Courant Lecture Notes Volume: 30
2020; 288 pp; Softcover
MSC: Primary 97; 15; 40; 20;
Print ISBN: 978-1-4704-5425-8
Product Code: CLN/30
This book is the second of two volumes on linear algebra for graduate students in mathematics, the sciences, and economics,
who have: a prior undergraduate course in the subject; a basic understanding of matrix algebra; and some proficiency with
mathematical proofs. Both volumes have been used for several years in a one-year course sequence, Linear Algebra I and II,
offered at New York University's Courant Institute.
The first three chapters of this second volume round out the coverage of traditional linear algebra topics: generalized
eigenspaces, further applications of Jordan form, as well as bilinear, quadratic, and multilinear forms. The final two
chapters are different, being more or less self-contained accounts of special topics that explore more advanced aspects of
modern algebra: tensor fields, manifolds, and vector calculus in Chapter 4 and matrix Lie groups in Chapter 5. The reader can
choose to pursue either chapter. Both deal with vast topics in contemporary mathematics. They include historical commentary
on how modern views evolved, as well as examples from geometry and the physical sciences in which these topics are important.
The book provides a nice and varied selection of exercises; examples are well-crafted and provide a clear understanding of
the methods involved.
Mathematical Surveys and Monographs Volume: 247
2020; 582 pp; Hardcover
MSC: Primary 16;
Print ISBN: 978-1-4704-5232-2
Product Code: SURV/247
This book is an introduction to Hopf algebras in braided monoidal categories with applications to Hopf algebras in the usual
sense. The main goal of the book is to present from scratch and with complete proofs the theory of Nichols algebras (or
quantum symmetric algebras) and the surprising relationship between Nichols algebras and generalized root systems.
In general, Nichols algebras are not classified by Cartan graphs and their root systems. However, extending partial results
in the literature, the authors were able to associate a Cartan graph to a large class of Nichols algebras. This allows them
to determine the structure of right coideal subalgebras of Nichols systems which generalize Nichols algebras. As applications
of these results, the book contains a classification of right coideal subalgebras of quantum groups and of the small quantum
groups, and a proof of the existence of PBW-bases that does not involve case by case considerations. The authors also include
short chapter summaries at the beginning of each chapter and historical notes at the end of each chapter.
The theory of Cartan graphs, Weyl groupoids, and generalized root systems appears here for the first time in a book form.
Hence, the book serves as an introduction to the modern classification theory of pointed Hopf algebras for advanced graduate
students and researchers working in categorial aspects and classification theory of Hopf algebras and their generalization.
Graduate students and researchers interested in category theory, Hopf algebras, and applications.
Contemporary Mathematics Volume: 749
2020; 388 pp; Softcover
MSC: Primary 14; 18; 19; 47;
Print ISBN: 978-1-4704-5026-7
Product Code: CONM/749
This volume contains the proceedings of the ICM 2018 satellite school and workshop K-theory conference in Argentina. The school was held from July 16 E0, 2018, in La Plata, Argentina, and the workshop was held from July 23 E7, 2018, in Buenos Aires, Argentina.
The volume showcases current developments in K-theory and related areas, including motives, homological algebra, index theory, operator algebras, and their applications and connections.
Papers cover topics such as K-theory of group rings, Witt groups of real algebraic varieties, coarse homology theories, topological cyclic homology, negative K-groups of monoid algebras, Milnor K-theory and regulators, noncommutative motives, the classification of C∁Ealgebras via Kasparov's K-theory, the comparison between full and reduced C∁Ecrossed products, and a proof of Bott periodicity using almost commuting matrices.
Graduate students and research mathematicians interested in K-theory and its applications to algebra, analysis, or topology.
Contemporary Mathematics Volume: 750
2020; 213 pp; Softcover
MSC: Primary 15; 16; 30; 46; 47;
Print ISBN: 978-1-4704-4693-2
Product Code: CONM/750
This volume contains the proceedings of the International Conference on Algebra and Related Topics, held from July 2 E, 2018, at Mohammed V University, Rabat, Morocco.
Linear reserver problems demand the characterization of linear maps between algebras that leave invariant certain properties or certain subsets or relations. One of the most intractable unsolved problems is Kaplansky's conjecture: every surjective unital invertibility preserving linear map between two semisimple Banach algebras is a Jordan homomorphism. Recently, there has been an upsurge of interest in nonlinear preservers, where the maps studied are no longer assumed linear but instead a weak algebraic condition is somehow involved through the preserving property.
This volume contains several articles on various aspects of preservers, including such topics as Jordan isomorphisms, Aluthge transform, joint numerical radius on C∁Ealgebras, advertible complete algebras, and Gelfand-Mazur algebras. The volume also contains a survey on recent progress on local spectrum-preserving maps.
Several articles in the volume present results about weighted spaces and algebras of holomorphic or harmonic functions, including biduality in weighted spaces of analytic functions, interpolation in the analytic Wiener algebra, and weighted composition operators on non-locally convex weighted spaces.
Graduate students and research mathematicians interested in linear analysis and function spaces.
Pure and Applied Undergraduate Texts Volume: 44
2020; 178 pp; Softcover
MSC: Primary 26; 40; 54; 37;
Print ISBN: 978-1-4704-5270-4
Product Code: AMSTEXT/44
This book is an introduction to the theory of calculus in the style of inquiry-based learning. The text guides students
through the process of making mathematical ideas rigorous, from investigations and problems to definitions and proofs. The
format allows for various levels of rigor as negotiated between instructor and students, and the text can be of use in a
theoretically oriented calculus course or an analysis course that develops rigor gradually. Material on topology (e.g., of
higher dimensional Euclidean spaces) and discrete dynamical systems can be used as excursions within a study of analysis or
as a more central component of a course. The themes of bisection, iteration, and nested intervals form a common thread
throughout the text.
The book is intended for students who have studied some calculus and want to gain a deeper understanding of the subject
through an inquiry-based approach.
Undergraduate students interested in an introduction to proof-based Elementary Topology and Analysis.
2020; 402 pp; Softcover
MSC: Primary 97; 00;
Print ISBN: 978-1-4704-5675-7
Product Code: MBK/131
This is the first of three volumes that, together, give an exposition of the mathematics of grades 9 E2 that is simultaneously mathematically correct and grade-level appropriate. The volumes are consistent with CCSSM (Common Core State Standards for Mathematics) and aim at presenting the mathematics of K E2 as a totally transparent subject.
The present volume begins with fractions, then rational numbers, then introductory geometry that can make sense of the slope of a line, then an explanation of the correct use of symbols that makes sense of “variables E and finally a systematic treatment of linear equations that explains why the graph of a linear equation in two variables is a straight line and why the usual solution method for simultaneous linear equations “by substitutions Eis correct.
This book should be useful for current and future teachers of K E2 mathematics, as well as for some high school students and for education professionals.
Teachers of middle school mathematics; students and professionals interested in mathematical education.