Popular features improved and updated in response to feedback from Matrix users. Systematic building of key vocabulary to cover up-to-date exam topics. Effective production: speaking practice in every lesson on a wide range of topics, and step-by-step guidance for writing a variety of text types. Grammar knowledge checked and activated in use. Strong focus on culture. Exam tips, techniques, and practice of exam-type tasks to give students confidence in the exam.

A series that prepares students for secondary school-leaving exams.

JETSTREAM is a brand new digital-age 6-level course for adult learners. Its carefully balanced pace and challenge offer a learning experience that is fun and motivating and which prepares students to use their English effectively in work and life.

A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

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.

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This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method, and automatic multilevel substructuring.