In the first paragraph of the preface of Mathematical Tools for Data Mining, the authors state that “we emphasize that this book is about mathematical tools for data mining, not data mining itself.” Mathematicians will be reassured to know that the authors hold true to their word. In addition to the set theory, partial orders, and combinatorics mentioned in the subtitle, readers will find solid presentations of topologies and measures, linear spaces, norms and inner products, lattices and Boolean algebras, and more.
The authors also hold true to their word when they note that the book “is intended as a reference for the working data miner,” though this reviewer would add one caveat. Data miners who intend to use the book as a reference must have a facility with mathematical notation prior to using the book. As long as they do, they will find that the chapters and their subsections are well labeled and organized. Further, the prose is clear and the comprehensive index facilitates ease of use.
Mathematics faculty may consider using the book as more than simply a reference. That is, this textbook is appropriate for an advanced undergraduate or graduate mathematics elective class. All theorems are proved, notation is standard, and ample exercise sets are included at the end of every chapter. The treatment of topics progresses quickly from the introductory — for example rank, multilinear forms, and determinants are covered in the chapter titled “Linear Spaces” — to less common topics such as topological linear spaces. Significant sections of the book present the math on its own terms, though readers will also discover applications, such as those to databases and data mining.
At 800+ pages, Mathematical Tools for Data Mining: Set Theory, Partial Orders, Combinatorics is more than just the data-mining reference book. It is highly readable textbook that successfully connects classic, theoretical mathematics to an enormously popular current application in modern society.
Susan D’Agostino is an Associate Professor of Mathematics at Southern New Hampshire University. She also serves on NH Governor Maggie Hassan’s STEM Education Task Force.