The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.

With cooperation of Aline Robert, Janine Rogalski, Maha Abboud-Blanchard, Claire Cazes, Monique Chappet-Pariès, Aurélie Chesnais, Christophe Hache, Julie Horoks, Eric Roditi & Nathalie Sayac. This book presents unique insights into a significant area of French research relating the learning and teaching of mathematics in school classrooms and their development. Having previously had only glimpses of this work, I have found the book fascinating in its breadth of theory, its links between epistemological, didactic and cognitive perspectives and its comprehensive treatment of student learning of mathematics, classroom activity, the work of teachers and prospective teacher development. Taking theoretical perspectives as their starting points, the authors of this volume present a rich array of theoretically embedded studies of mathematics teaching and learning in school classrooms. Throughout this book the reader is made aware of many unanswered questions and challenged to consider associated theoretical and methodological issues. For English-speaking communities who have lacked opportunity to access the French literature the book opens up a wealth of new ways of thinking about and addressing unresolved issues in mathematics learning, teaching and teacher education. I recommend it wholeheartedly! (Extract from Barbara Jaworski’s preface.)