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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

D.2 The geometric representation

We can represent complex numbers in ways other than the one in the definition. If you think about it, each number z = a + bi can be seen as an ordered pair (a,b). These can be visualized as vectors on the Cartesian plane.

PIC

Figure D.2: Complex numbers as vectors on the Cartesian plane

The absolute value |z| = √ ------- a2 + b2 of a complex number z = a + bi represents the length of the vector (a,b) from the origin, while conjugation z = abi corresponds to reflecting the point across the real axis.

This geometric view gives us a new algebraic way to represent complex numbers.

To see why, recall the relation of the unit circle and the trigonometric functions on the plane.

PIC

Figure D.3: Geometric representation of complex numbers

This means that every complex number with unit absolute value can be written in the form cos(φ) + isin(φ). From the geometric representation, we can see that every complex number is uniquely determined by its...

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Mathematics of Machine Learning
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