Mathematics Books

Book SynopsisFocuses on integrable systems and symmetries presents new results on applications of symmetries and integrability techniques to the case of equations defined on the lattice. This relatively new field has many applications, for example, in describing the evolution of crystals and molecular systems defined on lattices.Table of Contents Introduction Integrability and symmetries of nonlinear differential and difference equations in two independent variables Symmetries as integrability criteria Construction of lattice equations and their Lax pair Transformation groups for quad lattice equations Algebraic entropy of the nonautonomous Boll equations Translation from Russian of R. I. Yamilov, ''On the classification of discrete eqautions'', reference [841] No quad-graph equation can have a generalized symmetry given by the narita-Itoh-Bogoyavlensky equation Bibliography Subject Index

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Book SynopsisContains papers presented at a conference held in April 2007 at the CRM in Montreal honouring the remarkable contributions of John McKay. This title features the papers that cover a wide range of topics, including group theory, symmetries, modular functions, and geometry, with focus on 2 areas: 'Monstrous Moonshine' and the 'McKay Correspondence'.

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Book SynopsisAlgebraic curves and compact Riemann surfaces comprise the most developed and arguably the most beautiful portion of algebraic geometry. This book provides a foundation to proceed to advanced texts in general algebraic geometry, complex manifolds, and Riemann surfaces, as well as algebraic curves.Table of ContentsFundamental concepts The normalization theorem and its applications The Riemann-Roch theorem Applications of the Riemann-Roch theorem Abel's theorem and its applications.

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Book SynopsisContains a collection of mathematical applications of linear algebra, mainly in combinatorics, geometry, and algorithms. Each chapter covers a single main result with motivation and full proof, and assumes only a modest background in linear algebra. The topics include Hamming codes, the matrix-tree theorem, the Lovász bound on the Shannon capacity, and a counterexample to Borsuk's conjecture.Trade ReviewFinding examples of "linear algebra in action" that are both accessible and convincing is difficult. Thirty-three Miniatures is an attempt to present some usable examples. . . . For me, the biggest impact of the book came from noticing the tools that are used. Many linear algebra textbooks, including the one I use, delay discussion of inner products and transpose matrices till later in the course, which sometimes means they don't get discussed at all. Seeing how often the transpose matrix shows up in Matousek's miniatures made me realize space must be made for it. Similarly, the theorem relating the rank of the product of two matrices to the ranks of the factors plays a big role here. Most linear algebra instructors would benefit from this kind of insight. . . . Thirty-three Miniatures would be an excellent book for an informal seminar offered to students after their first linear algebra course. It may also be the germ of many interesting undergraduate talks. And it's fun as well." - Fernando Q. Gouvêa, MAA Reviews"[This book] is an excellent collection of clever applications of linear algebra to various areas of (primarily) discrete/combinatiorial mathematics. ... The style of exposition is very lively, with fairly standard usage of terminologies and notations. ... Highly recommended." - ChoiceTable of Contents Preface Notation Fibonacci numbers, quickly Fibonacci numbers, the formula The clubs of Oddtown Same-size intersections Error-correcting codes Odd distances Are these distances Euclidean? Packing complete bipartite graphs Equiangular lines Where is the triangle? Checking matrix multiplication Tiling a rectangle by squares Three Petersens are not enough Petersen, Hoffman–Singleton, and maybe 57 Only two distances Covering a cube minus one vertex Medium-size intersection is hard to avoid On the difficulty of reducing the diameter The end of the small coins Walking in the yard Counting spanning trees In how many ways can a man tile a board? More bricks—more walls? Perfect matchings and determinants Turning a ladder over a finite field Counting compositions Is it associative? The secret agent and umbrella Shannon capacity of the union: a tale of two fields Equilateral sets Cutting cheaply using eigenvectors Rotating the cube Set pairs and exterior products Index

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Book SynopsisTrade ReviewThe authors do an excellent job in bringing together the main techniques and results connected to the Erdős distance problem ... this is a useful book for the reader with sufficient mathematical experience who wishes to learn the principal techniques and results in the Erdős distance problem and related areas." - Mathematical Reviews"This book...achieves the remarkable feat of providing an extremely accessible treatment of a classic family of research problems. ...The book can be used for a reading course taken by an undergraduate student (parts of the book are accessible for talented high school students as well), or as introductory material for a graduate student who plans to investigate this area further...Highly recommended." - M. Bona, ChoiceTable of Contents Foreword Acknowledgments Introduction The √𝑛 theory The 𝑛^{2/3} theory The Cauchy-Schwarz inequality Graph theory and incidences The 𝑛^{4/5} theory The 𝑛^{6/7} theory Beyond 𝑛^{6/7} Information theory Dot products Vector spaces over finite fields Distances in vector spaces over finite fields Applications of the Erdős distance problem Hyperbolas in the plane Basic probability theory Jensen’s inequality Bibliography Biographical information Index of terminology

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Book SynopsisTrade ReviewThe presentation of the material is very clear and illustrated by a number of enlightening figures. Many motivating remarks and discussions are provided. A number of proofs in the more elementary chapters are omitted, but precise pointers to the literature are given. Also numerous exercises are posed as well as some more involved 'projects' which motivate the reader to get active herself." - R. Steinbauer, Monatshefte für Mathematik"This is a gentle introduction to Fourier analysis and wavelet theory that requires little background but still manages to explain some of the applications of Fourier and wavelet methods and touch on several current research topics. ... The authors have taken care to be accessible to undergraduate mathematicians. ... Compared to standard texts, this book is characterised by more personal and historical information, including footnotes. ... It comes with many projects for interested students, and lists a number of open-ended problems that suggest further developments and should engage interested students. ... In summary, this is a well-written and lively introduction to harmonic analysis that is accessible and stimulating for undergraduates and instructive and amusing for the more sophisticated reader. It could also be argued that the material herein should be part of the knowledge of most undergraduates in mathematics, given that the modern world relies more and more on data compression. It is therefore timely as well. It has certainly earned my enthusiastic recommendation." - Michael Cowling, Gazette of the Australian Mathematical Society"A wonderful introduction to harmonic analysis and applications. The book is intended for advanced undergraduate and beginning graduate students and it is right on target. Pereyra and Ward present in a captivating style a substantial amount of classical Fourier analysis as well as techniques and ideas leading to current research. ... It is a great achievement to be able to present material at this level with only a minimal prerequisite of advanced calculus and linear algebra and a set of Useful Tools included in the appendix. I recommend this excellent book with enthusiasm and I encourage every student majoring in math to take a look." - Florin Catrina, MAA Reviews"[T]he panorama of harmonic analysis presented in the book includes very recent achievements like the connection of the dyadic shift operator with the Hilbert transform. This gives to an interested reader a good chance to see concrete examples of contemporary research problems in harmonic analysis. I highly recommend this book as a good source for undergraduate and graduate courses as well as for individual studies." - Krzysztof Stempak, Zentralblatt MATHTable of Contents Contents List of figures List of tables IAS/Park City Mathematics Institute Preface Fourier series: Some motivation Interlude: Analysis concepts Pointwise convergence of Fourier series Summability methods Mean-square convergence of Fourier series A tour of discrete Fourier and Haar analysis The Fourier transform in paradise Beyond paradise From Fourier to wavelets, emphasizing Haar Zooming properties of wavelets Calculating with wavelets The Hilbert transform Useful tools Alexander’s dragon Bibliography Name index Subject index

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Book SynopsisPresents an exposition of fixed point theory. This work focuses on the problem of whether a closed interval, square, disk, or sphere has the fixed point property. It aims to show how fixed point theory uses combinatorial ideas related to decomposition of figures into distinct parts called faces, which adjoin each other in a regular fashion.Table of ContentsContinuous mappings of a closed interval and a square First combinatorial lemma Second combinatorial lemma, or walks through the rooms in a house Sperner's lemma Continuous mappings, homeomorphisms, and the fixed point property Compactness Proof of Brouwer's Theorem for a closed interval, the intermediate value theorem, and applications Proof of Brouwer's Theorem for a square The iteration method Retraction Continuous mappings of a circle, homotopy, and degree of a mapping Second definition of the degree of a mapping Continuous mappings of a sphere Lemma on equality of degrees.

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Book SynopsisTrade ReviewWritten by an eminent expert as the first monograph on this topic, this book can be recommended to anybody working on large networks and their applications in mathematics, computer science, social sciences, biology, statistical physics or chip design." - Zentralblatt Math"This is an amazing book: readable, deep, and lively. It sets out this emerging area, makes connections between old classical graph theory and graph limits, and charts the course of the future." - Persi Diaconis, Stanford University"It is always exciting when a mathematical theory turns out to be connected to a variety of other topics. This is the case with the recently developed subject of graph limits, which exhibits tight relations with a wide range of areas including statistical physics, analysis, algebra, extremal graph theory, and theoretical computer science. The book Large Networks and Graph Limits contains a comprehensive study of this active topic and an updated account of its present status. The author, Laszls Lovasz, initiated the subject, and together with his collaborators has contributed immensely to its development during the last decade. This is a beautiful volume written by an outstanding mathematician who is also an excellent expositor." - Noga Alon, Tel Aviv University, Israel"Modern combinatorics is by no means an isolated subject in mathematics, but has many rich and interesting connections to almost every area of mathematics and computer science. The research presented in Lovasz's book exemplifies this phenomenon by taking one of the most quintessentially combinatorial of objects--the finite graph--and through the process of taking limits of sequences of such graphs, reveals and clarifies connections to measure theory, analysis, statistical physics, metric geometry, spectral theory, property testing, algebraic geometry, and even Hilbert's tenth and seventeenth problems. Indeed, this book presents a wonderful opportunity for a student in combinatorics to explore other fields of mathematics, or conversely for experts in other areas of mathematics to become acquainted with some aspects of graph theory." - Terence Tao, University of California, Los Angeles, CA"László Lovász has written an admirable treatise on the exciting new theory of graph limits and graph homomorphisms, an area of great importance in the study of large networks. It is an authoritative, masterful text that reflects Lovász's position as the main architect of this rapidly developing theory. The book is a must for combinatorialists, network theorists, and theoretical computer scientists alike." - Bela Bollobas, Cambridge University, UKTable of Contents Preface Part 1. Large graphs: An informal introduction Very large networks Large graphs in mathematics and physics Part 2. The algebra of graph homomorphisms Notation and terminology Graph parameters and connection matrices Graph homomorphisms Graph algebras and homomorphism functions Part 3. Limits of dense graph sequences Kernels and graphons The cut distance Szemerédi partitions Sampling Convergence of dense graph sequences Convergence from the right On the structure of graphons The space of graphons Algorithms for large graphs and graphons Extremal theory of dense graphs Multigraphs and decorated graphs Part 4. Limits of bounded degree graphs Graphings Convergence of bounded degree graphs Right convergence of bounded degree graphs On the structure of graphings Algorithms for bounded degree graphs Part 5. Extensions: A brief survey Other combinatorial structures Appendix A Bibliography Author index Subject index Notation index

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Book SynopsisIn these volumes, a reader will find all of John Tate's published mathematical papers-spanning more than six decades-enriched by new comments made by the author. Included also is a selection of his letters. His letters give us a close view of how he works and of his ideas in process of formation.Table of Contents Part I: Fourier analysis in number fields and Hecke's zeta-functions by J. T. Tate A note on finite ring extensions by E. Artin and J. T. Tate On the relation between extremal points of convex sets and homomorphisms of algebras by J. Tate Genus change in inseparable extensions of function fields by J. Tate On Chevalley's proof of Luroth's theorem by S. Lang and J. Tate The higher dimensional cohomology groups of class field theory by J. Tate The cohomology groups of algebraic number fields by J. T. Tate On the Galois cohomology of unramified extensions of function fields in one variable by Y. Kawada and J. Tate On the characters of finite groups by R. Brauer and J. Tate Homology of Noetherian rings and local rings by J. Tate WC-groups over $p$-adic fields by J. Tate On the inequality of Castelnuovo-Severi by E. Artin and J. Tate On the inequality of Castelnuovo-Severi, and Hodge's theorem by J. Tate Principal homogeneous spaces over abelian varieties by S. Lang and J. Tate Principal homogeneous spaces for abelian varieties by J. Tate A different with an odd class by A. Frohlich, J.-P. Serre, and J. Tate Nilpotent quotient groups by J. Tate Duality theorems in Galois cohomology over number fields by J. Tate Ramification groups of local fields by S. Sen and J. Tate Formal complex multiplication in local fields by J. Lubin and J. Tate Algebraic cycles and poles of zeta functions by J. T. Tate Elliptic curves and formal groups by J. Lubin, J. Serre, and J. Tate On the conjectures of Birch and Swinnerton-Dyer and a geometric analog by J. Tate Formal moduli for one-parameter formal Lie groups by J. Lubin and J. Tate The cohomology groups of tori in finite Galois extensions of number fields by J. Tate Global class field theory by J. T. Tate Endomorphisms of abelian varieties over finite fields by J. Tate The rank of elliptic curves by J. T. Tate and I. R. Safarevic Residues of differentials on curves by J. Tate $p$-divisible groups by J. T. Tate The work of David Mumford by J. Tate Classes d'isogenie des varietes abeliennes sur un corps fini (d'apres T. Honda) by J. Tate Good reduction of abelian varieties by J.-P. Serre and J. Tate Group schemes of prime order by J. Tate and F. Oort Symbols in arithmetic by J. Tate Rigid analytic spaces by J. Tate The Milnor ring of a global field by H. Bass and J. Tate Appendix by H. Bass and J. Tate Letter from Tate to Iwasawa on a relation between $K_2$ and Galois cohomology by J. Tate Points of order 13 on elliptic curves by B. Mazur and J. Tate The arithmetic of elliptic curves by J. T. Tate The 1974 Fields Medals (I): An algebraic geometer by J. Tate Algorithm for determining the type of a singular fiber in an elliptic pencil by J. Tate Letters by J. Tate

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Book SynopsisAlgebraic Geometry has been at the centre of much of mathematics for hundreds of years. It is not an easy field to break into, despite its humble beginnings in the study of circles, ellipses, hyperbolas, and parabolas. This text consists of a series of exercises, plus some background information and explanations, starting with conics and ending with sheaves and cohomology.

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Book SynopsisPresents several new directions of mathematical research. All of these directions are based on numerical experiments conducted by the author, which led to new hypotheses that currently remain open. The hypotheses range from geometry and topology to combinatorics to algebra and number theory.Table of Contents Introduction The statistics of topology and algebra Combinatorial complexity and randomness Random permutations of Young diagrams of their cycles The geometry of Frobenius numbers for additive semigroups Bibliography

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Book SynopsisTrade Review[T]his is an extremely valuable textbook for graduate classical complex analysis in one variable both for lecturers and students not following the increasing standardization trends of student's curricula... The presentation style is excellent, a very well contemplated pleasant reading throughout, rich in interesting outlooks. I recommend this work to all the mathematical libraries at universities as an extremely helpful material in teaching or studying complex analysis." - László L. Stachó, ACTA Sci. Math.Table of Contents From i to z: the basics of complex analysis From z to the Riemann mapping theorem: some finer points of basic complex analysis Harmonic functions Riemann surfaces: definitions, examples, basic properties Analytic continuation, covering surfaces, and algebraic functions Differential forms on Riemann surfaces The theorems of Riemann-Roch, Abel, and Jacobi Uniformization Review of some basic background material Bibliography Index

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisForest mensuration provides data on aspects of length, mass and time of areas of forest, individual trees or parcels of felled timber. Such quantitative information is vital to sellers, buyers, planners, managers and researchers within forestry. This book is a revision of a successful text originally published in 1983 but written for students in Africa. The new edition is international in scope, and has also been changed and updated to reflect recent advances, particularly with respect to biomass and fodder measurement, sampling with unequal probabilities and growth modelling. The book covers both the theory and practice of forest mensuration and includes a number of worked examples of calculations. It is a basic textbook for students of forestry and will also be of value to practising foresters.Table of Contents1: Measurements 2: Measuring single trees 3: Measuring tree crops 4: Forest inventory 5: Statistical principles in forest inventory 6: Site assessment 7: Forest growth models

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Book SynopsisWritten by leading researchers from the USA, Canada and Europe, this is an essential reference tool for researchers and advanced students in animal nutrition. Farm livestock have evolved digestive systems that are capable of digesting fibrous materials and by-products unsuited for man. Throughout the world, production from farm livestock is concerned with providing food and clothing of animal origin for man. Animal production science underpins this goal and provides the scientific basis for livestock management practices. Feed evaluation concerns the use of methods to describe animal feedstuffs with respect to their ability to sustain different types and levels of animal performance. The main themes of the book are methods of feed evaluation, current feeding systems, and mechanistic mathematical modelling. No other title brings together methods, systems and models under one cover.Table of Contents1: Feed Evaluation for Animal Production, J France, MK Theodorou, RS Lowman and DE Beever 2: Feed Characterisation, A Chesson 3: Intake, Passage and Digestibility, DP Poppi, J France and SR McLennan 4: In Vitro and In Situ Methods for Estimating Digestibility with Reference to Protein Degradability, GA Broderick and RC Cochran 5: Measurement of Energy Metabolism, C K Reynolds 6: Feeding Systems for Dairy Cows, S Tamminga and G Hof 7: Feeding Systems for Beef Cattle, JG Buchanan-Smith and DG Fox 8: Feeding Systems for Sheep, LA Sinclair and RG Wilkinson 9: Feeding Systems for Pigs, LI Chiba 10: Feeding Systems for Poultry, S Leeson and JD Summers 11: Feeding Systems for Horses, D Cuddeford 12: Prediction of Response to Nutrients by Ruminants Through Mathematical Modelling and Improved Feed Characterization, DE Beever, J France and G Alderman 13: Analyses of Modelling Whole Rumen Function, J Dijkstra and A Bannink 14: Modelling the Lactating Dairy Cow, RL Baldwin and KC Donovan 15: Modelling Growth and Wool Production in Ruminants, WJ Gerrits and J Dijkstra 16: Modelling Growth and Lactation in Pigs, JL Black 17: Modelling the Utilization of Dietary Energy and Amino Acids by Poultry, MG MacLeod 18: Modelling Growth in Fish, Y Cui and S Xie 19: The Nutrition of Companion Animals, AC Longland, MK Theodorou and IH Burger 20: Index

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Book SynopsisIPM Systems need to be developed for agriculture to be economically and environmentallystrong, in production, storage, and food processing. Although the concept and philosophy ofintegrated pest management have been largely accepted for some time, its implementation iscomplex and faces numerous potential problems. If IPM is to enjoy widespread approval and adoption, it must be clearly defined and economically and socially acceptable. The topics covered in this book include a range of topics, such as: risk-benefit analysis, transgenic crops in IPM and consumer response to IPM.Trade Review"The editors have recruited a formidable team of authors to produce the thirteen information-packed chapters, each of which represents an amalgam of historical background, relevant science and present-day practice, together with as up-to-date a bibliography as possible." Derek Clifford, Pest Management Science, November 2004"Table of Contents1: Integrated Pest Management: Retrospect and prospect,G S Dhaliwal, O Koul and R Arora, Punjab Agricultural University, India 2: Cultural practices: Springboard to IPM, W I Bajwa and M Kogan, Oregon State University, USA 3: The relevance of modelling in successful implementation of IPM, D E Legg, University of Wyoming, USA 4: Manipulation of tritrophic interactions for IPM,R H J Verkerk, Imperial College London, UK 5: Behavior modifying chemicals: Prospects and constraints in IPM, L J Gut, L L Stelinski, Michigan State University,USA, D R Thomson, DJS Consulting, Washington State,USA and J R Miller, Michigan State University, USA 6: Transgenic insecticidal cultivars in Integrated Pest Management: Challenges and opportunities, J S Bernal,J Prasifka, M Sétamou and K M Heinz, Texas A&M University, USA 7: Plant resistance against pests: Issues and strategies,C M Smith, Kansas State University, USA 8: The pesticide paradox in IPM: Risk benefit analysis,P Guillebeau, University of Georgia Cooperative Extension Service, USA 9: Manipulation of host finding and acceptance behaviours in insects: Importance to IPM, R S Cowles, Connecticut Agricultural Experiment Station, USA 10: Integrated Pest Management in forestry: Potential and challenges, I S Otvos, Pacific Forestry Centre, Victoria,Canada 11: Consumer response to IPM: Potential and challenges,C S Hollingsworth and W M Coli, University of Massachusetts, USA 12: The essential role of IPM in promoting sustainability of agricultural production systems for future generations,G W Cuperus, R C Berberet and R T Noyes, Oklahoma State University, USA 13: Opportunities and challenges for IPM in developing Countries, D Bergvinson, CIMMYT, Mexico

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Book SynopsisGenomics has experienced a dramatic development during the last 15-20 years. Data from mammalian genomes such as the human, mouse and rat have already been published, while others such as the dog, cattle and chimpanzee will soon follow. This book summarizes the current knowledge of mammalian genomics and offers a comparative analysis of genomes known today. This analysis includes farm, companion and lab animals. Topics covered include structural and functional aspects of the mammalian genome, mechanisms of genomic changes at the molecular level, evolution of DNA sequences, comparative chromosome mapping and painting, genome databases, gene prediction and the use of genomic information to understand inherited diseases. Contributors include leading researchers from Europe, USA, Australia and Japan.Table of ContentsPart 1: Organization of the Mammalian Genome 1: Linkage mapping, 2: Mapping genomes at the chromosome level, 3: Mapping genomes at the molecular level, 4: DNA sequence of the human and other mammalian genomes, Part 2: Expression of the Mammalian Genome 5: The transcriptome, 6: The proteome, 7: The epigenome - epigenetic regulation of gene expression in mammalian species, 8: Regulation of genome activity and genetic networks in mammals, 9: Inducing alterations in the mammalian genome for investigating the function of genes, Part 3: Evolution of the Mammalian Genome 10: Mammalian genomes in context, 11: Elements and mechanisms of genome change, 12: DNA sequence evolution and phylogenetic footprinting, 13: The evolution of the mammalian karyotype, 14: Comparative gene mapping and chromosome painting in mammals and the reconstruction of the ancestral mammalian karyotype, Part 4: Genome Analysis and Bioinformatics 15: Bioinformatics: from computational analysis through to integrated systems, 16: Genetic databases, 17: Gene predictions and annotations, Part 5: The Fruits of Mammalian Genomics 18: Genomic research and progress in understanding inherited disorders in humans and other mammals, 19: Pharmacogenomics, 20: Genome scanning for quantitative trait loci, 21: Mammalian population genetics and genomics,

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Book SynopsisThis is a resource and guide for all who make decisions that affect the mathematics education of students from prekindergarten through grade 12. Recommendations are grounded in the belief that students should learn important mathematical concepts and processes with understanding.

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Book SynopsisPresents portraits of teaching by secondary school teachers who have closely observed classroom communication, conversation and discourse.

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Book SynopsisComplex Instruction (CI) is a response to the paradox that group work offers much potential but often creates circumstances where few students seem to learn. CI is a set of ideas and strategies that address the problems that confound group work, but that create powerful learning for children. This book offers guidance to readers on how to use these strategies and ideas.

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Book SynopsisThis collection of original articles is the start of a compelling conversation among some of the leading figures in critical and social justice mathematics, a number of teachers and educators who have been inspired by them and who have inspiring stories of their own to tell—and any reader interested in the intersection of education and social justice.

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Book SynopsisMathematics educators have long worked to help students to develop problem-solving skills. More recently, they have sought to provide students with the knowledge in the Common Core State Standards (CCSS). This volume is the second in a series from NCTM that equips classroom teachers with targeted, highly effective problems for achieving both goals at once.

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Book SynopsisThe Building a System of Tens Casebook was developed as the key resource for participants’ Developing Mathematical Ideas seminar experience. The thirty cases, written by teachers describing real situations and actual student thinking in their classrooms, provide the basis of each session’s investigation of specific mathematical concepts and teaching strategies.

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Book SynopsisPresents twenty-nine cases, written by teachers describing real situations and actual student thinking in their classrooms, that provide the basis of each session's investigation of specific mathematical concepts and teaching strategies.

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Book SynopsisPresents twenty-eight cases, written by teachers describing real situations and actual student thinking in their classrooms, that provide the basis of each session's investigation of specific mathematical concepts and teaching strategies.

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Book SynopsisAre you ready to take your teaching to the next level? Taking Action: Implementing Effective Mathematics Teaching Practices in Grades 6-8 offers a coherent set of professional learning experiences designed to foster teachers' understanding of the effective mathematics teaching practices and their ability to apply those practices in their own classrooms.

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Book SynopsisProvides the kind of mathematical knowledge and experiences that students will need for courses in other fields, such as biology, chemistry, business, finance, economics, and other areas that are heavily dependent on data either from laboratory experiments or from other studies. The focus is on the fundamental mathematical concepts and realistic problem-solving via mathematical modelling.Trade Review… On initial viewing, “Functions, Data and Models” may seem like a typical textbook, with all the usual key parts, including appendixes and answers to selected problems in the back of the book. However, on closer examination, readers will see and understand how the eight-chapter work differs from classic algebra books. The detailed preface includes messages for the student, messages for the instructor, and information on the book's philosophy. … The book would be a great resource for any algebra course. Highly recommended." - K.D. Holton, CHOICE Magazine"This textbook certainly sets the hook early when authors explain in the preface that the book's philosophy is to allow students to focus on mathematical ideas, not mathematical calculations. … As the authors point out in the introduction to this text, it contains enough material (in both depth and variety) to cover two semesters' worth of study. On the other hand, the interested instructor could easily design a syllabus covering a limited number of topics from the book to address the needs of a semester-long course. I highly recommend this text to instructors who seek to cultivate creativity and critical thinking in their college-algebra-level students" - Hilary Fletcher, Mathematics and Computer EducationTable of Contents Preface 1. Data Everywhere 2. Functions Everywhere 3. Linear Functions 4. More about Linear Functions 5. Families of Nonlinear Functions 6. Polynomial Functions 7. Extended Families of Functions 8. Modeling Periodic Phenomena Appendices Selected Short Answers About the Authors

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Book SynopsisMany situations exist in which solutions to problems are represented as function space integrals. Such representations can be used to study the qualitative properties of the solutions and to evaluate them numerically using Monte Carlo methods. The emphasis in this book is on the behavior of solutions in special situations when certain parameters get large or small.

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Book SynopsisA systematic, self-contained treatment of the theory of stochastic differential equations in infinite dimensional spaces. Included is a discussion of Schwartz spaces of distributions in relation to probability theory and infinite dimensional stochastic analysis, as well as the random variables and stochastic processes that take values in infinite dimensional spaces.

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Book SynopsisOrdinary Differential Equations covers the fundamentals of the theory of ordinary differential equations (ODEs), including an extensive discussion of the integration of differential inequalities, on which this theory relies heavily. In addition to these results, the text illustrates techniques involving simple topological arguments, fixed point theorems, and basic facts of functional analysis. Unlike many texts, which supply only the standard simplified theorems, Ordinary Differential Equations presents the basic theory of ODEs in a general way, making it a valuable reference. This SIAM reissue of the 1982 second edition covers invariant manifolds, perturbations, and dichotomies, making the text relevant to current studies of geometrical theory of differential equations and dynamical systems.

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Book SynopsisProvides the reader with a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems. It also addresses specialized topics such as image reconstruction, parameter identification, total variation methods, nonnegativity constraints, and regularization parameter selection methods.

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Book SynopsisBasic Concepts of Probability and Statistics provides a mathematically rigorous introduction to the fundamental ideas of modern statistics for readers without a calculus background. It is the only book at this level to introduce readers to modern concepts of hypothesis testing and estimation, covering basic concepts of finite, discrete models of probability and elementary statistical methods. Although published in 1970, it maintains a modern outlook, especially with such topics as models and model building, simple random and stratified survey sampling, experimental design, and nonparametric tests and its discussion of power. The book covers a wide range of applications in manufacturing, biology, and social science, including demographics, political science, and sociology. Each section offers extensive problem sets, with selected answers provided. Among the topics covered that readers may not expect in an elementary text are optimal design and a statement and proof of the fundamental (N

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Book SynopsisMathematical modeling - the ability to apply mathematical concepts and techniques to real-life systemsâhas expanded considerably over the last decades, making it impossible to cover all of its aspects in one course or textbook. Continuum Modeling in the Physical Sciences provides an extensive exposition of the general principles and methods of this growing field with a focus on applications in the natural sciences. The authors present a thorough treatment of mathematical modeling from the elementary level to more advanced concepts. Most of the chapters are devoted to a discussion of central issues such as dimensional analysis, conservation principles, balance laws, constitutive relations, stability, robustness, and variational methods, and are accompanied by numerous real-life examples. Readers will benefit from the exercises placed throughout the text and the Challenging Problems sections found at the ends of several chapters.

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Book SynopsisA novel approach to analysing initial-boundary value problems for integrable partial differential equations (PDEs) in two dimensions, based on ideas of the inverse scattering transform that the author introduced in 1997. This method is unique in also yielding novel integral representations for linear PDEs. Several new developments are addressed in the book, including a new transform method for linear evolution equations on the half-line and on the finite interval; analytical inversion of certain integrals such as the attenuated Radon transform and the Dirichlet-to-Neumann map for a moving boundary; integral representations for linear boundary value problems; analytical and numerical methods for elliptic PDEs in a convex polygon; and integrable nonlinear PDEs. An epilogue provides a list of problems on which the author's new approach has been used, offers open problems, and gives a glimpse into how the method might be applied to problems in three dimensions.

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Book SynopsisProvides an introduction to the applications, theory, and algorithms of linear and nonlinear optimization. The emphasis is on practical aspects - discussing modern algorithms, as well as the influence of theory on the interpretation of solutions or on the design of software. The book includes several examples of realistic optimization models that address important applications. The succinct style of this second edition is punctuated with numerous real-life examples and exercises, and the authors include accessible explanations of topics that are not often mentioned in textbooks, such as duality in nonlinear optimization, primal-dual methods for nonlinear optimization, filter methods, and applications such as support-vector machines. The book is designed to be flexible. It has a modular structure, and uses consistent notation and terminology throughout. It can be used in many different ways, in many different courses, and at many different levels of sophistication.

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Book SynopsisThe purpose of this book is to promote understanding of two phenomena: sensitivity of linear systems and least squares problems, and numerical stability of algorithms. Sensitivity and stability are analyzed as mathematical properties, without reference to finite precision arithmetic. The material is presented at a basic level, emphasizing ideas and intuition, but in a mathematically rigorous fashion. The derivations are simple and elegant, and the results are easy to understand and interpret. The book is self-contained. It was written for students in all areas of mathematics, engineering, and the computational sciences, but can easily be used for self-study. This text differs from other numerical linear algebra texts by offering the following: a systematic development of numerical conditioning; a simplified concept of numerical stability in exact arithmetic; simple derivations; a high-level view of algorithms; and results for complex matrices.

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Book SynopsisThis book addresses modern nonlinear programming concepts and algorithms, especially as they apply to challenging applications in chemical process engineering. It relates the material to real-world problem classes in process optimisation, thus bridging the gap between the mathematical material and the practical uses. Nonlinear Programming: Concepts, Algorithms, and Applications to Chemical Processes shows readers which methods are best suited for specific applications, how large-scale problems should be formulated and what features of these problems should be emphasised, and how existing NLP methods can be extended to exploit specific structures of large-scale optimisation models. The book serves a dual function: it will be useful to chemical engineers who wish to understand and use nonlinear programming; it will also be of interest to experts in mathematical optimisation who want to understand process engineering problems and develop better approaches to solving them.

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