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Machine Learning: An Applied Mathematics Introduction covers the essential mathematics behind all of the following topics

K Nearest Neighbours
K Means Clustering
Naïve Bayes Classifier
Regression Methods
Support Vector Machines
Self-Organizing Maps
Decision Trees
Neural Networks
Reinforcement Learning

The book includes many real-world examples from a variety of fields including

finance (volatility modelling)
economics (interest rates, inflation and GDP)
politics (classifying politicians according to their voting records, and using speeches to determine whether a politician is left or right wing)
biology (recognising flower varieties, and using heights and weights of adults to determine gender)
sociology (classifying locations according to crime statistics)
gambling (fruit machines and Blackjack)
business (classifying the members of his own website to see who will subscribe to his magazine!)

Paul Wilmott brings three decades of experience in mathematics education, and his inimitable style, to the hottest of subjects. This book is an accessible introduction for anyone who wants to understand the foundations but also wants to "get to the meat without having to eat too many vegetables."