Mathematics Books

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Book SynopsisIntended for the one- or two-semester course required of Education majors, MATHEMATICS FOR ELEMENTARY SCHOOL TEACHERS, 6E offers future teachers a comprehensive mathematics course designed to foster concept development through examples, investigations, and explorations. Visual icons throughout the main text allow instructors to easily connect content to the hands-on activities in the corresponding Explorations Manual. Bassarear presents real-world problems, problems that require active learning in a method similar to how archaeologists explore an archaeological find: they carefully uncover the site, slowly revealing more and more of the structure. The author demonstrates that there are many paths to solving a problem, and that sometimes, problems have more than one solution. With this exposure, future teachers will be better able to assess student needs using diverse approaches.Table of ContentsPreface. 1. Foundations for Learning Mathematics. Getting Started and Problem Solving. Process, Practice, and Content Standards. Questions to Summarize Big Ideas. Chapter 1 Summary. Chapter 1 Review Exercises. 2. Sets and Numeration. Sets. Numeration. Questions to Summarize Big Ideas. Chapter 2 Summary. Chapter 2 Review Exercises. 3. The Four Fundamental Operations of Arithmetic. Understanding Addition. Understanding Subtraction. Understanding Multiplication. Understanding Division. Questions to Summarize Big Ideas. Chapter 3 Summary. Chapter 3 Review Exercises. 4. Extending the Number System. Integers. Fractions and Rational Numbers. Understanding Operations with Fractions. Beyond Integers and Fractions. Questions to Summarize Big Ideas. Chapter 4 Summary. Chapter 4 Review Exercises. 5. Proportional Reasoning. Ratio and Proportion. Percents. Questions to Summarize Big Ideas. Chapter 5 Summary. Chapter 5 Review Exercises. 6. Algebraic Thinking. Understanding Patterns, Relations, and Functions. Represent and Analyze Math Situations and Structures Using Algebraic Symbols. Mathematical Models. Analyzing Change. Questions to Summarize Big Ideas. Chapter 6 Summary. Chapter 6 Review Exercises. 7. Uncertainty: Data and Chance. The Process of Collecting and Analyzing Data. Going Beyond the Basics. Concepts Related to Chance. Counting and Chance. Questions to Summarize Big Ideas. Chapter 7 Summary. Chapter 7 Review Exercises. 8. Geometry as Shape. Basic Ideas and Building Blocks. Two-Dimensional Figures. Three-Dimensional Figures. Questions to Summarize Big Ideas. Chapter 8 Summary. Chapter 8 Review Exercises. 9. Geometry as Measurement. Systems of Measurement. Perimeter and Area. Surface Area and Volume. Looking Back on Chapter 9. Chapter 9 Summary. Chapter 9 Review Exercises. 10. Geometry as Transforming Shapes. Congruence Transformations. Symmetry and Tessellations. Similarity. Questions to Summarize Big Ideas. Chapter 10 Summary. Chapter 10 Review Exercises. Appendix A: Selected Answers. Appendix B: Answers to Questions in Text. Endnotes. Photo Credits. Index.

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Book SynopsisIn recent years the development of new classification and regression algorithms based on deep learning has led to a revolution in the fields of artificial intelligence, machine learning, and data analysis. The development of a theoretical foundation to guarantee the success of these algorithms constitutes one of the most active and exciting research topics in applied mathematics. This book presents the current mathematical understanding of deep learning methods from the point of view of the leading experts in the field. It serves both as a starting point for researchers and graduate students in computer science, mathematics, and statistics trying to get into the field and as an invaluable reference for future research.Table of Contents1. The modern mathematics of deep learning Julius Berner, Philipp Grohs, Gitta Kutyniok and Philipp Petersen; 2. Generalization in deep learning Kenji Kawaguchi, Leslie Pack Kaelbling, and Yoshua Bengio; 3. Expressivity of deep neural networks Ingo Gühring, Mones Raslan and Gitta Kutyniok; 4. Optimization landscape of neural networks René Vidal, Zhihui Zhu and Benjamin D. Haeffele; 5. Explaining the decisions of convolutional and recurrent neural networks Wojciech Samek, Leila Arras, Ahmed Osman, Grégoire Montavon and Klaus-Robert Müller; 6. Stochastic feedforward neural networks: universal approximation Thomas Merkh and Guido Montúfar; 7. Deep learning as sparsity enforcing algorithms A. Aberdam and J. Sulam; 8. The scattering transform Joan Bruna; 9. Deep generative models and inverse problems Alexandros G. Dimakis; 10. A dynamical systems and optimal control approach to deep learning Weinan E, Jiequn Han and Qianxiao Li; 11. Bridging many-body quantum physics and deep learning via tensor networks Yoav Levine, Or Sharir, Nadav Cohen and Amnon Shashua.

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Book SynopsisThis monograph is the first to present the theory of global attractors of Hamiltonian partial differential equations. A particular focus is placed on the results obtained in the last three decades, with chapters on the global attraction to stationary states, to solitons, and to stationary orbits. The text includes many physically relevant examples and will be of interest to graduate students and researchers in both mathematics and physics. The proofs involve novel applications of methods of harmonic analysis, including Tauberian theorems, Titchmarsh''s convolution theorem, and the theory of quasimeasures. As well as the underlying theory, the authors discuss the results of numerical simulations and formulate open problems to prompt further research.Table of ContentsIntroduction; 1. Global attraction to stationary states; 2. Global attraction to solitons; 3. Global attraction to stationary orbits; 4. Asymptotic stability of stationary orbits and solitons; 5. Adiabatic effective dynamics of solitons; 6. Numerical simulation of solitons; 7. Dispersive decay; 8. Attractors and quantum mechanics; References; Index.

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Book SynopsisWritten for use in teaching and for self-study, this book provides a comprehensive and pedagogical introduction to groups, algebras, geometry, and topology. It assimilates modern applications of these concepts, assuming only an advanced undergraduate preparation in physics. It provides a balanced view of group theory, Lie algebras, and topological concepts, while emphasizing a broad range of modern applications such as Lorentz and Poincaré invariance, coherent states, quantum phase transitions, the quantum Hall effect, topological matter, and Chern numbers, among many others. An example based approach is adopted from the outset, and the book includes worked examples and informational boxes to illustrate and expand on key concepts. 344 homework problems are included, with full solutions available to instructors, and a subset of 172 of these problems have full solutions available to students.Trade Review'The whole of theoretical physics, and our general picture of the world, are based on symmetries. This book is devoted to symmetries and their manifestations in nature, and it allows students to develop a theoretical and experimental understanding of the fundamental properties of the Universe. This path is carefully paved by the authors.' Professor Vladimir Zelevinsky, Michigan State UniversityTable of ContentsPreface; Part I. Symmetry Groups and Algebras: 1. Introduction; 2. Some properties of groups; 3. Introduction to lie groups; 4. Permutation groups; 5. Electrons on periodic lattices; 6. The rotation group; 7. Classification of lie algebras; 8. Unitary and special unitary groups; 9. SU(3) flavor symmetry; 10. Harmonic oscillators and SU(3); 11. SU(3) matrix elements; 12. Introduction to non-compact groups; 13. The Lorentz group; 14. Lorentz covariant fields; 15. Poincaré invariance; 16. Gauge invariance; Part II. Broken Symmetry: 17. Spontaneous symmetry breaking; 18. The Higgs mechanism; 19. The standard model; 20. Dynamical symmetry; 21. Generalized coherent states; 22. Restoring symmetry by projection; 23. Quantum phase transitions; Part III. Topology and Geometry: 24. Topology, manifolds, and metrics; 25. Topological solitons; 26. Geometry and gauge theories; 27. Geometrical phases; 28. Topology of the quantum Hall effect; 29. Topological matter; Part IV. A Variety of Physical Applications: 30. Angular momentum recoupling; 31. Nuclear fermion dynamical symmetry; 32. Superconductivity and superfluidity; 33. Current algebra; 34. Grand unified theories; Appendix A. Second quantization; Appendix B. Natural units; Appendix C. Angular momentum tables; Appendix D. Lie algebras; References; Index.

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Book SynopsisSuitable for both postgraduate students and researchers in the field of operator theory, this book is an excellent resource providing the complete proof of the Brown-Douglas-Fillmore theorem. The book starts with a rapid introduction to the standard preparatory material in basic operator theory taught at the first year graduate level course. To quickly get to the main points of the proof of the theorem, several topics that aid in the understanding of the proof are included in the appendices. These topics serve the purpose of providing familiarity with a large variety of tools used in the proof and adds to the flexibility of reading them independently.Table of ContentsPreface; Overview; 1. Spectral Theory for Hilbert Space Operators; 2. Ext(X) as a Semigroup with Identity; 3. Splitting and the Mayer-Vietoris Sequence; 4. Determination of Ext(X); 5. Applications to Operator Theory; 6. Epilogue; Appendix A. Point Set Topology; Appendix B. Linear Analysis; Appendix C. The Spectral Theorem; Subject Index; Index of Symbols; References.

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Book SynopsisMaple is a powerful symbolic computation system that is widely used in universities around the world. This short introduction gives readers an insight into the rules that control how the system works, and how to understand, fix, and avoid common problems. Topics covered include algebra, calculus, linear algebra, graphics, programming, and procedures. Each chapter contains numerous illustrative examples, using mathematics that does not extend beyond first-year undergraduate material. Maple worksheets containing these examples are available for download from the author''s personal website. The book is suitable for new users, but where advanced topics are central to understanding Maple they are tackled head-on. Many concepts which are absent from introductory books and manuals are described in detail. With this book, students, teachers and researchers will gain a solid understanding of Maple and how to use it to solve complex mathematical problems in a simple and efficient way.Trade Review'Thompson (Univ. of Liverpool, UK) clearly knows the 'gotchas' that most often plague beginners (and others!) and provides pointed guidance; extracting the same vital information buried in longer and more systematic treatises and manuals can certainly prove a challenge. Summing Up: Recommended. Lower-division undergraduates and above; faculty and professionals.' D. V. Feldman, CHOICETable of Contents1. Introduction; 2. Getting started; 3. Algebra and calculus; 4. Solving equations; 5. Linear algebra; 6. Graphics; 7. Programming; 8. Procedures; 9. Example programs; Appendix A. Other ways to run Maple; Appendix B. Terminating characters; Index of Maple notation.

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Book SynopsisNew 2017 Cambridge A Level Maths and Further Maths resources help students with learning and revision. Written for the OCR AS/A Level Mathematics specifications for first teaching from 2017, this print Student Book and Cambridge Elevate edition covers the content for AS and first year of A Level. It balances accessible exposition with a wealth of worked examples, exercises and opportunities to test and consolidate learning, providing a clear and structured pathway for progressing through the course. It is underpinned by a strong pedagogical approach, with an emphasis on skills development and the synoptic nature of the course. Available online and on tablet devices through the Cambridge Elevate app. Includes answers to aid independent study.

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Book SynopsisA leading data visualisation expert explores the negativeand positive-influences that charts have on our perception of truth.Trade Review"[Alberto Cairo's] book reminds readers not to infer too much from a chart, especially when it shows them what they already wanted to see. Mr Cairo has sent a copy to the White House." -- The Economist

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Book SynopsisThis volume challenges the widespread belief that scientific knowledge as such is international. Employing case studies from Austria, Poland, the Czech lands, and Hungary, the authors show how scientists in the late Habsburg Monarchy simultaneously nationalized and internationalized their knowledge.Table of ContentsTable of Contents List of Tables and Figures The Authors The Nationalisation of Scientific Knowledge in Nineteenth-century Central Europe: An introduction; M.G.Ash & J.Surman Science and its Publics. Internationality and National Languages in Central Europe; J.Surman 'Staatsnation', 'Kulturnation', 'Nationalstaat'. The Role of National Politics in the Advancement of Science and Scholarship in Austria from 1848 to 1938; J.Feichtinger 'National Agreement' as Culture and Practice: The Geological Survey in Vienna and the Habsburg Empire (1849-1867); M.Klemun Scientific Nationalism: A Historical Approach to Nature in Late Nineteenth-century Hungary; G.Palló Acts of Creation: The Eötvös Family and the Rise of Science Education in Hungary; T.Frank Patriotism, Nationalism and Internationalism in Czech Science: Chemists in the Czech National Enlightenment; S.Štrbánová Fault Lines and Borderlands: Earthquake Spotting in Imperial Austria; D.R.Coen Nationalising Eugenics: The Hungarian Public Debate of 1910-1911; M.Turda The Politics of Fin-de-siècle Anatomy; T.Buklijas Index

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Book SynopsisLevel design connects the player to the game through challenges, experiences, and emotions. This book is an invaluable introduction to the evolving practices of Level Designers across the games industry. The increasingly complex role of the Level Designer requires technical and creative skill as it brings together architecture, art, player psychology, interaction design, usability, and experience design. This book explores in detail the principles designers employ when planning levels and building engaging spaces for the player. As well as practical approaches to level design, the book delves into the theoretical underpinnings of the processes and charts a path towards thinking like a Level Designer. Throughout the book you will be guided through the fundamentals of level design: each chapter builds on the types of research, ideation, best practices, and methodologies Level Designers employ when creating prototypes and shipped games. A series of interviews with designers and case studiTrade ReviewA pragmatic approach to level design that captures the critical elements needed to conceptualize and create meaningful player experiences. Michael Salmond uses practical and straightforward examples to clearly define and explore the key considerations of game and level designers alike. The content is diverse covering many topics, yet succinct and to the point. This book fills a critical void for video game education. * Johnny Luce, co-owner, software designer, and engineer at augzoo *This is an excellent book on level design, with a wealth of up-to-date and varied examples. It is highly visual and extremely readable, giving a comprehensive view of the area in a way that is colorful and engaging, whilst maintaining a good level of technicality. It is ideal for students studying game design, in order to develop their understanding of the theories and practices involved in level design as a specialism * J. Weinel, University of Greenwich, UK *Table of Contents1. What Is Level Design? 2. Creating Immersive, Believable Worlds 3. Design for Narrative 4. Environment Design vs Level Design 5. Building Worlds 6. Design for Single & Multiplayer 7. Level Design is Agile Design 8. The Language of Level Design 9. Prototyping Level Design 10. The Game Is the Level, the Level Is the Game 11. Communication and Final Touches 12. Where to Next?

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Book SynopsisThis book introduces the reader to Serres' unique manner of doing philosophy' that can be traced throughout his entire oeuvre: namely as a novel manner of bearing witness. It explores how Serres takes note of a range of epistemologically unsettling situations, which he understands as arising from the short-circuit of a proprietary notion of capital with a praxis of science that commits itself to a form of reasoning which privileges the most direct path (simple method) in order to expend minimal efforts while pursuing maximal efficiency. In Serres' universal economy, value is considered as a function of rarity, not as a stock of resources. This book demonstrates how Michel Serres has developed an architectonics that is coefficient with nature. Mathematic and Information in the Philosophy of Michel Serres acquaints the reader with Serres' monist manner of addressing the universality and the power of knowledge that is at once also the anonymous and empty faculty of incandescent, inveTrade ReviewWhat happens when we take mathematics not as the elementary basis upon which science must bloom, but as an ‘architectonics’ that unfolds the world as it informs mass, space and time? With great rigor, in content and style, Bühlmann reads the concepts that Michel Serres produced in his oeuvre through his mathematics and information theory, revealing his highly original, inclusive and affirmative philosophy of the 21st century. -- Rick Dolphijn, Associate Professor of Theories of Arts and Culture, Utrecht University, the NetherlandsThe importance of Serres’ philosophy has mostly gone unrecognized in continental philosophy, even though this philosopher had a critical influence on many of its key figures, such as Deleuze and Foucault. The dearth of informed commentary is now reduced by this scholar whose knowledge of mathematics is able to bridge both the analytical and continental traditions. -- Gregg Lambert, Dean’s Professor of Humanities, Syracuse University, USATable of ContentsForeword Chapter one: Introduction The plan of this book Chapter two: Quantum literacy Elementary indecision Communication versus production: Bearing witness, and literacy Cultivating indecision: The quantum domain’s domesticity Ciphers, zeroness, equations: Architectonics of nothing Chance-bound objects Taking ignorance into account: Quantifying strangeness Entropy and negentropy The price of information as a measure for an object’s strangeness Quantum literacy: Towards a novel theory of the subject ‘La Langue est une Puissance’ Chapter three: Chronopedia I: Counting time Meteora: The wisdom of the weather Code: A rosetta stone, a double staircase Time modelled as contemporaneity Counting time: Equinox and solstice The turning points for modelled beginnings and ends Of tables and models Sense means significance and direction Meteora A logos genuine to the world – ‘Le Logiciél Intra-Matériel’ Software, hardware Economy of maxima and minima: An anarchic logos Chapter four: Chronopedia II: Treasuring time Homothesis as the locus in quo of the universal’s presence 1st iteration (acquiring a space of possibility) 2nd iteration (learning to speak a language in which no one is native) 3rd iteration (setting the stage for thought to comprehend itself) 4th iteration (intelligence that is immanent and coextensive with the universe) 5th iteration (inventing a scale of reproduction) 6th iteration (the formula, a double-articulating application) The amorous nature of intellectual conception 1st iteration (marking all that is assumed to be constant with a cipher) 2nd iteration (confluence of multiple geneses) 3rd iteration (the residence of that which is genuinely migrational) 4th iteration (universal genitality) 5th iteration (mathematics is the circuit of cunning reason’s ruses) 6th iteration (the real as a black spectrum) Chapter five: Banking universality: The magnitudes of ageing Metaphysics The quickness of a magnanimous universe Invariance: Genericness in terms of entropy and negentropy Genuine and immanent to the all of time: Le ‘logiciel intra-matériel’ White metaphysics: How old does the world think it is? Freedom The neutral element: Materialism of identity (Pan’s) glossematics: The economy that deals with ‘purport’ Quanta of contemporaneity: Heat to incandescence, storage to bank account Quantum writing: Substitutes step in to address things themselves Chapter six: The incandescent Paraclete: Tables of plenty Equatoriality generalized Coming of age, liking sunset and sunrise How to combine precision with finesse or: euphoria contained by instruments that behave like cornucopia The (mathematical) inverse of Pantopia is not a utopia: Law in the panonymy of the whole world The objective mentality and character of instruments The vicarious order of knowledge that is authentic to the world Pan: The excitable subject of universal knowledge Generational con-sequentiality Blessed curiosity Exodic discourse Chapter seven: Sophistication and anamnesis: Retrograde movement of truth, remembering an abundant past The currency of knowledge The price of truth, and the price of information The convertibility of truth Classicism: Remembering contemporaneity Classical analysis, symbolical analysis Interlude: The Tower of Eiffel, archetypical symbol of existentialism? Building a cipher A corpus of intelligent forms The technical order of an object that is comfortable How to reason the sum total of all archetypes? Towards critique with regard to the symbolic alchemy of myth-making A realist classicism Familiarizing ourselves as strangers, native to the universe The domain of the quasi: Instructive analysis, character dispositions How can reason in general learn from singularities? Of genealogical and of tabular orders: Eating ‘next to’ (parasite) Heterogeneous scales, logistical uniformality (forms of operation) Indexical address: The referential of the centre Respecting order by challenging it Cunning ruses: The anarchic architectonic way of paying respect How to address the third-person singular? Augmentation, not authorship Anarchic civility, and the meanings of cultures Chapter eight Coda: Quantum literacy and architectonic dispositioning Architecture and philosophy Chapter zero: Instead of a conclusion: The static tripod Notes Bibliography

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Book SynopsisMax Maths Primary A Singapore Approach is a six-level course in mathematics for young learners. It offers a complete solution for schools following the Cambridge Primary maths curriculum framework, and has been specifically designed to support students who are learning in International and English-medium school settings.

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Book SynopsisBring the latest statistical tools to bear on predicting future variables and outcomes A huge range of fields rely on forecasts of how certain variables and causal factors will affect future outcomes, from product sales to inflation rates to demographic changes. Time series analysis is the branch of applied statistics which generates forecasts, and its sophisticated use of time oriented data can vastly impact the quality of crucial predictions. The latest computing and statistical methodologies are constantly being sought to refine these predictions and increase the confidence with which important actors can rely on future outcomes. Time Series Analysis and Forecasting presents a comprehensive overview of the methodologies required to produce these forecasts with the aid of time-oriented data sets. The potential applications for these techniques are nearly limitless, and this foundational volume has now been updated to reflect the most advanced tools. The result,

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Book SynopsisYou've Never Seen What You've Always Needed to Know Until Now Invisible forces are at work. They push and shove on everything you buy or sell. They affect every concept you want to take to market, all the suppliers you'll deal with, and every customer you'll ever see. To be successful, you need to understand them. See them in detail in ways not possible with other methods. Hypernomics: Using Hidden Dimensions to Solve Unseen Problems discovers that markets behave according to previously unknown laws set by the buyers and sellers within them. It reveals those rules and how to detect, describe, and deploy them to your advantage. It doesn't change economics so much as reveal it. It's like a microscope looking at pond water, a telescope tilted to the sky, sonar scanning the bottom of the ocean. Hypernomics lets you see into markets in ways you can't with the unaided eye. Sailors never navigate without a map. You shouldn't either, since your ship coulTable of ContentsIntroduction 1 CHAPTER 1 A Brief History of Position and Direction 9 Ancient Maps 9 Geography Begins 13 Math and Position Problems 13 Summary 26 Vignette: Restaurant Math 27 CHAPTER 2 Four-Dimensional Systems 29 Dot Plots Begin 29 "X" Marks the Spot 30 Most Markets Don't Address Commodities 31 Cartesian Systems and Negativity 33 Geography Is Never Negative 38 Plotting in Four Dimensions 52 Summary 56 CHAPTER 3 Five-Dimensional Systems 57 Physical Changes over Time 57 Economic Changes over Time 62 Summary 69 CHAPTER 4 Value 71 Human Traits 71 What Does Value Mean in Hypernomics? 75 Determining Value 77 The Market as Laboratory 79 Summary 91 Vignette: The Value of Expanding One's Limits 92 CHAPTER 5 Demand 95 Demand Frontiers 95 Aggregate Demand 102 Average Demand 104 Minimum Demand 105 Proxy Demand 106 Submarket, Sub-Submarket, and Mission Market Demand Curves 107 Product Demand Curves 109 Summary 110 A Hypernomics Vignette: The Value of and Demand for Money 111 CHAPTER 6 Price and Quantity Determination 121 The General Problem Calls for Specifics 121 The Neoclassical View: The Law of Supply and Demand 122 Ferrous Blunder: Universal Claim of Upward-Sloping Supply Curves 125 The Hypernomics View: The Law of Value and Demand 128 Summary 133 A Hypernomics Vignette: The Law of Value and Demand 134 CHAPTER 7 Market Mapping and Financial Cat Scans 137 Got Eggs? 137 Market Map Boundaries 141 Feature and Price Gap Maps 143 Financial Cat Scans 146 Summary 155 CHAPTER 8 Aiming and Missing 157 Neoclassical Aiming 157 Immediate Aiming 158 Immediate Aiming in Hypernomics 163 Ultimate Aiming 165 Ultimate Aiming in Hypernomics 167 Summary 170 CHAPTER 9 N-Dimensional Systems 173 Common Object 1—Pie 174 Common Object 2—Logarithmic Scaling 176 Common Object 3—Rolodex 178 Common Object 4—Concentric Circle 180 Common Object 5—Parallelograms (as in Extendable Mirrors) 181 Starting from (0,0,0,0. . .0) 182 Summary 200 CHAPTER 10 An Amazon Mining Expedition 201 Summary 210 CHAPTER 11 More 211 Vignette: What Do Markets Look Like to Viruses? 213 CHAPTER 12 Appendix: Using Hypernomics on Your Own 217 Stating the Problem 220 Data Collection 221 Data Entry 223 Data Manipulation 225 Data Interpretation 229 Summary 235 Vignette: The Importance of Going Deep into the Data 237 CHAPTER 13 Neoclassical Economics and Hypernomics Differences 241 Glossary 243 References 247 Index 279

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Book SynopsisMathematical Modeling for Computer Applications The mathematical sciences are part of nearly all aspects of everyday life. The discipline has underpinned such beneficial modern capabilities as internet searches, medical imaging, computer animation, numerical weather predictions, and all types of digital communications. This outstanding new volume in the series, Mathematics and Computer Science, examines the current state of mathematical science and explores the changes needed for the discipline to be in a strong position and able to maximize its contributions. Besides covering important practical applications for the areas where mathematics and computer science intersect, the editors of this new volume recommend that training for future generations of mathematical scientists should be re-assessed in light of the increasingly cross-disciplinary nature of the mathematical sciences. In addition, because of the valuable interplay between ideas and people from all parts of the mathematic

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

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Book SynopsisToday, 57 students are enrolled in the Physics Maitrise programme at the Joseph Fourier University in Grenoble, and 15 of them are foreign students. In that time interval, the total number of students enrolled in institutes of higher learning in mainland France rose from 309 700 (in 1960-1961) to 2 111 100 (in 2000-2001).Table of Contents1 / Watersheds.- 1. How and What to Spotlight.- 2. How Much Should be Explained.- 3. Images: Are they always useful?.- 4. Experiments: Are they supposed to help?.- Appendix 1: Some General Intentions Are Very Similar in the Various Syllabuses.- Appendix 2: Why the Pinhole Camera is no Longer on the Syllabus.- 2 / Contact, friction and propulsion.- 1. Laws that Run Counter to Common Sense.- 2. A Method of Spotlighting the Basics.- 3. A Way of Spotlighting Friction: goals and difficulties.- 4. First Elements of Static Friction: step by step.- 5. Analysing the Sequence: lines of attention.- 6. Evaluation of the Sequence with Students.- 7. Reactions of Trainee Teachers.- 8. What Conclusion Should We Draw?.- Appendix 1: The Technique of Fragmented Diagrams.- Appendix 2: Two Situations for Studying Kinetic Friction.- Appendix 3: Trainee Teachers’ Comments on the Sequence.- 3 / Pressure in Fluids in the Presence of Gravity.- 1. Questions About the Merits of a Microscopic Approach.- 2. The Macroscopic Level: what quantities “have to be”?.- 3. Fluid Statics: common ideas among students.- 4. A Proposal for the Teaching of Fluid Statics.- 5. Analysing the Sequence: lines of attention.- 6. Evaluation of the Sequence with Students.- 7. Teachers’ Reactions.- 8. Conclusion.- Appendix: Main Results of the External Evaluation.- 4 / Superposition of Electric Fields.- 1. Interaction at a Distance and Superposition.- 2. Charges, Fields and Superposition: selected aspects.- 3. Superposition and Causality: common forms of reasoning.- 4. Elements of a Teaching Sequence.- 5. Analysing the Sequence: lines of attention.- 6. Evaluation of the Sequence.- 7. Conclusion.- Appendix 1: Contents Previously Taught to Students Questioned in the Preliminary Survey.- Appendix 2: Electrostatics and Electric Circuits Disconnected: the field in wires.- 5 / Superposition of Waves and Optical Imaging.- 1. Choosing a Model.- 2. Common Difficulties and “Spotlighting” of the Content.- 3. Analysing the Proposal: some elements.- 4. Reactions of In-Service or Trainee Teachers.- 5. Conclusion.- 6 / Colour Phenomena.- 1. A Topic at a Crossroads.- 2. Colour Phenomena and Light: the chosen approach.- 3. Common Ideas: too exclusive a linkage.- 4. A Proposed Sequence.- 5. More Detail, Following the Lines of Attention.- 6. Evaluation of the Sequence.- 7. Teachers’ Reactions.- 8. Conclusion.- Appendix 1: Additive and Subtractive Mixing.- Appendix 2: Aspects of Knowledge Whose Acquisition is Evaluated One Year after the Sequence.- Conclusion.- Index of Names.

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Book SynopsisStarting with the most basic notions, Universal Algebra: Fundamentals and Selected Topics introduces all the key elements needed to read and understand current research in this field. Based on the author's two-semester course, the text prepares students for research work by providing a solid grounding in the fundamental constructions and concepts of universal algebra and by introducing a variety of recent research topics.The first part of the book focuses on core components, including subalgebras, congruences, lattices, direct and subdirect products, isomorphism theorems, a clone of operations, terms, free algebras, Birkhoff's theorem, and standard Maltsev conditions. The second part covers topics that demonstrate the power and breadth of the subject. The author discusses the consequences of Jónsson's lemma, finitely and nonfinitely based algebras, definable principal congruences, and the work of Foster and Pixley on primal and quasiprimal algebras. HeTrade Review… as far as I am concerned, the book under review, by Clifford Bergman, is most welcome: we need more of this sort of thing, both for potential universal algebraists and for people like me: fellow travelers to some degree, or mathematicians who both use and thoroughly adore algebra and its structural qualities, and find themselves growing more appreciative of this architectural elegance as they evolve in their work and studies. … it is clearly written and pleasant to read … the author provides motivation as well as examples and exercises galore. At first glance it looks to me like the exercises are well-structured and should do the job of bringing the student or reader along at a decent pace from ignorance to both an appreciation for the subject and some facility with it. It’s definitely an area worth pursuing for a graduate student with the right disposition.—Michael Berg, MAA Reviews, December 2011… excellently written and is highly recommended to all who are interested in universal algebra.—Mathematical ReviewsTable of ContentsFUNDAMENTALS OF UNIVERSAL ALGEBRA: Algebras. Lattices. The Nuts and Bolts of Universal Algebra. Clones, Terms, and Equational Classes. SELECTED TOPICS: Congruence Distributive Varieties. Arithmetical Varieties. Maltsev Varieties. Finite Algebras and Locally Finite Varieties. Bibliography. Index.

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Book SynopsisHistorical Introduction.- 1 The Fundamental Theorem of Arithmetic.- 2 Arithmetical Functions and Dirichlet Multiplication.- 3 Averages of Arithmetical Functions.- 4 Some Elementary Theorems on the Distribution of Prime Numbers.- 5 Congruences.- 6 Finite Abelian Groups and Their Characters.- 7 Dirichlet's Theorem on Primes in Arithmetic Progressions.- 8 Periodic Arithmetical Functions and Gauss Sums.- 9 Quadratic Residues and the Quadratic Reciprocity Law.- 10 Primitive Roots.- 11 Dirichlet Series and Euler Products.- 12 The Functions ?(s) and L(s, ?).- 13 Analytic Proof of the Prime Number Theorem.- 14 Partitions.- Index of Special Symbols.Trade ReviewFrom the reviews:T.M. ApostolIntroduction to Analytic Number Theory"This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enormous amount of material in little more than 300 pages. The presentation is invariably lucid and the book is a real pleasure to read."—MATHEMATICAL REVIEWS“After reading Introduction to Analytic Number Theory one is left with the impression that the author, Tom M. Apostal, has pulled off some magic trick. … I must admit that I love this book. The selection of topics is excellent, the exposition is fluid, the proofs are clear and nicely structured, and every chapter contains its own set of … exercises. … this book is very readable and approachable, and it would work very nicely as a text for a second course in number theory.” (Álvaro Lozano-Robledo, The Mathematical Association of America, December, 2011)Table of Contents1: The Fundamental Theorem of Arithmetic. 2: Arithmetical Functions and Dirichlet Multiplication. 3: Averages of Arithmetical Function. 4: Some Elementary Theorems on the Distribution of Prime Numbers. 5: Congruences. 6: Finite Abelian Groups and Their Characters. 7: Cirichlet's Theorem on Primes in Arithmetic Progressions. 8: Periodic Arithmetical Functions and Gauss Sums. 9: Quadratic Residues and the Quadratic Reciprocity Law. 10: Primitive Roots. 11: Dirichlet Series and Euler Products. 12: The Functions. 13: Analytic Proof of the Prime Number Theorem. 14: Partitions.

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Book SynopsisI Fundamentals.- 1 Ordinary Differential Equations.- 2 Difference Equations.- II Local Analysis.- 3 Approximate Solution of Linear Differential Equations.- 4 Approximate Solution of Nonlinear Differential Equations.- 5 Approximate Solution of Difference Equations.- 6 Asymptotic Expansion of Integrals.- III Perturbation Methods.- 7 Perturbation Series.- 8 Summation of Series.- IV Global Analysis.- 9 Boundary Layer Theory.- 10 WKB Theory.- 11 Multiple-Scale Analysis.Trade Review"This book is a reprint of the original published by McGraw-Hill \ref [MR0538168 (80d:00030)]. The only changes are the addition of the Roman numeral I to the title and the provision of a subtitle, "Asymptotic methods and perturbation theory". This latter improvement is much needed, as the original title suggested that this was a teaching book for undergraduate scientists and engineers. It is not, but is an excellent introduction to asymptotic and perturbation methods for master's degree students or beginning research students. Certain parts of it could be used for a course in asymptotics for final year undergraduates in applied mathematics or mathematical physics. This is a book that has stood the test of time and I cannot but endorse the remarks of the original reviewer. It is written in a fresh and lively style and the many graphs and tables, comparing the results of exact and approximate methods, were in advance of its time. I have owned a copy of the original for over twenty years, using it on a regular basis, and, after the original had gone out of print, lending it to my research students. Springer-Verlag has done a great service to users of, and researchers in, asymptotics and perturbation theory by reprinting this classic." (A.D. Wood, Mathematical Reviews) Table of ContentsI Preface. 1 Ordinary Differential Equations. 2 Difference Equations. 3 Approximate Solution of Linear Differential Equations. 4 Approximate Solution of Nonlinear Equations. 5 Approximate Solution of Difference Equations. 6 Asymptotic Expansion of Integrals. 7 Perturbation Series. 8 Summation of Series. 9 Boundary Layer Theory. 10 WKB Theory. 11 Multiple Scales Analysis. Appendix, References, Index

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Book SynopsisWith a fresh geometric approach that incorporates more than 250 illustrations, this textbook sets itself apart from all others in advanced calculus.  Besides the classical capstones--the change of variables formula, implicit and inverse function theorems, the integral theorems of Gauss and Stokes--the text treats other important topics in differential analysis, such as Morse''s lemma and the Poincaré lemma.  The ideas behind most topics can be understood with just two or three variables.  The book incorporates modern computational tools to give visualization real power.  Using 2D and 3D graphics, the book offers new insights into fundamental elements of the calculus of differentiable maps.  The geometric theme continues with an analysis of the physical meaning of the divergence and the curl at a level of detail not found in other advanced calculus books.  This is a textbook for undergraduates and graduate students in mathematics, the physical sciences, and economics.  Prerequisites are an introduction to linear algebra and multivariable calculus.  There is enough material for a year-long course on advanced calculus and for a variety of semester courses--including topics in geometry.  The measured pace of the book, with its extensive examples and illustrations, make it especially suitable for independent study.Trade ReviewFrom the reviews:“Many concepts in calculus and linear algebra have obvious geometric interpretations. … This book differs from other advanced calculus works … it can serve as a useful reference for professors. … it is the adopted course resource, its inclusion in a college library’s collection should be determined by the size and interests of the mathematics faculty. Summing Up … . Upper-division undergraduate through professional collections.” (C. Bauer, Choice, Vol. 48 (8), April, 2011)“The author of this book sees an opportunity to bring back a more geometric, visual and physically-motivated approach to the subject. … The author makes exceptionally good use of two and three-dimensional graphics. Drawings and figures are abundant and strongly support his exposition. Exercises are plentiful and they cover a range from routine computational work to proofs and extensions of results from the text. … Strong students … are likely to be attracted by the approach and the serious meaty content.” (William J. Satzer, The Mathematical Association of America, January, 2011)“A new geometric and visual approach to advanced calculus is presented. … The book can be useful a textbook for beginners as well as a source of supplementary material for university teachers in calculus and analysis. … the book meets a wide auditorium among undergraduate and graduate students in mathematics, physics, economics and in other fields which essentially use mathematical models. It is also very interesting for teachers and instructors in Calculus and Mathematical Analysis.” (Sergei V. Rogosin, Zentralblatt MATH, Vol. 1205, 2011)Table of Contents1 Starting Points.-1.1 Substitution.- Exercises.- 1.2 Work and path integrals.- Exercises.- 1.3 Polar coordinates.- Exercises.- 2 Geometry of Linear Maps.- 2.1 Maps from R2 to R2.- Exercises.- 2.2 Maps from Rn to Rn.- Exercises.- 2.3 Maps from Rn to Rp, n 6= p.- Exercises.- 3 Approximations.- 3.1 Mean-value theorems.- Exercises.- 3.2 Taylor polynomials in one variable.- Exercises.- 3.3 Taylor polynomials in several variables.- Exercises.- 4 The Derivative.- 4.1 Differentiability.- Exercises.- 4.2 Maps of the plane.- Exercises.- 4.3 Parametrized surfaces.- Exercises.- 4.4 The chain rule.- Exercises.- 5 Inverses.- 5.1 Solving equations.- Exercises.- 5.2 Coordinate Changes.- Exercises.- 5.3 The Inverse Function Theorem.- Exercises.- 6 Implicit Functions.- 6.1 A single equation.- Exercises.- 6.2 A pair of equations.- Exercises.- 6.3 The general case.- Exercises.- 7 Critical Points.- 7.1 Functions of one variable.- Exercises.- 7.2 Functions of two variables.- Exercises.- 7.3 Morse’s lemma.- Exercises.- 8 Double Integrals.- 8.1 Example: gravitational attraction.- Exercises.- 8.2 Area and Jordan content.- Exercises.- 8.3 Riemann and Darboux integrals.- Exercises.- 9 Evaluating Double Integrals.- 9.1 Iterated integrals.- Exercises.- 9.2 Improper integrals.- Exercises.- 9.3 The change of variables formula.- 9.4 Orientation.- Exercises.- 9.5 Green’s Theorem.- Exercises.- 10 Surface Integrals.- 10.1 Measuring flux.- Exercises.- 10.2 Surface area and scalar integrals.- Exercises.- 10.3 Differential forms.- Exercises.- 11 Stokes’ Theorem.- 11.1 Divergence.- Exercises.- 11.2 Circulation and Vorticity.- Exercises.- 11.3 Stokes’ Theorem.- 11.4 Closed and Exact Forms.- Exercises

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Book SynopsisRepresentation theory studies maps from groups into the general linear group of a finite-dimensional vector space.Trade ReviewFrom the reviews: "The book under review is an introduction to the modular representation theory of finite groups with a somehow balanced approach to the subject. ... the book is almost self-contained. It has the lightness of a gentle-paced lecture course and could be used with profit for an introduction to the methods of representation theory of finite groups, either in a formal course or for self-study." (Felipe Zaldivar, MAA Reviews, May, 2013)Table of ContentsPrerequisites in module theory.- The Cartan{Brauer triangle.- The Brauer character.- Green's theory of indecomposable modules.- Blocks.

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Book SynopsisThis book teaches the art of writing mathematics, an essential -and difficult- skill for any mathematics student.Table of ContentsSome writing tips.- Essential dictionary I.- Essential dictionary II.- Mathematical sentences.- Describing functions.- Writing well.- Forms of argument.- Induction.- Existence and definitions.- Writing a thesis.

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Book SynopsisChapter 1: Introduction: The nature and structure of the inventory problem.- Chapter 2: Review of the literature.- Chapter 3: Methodology.- Chapter 4: Analysis of inventory behaviour of OECD countries.- Chapter 5: Stability of macroeconomic variables.- Chapter 6: Inventory developments in individual countries.- Chapter 7: Summary and conclusions.Table of ContentsChapter 1: Introduction: The nature and structure of the inventory problem.- Chapter 2: Review of the literature.- Chapter 3: Methodology.- Chapter 4: Analysis of inventory behaviour of OECD countries.- Chapter 5: Stability of macroeconomic variables.- Chapter 6: Inventory developments in individual countries.- Chapter 7: Summary and conclusions.

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Book SynopsisIn its Second Edition, this in-depth study of the vibrations of fractal strings interlinks number theory, spectral geometry and fractal geometry. Includes a geometric reformulation of the Riemann hypothesis and a new final chapter on recent topics and results.Trade Review“This interesting volume gives a thorough introduction to an active field of research and will be very valuable to graduate students and researchers alike.” (C. Baxa, Monatshefte für Mathematik, Vol. 180, 2016)“In this research monograph the authors provide a mathematical theory of complex dimensions of fractal strings and its many applications. … The book is written in a self-contained manner the results … are completely proved. I appreciate that the book is useful for mathematicians, students, researchers, postgraduates, physicians and other specialists which are interested in studying the fractals and dimension theory.” (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, April, 2013)“The authors provide a mathematical theory of complex dimensions of fractal strings and its many applications. … The book is written in a self-contained manner, the results (including some fundamental ones) are completely proved. … the book will be useful to mathematicians, students, researchers, postgraduates, physicians and other specialists which are interested in studying fractals and dimension theory.” (Nicolae-Adrian Secelean, Zentralblatt MATH, Vol. 1261, 2013)"In this book the author encompasses a broad range of topics that connect many areas of mathematics, including fractal geometry, number theory, spectral geometry, dynamical systems, complex analysis, distribution theory and mathematical physics. The book is self containing, the material organized in chapters preceding by an introduction and finally there are some interesting applications of the theory presented. ...The book is very well written and organized and the subject is very interesting and actual and has many applications." -- Nicolae-Adrian Secelean for Zentralblatt MATH"This highly original self-contained book will appeal to geometers, fractalists, mathematical physicists and number theorists, as well as to graduate students in these fields and others interested in gaining insight into these rich areas either for its own sake or with a view to applications. They will find it a stimulating guide, well written in a clear and pleasant style." -- Mathematical Reviews (Review of previous book by authors)"It is the reviewera (TM)s opinion that the authors have succeeded in showing that the complex dimensions provide a very natural and unifying mathematical framework for investigating the oscillations in the geometry and the spectrum of a fractal string. The book is well written. The exposition is self-contained, intelligent and well paced." -- Bulletin of the London Mathematical Society (Review of previous book by authors)"The new approach and results on the important problems illuminated in this work will appeal to researchers and graduate students in number theory, fractal geometry, dynamical systems, spectral geometry, and mathematical physics." -- Simulation News Europe (Review of previous book by authors)Table of ContentsPreface.- Overview.- Introduction.- 1. Complex Dimensions of Ordinary Fractal Strings.- 2. Complex Dimensions of Self-Similar Fractal Strings.- 3. Complex Dimensions of Nonlattice Self-Similar Strings.- 4. Generalized Fractal Strings Viewed as Measures.- 5. Explicit Formulas for Generalized Fractal Strings.- 6. The Geometry and the Spectrum of Fractal Strings.- 7. Periodic Orbits of Self-Similar Flows.- 8. Fractal Tube Formulas.- 9. Riemann Hypothesis and Inverse Spectral Problems.- 10. Generalized Cantor Strings and their Oscillations.- 11. Critical Zero of Zeta Functions.- 12 Fractality and Complex Dimensions.- 13. Recent Results and Perspectives.- Appendix A. Zeta Functions in Number Theory.- Appendix B. Zeta Functions of Laplacians and Spectral Asymptotics.- Appendix C. An Application of Nevanlinna Theory.- Bibliography.- Author Index.- Subject Index.- Index of Symbols.- Conventions.- Acknowledgements.

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Book SynopsisStatistical Foundations of Data Science gives a thorough introduction to commonly used statistical models, contemporary statistical machine learning techniques and algorithms, along with their mathematical insights and statistical theories. It aims to serve as a graduate-level textbook and a research monograph on high-dimensional statistics, sparsity and covariance learning, machine learning, and statistical inference. It includes ample exercises that involve both theoretical studies as well as empirical applications.The book begins with an introduction to the stylized features of big data and their impacts on statistical analysis. It then introduces multiple linear regression and expands the techniques of model building via nonparametric regression and kernel tricks. It provides a comprehensive account on sparsity explorations and model selections for multiple regression, generalized linear models, quantile regression, robust regression, hazards regression, Trade Review"This book delivers a very comprehensive summary of the development of statistical foundations of data science. The authors no doubt are doing frontier research and have made several crucial contributions to the field. Therefore, the book offers a very good account of the most cutting-edge development. The book is suitable for both master and Ph.D. students in statistics, and also for researchers in both applied and theoretical data science. Researchers can take this book as an index of topics, as it summarizes in brief many significant research articles in an accessible way. Each chapter can be read independently by experienced researchers. It provides a nice cover of key concepts in those topics and researchers can benefit from reading the specific chapters and paragraphs to get a big picture rather than diving into many technical articles. There are altogether 14 chapters. It can serve as a textbook for two semesters. The book also provides handy codes and data sets, which is a great treasure for practitioners."~Journal of Time Series Analysis"This text—collaboratively authored by renowned statisticians Fan (Princeton Univ.), Li (Pennsylvania State Univ.), Zhang (Rutgers Univ.), and Zhou (Univ. of Minnesota)—laboriously compiles and explains theoretical and methodological achievements in data science and big data analytics. Amid today's flood of coding-based cookbooks for data science, this book is a rare monograph addressing recent advances in mathematical and statistical principles and the methods behind regularized regression, analysis of high-dimensional data, and machine learning. The pinnacle achievement of the book is its comprehensive exploration of sparsity for model selection in statistical regression, considering models such as generalized linear regression, penalized least squares, quantile and robust regression, and survival regression. The authors discuss sparsity not only in terms of various types of penalties but also as an important feature of numerical optimization algorithms, now used in manifold applications including deep learning. The text extensively probes contemporary high-dimensional data modeling methods such as feature screening, covariate regularization, graphical modeling, and principal component and factor analysis. The authors conclude by introducing contemporary statistical machine learning, spanning a range of topics in supervised and unsupervised learning techniques and deep learning. This book is a must-have bookshelf item for those with a thirst for learning about the theoretical rigor of data science."~Choice Review, S-T. Kim, North Carolina A&T State University, August 2021Table of Contents1. Introduction. 2. Multiple and Nonparametric Regression. 3. Introduction to Penalized Least-Squares. 4. Penalized Least Squares: Properties. 5. Generalized Linear Models and Penalized Likelihood. 6. Penalized M-estimators. 7. High Dimensional Inference 8. Feature Screening. 9. Covariance Regularization and Graphical Models. 10. Covariance Learning and Factor Models. 11. Applications of Factor Models and PCA. 12. Supervised Learning. 13. Unsupervised Learning. 14. An Introduction to Deep Learning.

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Book SynopsisRisk Analysis in Engineering and Economics is required reading for decision making under conditions of uncertainty. The author describes the fundamental concepts, techniques, and applications of the subject in a style tailored to meet the needs of students and practitioners of engineering, science, economics, and finance. Drawing on his extensive experience in uncertainty and risk modeling and analysis, the author covers everything from basic theory and key computational algorithms to data needs, sources, and collection. He emphasizes practical use of the methods presented and carefully examines the limitations, advantages, and disadvantages of each to help readers translate the discussed techniques into real-world solutions.This Second Edition: Introduces the topic of risk finance Incorporates homeland security applications throughout Offers additional material on predictive risk management Includes a wealth of neTrade ReviewPraise for the First Edition "This book ambitiously tackles risk analysis from the ground up. … an excellent reference for individuals studying in a variety of risk-related disciplines. … enlightening [examples]…attractive to students approaching risk studies from a variety of substantive backgrounds. … Advanced students are likely to find Ayyub's treatments…exceedingly valuable."—Journal of the American Statistical Association, June 2004, Vol. 99, No. 466 "… a good textbook and reference. The mix of engineering and economics is well balanced. … Valuable for students after college and useful for professional engineers."—Technometrics, August 2004, Vol. 46, No. 3 Praise for the Second Edition "… one of a kind in the market. … I am not aware of books that cover the subject in as comprehensive a manner."—Professor Nii O. Attoh-Okine, University of Delaware, Newark, USA Table of ContentsIntroduction. Risk Analysis Methods. System Definition and Structure. Reliability Assessment. Failure Consequences and Severity. Engineering Economics and Finance. Risk Control Methods. Data for Risk Studies. Fundamentals of Probability and Statistics. Failure Data. References and Bibliography. Index.

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Book SynopsisNew Tools to Solve Your Option Pricing ProblemsFor nonlinear PDEs encountered in quantitative finance, advanced probabilistic methods are needed to address dimensionality issues. Written by two leaders in quantitative researchincluding Risk magazine's 2013 Quant of the YearNonlinear Option Pricing compares various numerical methods for solving high-dimensional nonlinear problems arising in option pricing. Designed for practitioners, it is the first authored book to discuss nonlinear Black-Scholes PDEs and compare the efficiency of many different methods. Real-World Solutions for Quantitative Analysts The book helps quants develop both their analytical and numerical expertise. It focuses on general mathematical tools rather than specific financial questions so that readers can easily use the tools to solve their own nonlinear problems. The authors build intuition through numerous real-world examples of numTrade Review"... provides a wide overview of the advanced modern techniques applied in financial modeling. It gives an optimal combination of analytical and numerical tools in quantitative finance. It could provide guidance on the development of nonlinear methods of option pricing for practitioners as well as for analysts."—Nikita Y. Ratanov, from Mathematical Reviews Clippings, January 2015"… anyone with interest in quantitative finance and partial differential equations/continuous time stochastic analysis will not only greatly enjoy this book, but he or she will find both many numerical ideas of real practical interest as well as material for academic research, perhaps for years to come."—Peter Friz, The Bachelier Finance Society"This textbook provides a comprehensive treatment of numerical methods for nonlinear option pricing problems."—Zentralblatt MATH 1285"It is the only book of its kind. … The contribution of this book is threefold: (a) a practical, intuitive, and self-contained derivation of various of the latest derivative pricing models driven by diffusion processes; (b) an exposition of various advanced Monte Carlo simulation schemes for solving challenging nonlinear problems arising in financial engineering; (c) a clear and accessible survey of the theory of nonlinear PDEs. The authors have done a brilliant job providing just the right amount of rigorous theory required to understand the advanced methodologies they present. … Julien Guyon and Pierre Henry-Labordère, as befitting their reputations as star quants, have done an excellent job presenting the latest theory of nonlinear PDEs and their applications to finance. Much of the material in the book consists of the authors’ own original results. I highly recommend this book to seasoned mathematicians and experienced quants in the industry … Mathematicians will be able to see how practitioners argue heuristically to arrive at solutions of the toughest problems in financial engineering; practitioners of quantitative finance will find the book perfectly balanced between mathematical theory, financial modelling, and schemes for numerical implementation."—Quantitative Finance, 2014"Ever since Black and Scholes solved their eponymous linear PDE in 1969, the complexity of problems plaguing financial practitioners has exploded (non-linearly!). How fitting it is that nonlinear PDEs are now routinely used to extend the original framework. Written by two leading quants at two leading financial houses, this book is a tour de force on the use of nonlinear PDEs in financial valuation."—Peter Carr, PhD, Global Head of Market Modeling, Morgan Stanley, New York, and Executive Director of Masters in Mathematical Finance, Courant Institute of Mathematical Sciences, New York University "Finance used to be simple; you could go a long way with just linearity and positivity but this is not the case anymore. This superb book gives a wide array of modern methods for modern problems."—Bruno Dupire, Head of Quantitative Research, Bloomberg L.P."In this unique and impressive book, the authors apply sophisticated modern tools of pure and applied mathematics, such as BSDEs and particle methods, to solve challenging nonlinear problems of real practical interest, such as the valuation of guaranteed equity-linked annuity contracts and the calibration of local stochastic volatility models. Not only that, but sketches of proofs and implementation details are included. No serious student of mathematical finance, whether practitioner or academic, can afford to be without it."—Jim Gatheral, Presidential Professor, Baruch College, CUNY, and author of The Volatility Surface"Guyon and Henry-Labordère have produced an impressive textbook, which covers options and derivatives pricing from the point of view of nonlinear PDEs. This book is a comprehensive survey of nonlinear techniques, ranging from American options, uncertain volatility, and uncertain correlation models. It is aimed at graduate students or quantitative analysts with a strong mathematical background. They will find the book reasonably self-contained, i.e., discussing both the mathematical theory and the applications, in a very balanced approach. A must-read for the serious quantitative analyst."—Marco Avellaneda, Courant Institute of Mathematical Sciences, New York UniversityTable of ContentsSome Excursions in Option Pricing. Nonlinear PDEs: A Bit of Theory. Examples of Nonlinear Problems in Finance. Early Exercise Problems. Backward Stochastic Differential Equations. The Uncertain Lapse and Mortality Model. The Uncertain Volatility Model. McKean Nonlinear Stochastic Differential Equations. Calibration of Local Stochastic Volatility Models to Market Smiles. Calibration of Local Correlation Models to Market Smiles. Marked Branching Diffusions. References. Index.

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