The Soviet school, one of the glories of twentieth-century mathematics, faced a serious crisis in the summer of 1936. It was suffering from internal strains due to generational conflicts between the young talents and the old establishment. At the same time, Soviet leaders (including Stalin himself) were bent on “Sovietizing” all of science in the USSR by requiring scholars to publish their works in Russian in the Soviet Union, ending the nearly universal practice of publishing in the West. A campaign to “Sovietize” mathematics in the USSR was launched with an attack on Nikolai Nikolaevich Luzin, the leader of the Soviet school of mathematics, in Pravda. Luzin was fortunate in that only a few of the most ardent ideologues wanted to destroy him utterly. As a result, Luzin, though humiliated and frightened, was allowed to make a statement of public repentance and then let off with a relatively mild reprimand. A major factor in his narrow escape was the very abstractness of his research area (descriptive set theory), which was difficult to incorporate into a propaganda campaign aimed at the broader public.
The present book contains the transcripts of five meetings of the Academy of Sciences commission charged with investigating the accusations against Luzin, meetings held in July of 1936. Ancillary material from the Soviet press of the time is included to place these meetings in context.
History of Mathematics, Volume: 43
2016; 416 pp; Hardcover
ISBN: 978-1-4704-2608-8
Undergraduate and graduate students and research mathematicians interested in history
Matrix groups touch an enormous spectrum of the mathematical arena. This textbook brings them into the undergraduate curriculum. It makes an excellent one-semester course for students familiar with linear and abstract algebra and prepares them for a graduate course on Lie groups.
Matrix Groups for Undergraduates is concrete and example-driven, with geometric motivation and rigorous proofs. The story begins and ends with the rotations of a globe. In between, the author combines rigor and intuition to describe the basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, maximal tori, homogeneous spaces, and roots.
This second edition includes two new chapters that allow for an easier transition to the general theory of Lie groups.
Student Mathematical Library, Volume: 79
2016; 239 pp; Softcover
ISBN: 978-1-4704-2722-1
This book is a collection of three introductory tutorials coming out of three courses given at the CIMPA Research School “Galois Theory of Difference Equations” in Santa Marta, Columbia, July 23?August 1, 2012. The aim of these tutorials is to introduce the reader to three Galois theories of linear difference equations and their interrelations. Each of the three articles addresses a different galoisian aspect of linear difference equations. The authors motivate and give elementary examples of the basic ideas and techniques, providing the reader with an entry to current research. In addition each article contains an extensive bibliography that includes recent papers; the authors have provided pointers to these articles allowing the interested reader to explore further.
Mathematical Surveys and Monographs, Volume: 211
2016; 171 pp; Hardcover
Print ISBN: 978-1-4704-2655-2
Date Published: February 2016
format: Paperback
isbn: 9781611974195
Riemann-Hilbert problems are fundamental objects of study within complex analysis. Many problems in differential equations and integrable systems, probability and random matrix theory, and asymptotic analysis can be solved by reformulation as a Riemann-Hilbert problem. This book provides introductions to both computational complex analysis, as well as to the applied theory of Riemann-Hilbert problems from an analytical and numerical perspective. Following a full-discussion of applications to integrable systems, differential equations and special function theory, the authors include six fundamental examples and five more sophisticated examples of the analytical and numerical Riemann-Hilbert method, each of mathematical or physical significance, or both. As the most comprehensive book to date on the applied and computational theory of Riemann-Hilbert problems, this book is ideal for graduate students and researchers interested in a computational or analytical introduction to the Riemann-Hilbert method.
Preface
Notation and abbreviations
Part I. Riemann-Hilbert Problems:
1. Classical applications of Riemann-Hilbert problems
2. Riemann-Hilbert problems
3. Inverse scattering and nonlinear steepest descent
Part II. Numerical Solution of Riemann-Hilbert Problems:
4. Approximating functions
5. Numerical computation of Cauchy transforms
6. The numerical solution of Riemann-Hilbert problems
7. Uniform approximation theory for Riemann-Hilbert problems
Part III. The Computation of Nonlinear Special Functions and Solutions of Nonlinear PDEs:
8. The Korteweg-de Vries and modified Korteweg-de Vries equations
9. The focusing and defocusing nonlinear Schrodinger equations
10. The Painleve II transcendents
11. The finite-genus solutions of the Korteweg-de Vries equation
12. The dressing method and nonlinear superposition
Part IV. Appendices: A. Function spaces and functional analysis
B. Fourier and Chebyshev series
C. Complex analysis
D. Rational approximation
E. Additional KdV results
Bibliography
Index.
available from June 2016
format: Hardback
isbn: 9781107103856
format: Paperback
isbn: 9781107503823
Like its predecessor, 200 Puzzling Physics Problems, this book is aimed at strengthening students' grasp of the laws of physics by applying them to situations that are practical, and to problems that yield more easily to intuitive insight than to brute-force methods and complex mathematics. The problems are chosen almost exclusively from classical, non-quantum physics, but are no easier for that. They are intriguingly posed in accessible non-technical language, and require readers to select an appropriate analysis framework and decide which branches of physics are involved. The general level of sophistication needed is that of the exceptional school student, the good undergraduate, or the competent graduate student; some physics professors may find some of the more difficult questions challenging. By contrast, the mathematical demands are relatively minimal, and seldom go beyond elementary calculus. This further book of physics problems is not only instructive and challenging, but also enjoyable.
Preface
How to use this book
Thematic order of the problems
Problems
Hints
Solutions
Appendix.