Many paths lead into Euclidean plane geometry. Geometry Transformed offers an expeditious yet rigorous route using axioms based on rigid motions and dilations. Since transformations are available at the outset, interesting theorems can be proved sooner; and proofs can be connected to visual and tactile intuition about symmetry and motion. The reader thus gains valuable experience thinking with transformations, a skill that may be useful in other math courses or applications. For students interested in teaching mathematics at the secondary school level, this approach is particularly useful since geometry in the Common Core State Standards is based on rigid motions.
The only prerequisite for this book is a basic understanding of functions. Some previous experience with proofs may be helpful, but students can also learn about proofs by experiencing them in this book?in a context where they can draw and experiment. The eleven chapters are organized in a flexible way to suit a variety of curriculum goals. In addition to a geometrical core that includes finite symmetry groups, there are additional topics on circles and on crystallographic and frieze groups, and a final chapter on affine and Cartesian coordinates. The exercises are a mixture of routine problems, experiments, and proofs.
Undergraduate and graduate students interested in geometry aligned with Common Core standards (CCSSM).
Pure and Applied Undergraduate Texts, Volume: 51
2021; 282 pp; Softcover
MSC: Primary 51; 97; 20;
Print ISBN: 978-1-4704-6307-6
Product Code: AMSTEXT/51
Not yet published
Expected publication date April 21, 2021
The generalized Ricci flow is a geometric evolution equation which has recently emerged from investigations into mathematical physics, Hitchin's generalized geometry program, and complex geometry. This book gives an introduction to this new area, discusses recent developments, and formulates open questions and conjectures for future study.
The text begins with an introduction to fundamental aspects of generalized Riemannian, complex, and Kahler geometry. This leads to an extension of the classical Einstein-Hilbert action, which yields natural extensions of Einstein and Calabi-Yau structures as ecanonical metricsf in generalized Riemannian and complex geometry. The book then introduces generalized Ricci flow as a tool for constructing such metrics and proves extensions of the fundamental Hamilton/Perelman regularity theory of Ricci flow. These results are refined in the setting of generalized complex geometry, where the generalized Ricci flow is shown to preserve various integrability conditions, taking the form of pluriclosed flow and generalized Kahler-Ricci flow, leading to global convergence results and applications to complex geometry. Finally, the book gives a purely mathematical introduction to the physical idea of T-duality and discusses its relationship to generalized Ricci flow.
The book is suitable for graduate students and researchers with a background in Riemannian and complex geometry who are interested in the theory of geometric evolution equations.
Graduate students and researchers interested in the generalized Ricci Flow and mathematical physics.
University Lecture Series, Volume: 76
2021; 256 pp; Softcover
MSC: Primary 53;
Print ISBN: 978-1-4704-6258-1
Product Code: ULECT/76
Not yet published
Expected publication date May 6, 2021
This two-volume set containts parts I and II.
Each volume is a collection of articles written in memory of Boris Dubrovin (1950?2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher.
The contributions are split into two parts: gIntegrable Systemsh and gQuantum Theories and Algebraic Geometryh, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.
Graduate students and researchers interested in mathematical physics, enumerative and differential geometry, and geometric representation theory.
Proceedings of Symposia in Pure Mathematics Volume: 103
2021; 983 pp; Softcover
Print ISBN: 978-1-4704-5590-3
Product Code: PSPUM/103
Not yet published
Expected publication date May 5, 2021
How do biological objects communicate, make structures, make measurements and decisions, search for food, i.e., do all the things necessary for survival? Designed for an advanced undergraduate audience, this book uses mathematics to begin to tell that story. It builds on a background in multivariable calculus, ordinary differential equations, and basic stochastic processes and uses partial differential equations as the framework within which to explore these questions.
Undergraduate and graduate students and researchers interested in mathematical biology and PDEs.
This book tells the story of living processes that change in time and space. Driven by scientific inquiry, methods from partial differential equations, stochastic processes, dynamical systems, and numerical methods are brought to bear on the subject, and their exposition seems effortless in the pursuit of deeper biological understanding. With subjects ranging from spruce budworm populations to calcium dynamics and from tiger bush patterns to collective behavior, this is a must-read for anyone who is serious about modern mathematical biology.
-- Mark Lewis, University of Alberta
Prof. Keener is one of the Great Minds in Math Biology who has trained generations of fine scientists and mathematicians over the years.
-- Leah Edelstein-Keshet, University of British Columbia
This is a fantastic book for those of us who teach mathematical modelling of spatiotemporal phenomena in biology, and for anyone who wishes to move into the field. It guides the reader on how one should tackle the art of modelling and, in a very systematic and natural way, introduces many of the necessary mathematical and computational approaches, seamlessly integrating them with the biology. It is a pleasure to read.
-- Philip Maini, University of Oxford
Mathematical Biology has few foundational texts. But this is one.
-- Michael C. Reed, Duke University
Pure and Applied Undergraduate Texts, Volume: 50
2021; 314 pp; Softcover
MSC: Primary 92; 35; Secondary 34; 60; 65
Print ISBN: 978-1-4704-5428-9
Not yet published
Expected publication date June 2, 2021
Part of Acta Numerica
Not yet published - available from March 2021
FORMAT: HardbackISBN: 9781108843362
Acta Numerica is an annual publication containing invited survey papers by leading researchers in numerical mathematics and scientific computing. The papers present overviews of recent developments in their area and provide state-of-the-art techniques and analysis.
The latest issue of the leading review in mathematics as measured by Impact factor
Outstanding contributors provide state-of-art surveys in important topics of contemporary interest
Covers a broad range of fields from data-driven science, to engineering, to computational physics
PUBLICATION PLANNED FOR: March 2021
FORMAT: HardbackISBN: 9781108843362
LENGTH: 768 pagesDIMENSIONS: 253 x 180 x 35 mmWEIGHT: 1.5kg
1. Numerical methods for nonlocal and fractional models Marta D'Elia, Qiang Du, Christian Glusa, Max Gunzburger, Xiaochuan Tian and Zhi Zhou
2. The numerics of phase retrieval Albert Fannjiang and Thomas Strohmer
3. Computing quantum dynamics in the semiclassical regime Caroline Lasser and Christian Lubich
4. Randomized numerical linear algebra: foundations and algorithms Per-Gunnar Martinsson and Joel A. Tropp
5. Fast algorithms using orthogonal polynomials Sheehan Olver, Richard Mikael Slevinsky and Alex Townsend
6. Essentially non-oscillatory and weighted essentially non-oscillatory schemes Chi-Wang Shu.
PUBLICATION PLANNED FOR: August 2021
Not yet published - available from August 2021
FORMAT: HardbackI SBN: 9781108831833
FORMAT: Paperback ISBN: 9781108927406
Description
Paul Erd?s published more papers during his lifetime than any other mathematician, especially in discrete mathematics. He had a nose for beautiful, simply-stated problems with solutions that have far-reaching consequences across mathematics. This captivating book, written for students, provides an easy-to-understand introduction to discrete mathematics by presenting questions that intrigued Erd?s, along with his brilliant ways of working toward their answers. It includes young Erd?s's proof of Bertrand's postulate, the Erd?s-Szekeres Happy End Theorem, De Bruijn-Erd?s theorem, Erd?s-Rado delta-systems, Erd?s-Ko-Rado theorem, Erd?s-Stone theorem, the Erd?s-Renyi-Sos Friendship Theorem, Erd?s-Renyi random graphs, the Chvatal-Erd?s theorem on Hamilton cycles, and other results of Erd?s, as well as results related to his work, such as Ramsey's theorem or Deza's theorem on weak delta-systems. Its appendix covers topics normally missing from introductory courses. Filled with personal anecdotes about Erd?s, this book offers a behind-the-scenes look at interactions with the legendary collaborator.
Foreword
Preface
Acknowledgments
Introduction
1. A glorious beginning ? Bertrand's postulate
2. Discrete geometry and spinoffs
3. Ramsey's theorem
4. Delta-systems
5. Extremal set theory
6. Van der Waerden's theorem
7. Extremal graph theory
8. The friendship theorem
9. Chromatic number
10. Thresholds of graph properties
11. Hamilton cycles
Appendix A. A few tricks of the trade
Appendix B. Definitions, terminology, notation
Appendix C. More on Erd?s
References
Index.