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Add the vital warm-up process to your algebra lessons with these workouts designed to capture students’ interest and reinforce their skills. A broad range of concepts is covered from linear equations to factoring to pure fun. Each workout is easily reproducible and includes an answer key or mini-lesson demonstrating how to solve each problem. Essential teaching tips for the algebra classroom are also included.
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.
Includes 100 algebraic exercises as well as essential teaching tips.
This book will help "turn on the light" as each workout is designed to engage students' exploration of algebra as they complete each thought-provoking, skill-building activity. Each workout is easily reproducible and includes an answer key or mini-lesson that demonstrates how to solve each problem. 14 practical teaching tips are included.
Add the vital warm-up process to your algebra lessons with these workouts designed to capture students’ interest and reinforce their skills. A broad range of concepts is covered from linear equations to factoring to pure fun. Each workout is easily reproducible and includes an answer key or mini-lesson demonstrating how to solve each problem. Essential teaching tips for the algebra classroom are also included.
Add the vital warm-up process to your algebra lessons with these workouts designed to capture students’ interest and reinforce their skills. A broad range of concepts is covered from linear equations to factoring to pure fun. Each workout is easily reproducible and includes an answer key or mini-lesson demonstrating how to solve each problem. Essential teaching tips for the algebra classroom are also included.
Mathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general. This book is designed for students who plan to specialize in logic, as well as for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginning graduate-level course. There are three main chapters: Set Theory, Model Theory, and Recursion Theory. The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms. It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals. The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Lowenheim-Skolem Theorems, elementary submodels, model completeness, and applications to algebra. This chapter also continues the foundational issues begun in the set theory chapter. Mathematics can now be viewed as formal proofs from ZFC. Also, model theory leads to models of set theory. This includes a discussion of absoluteness, and an analysis of models such as H( ) and R( ). The Recursion Theory chapter develops some basic facts about computable functions, and uses them to prove a number of results of foundational importance; in particular, Church's theorem on the undecidability of logical consequence, the incompleteness theorems of Godel, and Tarski's theorem on the non-definability of truth.
Add the vital warm-up process to your algebra lessons with these workouts designed to capture students’ interest and reinforce their skills. A broad range of concepts is covered from linear equations to factoring to pure fun. Each workout is easily reproducible and includes an answer key or mini-lesson demonstrating how to solve each problem. Essential teaching tips for the algebra classroom are also included.