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ABCD springer.com JMM 2012 Titles on Display springer.com 2 ▶$69.95 algebraic topology, both of which provide applications of the main results. More on www.springer.com/978-3-642-19579-2 S. Abbott, Middlebury College, Middlebury, VT, USA Usually dispatched within 3 to 5 business days 2011. VIII, 122 p. 15 illus., 9 in color. (École d'Été de Understanding Analysis Probabilités de Saint-Flour, Vol. 2019) Softcover This book outlines an elementary, one-semester 978-3-642-19579-2 course which exposes students to both the process of ▶$49.95 rigor, and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim of a course in real analysis should be to M. Abate, Università di Pisa, Italia; F. Tovena, Università Tor challenge and improve mathematical intuition rather Vergata, Roma, Italia than to verify it. The philosophy of this book is to focus attention on questions which give analysis its Curves and Surfaces inherent fascination. The book provides an introduction to Differential More on www.springer.com/978-0-387-95060-0 Geometry of Curves and Surfaces. The theory of Usually dispatched within 3 to 5 business days curves starts with a discussion of possible definitions of the concept of curve, proving in particular the 2001. XII, 257 p. 32 illus. (Undergraduate Texts in classification of 1-dimensional manifolds. We then Mathematics) Hardcover present the classical local theory of parametrized 978-0-387-95060-0 plane and space curves (curves in n-dimensional ▶$54.95 space are discussed in the complementary material): R.P. Agarwal, Florida Institute of Technology, Melbourne, FL, curvature, torsion, Frenet’s formulas and the USA; K. Perera, Florida Institute of Technology, Melbourne, fundamental theorem of the local theory of FL, USA; S. Pinelas, Universidade dos Açores, Ponta Delgada, Portugal curves. Then, after a self-contained presentation of degree theory for continuous self-maps of the circumference, we study the global theory of plane An Introduction to Complex curves, introducing winding and rotation numbers, Analysis and proving the Jordan curve theorem for curves of class C2, and Hopf theorem on the rotation This textbook introduces the subject of complex number of closed simple curves. The local theory of analysis to advanced undergraduate and graduate surfaces begins with a comparison of the concept students in a clear and concise manner. Key features of parametrized (i.e., immersed) surface with the of this textbook:-Effectively organizes the subject concept of regular (i.e., embedded) surface. We then into easily manageable sections in the form of 50 develop the basic differential geometry of surfaces class-tested lectures- Uses detailed examples to drive in R3: definitions, examples, differentiable maps the presentation -Includes numerous exercise sets R.J. Adler, Technion - Israel Institute of Technology, Haifa, and functions, tangent vectors (presented both that encourage pursuing extensions of the material, Israel; J.E. Taylor, Stanford University, Stanford, USA as vectors tangent to curves in the surface and as each with an “Answers or Hints” section -covers an derivations on germs of differentiable functions; we Topological Complexity of array of advanced topics which allow for flexibility in shall consistently use both approaches in the whole developing the subject beyond the basics -Provides a book) and orientation. Next we study the several Smooth Random Functions concise history of complex numbers An Introduction to Complex Analysis will be valuable to students in notions of curvature on a surface, stressing both the École d'Été de Probabilités de Saint-Flour mathematics, engineering and other applied sciences. geometrical meaning of the objects introduced and XXXIX-2009 the algebraic/analytical methods needed to study Prerequisites include a course in calculus. them via the Gauss map, up to the proof of Gauss’ These notes, based on lectures delivered in Saint More on www.springer.com/978-1-4614-0194-0 Flour, provide an easy introduction to the authors’ Teorema Egregium. Then we introduce vector fields Usually dispatched within 3 to 5 business days on a surface (flow, first integrals, integral curves) 2007 Springer monograph “Random Fields and Geometry.” While not as exhaustive as the full and geodesics (definition, basic properties, geodesic 2011. XIV, 331 p. 94 illus. Hardcover curvature, and, in the complementary material, a monograph, they are also less exhausting, while 978-1-4614-0194-0 still covering the basic material, typically at a more full proof of minimizing properties of geodesics ▶$74.95 and of the Hopf-Rinow theorem for surfaces). intuitive and less technical level. They also cover Then we shall present a proof of the celebrated some more recent material relating to random Gauss-Bonnet theorem, both in its local and in its algebraic topology and statistical applications. The global form, using basic properties (fully proved notes include an introduction to the general theory in the complementary material) of triangulations of Gaussian random fields, treating classical topics of surfaces. As an application, we shall prove the such as continuity and boundedness. This is followed Poincaré-Hopf theorem on zeroes of vector fields. by a quick review of geometry, both integral and Finally, the last chapter will be devoted to several Riemannian, with an emphasis on tube formulae, important results on the global theory of surfaces, to provide the reader with the material needed to like for instance the characterization of surfaces with understand and use the Gaussian kinematic formula, constant Gaussian curvature, and the orientability of the main result of the notes. This is followed by compact surfaces in R3. chapters on topological inference and random More on www.springer.com/978-88-470-1940-9 Due: November 25, 2011 2012. XIII, 393 p. 65 illus. (La Matematica per il 3+2) Softcover 978-88-470-1940-9 springer.com 3 Ziegler... write: "... all we offer is the examples that J. Akiyama, Tokai University, Shibuya-ku, Japan; M. Kano, we have selected, hoping that our readers will share Ibaraki University, Hitachi, Japan our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the Factors and Factorizations of AMS, August 1999 "... This book is a pleasure to hold Graphs and to look at: ample margins, nice photos, instructive pictures, and beautiful drawings ... It is a pleasure to Proof Techniques in Factor Theory read as well: the style is clear and entertaining, the This book chronicles the development of graph level is close to elementary, the necessary background factors and factorizations. It pursues a comprehensive is given separately, and the proofs are brilliant. approach, addressing most of the important results Moreover, the exposition makes them transparent. ..." from hundreds of findings over the last century. One LMS Newsletter, January 1999 of the main themes is the observation that many M. Aigner, Freie Universität Berlin, Germany More on www.springer.com/978-3-642-00855-9 theorems can be proved using only a few standard proof techniques. This stands in marked contrast to Title available online only, not as print version. A Course in Enumeration the seemingly countless, complex proof techniques offered by the extant body of papers and books. In Combinatorial enumeration is a readily accessible 2010. VIII, 274 p. 250 illus., 6 in color. Hardcover subject full of easily stated, but sometimes 978-3-642-00855-9 addition to covering the history and development of this area, the book offers conjectures and discusses tantalizingly difficult problems. This book leads ▶$49.95 the reader in a leisurely way from the basic notions open problems. It also includes numerous explanatory of combinatorial enumeration to a variety of figures that enable readers to progressively and topics, ranging from algebra to statistical physics. intuitively understand the most important notions The aim of the author is to introduce readers to a and proofs in the area of factors and factorization. fascinating field, and to offer a sophisticated source of More on www.springer.com/978-3-642-21918-4 information for the professional mathematician who Usually dispatched within 3 to 5 business days wants to learn more about the subject. The book is 2011. XII, 353 p. 153 illus. (Lecture Notes in Mathematics, organized in three parts: Basics, Methods, and Topics. Vol. 2031) Softcover There are 666 exercises, and as a special feature every 978-3-642-21918-4 chapter ends with a highlight section, discussing in $89.95 detail a particularly beautiful or famous result. ▶ More on www.springer.com/978-3-540-39032-9 Online orders shipping within 2-3 days 2007. X, 565 p. 55 illus. (Graduate Texts in M. Akhmet, Middle East Technical University, Ankara, Turkey Mathematics, Vol. 238) Hardcover 978-3-540-39032-9 Nonlinear Hybrid Continuous/ ▶$89.95 Discrete-Time Models The book is mainly about hybrid systems with continuous/discrete-time dynamics. The major part of the book consists of the theory of equations with piece-wise constant argument of generalized type. The systems as well as technique of investigation were introduced by the author very recently. They both A.G. Aksoy, Claremont McKenna College, Claremont, CA, generalized known theory about differential equations USA; M.A. Khamsi, University of Texas at El Paso, El Paso, TX, with piece-wise constant argument, introduced USA by K. Cook and J. Wiener in the 1980s. Moreover, differential equations with fixed and variable A Problem Book in Real Analysis moments of impulses are used to model real world problems. We consider models of neural networks, Today, nearly every undergraduate mathematics M. Aigner, Freie Universität Berlin, Germany; G.M. Ziegler, blood pressure distribution and a generalized model program requires at least one semester of real Technische Universität Berlin, Germany of the cardiac pacemaker. All the results of the analysis.