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Books in Mathematics

The Mathematics collection presents a range of foundational and advanced research content across applied and discrete mathematics, including fields such as Computational Mathematics; Differential Equations; Linear Algebra; Modelling & Simulation; Numerical Analysis; Probability & Statistics.

  • Nonlinear Partial Differential Equations and Their Applications

    College de France Seminar Volume XIV
    • 1st Edition
    • Volume 31
    • Doina Cioranescu + 1 more
    • English
    This book contains the written versions of lectures delivered since 1997 in the well-known weekly seminar on Applied Mathematics at the Collège de France in Paris, directed by Jacques-Louis Lions. It is the 14th and last of the series, due to the recent and untimely death of Professor Lions. The texts in this volume deal mostly with various aspects of the theory of nonlinear partial differential equations. They present both theoretical and applied results in many fields of growing importance such as Calculus of variations and optimal control, optimization, system theory and control, operations research, fluids and continuum mechanics, nonlinear dynamics, meteorology and climate, homogenization and material science, numerical analysis and scientific computations The book is of interest to everyone from postgraduate, who wishes to follow the most recent progress in these fields.

  • Complex Numbers in n Dimensions

    • 1st Edition
    • Volume 190
    • S. Olariu
    • English
    Two distinct systems of hypercomplex numbers in n dimensions are introduced in this book, for which the multiplication is associative and commutative, and which are rich enough in properties such that exponential and trigonometric forms exist and the concepts of analytic n-complex function, contour integration and residue can be defined.The first type of hypercomplex numbers, called polar hypercomplex numbers, is characterized by the presence in an even number of dimensions greater or equal to 4 of two polar axes, and by the presence in an odd number of dimensions of one polar axis. The other type of hypercomplex numbers exists as a distinct entity only when the number of dimensions n of the space is even, and since the position of a point is specified with the aid of n/2-1 planar angles, these numbers have been called planar hypercomplex numbers.The development of the concept of analytic functions of hypercomplex variables was rendered possible by the existence of an exponential form of the n-complex numbers. Azimuthal angles, which are cyclic variables, appear in these forms at the exponent, and lead to the concept of n-dimensional hypercomplex residue. Expressions are given for the elementary functions of n-complex variable. In particular, the exponential function of an n-complex number is expanded in terms of functions called in this book n-dimensional cosexponential functionsof the polar and respectively planar type, which are generalizations to n dimensions of the sine, cosine and exponential functions.In the case of polar complex numbers, a polynomial can be written as a product of linear or quadratic factors, although it is interesting that several factorizations are in general possible. In the case of planar hypercomplex numbers, a polynomial can always be written as a product of linear factors, although, again, several factorizations are in general possible.The book presents a detailed analysis of the hypercomplex numbers in 2, 3 and 4 dimensions, then presents the properties of hypercomplex numbers in 5 and 6 dimensions, and it continues with a detailed analysis of polar and planar hypercomplex numbers in n dimensions. The essence of this book is the interplay between the algebraic, the geometric and the analytic facets of the relations.

  • Almost Free Modules

    Set-theoretic Methods
    • 1st Edition
    • Volume 65
    • P.C. Eklof + 1 more
    • English
    This book provides a comprehensive exposition of the use of set-theoretic methods in abelian group theory, module theory, and homological algebra, including applications to Whitehead's Problem, the structure of Ext and the existence of almost-free modules over non-perfect rings. This second edition is completely revised and udated to include major developments in the decade since the first edition. Among these are applications to cotorsion theories and covers, including a proof of the Flat Cover Conjecture, as well as the use of Shelah's pcf theory to constuct almost free groups. As with the first edition, the book is largely self-contained, and designed to be accessible to both graduate students and researchers in both algebra and logic. They will find there an introduction to powerful techniques which they may find useful in their own work.

  • Mathematics

    A Second Start
    • 2nd Edition
    • S. Page + 2 more
    • English
    Provides less mathematically minded students with a gentle introduction to basic mathematics and some more advanced topics. Covering algebra, trigonometry, calculus and statistics, it manages to combine clarity of presentation with liveliness of style and sympathy for students’ needs. It is straightforward, pragmatic and packed full of illustrative examples, exercises and self-test questions. The essentials of formal mathematics are lucidly explained, with terms such as ‘integral’ or ‘differential equation’ fully clarified.

  • Mathematics Teaching Practice

    Guide for University and College Lecturers
    • 1st Edition
    • J H Mason
    • English
    Mathematics; Clarifying the distinction between mathematical research and mathematics education, this book offers hundreds of suggestions for making small and medium sized changes for lectures, tutorials, task design, or problem solving. Here is guidance and inspiration for effective mathematics teaching in a modern technological environment, directed to teachers who are unhappy with results or experience, or those now in teacher training or new to the profession. Commencing with a range of student behaviours and attitudes that have struck and amazed tutors and lecturers, Professor Mason offers a wealth of partial diagnoses, followed by specific advice and suggestions for remedial actions.

  • Manifold Theory

    An Introduction for Mathematical Physicists
    • 1st Edition
    • D. Martin
    • English
    This account of basic manifold theory and global analysis, based on senior undergraduate and post-graduate courses at Glasgow University for students and researchers in theoretical physics, has been proven over many years. The treatment is rigorous yet less condensed than in books written primarily for pure mathematicians. Prerequisites include knowledge of basic linear algebra and topology. Topology is included in two appendices because many courses on mathematics for physics students do not include this subject.

  • Mathematical Models for Society and Biology

    • 1st Edition
    • Edward Beltrami
    • English
    Mathematical Modeling for Society and Biology engagingly relates mathematics to compelling real-life problems in biology and contemporary society. It shows how mathematical tools can be used to gain insight into these modern, common problems to provide effective, real solutions. Beltrami's creative, non-threatening approach draws on a wealth of interesting examples pertaining to current social and biological issues. Central ideas appear again in different contexts throughout the book, showing the general unity of the modeling process. The models are strikingly novel and based on issues of real concern. Most have never appeared in book form. Through the relevance of these models mathematics becomes not just figures and numbers, but a means to a more refined understanding of the world.

  • Handbook of Geometric Topology

    • 1st Edition
    • R.B. Sher + 1 more
    • English
    Geometric Topology is a foundational component of modern mathematics, involving the study of spacial properties and invariants of familiar objects such as manifolds and complexes. This volume, which is intended both as an introduction to the subject and as a wide ranging resouce for those already grounded in it, consists of 21 expository surveys written by leading experts and covering active areas of current research. They provide the reader with an up-to-date overview of this flourishing branch of mathematics.

  • Mathematical Logic

    • 1st Edition
    • Volume 4
    • R.O. Gandy + 1 more
    • English
    Mathematical Logic is a collection of the works of one of the leading figures in 20th-century science. This collection of A.M. Turing's works is intended to include all his mature scientific writing, including a substantial quantity of unpublished material. His work in pure mathematics and mathematical logic extended considerably further; the work of his last years, on morphogenesis in plants, is also of the greatest originality and of permanent importance. This book is divided into three parts. The first part focuses on computability and ordinal logics and covers Turing's work between 1937 and 1938. The second part covers type theory; it provides a general introduction to Turing's work on type theory and covers his published and unpublished works between 1941 and 1948. Finally, the third part focuses on enigmas, mysteries, and loose ends. This concluding section of the book discusses Turing's Treatise on the Enigma, with excerpts from the Enigma Paper. It also delves into Turing's papers on programming and on minimum cost sequential analysis, featuring an excerpt from the unpublished manuscript. This book will be of interest to mathematicians, logicians, and computer scientists.

  • Mathematics for Chemistry and Physics

    • 1st Edition
    • George Turrell
    • English
    Chemistry and physics share a common mathematical foundation. From elementary calculus to vector analysis and group theory, Mathematics for Chemistry and Physics aims to provide a comprehensive reference for students and researchers pursuing these scientific fields. The book is based on the authors many classroom experience. Designed as a reference text, Mathematics for Chemistry and Physics will prove beneficial for students at all university levels in chemistry, physics, applied mathematics, and theoretical biology. Although this book is not computer-based, many references to current applications are included, providing the background to what goes on "behind the screen" in computer experiments.

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