Date Published: August 2016
availability: Temporarily unavailable - available from March 2017
format: Hardback
isbn: 9780980232776
Linear algebra is something all mathematics undergraduates and many other students, in subjects ranging from engineering to economics, have to learn. The fifth edition of this hugely successful textbook retains all the qualities of earlier editions while at the same time seeing numerous minor improvements and major additions. The latter include: ? A new chapter on singular values and singular vectors, including ways to analyze a matrix of data ? A revised chapter on computing in linear algebra, with professional-level algorithms and code that can be downloaded for a variety of languages ? A new section on linear algebra and cryptography ? A new chapter on linear algebra in probability and statistics. A dedicated and active website also offers solutions to exercises as well as new exercises from many different sources (e.g. practice problems, exams, development of textbook examples), plus codes in MATLAB, Julia, and Python.
1. Introduction to vectors
2. Solving linear equations
3. Vector spaces and subspaces
4. Orthogonality
5. Determinants
6. Eigenvalues and eigenvectors
7. The singular value decomposition (SVD)
8. Linear transformations
9. Complex vectors and matrices
10. Applications
11. Numerical linear algebra
12. Linear algebra in probability and statistics
Matrix factorizations
Index
Six great theorems/linear algebra in a nutshell.
To Be Published: 20 January 2017
Publisher: International Press of Boston, Inc.
Paperback
192 pages
Description
Papers based on selected lectures given at the Current Development Mathematics
Conference,
held in November 2015 at Harvard University.
Series: Developments in Mathematics, Vol. 42
1st ed. 2015, X, 172 p. 123 illus., 39 illus. in
color.
Printed book
Hardcover
ISBN 978-1-4939-3081-4
* Presents an exciting playing field for graduate students and
researchers in mathematics, physics, and computer science, to
expand their knowledge in the field of algebraic geometry
* Comprehensive treatment brings graduate students and new
researchers to the forefront of the field
* Serves as excellent supplementary material for a graduate course on
Grassmannian varieties
This book gives a comprehensive treatment of the Grassmannian varieties and their
Schubert subvarieties, focusing on the geometric and representation-theoretic aspects of
Grassmannian varieties. Research of Grassmannian varieties is centered at the crossroads
of commutative algebra, algebraic geometry, representation theory, and combinatorics.
Therefore, this text uniquely presents an exciting playing field for graduate students
and researchers in mathematics, physics, and computer science, to expand their
knowledge in the field of algebraic geometry. The standard monomial theory (SMT) for
the Grassmannian varieties and their Schubert subvarieties are introduced and the text
presents some important applications of SMT including the Cohen?Macaulay property,
normality, unique factoriality, Gorenstein property, singular loci of Schubert varieties, toric
degenerations of Schubert varieties, and the relationship between Schubert varieties and
classical invariant theory.
This text would serve well as a reference book for a graduate work on Grassmannian
varieties and would be an excellent supplementary text for several courses including
those in geometry of spherical varieties, Schubert varieties, advanced topics in geometric
and differential topology, representation theory of compact and reductive groups, Lie
theory, toric varieties, geometric representation theory, and singularity theory. The reader
should have some familiarity with commutative algebra and algebraic geometry.
Series: Springer Undergraduate Texts in Mathematics and Technology
2017, XVII, 303 p. 40 illus.
Printed book
Hardcover
ISBN 978-3-319-50223-6
* Second edition includes a new chapter on numerical methods of
solution
* Second edition includes 246 worked examples and over 1000
exercises
* Discusses essential topics completely, concisely, and succinctly, in
"everyday classroom language" without unnecessary embellishment
* Text to be used both independently by average students and as
a basic framework in the fundamentals of the subject for more
advanced students
This textbook is designed with the needs of today’s student in mind. It is the ideal
textbook for a first course in elementary differential equations for future engineers and
scientists, including mathematicians. This book is accessible to anyone who has a basic
knowledge of precalculus algebra and differential and integral calculus. Its carefully
crafted text adopts a concise, simple, no-frills approach to differential equations, which
helps students acquire a solid experience in many classical solution techniques. With
a lighter accent on the physical interpretation of the results, a more manageable page
count than comparable texts, a highly readable style, and over 1000 exercises designed
to be solved without a calculating device, this book emphasizes the understanding and
practice of essential topics in a succinct yet fully rigorous fashion. Apart from several other
enhancements, the second edition contains one new chapter on numerical methods of
solution.
The book formally splits the "pure" and "applied" parts of the contents by placing the
discussion of selected mathematical models in separate chapters. At the end of most
of the 246 worked examples, the author provides the commands in MathematicaR
for verifying the results. The book can be used independently by the average student
to learn the fundamentals of the subject, while those interested in pursuing more
advanced material can regard it as an easily taken first step on the way to the next level.
Additionally, practitioners who encounter differential equations in their professional work
will find this text to be a convenient source of reference.
Other Springer publications by Christian Constanda: Dude, Can you Count? ISBN:
978-1-84882-538-3; (with D. Doty and W.
Series: SpringerBriefs in Quantitative Finance
1st ed. 2017, VIII, 142 p. 24 illus. in color.
Printed book
Softcover
ISBN 978-3-319-50967-9
* User-friendly presentation of the main theoretical properties
of the Fourier-Malliavin volatility estimation and its possible
extensionsProvides details to efficiently implement the proposed
estimators in real cases
* Includes codes for reproducing numerical results
This volume is a user-friendly presentation of the main theoretical properties of the
Fourier-Malliavin volatility estimation, allowing the readers to experience the potential
of the approach and its application in various financial settings. Readers are given
examples and instruments to implement this methodology in various financial settings
and applications of real-life data. A detailed bibliographic reference is included to permit
an in-depth study.
Series: Algebra and Applications, Vol. 22
1st ed. 2016, XX, 699 p. 273 illus.
Printed book
Hardcover
ISBN 978-981-10-3336-0
* Provides a self-contained treatment of commutative ring theory at
the graduate level
* Deals with recent hot topics including w-operation theory (which is
related to a special torsion theory) and relative homological algebra
* Includes many exercises for self-testing
This book provides an introduction to the basics and recent developments of
commutative algebra. A glance at the contents of the first five chapters shows that
the topics covered are ones that usually are included in any commutative algebra text.
However, the contents of this book differ significantly from most commutative algebra
texts: namely, its treatment of the Dedekind?Mertens formula, the (small) finitistic
dimension of a ring, Gorenstein rings, valuation overrings and the valuative dimension,
and Nagata rings. Going further, Chapter 6 presents w-modules over commutative rings
as they can be most commonly used by torsion theory and multiplicative ideal theory.
Chapter 7 deals with multiplicative ideal theory over integral domains. Chapter 8 collects
various results of the pullbacks, especially Milnor squares and D+M constructions, which
are probably the most important example-generating machines. In Chapter 9, coherent
rings with finite weak global dimensions are probed, and the local ring of weak global
dimension two is elaborated on by combining homological tricks and methods of star
operation theory. Chapter 10 is devoted to the Grothendieck group of a commutative ring.
In particular, the Bass?Quillen problem is discussed. Finally, Chapter 11 aims to introduce
relative homological algebra, especially where the related concepts of integral domains
which appear in classical ideal theory are defined and investigated by using the class
of Gorenstein projective modules. Each section of the book is followed by a selection of
exercises of varying degrees of difficulty. This book will appeal to a wide readership from
graduate students to academic researchers who are interested in studying commutative
algebra.