Bøger af Michael L. (College of DuPage) O'Leary

LINEAR ALGEBRAEXPLORE A COMPREHENSIVE INTRODUCTORY TEXT IN LINEAR ALGEBRA WITH COMPELLING SUPPLEMENTARY MATERIALS, INCLUDING A COMPANION WEBSITE AND SOLUTIONS MANUALSLinear Algebra delivers a fulsome exploration of the central concepts in linear algebra, including multidimensional spaces, linear transformations, matrices, matrix algebra, determinants, vector spaces, subspaces, linear independence, basis, inner products, and eigenvectors. While the text provides challenging problems that engage readers in the mathematical theory of linear algebra, it is written in an accessible and simple-to-grasp fashion appropriate for junior undergraduate students.An emphasis on logic, set theory, and functions exists throughout the book, and these topics are introduced early to provide students with a foundation from which to attack the rest of the material in the text. Linear Algebra includes accompanying material in the form of a companion website that features solutions manuals for students and instructors. Finally, the concluding chapter in the book includes discussions of advanced topics like generalized eigenvectors, Schur's Lemma, Jordan canonical form, and quadratic forms. Readers will also benefit from the inclusion of:* A thorough introduction to logic and set theory, as well as descriptions of functions and linear transformations* An exploration of Euclidean spaces and linear transformations between Euclidean spaces, including vectors, vector algebra, orthogonality, the standard matrix, Gauss-Jordan elimination, inverses, and determinants* Discussions of abstract vector spaces, including subspaces, linear independence, dimension, and change of basis* A treatment on defining geometries on vector spaces, including the Gram-Schmidt processPerfect for undergraduate students taking their first course in the subject matter, Linear Algebra will also earn a place in the libraries of researchers in computer science or statistics seeking an accessible and practical foundation in linear algebra.

Rather than teach mathematics and the structure of proofssimultaneously, this book first introduces logic as the foundationof proofs and then demonstrates how logic applies to mathematicaltopics. This method ensures that readers gain a firmunderstanding of how logic interacts with mathematics and empowersthem to solve more complex problems.

* Highlights from the history of geometry are intertwined with explanations on how to read and write proofs. * This is the first book to present the works of Euclid and Hilbert in addition to other geometers in chronological order, all in an effort to show how the subject matter developed over time.

Based on the premise that in order to write proofs, one needs to read finished proofs as well as study both their logic and grammar, Revolutions in Geometry depicts how to write basic proofs in various fields of geometry.