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This classic treatment of linear algebra presents the fundamentals
in the clearest possible way, examining basic ideas by means of
computational examples and geometrical interpretation. It proceeds
from familiar concepts to the unfamiliar, from the concrete to the
abstract. Readers consistently praise this outstanding text for its
expository style and clarity of presentation.
Clear, accessible, step-by-step explanations make the
material crystal... more...

Reinforces student understanding and aids in test preparation with
detailed explanations, worked-out examples, and practice problems.
Lists key ideas to master and builds problem-solving skills.
Includes worked solutions to the odd-numbered problems in the text.

This is a book of entertaining problems that can be solved through
the use of algebra, problems with intriguing plots to excite the
readers curiosity, amusing excursions into the history of
mathematics, unexpected uses that algebra is put to in everyday
affairs, and more. Algebra Can Be Fun has brought hundreds of
thousands of youngsters into the fold of mathematics and its
wonders. It is written in the form of lively sketches that discuss
the... more...

Eine verständliche, konzise und immer flüssige Einführung in die
Algebra, die insbesondere durch ihre sorgfältige didaktische
Aufbereitung bei vielen Studenten Freunde findet. Die vorliegende
Auflage bietet neben zahlreichen Aufgaben (mit Lösungshinweisen)
sowie einführenden und motivierenden Vorbemerkungen auch
Ausblicke auf neuere Entwicklungen. Auch selten im Lehrbuch
behandelte Themen wie Resultanten, Diskriminanten,... more...

This book describes the history of Jordan algebras and describes in
full mathematical detail the recent structure theory for Jordan
algebras of arbitrary dimension due to Efim Zel'manov. Jordan
algebras crop up in many surprising settings, and find application
to a variety of mathematical areas. No knowledge is required beyond
standard first-year graduate algebra courses.

A clear, efficient exposition of this topic with complete proofs
and exercises, covering cubic and quartic formulas; fundamental
theory of Galois theory; insolvability of the quintic; Galoiss
Great Theorem; and computation of Galois groups of cubics and
quartics. Suitable for first-year graduate students, either as a
text for a course or for study outside the classroom, this new
edition has been completely rewritten in an attempt to make proofs
clearer... more...

This is intended for a graduate course on Siegel modular forms,
Hecke operators, and related zeta functions. The author’s aim is to
present a concise and self-contained introduction to an important
and developing area of number theory that will serve to attract
young researchers to this beautiful field. Topics include: *
analytical properties of radial Dirichlet series attached to
modular forms of genuses 1 and 2; * the abstract theory of... more...

Here we present a nearly complete treatment of the Grand Universe
of linear and weakly nonlinear regression models within the first 8
chapters. Our point of view is both an algebraic view as well as a
stochastic one. For example, there is an equivalent lemma between a
best, linear uniformly unbiased estimation (BLUUE) in a
Gauss-Markov model and a least squares solution (LESS) in a system
of linear equations. While BLUUE is a stochastic regression... more...

This (post) graduate text gives a broad introduction to Lie groups
and algebras with an emphasis on differential geometrical methods.
It analyzes the structure of compact Lie groups in terms of the
action of the group on itself by conjugation, culminating in the
classification of the representations of compact Lie groups and
their realization as sections of holomorphic line bundles over flag
manifolds. Appendices provide background reviews.

Tilting theory originates in the representation theory of finite
dimensional algebras. Today the subject is of much interest in
various areas of mathematics, such as finite and algebraic group
theory, commutative and non-commutative algebraic geometry, and
algebraic topology. The aim of this book is to present the basic
concepts of tilting theory as well as the variety of applications.
It contains a collection of key articles, which together form a... more...