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GENERAL PURE AND APPLIED MATHEMATICS
Textbook LECTURES ON LINEAR ALGEBRA
by Donald S Passman (University of Wisconsin-Madison, USA)
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The book consists of expanded notes of an upper level linear algebra course the author offered. Each section, or lecture, covers about a week’s worth of material and includes a mixture of exercises of interest. So it feels like a series of lectures that is very readable. The notes cover all the basics of linear algebra but from a mature point of view. The author starts by briefly discussing fields and use these axioms to define and explain vector spaces, then carefully explores the relationship between linear transformations and matrices in an easy to understand manner. Determinants are introduced as volume functions and ways to determine whether vectors are linearly independent. Also included is a full chapter on bilinear forms and a brief chapter on infinite dimensional spaces.
The book is very well written, with numerous examples and exercises. It includes proofs and techniques that the author has developed over the years to make the material easier to understand and to compute.
Contents: Vector Spaces; Linear Transformations; Determinants; Bilinear Forms; Infinite Dimensional Spaces.
Readership: Upper level undergraduate math majors and graduate students.
250pp May 2022 978-981-125-484-0 US$88 £70 978-981-125-499-4(pbk) US$48 £40
Textbook
Essential Textbooks in Mathematics
ANALYSIS IN EUCLIDEAN SPACE
by Joaquim Bruna (Universitat Autònoma de Barcelona, Spain & Barcelona Graduate School of Mathematics, Spain) Based on notes written during the teacher’s many years of teaching, Analysis in Euclidean Space mainly covers Differentiation and Integration theory in several real variables, but also an array of closely related areas including measure theory, differential geometry, classical theory of curves geometric measure theory, integral geometry, and others. With several original results, new approaches and an emphasis on concepts and rigorous proofs, the book is suitable for undergraduate students, particularly in mathematics and physics, who are interested in acquiring a solid grounding in analysis and expanding their background. There are many examples and exercises inserted in the text for the student to work independently. Featured Contents: Introduction; Euclidean Space; Continuous Functions; Coordinate Systems, Curves and Surfaces; Differentiation; Higher Order Derivatives; The Inverse and Implicit Function Theorems; Regular SubManifolds; Ordinary Differential Equations; Linear Partial Differential Equations; Orthogonal Families of Curves and Surfaces; Measuring Sets: The Riemann Integral; The Lebesgue Integral; Fubini’s Theorem and Change of Variables; Integration on Sub-Manifolds; Line Integrals and Flux; and others. Readership: Undergraduate and graduate students.
