Every Data Scientist Should Know

Recap of Mathematical Notation and Terminology

Our tour of math concepts will start properly in Chapter 2. Before we begin that tour, we’ll start by recapping some mathematical notation and terminology. Mathematics is a language, and mathematical symbols and notation are its alphabet. Therefore, we must be comfortable with and understand the basics of this alphabet.

In this chapter, we will recap the most common core notation and terminology that we are likely to use repeatedly throughout the book. We have grouped the recap into six main math areas or topics. Those topics are as follows:

  • Number systems: In this section, we introduce notation for real and complex numbers
  • Linear algebra: In this section, we introduce notation for describing vectors and matrices
  • Sums, products, and logarithms: In this section, we introduce notation for succinctly representing sums and products, and we introduce rules for logarithms
  • Differential and integral calculus: In this...

Technical requirements

As this chapter solely recaps some of the mathematical notation we will use in later chapters, there are no code examples given and hence no technical requirements for this particular chapter.

For later chapters, you will be able to find code examples at the GitHub repository: https://github.com/PacktPublishing/15-Math-Concepts-Every-Data-Scientist-Should-Know

Number systems

In this section, we introduce notation for describing sets of numbers. We will focus on the real numbers and the complex numbers.

Notation for numbers and fields

As this is a book about data science, we will be dealing with numbers. So, it will be worthwhile recapping the notation we use to refer to the most common sets of numbers.

Most of the numbers we will deal with in this book will be real numbers, such as 4.6, 1, or -2.3. We can think of them as “living” on the real number line shown in Figure 1.1. The real number line is a one-dimensional continuous structure. There are an infinite number of real numbers. We denote the set of all real numbers by the symbol .

Figure 1.1: The real number line

Figure 1.1: The real number line

Obviously, there will be situations where we want to restrict our datasets to, say, just integer-valued numbers. This would be the case if we were analyzing count data, such as the number of items of a particular...

Linear algebra

In this section, we introduce notation to describe vectors and matrices, which are key mathematical objects that we will encounter again and again throughout this book.

Vectors

In many circumstances, we will want to represent a set of numbers together. For example, the numbers 7.3 and 1.2 might represent the values of two features that correspond to a data point in a training set. We often group these numbers together in brackets and write them as (7.3, 1.2) or [7.3, 1.2]. Because of the similarity to the way we write spatial coordinates, we tend to call a collection of numbers that are held together a vector. A vector can be two-dimensional, as in the example just given, or d-dimensional, meaning it contains d components, and so might look like <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mfenced separators="|"><mml:mrow><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfenced></mml:math>.

We can write a vector in two ways. We can write it as a row vector, going across the page, such as the following vector:

<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mfenced open="(" close=")"><mrow><msub><mi>x</mi><mn>1</mn></msub><mo>,</mo><msub><mi>x</mi><mn>2</mn></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mi>x</mi><mi>d</mi></msub></mrow></mfenced><mo>=</mo><mtext>a</mtext></mrow></mrow></math> d-dimensional row vector

Eq. 8

Alternatively, we can write it as a column vector going...

Sums, products, and logarithms

In this section, we introduce notation for doing the most basic operations we can do with numbers, namely adding them together or multiplying them together. We’ll then introduce notation for working with logarithms.

Sums and the 𝚺 notation

When we want to add several numbers together, we can use the summation, or <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi mathvariant="normal">Σ</mml:mi></mml:math>, notation. For example, if we want to represent the addition of the numbers <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant="normal">x</mml:mi></mml:mrow><mml:mrow><mml:mn>5</mml:mn></mml:mrow></mml:msub></mml:math>, we use the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi mathvariant="normal">Σ</mml:mi></mml:math> notation to write this as follows:

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mrow><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>i</mi><mo>=</mo><mn>5</mn></mrow></munderover><msub><mi>x</mi><mi>i</mi></msub></mrow></mrow></math>

Eq. 13

This notation is shorthand for writing <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>5</mml:mn></mml:mrow></mml:msub></mml:math>. This essentially defines what the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi mathvariant="normal">Σ</mml:mi></mml:math> notation represents – that is, the following:

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mrow><mrow><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>i</mi><mo>=</mo><mn>5</mn></mrow></munderover><msub><mi>x</mi><mi>i</mi></msub></mrow><mo>=</mo><msub><mi>x</mi><mn>1</mn></msub><mo>+</mo><msub><mi>x</mi><mn>2</mn></msub><mo>+</mo><msub><mi>x</mi><mn>3</mn></msub><mo>+</mo><msub><mi>x</mi><mn>4</mn></msub><mo>+</mo><msub><mi>x</mi><mn>5</mn></msub></mrow></mrow></math>

Eq. 14

In the left-hand side (LHS) of Eq. 14, the integer indexing variable, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>i</mml:mi></mml:math>, takes the values between 1 (indicated beneath the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi mathvariant="normal">Σ</mml:mi></mml:math> symbol) and 5 (indicated above the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi mathvariant="normal">Σ</mml:mi></mml:math> symbol) and we interpret the LHS as “take all the numbers <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math> for the values of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>i</mml:mi></mml:math> indicated by the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi mathvariant="normal">Σ</mml:mi></mml:math> symbol and add them together.”

You may wonder whether the shorthand...

Differential and integral calculus

In this section, we won’t go into the fundamentals of differential calculus, but instead just recap some basic results and notation. Therefore, we are assuming you already have some basic familiarity with differentiation and integration.

Differentiation

Let’s start with what the derivative of a function or curve <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>y</mml:mi><mml:mfenced separators="|"><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:mfenced></mml:math> intuitively represents. An example curve is shown in Figure 1.5. The derivative of this function is denoted by the following symbol:

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mfrac><mrow><mi>d</mi><mi>y</mi></mrow><mrow><mi>d</mi><mi>x</mi></mrow></mfrac></mrow></math>

Eq. 29

The derivative of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>y</mml:mi><mml:mfenced separators="|"><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:mfenced></mml:math> is itself a function of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>x</mml:mi></mml:math>. The numerical value of the derivative evaluated at a particular value of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>x</mml:mi></mml:math>, let’s say at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>x</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math>, is the gradient (or slope) of the tangent to the curve <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>y</mml:mi><mml:mfenced separators="|"><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:mfenced></mml:math> at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>x</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math>. As such, we can think of the derivative as defining the local gradient value of the curve. This is illustrated in Figure 1.5 as well:

Figure 1.5: The derivative as the gradient of the tangent to the curve

Figure 1.5: The derivative as the gradient of the tangent to the curve

Sometimes, when we want to be explicit...

Analysis

In this section, we recap the notation that is used in analyzing and describing the behavior of functions. This includes notation for describing limits, notation for describing the relative ordering of functions, and notation for describing standard approximations of functions.

Limits

When we are talking about limits, we are talking about the mathematical behavior of some quantity, often a function, as some other quantity approaches a particular value, often infinity. Let’s make that more concrete. Consider the function <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>f</mml:mi><mml:mfenced separators="|"><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:mfenced><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:mfrac></mml:math> . As <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>x</mml:mi></mml:math> gets bigger and bigger, then clearly, the value of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>f</mml:mi><mml:mfenced separators="|"><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:mfenced></mml:math> gets smaller and smaller, until eventually, as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>x</mml:mi></mml:math> becomes infinitely large, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>f</mml:mi><mml:mfenced separators="|"><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:mfenced></mml:math> becomes zero. We say that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>f</mml:mi><mml:mfenced separators="|"><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:mfenced></mml:math> approaches its limit of 0 as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>x</mml:mi></mml:math> approaches <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi mathvariant="normal">∞</mml:mi></mml:math>. Mathematically, we write this as follows:

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mrow><munder><mi>lim</mi><mrow><mi>x</mi><mo>→</mo><mi mathvariant="normal">∞</mi></mrow></munder><mi>f</mi><mfenced open="(" close=")"><mi>x</mi></mfenced><mo>=</mo><mn>0</mn></mrow></mrow></math>

Eq. 46

The word lim denotes the fact that we are talking about a limit, while the symbols <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>x</mml:mi><mml:mo>→</mml:mo><mml:mi mathvariant="normal">∞</mml:mi></mml:math> describe what limit we are talking about. The RHS of Eq. 46 gives the actual limiting value.

Sometimes...

Combinatorics

Our final section regards binomial coefficients. They are part of the mathematical field of combinatorics, but we will introduce them in the context of the binomial distribution, which we will meet multiple times in the book.

Binomial coefficients

Along with the normal or Gaussian distribution, the binomial distribution is one of the most common distributions we will encounter as data scientists. It is the distribution of the number of times, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>n</mml:mi></mml:math>, we observe a particular outcome in a set of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>N</mml:mi></mml:math> observations, where in each observation there are only two possibilities that can occur. Given we are interested only in the total number, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>n</mml:mi></mml:math>, of successful outcomes of a particular type, a large part of calculating the associated probability comes down to calculating how many ways we can distribute or arrange the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>n</mml:mi></mml:math> successes between the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>N</mml:mi></mml:math> observations. The answer is given by the binomial coefficient <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mfenced separators="|"><mml:mrow><mml:mfrac linethickness="0pt"><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:mfenced></mml:math>. This is defined mathematically as follows:

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mrow><mfenced open="(" close=")"><mfrac><mi>N</mi><mi>n</mi></mfrac></mfenced><mo>=</mo><mfrac><mrow><mi>N</mi><mo>!</mo></mrow><mrow><mi>n</mi><mo>!</mo><mfenced open="(" close=")"><mrow><mi>N</mi><mo>−</mo><mi>n</mi></mrow></mfenced><mo>!</mo></mrow></mfrac></mrow></mrow></math>

Eq. 62

Here, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>n</mml:mi><mml:mo>!</mml:mo></mml:math> means <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>n</mml:mi></mml:math> factorial...

Summary

We have completed our brief recap of the main notation and terminology that we will need for our tour of math concepts in data science. We are now ready for that tour, so let’s begin.

In the next chapter, we will meet our first key math concept when we learn about random variables and probability distributions.

Notes and further reading

  1. An example of one of the more well-known “big book of integrals” is Table of Integrals, Series, and Products by I.S. Gradshteyn and I.M. Ryzhik, 8th Edition, Daniel Zwillinger (Editor), Academic Press (Cambridge, Massachusetts, USA), 2014. This is the book of integrals that I use.
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Data science combines the power of data with the rigor of scientific methodology, with mathematics providing the tools and frameworks for analysis, algorithm development, and deriving insights. As machine learning algorithms become increasingly complex, a solid grounding in math is crucial for data scientists. David Hoyle, with over 30 years of experience in statistical and mathematical modeling, brings unparalleled industrial expertise to this book, drawing from his work in building predictive models for the world's largest retailers. Encompassing 15 crucial concepts, this book covers a spectrum of mathematical techniques to help you understand a vast range of data science algorithms and applications. Starting with essential foundational concepts, such as random variables and probability distributions, you’ll learn why data varies, and explore matrices and linear algebra to transform that data. Building upon this foundation, the book spans general intermediate concepts, such as model complexity and network analysis, as well as advanced concepts such as kernel-based learning and information theory. Each concept is illustrated with Python code snippets demonstrating their practical application to solve problems. By the end of the book, you’ll have the confidence to apply key mathematical concepts to your data science challenges.

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Table of Contents

20 Chapters
Part 1: Essential Concepts Chevron down icon Chevron up icon
Chapter 1: Recap of Mathematical Notation and Terminology Chevron down icon Chevron up icon
Chapter 2: Random Variables and Probability Distributions Chevron down icon Chevron up icon
Chapter 3: Matrices and Linear Algebra Chevron down icon Chevron up icon
Chapter 4: Loss Functions and Optimization Chevron down icon Chevron up icon
Chapter 5: Probabilistic Modeling Chevron down icon Chevron up icon
Part 2: Intermediate Concepts Chevron down icon Chevron up icon
Chapter 6: Time Series and Forecasting Chevron down icon Chevron up icon
Chapter 7: Hypothesis Testing Chevron down icon Chevron up icon
Chapter 8: Model Complexity Chevron down icon Chevron up icon
Chapter 9: Function Decomposition Chevron down icon Chevron up icon
Chapter 10: Network Analysis Chevron down icon Chevron up icon
Part 3: Selected Advanced Concepts Chevron down icon Chevron up icon
Chapter 11: Dynamical Systems Chevron down icon Chevron up icon
Chapter 12: Kernel Methods Chevron down icon Chevron up icon
Chapter 13: Information Theory Chevron down icon Chevron up icon
Chapter 14: Non-Parametric Bayesian Methods Chevron down icon Chevron up icon
Chapter 15: Random Matrices Chevron down icon Chevron up icon
Index Chevron down icon Chevron up icon
Other Books You May Enjoy Chevron down icon Chevron up icon

Customer reviews

Top Reviews
Rating distribution
Full star icon Full star icon Full star icon Full star icon Half star icon 4.3
(6 Ratings)
5 star 83.3%
4 star 0%
3 star 0%
2 star 0%
1 star 16.7%
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Top Reviews

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Pablo Cepeda Oct 26, 2024
Full star icon Full star icon Full star icon Full star icon Full star icon 5
Nice book
Feefo Verified review Feefo
Amazon Customer Sep 22, 2024
Full star icon Full star icon Full star icon Full star icon Full star icon 5
The book is structured around 15 crucial concepts that form the bedrock of data science. From the very beginning, readers are introduced to foundational topics like random variables and probability distributions. Hoyle's clear explanations help readers grasp why data varies, setting a solid groundwork for the more complex ideas that follow. The transition into matrices and linear algebra is seamless, making complex mathematical concepts accessible even to those who may not have a strong math background.The progression from essential to advanced topics — such as kernel methods, information theory, and Bayesian non-parametric methods — is methodical and well-paced. The inclusion of topics like time series forecasting and network analysis further enriches the book, catering to a diverse range of interests within the data science community.Overall, this book is a significant contribution to the field of data science literature. It not only elucidates the mathematical principles that underpin various algorithms but also empowers readers to become more proficient in applying these concepts to real-world scenarios. For anyone serious about mastering data science, Hoyle’s work is a must-read, offering a blend of theory and practice that is sure to enhance your analytical capabilities.
Amazon Verified review Amazon
Gabriel Preda Sep 27, 2024
Full star icon Full star icon Full star icon Full star icon Full star icon 5
If you got here, you are planning probably to buy and read this book. Which will be an excellent idea, because is giving you the best value for money for this type of books. Let's see why the book structure, its content quality, the quality of printing, all are providing good reasons to do it.Structure: The book is structured in three parts, covering concepts gradually increasing in difficulty, from basic and introductory notions to intermediate and advanced. In the first part the basic principles in random numbers and probability distribution, matrices and linear algebra, loss functions, optimisation, probabilistic modeling are covered. In the second part, the book will tackle time series and forecasting, hypothesis testing, and model complexity, followed by function decomposition, and network analysis. In the last part, the more advanced topics of dynamical systems, kernel methods, information theory, non-parametric Bayesian methods and random matrices are covered.Content quality: The author is a former university professor and you can see that in the consistency of the material he included, as well as in the clear explanations of the notions, so that you can keep pace not only with the introductory chapters but also with the most advanced ones. The book is well documented, the notations are carefully edited, the narative is clear and easy to follow. This easiness to follow the content is supported by the author’s choice to add summaries, example, and further reading recommendations, depending on what is adequate in the specific case, to the end of each chapter. This helps the reader to crystallise his recently learned topics.Typography: When you read this book, you enjoy not only the quality of the content and the way that the author explains rather complex notions so that you can follow, but also the quality of the typography. A beautiful font (I read it on a paperback copy), with clear tables and beautifully rendered images, in color (which for a technical book, especially when graph are presented, is a very useful feature).Summary: An easy to read, well documented, highly recommended reference for those of you that takes seriously the Data Science specialisation. And an excellent introduction in the basic tools for the Data Scientist.
Amazon Verified review Amazon
Steven Fernandes Sep 12, 2024
Full star icon Full star icon Full star icon Full star icon Full star icon 5
Title: Elevate Your Data Science Skills: A Comprehensive GuideReview:This book is a comprehensive toolkit for anyone looking to deepen their data science expertise. It covers foundational concepts and advanced techniques, using real-world challenges to illustrate the application of theories. Practical implementations using Python libraries like NumPy, SciPy, and sci-kit-learn are detailed, alongside guidance on building predictive models and mastering Bayesian methods. It’s especially valuable for those interested in time series and network data. A must-have for aspiring and seasoned data scientists alike.
Amazon Verified review Amazon
Sai Kumar Bysani Oct 18, 2024
Full star icon Full star icon Full star icon Full star icon Full star icon 5
The book encompasses a wide array of mathematical concepts essential for data science, including:1. 𝐑𝐚𝐧𝐝𝐨𝐦 𝐕𝐚𝐫𝐢𝐚𝐛𝐥𝐞𝐬 & 𝐏𝐫𝐨𝐛𝐚𝐛𝐢𝐥𝐢𝐭𝐲 𝐃𝐢𝐬𝐭𝐫𝐢𝐛𝐮𝐭𝐢𝐨𝐧𝐬: Understanding the foundations of randomness and how different distributions impact data interpretation.2. 𝐋𝐢𝐧𝐞𝐚𝐫 𝐀𝐥𝐠𝐞𝐛𝐫𝐚: Key concepts like matrices and vectors that form the backbone of many algorithms used in machine learning and data analysis.3. 𝐋𝐨𝐬𝐬 𝐅𝐮𝐧𝐜𝐭𝐢𝐨𝐧𝐬 & 𝐎𝐩𝐭𝐢𝐦𝐢𝐳𝐚𝐭𝐢𝐨𝐧: Insight into how these elements are crucial for training models and making predictions.4. 𝐏𝐫𝐨𝐛𝐚𝐛𝐢𝐥𝐢𝐬𝐭𝐢𝐜 𝐌𝐨𝐝𝐞𝐥𝐢𝐧𝐠: Techniques for making inferences and predictions based on observed data.5. 𝐇𝐲𝐩𝐨𝐭𝐡𝐞𝐬𝐢𝐬 𝐓𝐞𝐬𝐭𝐢𝐧𝐠: A fundamental aspect of data science that helps in validating assumptions and claims based on data.6. 𝐓𝐢𝐦𝐞 𝐒𝐞𝐫𝐢𝐞𝐬 𝐀𝐧𝐚𝐥𝐲𝐬𝐢𝐬: Methods for analyzing data points collected or recorded at specific time intervals, essential for forecasting....and many more important math concepts!I like how the book combines theory with practical application, providing Python code snippets that help readers see how these concepts are applied in real-world scenarios. This practical focus makes the book particularly beneficial for those who learn best by doing.Whether you’re new to data science or looking to sharpen your skills, this book serves as a solid reference guide and a stepping stone to deeper understanding. It encourages readers to not only grasp the math but to apply it effectively in their data science projects.In conclusion, if you're looking to enhance your mathematical toolkit and elevate your data science skills, I highly recommend picking up this book. It’s a great addition to any data scientist’s library and a fantastic resource for professional growth.
Amazon Verified review Amazon
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Premium: Trackable delivery to most EU destinations within 4-9 business days.

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Economy: Can deliver to P. O. Boxes and private residences.
Trackable service with delivery to addresses in Australia only.
Delivery time ranges from 7-9 business days for VIC and 8-10 business days for Interstate metro
Delivery time is up to 15 business days for remote areas of WA, NT & QLD.

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Rest of the World:

Premium: Countries in the American continent: Trackable delivery to most countries within 4-7 business days

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Premium: Delivery to most Asian addresses within 5-9 business days

Disclaimer:
All orders received before 5 PM U.K time would start printing from the next business day. So the estimated delivery times start from the next day as well. Orders received after 5 PM U.K time (in our internal systems) on a business day or anytime on the weekend will begin printing the second to next business day. For example, an order placed at 11 AM today will begin printing tomorrow, whereas an order placed at 9 PM tonight will begin printing the day after tomorrow.


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