Contemporary Mathematics, Volume: 627
2014; 174 pp; softcover
ISBN-13: 978-1-4704-1078-0
Expected publication date is December 4, 2014.
This volume contains the proceedings of an international conference to commemorate the 125th anniversary of Ramanujan's birth, held from November 5-7, 2012, at the University of Florida, Gainesville, Florida.
Srinivasa Ramanujan was India's most famous mathematician. This volume contains research and survey papers describing recent and current developments in the areas of mathematics influenced by Ramanujan. The topics covered include modular forms, mock theta functions and harmonic Maass forms, continued fractions, partition inequalities, q-series, representations of affine Lie algebras and partition identities, highly composite numbers, analytic number theory and quadratic forms.
Graduate students and research mathematicians interested in number theory.
Clay Mathematics Proceedings, Volume: 20
2014; 340 pp; softcover
ISBN-13: 978-0-8218-8982-4
Expected publication date is January 16, 2015.
Resolution of Singularities has long been considered as being a difficult to access area of mathematics. The more systematic and simpler proofs that have appeared in the last few years in zero characteristic now give us a much better understanding of singularities. They reveal the aesthetics of both the logical structure of the proof and the various methods used in it. The present volume is intended for readers who are not yet experts but always wondered about the intricacies of resolution. As such, it provides a gentle and quite comprehensive introduction to this amazing field. The book may tempt the reader to enter more deeply into a topic where many mysteries--especially the positive characteristic case--await to be disclosed.
Graduate students and research mathematicians interested in algebraic geometry, commutative geometry, singularity theory, and local analytic geometry.
H. Hauser -- Blowups and resolution
A. Bravo and O. E. Villamayor U. -- On the behavior of the multiplicity on schemes: Stratification and blow ups
J. Schicho -- A simplified game for resolution of singularities
S. D. Cutkosky -- Resolution of singularities in char p and monomialization
S. Encinas -- Resolution of toric varieties
A. Fruhbis-Kruger -- Desingularization in computational applications and experiments
H. Kawanoue -- Introduction to the idealistic filtration program with emphasis on the radical saturation
J. Schicho and J. Top -- Algebraic approaches to FlipIt
T. Yasuda -- Higher Semple-Nash blowups and F-blowups
Pure and Applied Undergraduate Texts, Volume: 22
2014; 388 pp; hardcover
ISBN-13: 978-1-4704-1560-0
Expected publication date is January 19, 2015.
Fourier Analysis is an important area of mathematics, especially in light of its importance in physics, chemistry, and engineering. Yet it seems that this subject is rarely offered to undergraduates. This book introduces Fourier Analysis in its three most classical settings: The Discrete Fourier Transform for periodic sequences, Fourier Series for periodic functions, and the Fourier Transform for functions on the real line.
The presentation is accessible for students with just three or four terms of calculus, but the book is also intended to be suitable for a junior-senior course, for a capstone undergraduate course, or for beginning graduate students. Material needed from real analysis is quoted without proof, and issues of Lebesgue measure theory are treated rather informally. Included are a number of applications of Fourier Series, and Fourier Analysis in higher dimensions is briefly sketched. A student may eventually want to move on to Fourier Analysis discussed in a more advanced way, either by way of more general orthogonal systems, or in the language of Banach spaces, or of locally compact commutative groups, but the experience of the classical setting provides a mental image of what is going on in an abstract setting.
Undergraduate and graduate students interested in learning Fourier analysis.
Background
Complex numbers
The discrete Fourier transform
Fourier coefficients and first Fourier series
Summability of Fourier series
Fourier series in mean square
Trigonometric polynomials
Absolutely convergent Fourier series
Convergence of Fourier series
Applications of Fourier series
The Fourier transform
Higher dimensions
Appendix B. The binomial theorem
Appendix C. Chebyshev polynomials
Appendix F. Applications of the fundamental theorem of algebra
Appendix I. Inequalities
Appendix L. Topics in linear algebra
Appendix O. Orders of magnitude
Appendix T. Trigonometry
References
Notation
Index
2014; 368 pp; hardcover
ISBN-13: 978-93-80250-64-9
Expected publication date is January 21, 2015.
This is part one of a two-volume introduction to real analysis and is intended for honours undergraduates who have already been exposed to calculus. The emphasis is on rigour and on foundations. The material starts at the very beginning--the construction of the number systems and set theory--then goes on to the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and finally to the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. There are also appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of twenty-five to thirty lectures each.
The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.
In the third edition, several typos and other errors have been corrected and a few new exercises have been added.
Undergraduate and graduate students interested in analysis.
Volume 1
Introduction
Starting at the beginning: The natural numbers
Set theory
Integers and rationals
The real numbers
Limits of sequences
Series
Infinite sets
Continuous functions on R
Differentiation of functions
The Riemann integral
Appendix A: The basics of mathematical logic
Appendix B: The decimal system
2014; 236 pp; hardcover
ISBN-13: 978-93-80250-65-6
Expected publication date is January 21, 2015.
This is part two of a two-volume introduction to real analysis and is intended for honours undergraduates who have already been exposed to calculus. The emphasis is on rigour and on foundations. The material starts at the very beginning--the construction of the number systems and set theory--then goes on to the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and finally to the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. There are also appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of twenty-five to thirty lectures each.
The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.
In the third edition, several typos and other errors have been corrected and a few new exercises have been added.
Undergraduate and graduate students interested in analysis.
Volume 2
Metric spaces
Continuous functions on metric spaces
Uniform convergence
Power series
Fourier series
Several variable differential calculus
Lebesgue measure
Lebesgue integratio