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Mathematics of Machine Learning

Mathematics of Machine Learning

By : Tivadar Danka
3 (2)
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Mathematics of Machine Learning

Mathematics of Machine Learning

3 (2)
By: Tivadar Danka

Overview of this book

Mathematics of Machine Learning provides a rigorous yet accessible introduction to the mathematical underpinnings of machine learning, designed for engineers, developers, and data scientists ready to elevate their technical expertise. With this book, you’ll explore the core disciplines of linear algebra, calculus, and probability theory essential for mastering advanced machine learning concepts. PhD mathematician turned ML engineer Tivadar Danka—known for his intuitive teaching style that has attracted 100k+ followers—guides you through complex concepts with clarity, providing the structured guidance you need to deepen your theoretical knowledge and enhance your ability to solve complex machine learning problems. Balancing theory with application, this book offers clear explanations of mathematical constructs and their direct relevance to machine learning tasks. Through practical Python examples, you’ll learn to implement and use these ideas in real-world scenarios, such as training machine learning models with gradient descent or working with vectors, matrices, and tensors. By the end of this book, you’ll have gained the confidence to engage with advanced machine learning literature and tailor algorithms to meet specific project requirements. *Email sign-up and proof of purchase required
Table of Contents (36 chapters)
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2
Part 1: Linear Algebra
11
References
12
Part 2: Calculus
19
References
20
Part 3: Multivariable Calculus
24
References
25
Part 4: Probability Theory
29
References
30
Part 5: Appendix
31
Other Books You May Enjoy
32
Index

C.2 Operations on sets

Describing more complex sets with only these two methods (listing their members or using the set-builder notation) is extremely difficult. To make the job easier, we define operations on sets.

C.2.1 Union, intersection, difference

The most basic operations are the union, intersection, and difference. You are probably familiar with these, as they are encountered frequently as early as high school. Even if you are familiar with them, check out the formal definition next.

Definition 109. (Set operations)

Let A and B be two sets. We define

(a) their union by A B := {x : x A or x B},

(b) their intersection by A B := {x : x A and x B},

(c) and their difference by A B := {x : x A and x∈∕B}.

We can easily visualize these with Venn diagrams, as you can see below.

PIC

Figure C.1: Set operations visualized in Venn diagrams

We can express set operations in plain English as well. For example, A∪...

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Mathematics of Machine Learning
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