Introduction section of Mathematical foundations of data science

This is the introduction section of my book - Mathematical foundations of data science.

If you are curious about the image - see below!

Introduction

There is a beautiful German word called ‘Leitmotif’. Roughly, it translates as a common theme in music that repeats again across the music composition. I think mathematics is like a leitmotif. Mathematics comprises a few ideas that repeat. If you understand these ideas and how they apply to a domain, you can use them to learn complex topics, in our case, Artificial Intelligence.?

In a nutshell, Artificial intelligence (AI) is the ability of a machine to perform complex tasks at the same ability as a human would. Historically these tasks could only be performed by humans and not machines. Today, we are living in a world dominated by AI tools like chatGPT. Most of us now appreciate that this world where AI dominates most aspects of society will soon be upon us.? Some say in five years - others in twenty years. But in either case, most people agree it will appear in our lifetime.?

We also know that AI will be highly disruptive to humans. Disruption creates opportunities but also challenges. I take an optimistic view of AI. To make the best of AI opportunities, we need to find new ways of accelerating the learning of AI itself. This book uses the idea of maths foundations to learn AI. In the age of chatGPT talking a maths-based approach to learning AI may seem counter intuitive - but I offer three reasons for doing so.

Firstly, the maths concepts I use here are probably known to many people especially if they have studied a maths or a science based degree. The book is based on an understanding of functions, probability theory, statistics, linear algebra and optimization. These ideas are familiar to most people in the first year of a Bachelor’s degree (age 18).?

Secondly, chatGPT and other tools make it easier to learn topics - even coding. But that ease makes it all the more important to understand the fundamentals of AI. Maths offers you the best way to learn the fundamentals of AI.?

Finally, chatgPT could actually help you to understand this book. In fact, I assume,you will use a similar tool to learn many concepts that you need to brush up if needed. It also allows me to keep the book concise. ?

In fact, I have made a conscious attempt to keep the book concise. It would have been easier to create a bigger book by explaining concepts like vectros, matrices, matrix transpose etc. But these ideas are probably known to you and you can brush them up easily. It is in fact more important to understand how these concepts fit together in context of machine learning and deep learning. For the same reason, I have avoided including equations or diagrams unnecessarily.?

The audience for this book is neither mathematicians nor developers. The audience is anyone who wants to use certain key maths concepts to understand machine learning and deep learning - whether they are studying these ideas now or they have studied these ideas decades ago.

I am to keep the book concise - about 125 A4 pages (which makes about less than 200 page book)

The book has three sections:

Section One - Fundamentals

Section Two - Conceptions and Misconceptions - ideas about machine learning and deep learning that people typically get wrong and?

Section Three Mathematical foundations of machine learning and deep learning - where we see how the core maths ideas underpin various aspects of machine learning and deep learning.?

The book is based on my teaching - but is not associated with any university?

Finally, ending this introduction on a musical note. Despite the best efforts of my German friends, I have never quite gotten the hang of classical music. So, from a musical perspective, the real tribute goes to the music I listen to that keeps me going for long hours: AC/DC, Guns and Roses, Metallica, Iron Maiden and Pink Floyd!

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