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Mathematics of Machine Learning

Mathematics of Machine Learning

By : Tivadar Danka
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Mathematics of Machine Learning

Mathematics of Machine Learning

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.
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

14
Integration

When we first encountered the concept of derivatives in Chapter 12, we introduced it through an example from physics. As Newton created it, the derivative describes the velocity of a moving object as calculated from its time-distance graph. In other words, the velocity can be derived from the time-distance information.

Can the distance be reconstructed given the velocity? In a sense, this is the inverse of differentiation.

Questions such as these are hard to answer if we only look at the most general case, so let’s consider a special one. Suppose that our object is moving with a constant velocity v(t) = v0ms-, for a duration of T seconds. With some elementary logic, we can conclude that the total distance traveled is v0T meters.

When taking a look at the time-velocity plot, we can immediately see that the distance is the area under the time-velocity function graph v(t) = v0.

The graph of v(t) describes a rectangle with width v0 and length T, hence its area is indeed...

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Mathematics of Machine Learning
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