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.

Reflecting the latest technology and tools of the trade, MATHEMATICS FOR MACHINE TECHNOLOGY, 7e provides the mathematical skills and practice that students and apprentices will use on the job in the machine trades and manufacturing fields. This comprehensive book combines math concepts with relevant machine applications through industry-specific examples, realistic illustrations, and actual machine applications. Problems and examples progress from the simple to the relatively complex, from general math to trigonometry and solid geometry, and relate directly to how the math is used in machine trades and manufacturing fields. The new Seventh Edition also includes all-new units on electronic calipers, height gages, and electronic micrometers, as well as thorough coverage of measuring in both metric and customary systems. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

This book covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.

From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

Math for Machinists provides students with a review of basic math operations (whole numbers, fractions, decimals, percentages) and measurements, and additional math topics directly applicable to machining and manufacturing, such as precision measurements, angles, area, volume, gear calculations, trigonometry, and working with coordinate systems. Creative machine shop-related problems and pertinent exercises help students develop their math skills, troubleshooting skills, and their knowledge of the trade. Updated by new author John Templeton, this edition includes eight new units, hundreds of additional applied practice problems, plus many new end-of-unit review questions throughout the text. Answers to odd-numbered problems are listed in the back of the text for self-assessment.

Advances in Mathematics for Industry 4.0 examines key tools, techniques, strategies, and methods in engineering applications. By covering the latest knowledge in technology for engineering design and manufacture, chapters provide systematic and comprehensive coverage of key drivers in rapid economic development. Written by leading industry experts, chapter authors explore managing big data in processing information and helping in decision-making, including mathematical and optimization techniques for dealing with large amounts of data in short periods. - Focuses on recent research in mathematics applications for Industry 4.0 - Provides insights on international and transnational scales - Identifies mathematics knowledge gaps for Industry 4.0 - Describes fruitful areas for further research in industrial mathematics, including forthcoming international studies and research