This is a textbook to help readers understand the steps that lead to deep learning. Linear algebra comes first especially singular values, least squares, and matrix factorizations. Often the goal is a low rank approximation A = CR (column-row) to a large matrix of data to see its most important part. This uses the full array of applied linear algebra, including randomization for very large matrices. Then deep learning creates a large-scale optimization problem for the weights solved by gradient descent or better stochastic gradient descent. Finally, the book develops the architectures of fully connected neural nets and of Convolutional Neural Nets (CNNs) to find patterns in data. Audience: This book is for anyone who wants to learn how data is reduced and interpreted by and understand matrix methods. Based on the second linear algebra course taught by Professor Strang, whose lectures on the training data are widely known, it starts from scratch (the four fundamental subspaces) and is fully accessible without the first text.

Linear Algebra and Learning from Data

Computers & Technology

Strang, Gilbert

Computer Science

Wellesley-Cambridge Press

Renowned applied mathematician Gilbert Strang teaches applied mathematics with the clear explanations, examples and insights of an experienced teacher. This book progresses steadily through a range of topics from symmetric linear systems to differential equations to least squares and Kalman filtering and optimization. It clearly demonstrates the power of matrix algebra in engineering problem solving. This is an ideal book (beloved by many readers) for a first course on applied mathematics and a reference for more advanced applied mathematicians. The only prerequisite is a basic course in linear algebra.

Introduction to Applied Mathematics

Science & Math

Mathematics

Encompasses the full range of computational science and engineering from modelling to solution, both analytical and numerical. It develops a framework for the equations and numerical methods of applied mathematics. Gilbert Strang has taught this material to thousands of engineers and scientists (and many more on MIT's OpenCourseWare 18.085-6). His experience is seen in his clear explanations, wide range of examples, and teaching method. The book is solution-based and not formula-based: it integrates analysis and algorithms and MATLAB codes to explain each topic as effectively as possible. The topics include applied linear algebra and fast solvers, differential equations with finite differences and finite elements, Fourier analysis and optimization. This book also serves as a reference for the whole community of computational scientists and engineers. Supporting resources, including MATLAB codes, problem solutions and video lectures from Gilbert Strang's 18.085 courses at MIT, are provided at math.mit.edu/cse.

Computational Science and Engineering

Gilbert Strang's Calculus textbook is ideal both as a course companion and for self study. The author has a direct style. His book presents detailed and intensive explanations. Many diagrams and key examples are used to aid understanding, as well as the application of calculus to physics and engineering and economics. The text is well organized, and it covers single variable and multivariable calculus in depth. An instructor's manual and student guide are available online at http://ocw.mit.edu/ans7870/resources/Strang/strangtext.htm.

Calculus

First edition of a long series of editions of this text. Although not applicable for class instruction, provides an excellent introduction to the following topics to the lay reader. 1. Vectors and Matrices 2 Solving Linear Equations 3 Vector Spaces and Subspaces 4 Orthgonality 5 Determinants 6 Eigenvalues and Eigenvectors 7 Linear Transformations 8 Applications 9 Numerical Linear Algebra 10 Complex Vectors and Complex Matrices

Introduction to Linear Algebra

Gilbert Strang

This book explains wavelets to both engineers and mathematicians. It approaches the subject with a major emphasis on the filter structures attached to wavelets. Those filters are the key to algorithmic efficiency and they are well developed throughout signal processing. Now they make possible major achievements in data analysis and compression. The explanations of difficult topics are direct, rigorous and very approachable. Many practical applications are discussed. The book is ideal as an introduction to the principles of wavelets and as a reference for the analysis and applications. Also included in Wavelets and Filter Banks are many examples to make effective use of the MATLAB Wavelet Toolbox.

Wavelets and Filter Banks

Nguyen, Truong

This informally written text provides students with a clear introduction into the subject of linear algebra. Topics covered include matrix multiplication, row reduction, matrix inverse, orthogonality and computation. The self-teaching book is loaded with examples and graphics and provides a wide array of probing problems, accompanying solutions, and a glossary. 
 Chapter 1: Introduction to Vectors; Chapter 2: Solving Linear Equations; Chapter 3: Vector Spaces and Subspaces; Chapter 4: Orthogonality; Chapter 5: Determinants; Chapter 6: Eigenvalues and Eigenvectors; Chapter 7: Linear Transformations; Chapter 8: Applications; Chapter 9: Numerical Linear Algebra; Chapter 10: Complex Vectors and Matrices; Solutions to Selected Exercises; Final Exam. Matrix Factorizations. Conceptual Questions for Review. Glossary: A Dictionary for Linear Algebra Index Teaching Codes Linear Algebra in a Nutshell.

Introduction to Linear Algebra, Third Edition

This second edition has two parts. The first part is the complete classic by Gilbert Strang and George Fix, first published in 1973. The original book demonstrates the solid mathematical foundation of the finite element idea, and the reasons for its success. The second part is a new textbook by Strang. It provides examples, codes, and exercises to connect the theory of the Finite Element Method directly to the applications. The reader will learn how to assemble the stiffness matrix K and solve the finite element equations KU=F. Discontinuous Galerkin methods with a numerical flux function are now included. Strang's approach is direct and focuses on learning finite elements by using them.

An Analysis of the Finite Element Method

Fix, George

This leading textbook for first courses in linear algebra comes from the hugely experienced MIT lecturer and author Gilbert Strang. The book's tried and tested approach is direct, offering practical explanations and examples, while showing the beauty and variety of the subject. Unlike most other linear algebra textbooks, the approach is not a repetitive drill. Instead it inspires an understanding of real mathematics. The book moves gradually and naturally from numbers to vectors to the four fundamental subspaces. This new edition includes challenge problems at the end of each section. Preview five complete sections at math.mit.edu/linearalgebra. Readers can also view freely available online videos of Gilbert Strang's 18.06 linear algebra course at MIT, via OpenCourseWare (ocw.mit.edu), that have been watched by over a million viewers. Also on the web (http://web.mit.edu/18.06/www/), readers will find years of MIT exam questions, MATLAB help files and problem sets to practise what they have learned.

The emergence of satellite technology has changed the lives of millions of people. In particular, GPS has brought an unprecedented level of accuracy to the field of geodesy. This text is a guide to the algorithms and mathematical principles that account for the success of GPS technology and replaces the authors' previous work, Linear Algebra, Geodesy, and GPS (1997). An initial discussion of the basic concepts, characteristics and technical aspects of different satellite systems is followed by the necessary mathematical content which is presented in a detailed and self-contained fashion. At the heart of the matter are the positioning algorithms on which GPS technology relies, the discussion of which will affirm the mathematical contents of the previous chapters. Numerous ready-to-use MATLAB codes are included for the reader. This comprehensive guide will be invaluable for engineers and academic researchers who wish to master the theory and practical application of GPS technology.

Algorithms for Global Positioning

Borre, Kai

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Books by Wellesley-Cambridge Press

See the best price to sell, buy or rent books by the Wellesley-Cambridge Press publisher. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Linear Algebra and Learning from Data

Introduction to Applied Mathematics

Computational Science and Engineering

Calculus

Introduction to Linear Algebra

Wavelets and Filter Banks

Introduction to Linear Algebra, Third Edition

An Analysis of the Finite Element Method

Introduction to Linear Algebra

Algorithms for Global Positioning