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  • - From Euclidean Surfaces to Hyperbolic Knots
    av Francis Bonahon
    850,-

    The study of 3-dimensional spaces brings together elements from several areas of mathematics. The most notable are topology and geometry, but elements of number theory and analysis also make appearances. There have been striking developments in the mathematics of 3-dimensional manifolds. This book introduces some of these important developments.

  • av Iva Stavrov
    930,-

    This book introduces advanced undergraduates to Riemannian geometry and mathematical general relativity. The overall strategy of the book is to explain the concept of curvature via the Jacobi equation which, through discussion of tidal forces, further helps motivate the Einstein field equations. After addressing concepts in geometry such as metrics, covariant differentiation, tensor calculus and curvature, the book explains the mathematical framework for both special and general relativity. Relativistic concepts discussed include (initial value formulation of) the Einstein equations, stress-energy tensor, Schwarzschild space-time, ADM mass and geodesic incompleteness. The concluding chapters of the book introduce the reader to geometric analysis: original results of the author and her undergraduate student collaborators illustrate how methods of analysis and differential equations are used in addressing questions from geometry and relativity. The book is mostly self-contained and the reader is only expected to have a solid foundation in multivariable and vector calculus and linear algebra. The material in this book was first developed for the 2013 summer program in geometric analysis at the Park City Math Institute, and was recently modified and expanded to reflect the author's experience of teaching mathematical general relativity to advanced undergraduates at Lewis & Clark College.

  • - Selected Topics Beyond the Basic Courses
    av Ida Kantor
    850,-

  • av C.E. Silva
    850,-

    Gives an introduction to basic concepts in ergodic theory such as recurrence, ergodicity, the ergodic theorem, mixing, and weak mixing. In particular, this book includes a detailed construction of the Lebesgue measure on the real line and an introduction to measure spaces up to the Caratheodory extension theorem.

  • av David E. Blair
    712,-

    It is rarely taught in undergraduate or graduate curricula that the only conformal maps in Euclidean space of dimension greater than 2 are those generated by similarities and inversions in spheres. This is in stark contrast to the conformal maps in the plane. This book gives a treatment of this paucity of conformal maps in higher dimensions.

  • av A.B. Sossinsky
    850,-

    This is an innovative modern exposition of geometry, or rather, of geometries; it is the first textbook in which Felix Klein's Erlangen Program (the action of transformation groups) is systematically used as the basis for defining various geometries. The course of study presented is dedicated to the proposition that all geometries are created equal - although some remain more equal than others.

  • - Continuity and Differentiation
    av W.J. Kaczor
    850,-

    Helps in the understanding of continuous and differentiable functions. This book emphasises on real functions of a single variable. It contains topics that include: continuous functions, the intermediate value property, uniform continuity, mean value theorems, Taylors formula, convex functions, and sequences and series of functions.

  • av Bruce M. Landman
    850,-

  • av Gary L. Mullen & Carl Mummert
    850,-

    Offers an introduction to the theory of finite fields and to some of their many practical applications. After covering their construction and elementary properties, the authors discuss the trace and norm functions, bases for finite fields, and properties of polynomials over finite fields. Each of the remaining chapters details applications.

  • av Joel Spencer
    850,-

  • av Joel H. Shapiro
    850,-

    Introduces functional analysis to undergraduate mathematics students who possess a basic background in analysis and linear algebra. By studying how the Volterra operator acts on vector spaces of continuous functions, its readers will sharpen their skills, reinterpret what they already know, and learn fundamental Banach-space techniques.

  • av Rekha R. Thomas
    850,-

    Presents a course in the geometry of convex polytopes in arbitrary dimension, suitable for an advanced undergraduate or beginning graduate student. This book starts with the basics of polytope theory. It introduces Schlegel and Gale diagrams as geometric tools to visualize polytopes in high dimension and to unearth bizarre phenomena in polytopes.

  • av Charles Radin
    712,-

    Tries to display the value (and joy!) of starting from a mathematically amorphous problem and combining ideas from diverse sources to produce new and significant mathematics - mathematics unforeseen from the motivating problem. This book focuses on aperiodic tilings; the best-known example is the 'kite and dart' tiling.

  • av A.R. Wadsworth
    850,-

    Presents problems in abstract algebra for strong undergraduates or beginning graduate students. The book contains problems on groups (including the Sylow Theorems, solvable groups, presentation of groups by generators and relations); rings (including basic ideal theory and factorization in integral domains); linear algebra (emphasizing linear transformations); and fields (including Galois theory).

  • av Gail S. Nelson
    850,-

    Provides a bridge between an undergraduate course in Real Analysis and a first graduate-level course in Measure Theory and Integration. The main goal of this book is to prepare students for what they may encounter in graduate school, but will be useful for many beginning graduate students as well.

  • - Connecting Algebra, Combinatorics, and Geometry
    av Emily H. Moore
    850,-

  • av Gerald Tenenbaum & Michel Mendes France
    712,-

    We have been curious about numbers - and prime numbers - since antiquity. One notable direction this century in the study of primes has been the influx of ideas from probability. This book intends to provide insights into the prime numbers and to describe how a sequence so tautly determined can incorporate such a striking amount of randomness.

  • av Gregory F. Lawler
    850,-

    Introducing the heat equation and the closely related notion of harmonic functions from a probabilistic perspective, this book includes chapters on: the discrete case, random walk and the heat equation on the integer lattice; the continuous case, Brownian motion and the usual heat equation; and martingales and fractal dimension.

  • av Charles M. Grinstead
    850,-

  • av Rebecca Weber
    850,-

  • av L.d. Faddeev
    850,-

    Describes the relation between classical and quantum mechanics. This book contains a discussion of problems related to group representation theory and to scattering theory. It intends to give a mathematically oriented student the opportunity to grasp the main points of quantum theory in a mathematical framework.

  • av Yitzhak Katznelson & Yonatan R. Katznelson
    850,-

    Linear algebra is the study of vector spaces and the linear maps between them. It underlies much of modern mathematics and is widely used in applications. Written for students with some mathematical maturity and an interest in abstraction and formal reasoning, this book is suitable for an advanced undergraduate course in linear algebra.

  • av Svetlana Katok
    850,-

    Introduces $p$-adic numbers from the point of view of number theory, topology, and analysis. Covering several topics from real analysis and elementary topology, this book includes totally disconnected spaces and Cantor sets, points of discontinuity of maps and the Baire Category Theorem, and surjectivity of isometries of compact metric spaces.

  • av Bruce C. Berndt
    850,-

    Ramanujan is recognized as one of the great number theorists of the twentieth century. This book provides an introduction to his work in number theory. It also examines subjects that have a rich history dating back to Euler and Jacobi, and they continue to be focal points of contemporary mathematical research.

  • av Gregory F. Lawler
    712,-

    Based on classes in probability for advanced undergraduates held at the IAS/Park City Mathematics Institute (Utah), this title is derived from both lectures (Chapters 1-10) and computer simulations (Chapters 11-13) that were held during the program. It concludes with a number of problems ranging from routine to very difficult.

  • av Sheldon Katz
    850,-

    Perhaps the most famous example of how ideas from modern physics have revolutionized mathematics is the way string theory has led to an overhaul of enumerative geometry, an area of mathematics that started in the eighteen hundreds. The book begins with an insightful introduction to enumerative geometry.

  • av Sara Neusel
    850,-

    Presents the characteristic zero invariant theory of finite groups acting linearly on polynomial algebras. The author assumes basic knowledge of groups and rings, and introduces more advanced methods from commutative algebra along the way. The theory is illustrated by numerous examples.

  • - A Case Studies Approach
    av Reinhard Illner, C.Sean Bohun, Samantha McCollum & m.fl.
    850,-

    Mathematical modelling is a subject without boundaries. This book explains the process of modelling real situations to obtain mathematical problems that can be analyzed, thus solving the original problem. It is suitable for a one-term course for advanced undergraduates.

  • av A. Shen
    712,-

    Suitable for undergraduate students as well as professional mathematicians who want to finally find out what transfinite induction is and why it is always replaced by Zorn's Lemma, this text introduces the main subjects of 'naive' (nonaxiomatic) set theory: functions, cardinalities, ordered and well-ordered sets, and operations on ordinals.

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