• -Preface for the Instructor-Preface for the Student-Acknowledgments-1. Vector Spaces-
• 2. Finite-Dimensional Vector Spaces-
• 3. Linear Maps-
• 4. Polynomials-
• 5. Eigenvalues, Eigenvectors, and Invariant Subspaces-
• 6. Inner Product Spaces-
• 7. Operators on Inner Product Spaces-
• 8. Operators on Complex Vector Spaces-
• 9. Operators on Real Vector Spaces-
• 10. Trace and Determinant-Photo Credits-Symbol Index-Index.
• (source: Nielsen Book Data)

This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have been added since the previous edition. Many new examples have been added to illustrate the key ideas of linear algebra. New topics covered in the book include product spaces, quotient spaces, and dual spaces. Beautiful new formatting creates pages with an unusually pleasant appearance in both print and electronic versions. No prerequisites are assumed other than the usual demand for suitable mathematical maturity. Thus the text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator. From reviews of previous editions: "...a didactic masterpiece" -Zentralblatt MATH "...a tour de force in the service of simplicity and clarity ...The most original linear algebra book to appear in years, it certainly belongs in every undergraduate library." -CHOICE "The determinant-free proofs are elegant and intuitive." -American Mathematical Monthly "Clarity through examples is emphasized ...the text is ideal for class exercises ...I congratulate the author and the publisher for a well-produced textbook on linear algebra." -Mathematical Reviews.
(source: Nielsen Book Data)

• Preface.- 1 The Real Numbers.- 2 Sequences and Series.- 3 Basic Topology of R.- 4 Functional Limits and Continuity.- 5 The Derivative.- 6 Sequences and Series of Functions.- 7 The Riemann Integral.- 8 Additional Topics.- Bibliography.- Index.
• (source: Nielsen Book Data)

This lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of them. By focusing on the unifying themes of approximation and the resolution of paradoxes that arise in the transition from the finite to the infinite, the text turns what could be a daunting cascade of definitions and theorems into a coherent and engaging progression of ideas. Acutely aware of the need for rigor, the student is much better prepared to understand what constitutes a proper mathematical proof and how to write one. Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition. Roughly 150 new exercises join a selection of the best exercises from the first edition, and three more project-style sections have been added. Investigations of Euler's computation of zeta(2), the Weierstrass Approximation - Theorem, and the gamma function are now among the book's cohort of seminal results serving as motivation and payoff for the beginning student to master the methods of analysis. Review of the first edition: "This is a dangerous book. Understanding Analysis is so well-written and the development of the theory so well-motivated that exposing students to it could well lead them to expect such excellence in all their textbooks...Understanding Analysis is perfectly titled; if your students read it, that's what's going to happen...This terrific book will become the text of choice for the single-variable introductory analysis course ..." - Steve Kennedy, MAA Reviews.
(source: Nielsen Book Data)