A Mathematical Introduction to Data Science with Python

This textbook serves as a companion to "A Mathematical Introduction to Data Science". It uses Python programming to provide a comprehensive foundation in the mathematics needed for data science. It is designed for anyone with a basic mathematical background, including students and self-learners interested in understanding the principles behind the computational algorithms used in data science. The focus of this book is to demonstrate how programming can aid in this understanding and be used in solving mathematical problems. It is written using Python as its programming language, but readers do not need prior knowledge of Python to benefit from it.

Some examples from "A Mathematical Introduction to Data Science" are used to illustrate key concepts such as sets, functions, linear algebra, calculus, and probability and statistics, through Python programming, though it is not necessary to have seen the examples before. Further, this textbook shows how those mathematical concepts can be applied in widely used computational algorithms, such as Principal Component Analysis, Singular Value Decomposition, Linear Regression in two and more dimensions, Simple Neural Networks, Maximum Likelihood Estimation, Logistic Regression and Ridge Regression.

This textbook is designed with the assumption that readers have no prior knowledge of Python but possess a basic understanding of programming concepts, such as control flow. Ideally, readers should have both this book and its companion, "A Mathematical Introduction to Data Science". However, those with a strong mathematical background and an interest in programming implementations can benefit from reading this textbook alone.

A hands-on Python companion to the maths book, applying concepts through practical coding exercises for deeper learning Provides a complete Python code listing for each example and exercise Early chapters detail code walkthroughs; later chapters focus on new Python functions, classes, and mathematical ideas https://github.com/sn-code-inside/MIDS-Python-Book

Autorentext

Dr. Yi Sun: Reader in Data Science, in the Department of Computer Science, at the University of Hertfordshire. She has extensive teaching experience in machine learning and data science since 2006. Her research focuses on machine learning applications, with additional interests in image processing, natural language processing, and time series analysis.

Prof. Rod Adams: Emeritus Professor, in the Department of Computer Science, at University of Hertfordshire. He has extensive experience in teaching both mathematics and computer science since the 1970s. His initial research was in mathematical logic and the maths behind compilers, especially for functional languages. Most of his research, however, has centred on neural modelling and machine learning in many application domains.

Inhalt

Chapter 1 Introduction.- Chapter 2 Sets and Functions.- Chapter 3 Liner Algebra.- Chapter 4 Matrix Decomposition.- Chapter 5 Calculus.- Chapter 6 Advanced Calculus.- Chapter 7 Algorithms 1 Principal Component Analysis.- Chapter 8 Algorithms 2 Liner Regression.- Chapter 9 Algorithms 3 Neural Networks.- Chapter 10 Probability.- Chapter 11 Further Probability.- Chapter 12 Elements of Statistics.- Chapter 13 Algorithms 4 Maximum Likelihood Estimation and Its Application to Regression.- Chapter 14 Data Modelling in Practice.