Problem Books Volume: 33
2002; 337 pp; Softcover
Print ISBN: 978-1-4704-5124-0
MAA Press: An Imprint of the American Mathematical Society
This third volume of problems from the William Lowell Putnam Competition is unlike the previous two in that it places the problems in the context of important mathematical themes. The authors highlight connections to other problems, to the curriculum and to more advanced topics. The best problems contain kernels of sophisticated ideas related to important current research, and yet the problems are accessible to undergraduates. The solutions have been compiled from the American Mathematical Monthly, Mathematics Magazine and past competitors. Multiple solutions enhance the understanding of the audience, explaining techniques that have relevance to more than the problem at hand. In addition, the book contains suggestions for further reading, a hint to each problem, separate from the full solution and background information about the competition.
The book will appeal to students, teachers, professors and indeed anyone interested in problem solving as a gateway to a deep understanding of mathematics.
Each chapter solves several realistic problems while introducing the modelling optimization techniques and simulation as required. This allows readers to see how the methods are used, making it easier to grasp the basics.
-- CERN Courier
The book will be invaluable for anybody with an interest in mathematical competitions or just trying his or her hand at challenging Mathematics at university level. All theories begin with simple, easy to state and beautiful problems and this book has an abundant supply of those.
-- The London Mathematical Society
AMS/MAA Textbooks Volume: 59;
2020; 354 pp; Hardcover
MSC: Primary 26; 42;
Print ISBN: 978-1-4704-5145-5
Product Code: TEXT/59
MAA Press: An Imprint of the American Mathematical Society
Fourier Series, Fourier Transforms, and Function Spaces is designed as a textbook for a second course or capstone course in analysis for advanced undergraduate or beginning graduate students. By assuming the existence and properties of the Lebesgue integral, this book makes it possible for students who have previously taken only one course in real analysis to learn Fourier analysis in terms of Hilbert spaces, allowing for both a deeper and more elegant approach. This approach also allows junior and senior undergraduates to study topics like PDEs, quantum mechanics, and signal processing in a rigorous manner.
Students interested in statistics (time series), machine learning (kernel methods), mathematical physics (quantum mechanics), or electrical engineering (signal processing) will find this book useful. With 400 problems, many of which guide readers in developing key theoretical concepts themselves, this text can also be adapted to self-study or an inquiry-based approach. Finally, of course, this text can also serve as motivation and preparation for students going on to further study in analysis.
Undergraduate and graduate students and researchers interested in analysis, differential equations, and applied math.
with contributions by Carlos D'Andrea, Alicia Dickenstein, Jonathan Hauenstein, Hal Schenck, and Jessica Sidman.
CBMS Regional Conference Series in Mathematics Volume: 134;
2020; 250 pp; Softcover
MSC: Primary 13; 14; Secondary 52; 62; 65; 68; 92
Print ISBN: 978-1-4704-5137-0
Product Code: CBMS/134
Systems of polynomial equations can be used to model an astonishing variety of phenomena. This book explores the geometry and algebra of such systems and includes numerous applications. The book begins with elimination theory from Newton to the twenty-first century and then discusses the interaction between algebraic geometry and numerical computations, a subject now called numerical algebraic geometry. The final three chapters discuss applications to geometric modeling, rigidity theory, and chemical reaction networks in detail. Each chapter ends with a section written by a leading expert.
Examples in the book include oil wells, HIV infection, phylogenetic models, four-bar mechanisms, border rank, font design, Stewart-Gough platforms, rigidity of edge graphs, Gaussian graphical models, geometric constraint systems, and enzymatic cascades. The reader will encounter geometric objects such as Bezier patches, Cayley-Menger varieties, and toric varieties; and algebraic objects such as resultants, Rees algebras, approximation complexes, matroids, and toric ideals. Two important subthemes that appear in multiple chapters are toric varieties and algebraic statistics. The book also discusses the history of elimination theory, including its near elimination in the middle of the twentieth century.
The main goal is to inspire the reader to learn about the topics covered in the book. With this in mind, the book has an extensive bibliography containing over 350 books and papers.
Graduate students and researchers interested in applications of algebraic geometry.
Contemporary Mathematics Volume: 743;
2020; 280 pp; Softcover
MSC: Primary 30; 44; 46; 47;
Print ISBN: 978-1-4704-4692-5
Product Code: CONM/743
A co-publication of the AMS and Centre de Recherches Mathematiques
This volume contains the proceedings of the Conference on Complex Analysis and Spectral Theory, in celebration of Thomas Ransford's 60th birthday, held from May 21?25, 2018, at Laval University, Quebec, Canada.
Spectral theory is the branch of mathematics devoted to the study of matrices and their eigenvalues, as well as their infinite-dimensional counterparts, linear operators and their spectra. Spectral theory is ubiquitous in science and engineering because so many physical phenomena, being essentially linear in nature, can be modelled using linear operators. On the other hand, complex analysis is the calculus of functions of a complex variable. They are widely used in mathematics, physics, and in engineering. Both topics are related to numerous other domains in mathematics as well as other branches of science and engineering. The list includes, but is not restricted to, analytical mechanics, physics, astronomy (celestial mechanics), geology (weather modeling), chemistry (reaction rates), biology, population modeling, economics (stock trends, interest rates and the market equilibrium price changes).
There are many other connections, and in recent years there has been a tremendous amount of work on reproducing kernel Hilbert spaces of analytic functions, on the operators acting on them, as well as on applications in physics and engineering, which arise from pure topics like interpolation and sampling. Many of these connections are discussed in articles included in this book.
Graduate students and research mathematicians interested in functional analysis, complex analysis, and Fourier anaylsis.
Contemporary Mathematics Volume: 744;
2020; 347 pp; Softcover
MSC: Primary 11; 20; 22; 30; 37; 54; 60;
Print ISBN: 978-1-4704-5100-4
Product Code: CONM/744
This volume contains the proceedings of the conference Dynamics: Topology and Numbers, held from July 2?6, 2018, at the Max Planck Institute for Mathematics, Bonn, Germany.
The papers cover diverse fields of mathematics with a unifying theme of relation to dynamical systems. These include arithmetic geometry, flat geometry, complex dynamics, graph theory, relations to number theory, and topological dynamics.
The volume is dedicated to the memory of Sergiy Kolyada and also contains some personal accounts of his life and mathematics.
Graduate students and research mathematicians interested in dynamical systems and related topics.
Paperback ISBN: 9780128182178
Imprint: Academic Press
Published Date: 1st May 2020
Page Count: 548
A Modern Introduction to Differential Equations, Third Edition, provides an introduction to the basic concepts of differential equations. The book begins by introducing the basic concepts of differential equations, focusing on the analytical, graphical and numerical aspects of first-order equations, including slope fields and phase lines. The comprehensive resource then covers methods of solving second-order homogeneous and nonhomogeneous linear equations with constant coefficients, systems of linear differential equations, the Laplace transform and its applications to the solution of differential equations and systems of differential equations, and systems of nonlinear equations.
Throughout the text, valuable pedagogical features support learning and teaching. Each chapter concludes with a summary of important concepts, and figures and tables are provided to help students visualize or summarize concepts. The book also includes examples and updated exercises drawn from biology, chemistry, and economics, as well as from traditional pure mathematics, physics, and engineering.
Offers an accessible and highly readable resource to engage students
Introduces qualitative and numerical methods early to build understanding
Includes a large number of exercises from biology, chemistry, economics, physics and engineering
Provides exercises that are labeled based on difficulty/sophistication and end-of-chapter summaries
Upper level undergraduate and graduate students from a variety of majors taking courses typically titled (Introductory) Differential Equations, (Introductory) Partial Differential Equations, Applied Mathematics, Fourier Series and Boundary Value Problems
1. Introduction to Differential Equations
2. First-Order Differential Equations