A mathematical introduction to the theory and applications of logic and set theory with an emphasis on writing proofs Highlighting the applications and notations of basic mathematical concepts within the framework of logic and set theory, A First Course in Mathematical Logic and Set Theory introduces how logic is used to prepare and structure proofs and solve more complex problems. The book begins with propositional logic, including two-column proofs and truth table applications, followed by first-order logic, which provides the structure for writing mathematical proofs. Set theory is then introduced and serves as the basis for defining relations, functions, numbers, mathematical induction, ordinals, and cardinals. The book concludes with a primer on basic model theory with applications to abstract algebra. A First Course in Mathematical Logic and Set Theory also includes: <ul>
<li>Section exercises designed to show the interactions between topics and reinforce the presented ideas and concepts</li> <li>Numerous examples that illustrate theorems and employ basic concepts such as Euclid’s lemma, the Fibonacci sequence, and unique factorization</li> <li>Coverage of important theorems including the well-ordering theorem, completeness theorem, compactness theorem, as well as the theorems of Löwenheim–Skolem, Burali-Forti, Hartogs, Cantor–Schröder–Bernstein, and König</li> </ul>
An excellent textbook for students studying the foundations of mathematics and mathematical proofs, A First Course in Mathematical Logic and Set Theory is also appropriate for readers preparing for careers in mathematics education or computer science. In addition, the book is ideal for introductory courses on mathematical logic and/or set theory and appropriate for upper-undergraduate transition courses with rigorous mathematical reasoning involving algebra, number theory, or analysis.

A First Course in Mathematical Logic and Set Theory

Science & Math

O'Leary, Michael L.

Mathematics

wiley

A text for a junior and senior level courses in modern geometryand/or history of mathematics for mathematics majors as well assecondary education students (this book meets the state geometrystandards for California, Florida, Illinois, New York, andTexas).  A prerequisite for this book includes completion ofthe introductory calculus sequence.  While there is minimalcalculus content in the book, the study of proofs does becomerather involved.•Highlights from the history of geometry are intertwined withexplanations on how to read and write proofs.•This is the first book to present the works of Euclid andHilbert in addition to other geometers in chronological order, allin an effort to show how the subject matter developed overtime.•Hints and both partial and complete solutions are includedat the end of the book as an aid for selected exercises.•This book develops ideas with careful attention to logic andfollows the development of the field through time.•An Instructor's Solutions Manual is available uponrequest.

Revolutions of Geometry Book and Solutions Set (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts)

LINEAR ALGEBRA EXPLORE A COMPREHENSIVE INTRODUCTORY TEXT IN LINEAR ALGEBRA WITH COMPELLING SUPPLEMENTARY MATERIALS, INCLUDING A COMPANION WEBSITE AND SOLUTIONS MANUALS Linear 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: <ul> <li>A thorough introduction to logic and set theory, as well as descriptions of functions and linear transformations</li> <li>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</li> <li>Discussions of abstract vector spaces, including subspaces, linear independence, dimension, and change of basis</li> <li>A treatment on defining geometries on vector spaces, including the Gram-Schmidt process</li> </ul> Perfect 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.

Linear Algebra

See the best price to sell, buy, or rent books by O'Leary, Michael L.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by O'Leary, Michael L.

See the best price to sell, buy, or rent books by O'Leary, Michael L.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

A First Course in Mathematical Logic and Set Theory

Revolutions of Geometry Book and Solutions Set (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts)

Linear Algebra