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| felix zhang ap calculus: Learning Queena N. Lee-Chua, 2010-09-02 Parents are unsure about many things. How can they help their kids with homeworks? How can they discipline their children, yet treat them with love and respect? How can they strike a balance between family and career? How can they ensure that their kids love learning? |
| felix zhang ap calculus: The Schur Complement and Its Applications Fuzhen Zhang, 2006-03-30 This book describes the Schur complement as a rich and basic tool in mathematical research and applications and discusses many significant results that illustrate its power and fertility. Coverage includes historical development, basic properties, eigenvalue and singular value inequalities, matrix inequalities in both finite and infinite dimensional settings, closure properties, and applications in statistics, probability, and numerical analysis. |
| felix zhang ap calculus: Helping Children Learn Mathematics National Research Council, Division of Behavioral and Social Sciences and Education, Center for Education, Mathematics Learning Study Committee, 2002-07-31 Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society. |
| felix zhang ap calculus: Photonic Crystals John D. Joannopoulos, Steven G. Johnson, Joshua N. Winn, Robert D. Meade, 2011-10-30 Since it was first published in 1995, Photonic Crystals has remained the definitive text for both undergraduates and researchers on photonic band-gap materials and their use in controlling the propagation of light. This newly expanded and revised edition covers the latest developments in the field, providing the most up-to-date, concise, and comprehensive book available on these novel materials and their applications. Starting from Maxwell's equations and Fourier analysis, the authors develop the theoretical tools of photonics using principles of linear algebra and symmetry, emphasizing analogies with traditional solid-state physics and quantum theory. They then investigate the unique phenomena that take place within photonic crystals at defect sites and surfaces, from one to three dimensions. This new edition includes entirely new chapters describing important hybrid structures that use band gaps or periodicity only in some directions: periodic waveguides, photonic-crystal slabs, and photonic-crystal fibers. The authors demonstrate how the capabilities of photonic crystals to localize light can be put to work in devices such as filters and splitters. A new appendix provides an overview of computational methods for electromagnetism. Existing chapters have been considerably updated and expanded to include many new three-dimensional photonic crystals, an extensive tutorial on device design using temporal coupled-mode theory, discussions of diffraction and refraction at crystal interfaces, and more. Richly illustrated and accessibly written, Photonic Crystals is an indispensable resource for students and researchers. Extensively revised and expanded Features improved graphics throughout Includes new chapters on photonic-crystal fibers and combined index-and band-gap-guiding Provides an introduction to coupled-mode theory as a powerful tool for device design Covers many new topics, including omnidirectional reflection, anomalous refraction and diffraction, computational photonics, and much more. |
| felix zhang ap calculus: Making Mathematics Come to Life Oleg A. Ivanov, 2009-12-16 ``It is difficult to define the genre of the book. It is not a problem book, nor a textbook, nor a `book for reading about mathematics'. It is most of all reminiscent of a good lecture course, from which a thoughtful student comes away with more than was actually spoken about in the lectures.'' --from the Preface by A. S. Merkurjev If you are acquainted with mathematics at least to the extent of a standard high school curriculum and like it enough to want to learn more, and if, in addition, you are prepared to do some serious work, then you should start studying this book. An understanding of the material of the book requires neither a developed ability to reason abstractly nor skill in using the refined techniques of mathematical analysis. In each chapter elementary problems are considered, accompanied by theoretical material directly related to them. There are over 300 problems in the book, most of which are intended to be solved by the reader. In those places in the book where it is natural to introduce concepts outside the high school syllabus, the corresponding definitions are given with examples. And in order to bring out the meaning of such concepts clearly, appropriate (but not too many) theorems are proved concerning them. Unfortunately, what is sometimes studied at school under the name ``mathematics'' resembles real mathematics not any closer than a plucked flower gathering dust in a herbarium or pressed between the pages of a book resembles that same flower in the meadow besprinkled with dewdrops sparkling in the light of the rising sun. |
| felix zhang ap calculus: Machine Learning Refined Jeremy Watt, Reza Borhani, Aggelos K. Katsaggelos, 2020-01-09 An intuitive approach to machine learning covering key concepts, real-world applications, and practical Python coding exercises. |
| felix zhang ap calculus: History in Mathematics Education John Fauvel, J.A. van Maanen, 2006-04-11 This ground-breaking book investigates how the learning and teaching of mathematics can be improved through integrating the history of mathematics into all aspects of mathematics education: lessons, homework, texts, lectures, projects, assessment, and curricula. It draws upon evidence from the experience of teachers as well as national curricula, textbooks, teacher education practices, and research perspectives across the world. It includes a 300-item annotated bibliography of recent work in the field in eight languages. |
| felix zhang ap calculus: Parameterized Algorithms Marek Cygan, Fedor V. Fomin, Łukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Michał Pilipczuk, Saket Saurabh, 2015-07-20 This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area. The book covers many of the recent developments of the field, including application of important separators, branching based on linear programming, Cut & Count to obtain faster algorithms on tree decompositions, algorithms based on representative families of matroids, and use of the Strong Exponential Time Hypothesis. A number of older results are revisited and explained in a modern and didactic way. The book provides a toolbox of algorithmic techniques. Part I is an overview of basic techniques, each chapter discussing a certain algorithmic paradigm. The material covered in this part can be used for an introductory course on fixed-parameter tractability. Part II discusses more advanced and specialized algorithmic ideas, bringing the reader to the cutting edge of current research. Part III presents complexity results and lower bounds, giving negative evidence by way of W[1]-hardness, the Exponential Time Hypothesis, and kernelization lower bounds. All the results and concepts are introduced at a level accessible to graduate students and advanced undergraduate students. Every chapter is accompanied by exercises, many with hints, while the bibliographic notes point to original publications and related work. |
| felix zhang ap calculus: Mathematics under the Microscope Alexandre Borovik, 2010 Discusses, from a working mathematician's point of view, the mystery of mathematical intuition: Why are certain mathematical concepts more intuitive than others? And to what extent does the 'small scale' structure of mathematical concepts and algorithms reflect the workings of the human brain? |
| felix zhang ap calculus: Black Holes in Higher Dimensions Gary T. Horowitz, 2012-04-19 The first book devoted to black holes in more than four dimensions, for graduate students and researchers. |
| felix zhang ap calculus: A Mathematical Gift, III Koji Shiga, Toshikazu Sunada, 2005-07-18 This book brings the beauty and fun of mathematics to the classroom. It offers serious mathematics in a lively, reader-friendly style. Included are exercises and many figures illustrating the main concepts. The first chapter talks about the theory of manifolds. It includes discussion of smoothness, differentiability, and analyticity, the idea of local coordinates and coordinate transformation, and a detailed explanation of the Whitney imbedding theorem (both in weak and in strong form).The second chapter discusses the notion of the area of a figure on the plane and the volume of a solid body in space. It includes the proof of the Bolyai-Gerwien theorem about scissors-congruent polynomials and Dehn's solution of the Third Hilbert Problem. This is the third volume originating from a series of lectures given at Kyoto University (Japan). It is suitable for classroom use for high school mathematics teachers and for undergraduate mathematics courses in the sciences and liberal arts. The first and second volumes are available as Volume 19 and Volume 20 in the AMS series, Mathematical World. |
| felix zhang ap calculus: Uniform Central Limit Theorems R. M. Dudley, 1999-07-28 This treatise by an acknowledged expert includes several topics not found in any previous book. |
| felix zhang ap calculus: 5000 Years of Geometry Christoph J. Scriba, Peter Schreiber, 2015-04-22 The present volume provides a fascinating overview of geometrical ideas and perceptions from the earliest cultures to the mathematical and artistic concepts of the 20th century. It is the English translation of the 3rd edition of the well-received German book “5000 Jahre Geometrie,” in which geometry is presented as a chain of developments in cultural history and their interaction with architecture, the visual arts, philosophy, science and engineering. Geometry originated in the ancient cultures along the Indus and Nile Rivers and in Mesopotamia, experiencing its first “Golden Age” in Ancient Greece. Inspired by the Greek mathematics, a new germ of geometry blossomed in the Islamic civilizations. Through the Oriental influence on Spain, this knowledge later spread to Western Europe. Here, as part of the medieval Quadrivium, the understanding of geometry was deepened, leading to a revival during the Renaissance. Together with parallel achievements in India, China, Japan and the ancient American cultures, the European approaches formed the ideas and branches of geometry we know in the modern age: coordinate methods, analytical geometry, descriptive and projective geometry in the 17th an 18th centuries, axiom systems, geometry as a theory with multiple structures and geometry in computer sciences in the 19th and 20th centuries. Each chapter of the book starts with a table of key historical and cultural dates and ends with a summary of essential contents of geometr y in the respective era. Compelling examples invite the reader to further explore the problems of geometry in ancient and modern times. The book will appeal to mathematicians interested in Geometry and to all readers with an interest in cultural history. From letters to the authors for the German language edition I hope it gets a translation, as there is no comparable work. Prof. J. Grattan-Guinness (Middlesex University London) Five Thousand Years of Geometry - I think it is the most handsome book I have ever seen from Springer and the inclusion of so many color plates really improves its appearance dramatically! Prof. J.W. Dauben (City University of New York) An excellent book in every respect. The authors have successfully combined the history of geometry with the general development of culture and history. ... The graphic design is also excellent. Prof. Z. Nádenik (Czech Technical University in Prague) |
| felix zhang ap calculus: Mathematical Conversations Robin Wilson, Jeremy Gray, 2012-12-06 Approximately fifty articles that were published in The Mathematical Intelligencer during its first eighteen years. The selection demonstrates the wide variety of attractive articles that have appeared over the years, ranging from general interest articles of a historical nature to lucid expositions of important current discoveries. Each article is introduced by the editors. ...The Mathematical Intelligencer publishes stylish, well-illustrated articles, rich in ideas and usually short on proofs. ...Many, but not all articles fall within the reach of the advanced undergraduate mathematics major. ... This book makes a nice addition to any undergraduate mathematics collection that does not already sport back issues of The Mathematical Intelligencer. D.V. Feldman, University of New Hamphire, CHOICE Reviews, June 2001. |
| felix zhang ap calculus: The Text Mining Handbook Ronen Feldman, James Sanger, 2007 Publisher description |
| felix zhang ap calculus: The Shape of Inner Space Shing-Tung Yau, Steven J. Nadis, 2010-09-07 The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations. |
| felix zhang ap calculus: Anachronisms in the History of Mathematics Niccolò Guicciardini, 2021-07-22 The controversial matters surrounding the notion of anachronism are difficult ones: they have been broached by literary and art critics, by philosophers, as well as by historians of science. This book adopts a bottom-up approach to the many problems concerning anachronism in the history of mathematics. Some of the leading scholars in the field of history of mathematics reflect on the applicability of present-day mathematical language, concepts, standards, disciplinary boundaries, indeed notions of mathematics itself, to well-chosen historical case studies belonging to the mathematics of the past, in European and non-European cultures. A detailed introduction describes the key themes and binds the various chapters together. The interdisciplinary and transcultural approach adopted allows this volume to cover topics important for history of mathematics, history of the physical sciences, history of science, philosophy of mathematics, history of philosophy, methodology of history, non-European science, and the transmission of mathematical knowledge across cultures. |
| felix zhang ap calculus: Number Theory and Modular Forms Bruce C. Berndt, Ken Ono, 2003-11-30 Robert A. Rankin, one of the world's foremost authorities on modular forms and a founding editor of The Ramanujan Journal, died on January 27, 2001, at the age of 85. Rankin had broad interests and contributed fundamental papers in a wide variety of areas within number theory, geometry, analysis, and algebra. To commemorate Rankin's life and work, the editors have collected together 25 papers by several eminent mathematicians reflecting Rankin's extensive range of interests within number theory. Many of these papers reflect Rankin's primary focus in modular forms. It is the editors' fervent hope that mathematicians will be stimulated by these papers and gain a greater appreciation for Rankin's contributions to mathematics. This volume would be an inspiration to students and researchers in the areas of number theory and modular forms. |
| felix zhang ap calculus: Problems in Real Analysis Teodora-Liliana Radulescu, Vicentiu D. Radulescu, Titu Andreescu, 2009-06-12 Problems in Real Analysis: Advanced Calculus on the Real Axis features a comprehensive collection of challenging problems in mathematical analysis that aim to promote creative, non-standard techniques for solving problems. This self-contained text offers a host of new mathematical tools and strategies which develop a connection between analysis and other mathematical disciplines, such as physics and engineering. A broad view of mathematics is presented throughout; the text is excellent for the classroom or self-study. It is intended for undergraduate and graduate students in mathematics, as well as for researchers engaged in the interplay between applied analysis, mathematical physics, and numerical analysis. |
| felix zhang ap calculus: The Cloud-to-Thing Continuum Theo Lynn, John G. Mooney, Brian Lee, Patricia Takako Endo, 2020-07-07 The Internet of Things offers massive societal and economic opportunities while at the same time significant challenges, not least the delivery and management of the technical infrastructure underpinning it, the deluge of data generated from it, ensuring privacy and security, and capturing value from it. This Open Access Pivot explores these challenges, presenting the state of the art and future directions for research but also frameworks for making sense of this complex area. This book provides a variety of perspectives on how technology innovations such as fog, edge and dew computing, 5G networks, and distributed intelligence are making us rethink conventional cloud computing to support the Internet of Things. Much of this book focuses on technical aspects of the Internet of Things, however, clear methodologies for mapping the business value of the Internet of Things are still missing. We provide a value mapping framework for the Internet of Things to address this gap. While there is much hype about theInternet of Things, we have yet to reach the tipping point. As such, this book provides a timely entrée for higher education educators, researchers and students, industry and policy makers on the technologies that promise to reshape how society interacts and operates. |
| felix zhang ap calculus: Games, Strategies and Decision Making Joseph Harrington, 2009 This book on game theory introduces and develops the key concepts with a minimum of mathematics. Students are presented with empirical evidence, anecdotes and strategic situations to help them apply theory and gain a genuine insight into human behaviour. The book provides a diverse collection of examples and scenarios from history, literature, sports, crime, theology, war, biology, and everyday life. These examples come with rich context that adds real-world meat to the skeleton of theory. Each chapter begins with a specific strategic situation and is followed with a systematic treatment that gradually builds understanding of the concept. |
| felix zhang ap calculus: Mathematics of Wave Phenomena Willy Dörfler, Marlis Hochbruck, Dirk Hundertmark, Wolfgang Reichel, Andreas Rieder, Roland Schnaubelt, Birgit Schörkhuber, 2020-10-01 Wave phenomena are ubiquitous in nature. Their mathematical modeling, simulation and analysis lead to fascinating and challenging problems in both analysis and numerical mathematics. These challenges and their impact on significant applications have inspired major results and methods about wave-type equations in both fields of mathematics. The Conference on Mathematics of Wave Phenomena 2018 held in Karlsruhe, Germany, was devoted to these topics and attracted internationally renowned experts from a broad range of fields. These conference proceedings present new ideas, results, and techniques from this exciting research area. |
| felix zhang ap calculus: Proof and Proving in Mathematics Education Gila Hanna, Michael de Villiers, 2012-06-14 *THIS BOOK IS AVAILABLE AS OPEN ACCESS BOOK ON SPRINGERLINK* One of the most significant tasks facing mathematics educators is to understand the role of mathematical reasoning and proving in mathematics teaching, so that its presence in instruction can be enhanced. This challenge has been given even greater importance by the assignment to proof of a more prominent place in the mathematics curriculum at all levels. Along with this renewed emphasis, there has been an upsurge in research on the teaching and learning of proof at all grade levels, leading to a re-examination of the role of proof in the curriculum and of its relation to other forms of explanation, illustration and justification. This book, resulting from the 19th ICMI Study, brings together a variety of viewpoints on issues such as: The potential role of reasoning and proof in deepening mathematical understanding in the classroom as it does in mathematical practice. The developmental nature of mathematical reasoning and proof in teaching and learning from the earliest grades. The development of suitable curriculum materials and teacher education programs to support the teaching of proof and proving. The book considers proof and proving as complex but foundational in mathematics. Through the systematic examination of recent research this volume offers new ideas aimed at enhancing the place of proof and proving in our classrooms. |
| felix zhang ap calculus: Inorganic Polyphosphates Heinz C. Schröder, Werner E.G. Müller, 2012-10-12 Inorganic polyphosphates - polymers of orthophosphate linked by high-energy phosphoanhydride bonds - have been found in apparently all forms of life, from bacteria, yeasts and fungi to higher plants and animals. These polymers, which had been neglected for a long time, have become a fascinating area of research in the last few years. This volume summarizes the present state of knowledge about the metabolism and function of inorganic polyphosphates. In addition, the methods to study these polymers as well as the biotechnological applications of inorganic polyphosphates are described. The 15 chapters of this volume, dealing with different aspects of polyphosphate research, are written by experts in the field. This book represents a valuable source of information not only for researchers working on this subject, but also for scientists interested in fundamental aspects of cell and energy metabolism. |
| felix zhang ap calculus: Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) Boyan Sirakov, Paulo Ney De Souza, Marcelo Viana, 2019-02-27 The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios. |
| felix zhang ap calculus: Proceedings of the International Conference on Mathematics Textbook Research and Development (ICMT-2014) Christian Bokhove, Albert Geoffrey Howson, Lianghuo Fan, 2014 ICMT-2014, the International Conference on Mathematics Textbook Research and Development, brought together mathematics educators, textbook researchers and developers, and policy makers from different parts of the world to share their research results, development experiences and reform ideas, and discuss issues and directions concerning mathematics textbook research and development. These proceedings contain all the papers presented at the conference, including the plenary presentations and plenary panel, as well as the symposia, research papers, and workshops. This volume provides a comprehensive record of the ICMT-2014 conference and serves as an essential reference for education researchers, practitioners, and policy makers and curriculum developers interested in mathematics textbook research and development. |
| felix zhang ap calculus: Pattern Recognition and Machine Learning Christopher M. Bishop, 2016-08-23 This is the first textbook on pattern recognition to present the Bayesian viewpoint. The book presents approximate inference algorithms that permit fast approximate answers in situations where exact answers are not feasible. It uses graphical models to describe probability distributions when no other books apply graphical models to machine learning. No previous knowledge of pattern recognition or machine learning concepts is assumed. Familiarity with multivariate calculus and basic linear algebra is required, and some experience in the use of probabilities would be helpful though not essential as the book includes a self-contained introduction to basic probability theory. |
| felix zhang ap calculus: Stamping through Mathematics Robin J. Wilson, 2006-05-07 The astonishing variety and beauty of mathematical elements in stamp design is brought to life in this collection of more than 350 stamps, illustrated with mathematical figures, people, and content, each reproduced in enlarged format, in full color. It's a perfect gift book for anyone interested in stamps, or in the surprising use of mathematics in the real world. The author is widely known in the math community for his regular column on stamps in the magazine The Mathematical Intelligencer. |
| felix zhang ap calculus: An Introduction to the Theory of Functional Equations and Inequalities Marek Kuczma, 2009-03-12 Marek Kuczma was born in 1935 in Katowice, Poland, and died there in 1991. After finishing high school in his home town, he studied at the Jagiellonian University in Kraków. He defended his doctoral dissertation under the supervision of Stanislaw Golab. In the year of his habilitation, in 1963, he obtained a position at the Katowice branch of the Jagiellonian University (now University of Silesia, Katowice), and worked there till his death. Besides his several administrative positions and his outstanding teaching activity, he accomplished excellent and rich scientific work publishing three monographs and 180 scientific papers. He is considered to be the founder of the celebrated Polish school of functional equations and inequalities. The second half of the title of this book describes its contents adequately. Probably even the most devoted specialist would not have thought that about 300 pages can be written just about the Cauchy equation (and on some closely related equations and inequalities). And the book is by no means chatty, and does not even claim completeness. Part I lists the required preliminary knowledge in set and measure theory, topology and algebra. Part II gives details on solutions of the Cauchy equation and of the Jensen inequality [...], in particular on continuous convex functions, Hamel bases, on inequalities following from the Jensen inequality [...]. Part III deals with related equations and inequalities (in particular, Pexider, Hosszú, and conditional equations, derivations, convex functions of higher order, subadditive functions and stability theorems). It concludes with an excursion into the field of extensions of homomorphisms in general. (Janos Aczel, Mathematical Reviews) This book is a real holiday for all the mathematicians independently of their strict speciality. One can imagine what deliciousness represents this book for functional equationists. (B. Crstici, Zentralblatt für Mathematik) |
| felix zhang ap calculus: An Introduction to Causal Inference Judea Pearl, 2015 This paper summarizes recent advances in causal inference and underscores the paradigmatic shifts that must be undertaken in moving from traditional statistical analysis to causal analysis of multivariate data. Special emphasis is placed on the assumptions that underly all causal inferences, the languages used in formulating those assumptions, the conditional nature of all causal and counterfactual claims, and the methods that have been developed for the assessment of such claims. These advances are illustrated using a general theory of causation based on the Structural Causal Model (SCM) described in Pearl (2000a), which subsumes and unifies other approaches to causation, and provides a coherent mathematical foundation for the analysis of causes and counterfactuals. In particular, the paper surveys the development of mathematical tools for inferring (from a combination of data and assumptions) answers to three types of causal queries: (1) queries about the effects of potential interventions, (also called causal effects or policy evaluation) (2) queries about probabilities of counterfactuals, (including assessment of regret, attribution or causes of effects) and (3) queries about direct and indirect effects (also known as mediation). Finally, the paper defines the formal and conceptual relationships between the structural and potential-outcome frameworks and presents tools for a symbiotic analysis that uses the strong features of both. The tools are demonstrated in the analyses of mediation, causes of effects, and probabilities of causation. -- p. 1. |
| felix zhang ap calculus: The Distribution of Prime Numbers Albert Edward Ingham, 1990-09-28 Originally published in 1934, this volume presents the theory of the distribution of the prime numbers in the series of natural numbers. Despite being long out of print, it remains unsurpassed as an introduction to the field. |
| felix zhang ap calculus: Perspectives on the Teaching of Geometry for the 21st Century C. Mammana, V. Villani, 2012-12-06 In recent years geometry seems to have lost large parts of its former central position in mathematics teaching in most countries. However, new trends have begun to counteract this tendency. There is an increasing awareness that geometry plays a key role in mathematics and learning mathematics. Although geometry has been eclipsed in the mathematics curriculum, research in geometry has blossomed as new ideas have arisen from inside mathematics and other disciplines, including computer science. Due to reassessment of the role of geometry, mathematics educators and mathematicians face new challenges. In the present ICMI study, the whole spectrum of teaching and learning of geometry is analysed. Experts from all over the world took part in this study, which was conducted on the basis of recent international research, case studies, and reports on actual school practice. This book will be of particular interest to mathematics educators and mathematicians who are involved in the teaching of geometry at all educational levels, as well as to researchers in mathematics education. |
| felix zhang ap calculus: Evolution Equations Gisele Ruiz Goldstein, Rainer Nagel, Silvia Romanelli, 2003-06-24 Celebrating the work of renowned mathematician Jerome A. Goldstein, this reference compiles original research on the theory and application of evolution equations to stochastics, physics, engineering, biology, and finance. The text explores a wide range of topics in linear and nonlinear semigroup theory, operator theory, functional analysis, and linear and nonlinear partial differential equations, and studies the latest theoretical developments and uses of evolution equations in a variety of disciplines. Providing nearly 500 references, the book contains discussions by renowned mathematicians such as H. Brezis, G. Da Prato, N.E. Gretskij, I. Lasiecka, Peter Lax, M. M. Rao, and R. Triggiani. |
| felix zhang ap calculus: Evolution of Mathematical Concepts Raymond L. Wilder, 2013-01-01 Accessible to students and relevant to specialists, this remarkable book by a prominent educator offers a unique perspective on the evolutionary development of mathematics. Rather than conducting a survey of the history or philosophy of mathematics, Raymond L. Wilder envisions mathematics as a broad cultural phenomenon. His treatment examines and illustrates how such concepts as number and length were affected by historic and social events. Starting with a brief consideration of preliminary notions, this study explores the early evolution of numbers, the evolution of geometry, and the conquest of the infinite as embodied by real numbers. A detailed look at the processes of evolution concludes with an examination of the evolutionary aspects of modern mathematics. |
| felix zhang ap calculus: Finite Mathematics as the Foundation of Classical Mathematics and Quantum Theory Felix Lev, 2020-11-03 This book delves into finite mathematics and its application in physics, particularly quantum theory. It is shown that quantum theory based on finite mathematics is more general than standard quantum theory, whilst finite mathematics is itself more general than standard mathematics.As a consequence, the mathematics describing nature at the most fundamental level involves only a finite number of numbers while the notions of limit, infinite/infinitesimal and continuity are needed only in calculations that describe nature approximately. It is also shown that the concepts of particle and antiparticle are likewise approximate notions, valid only in special situations, and that the electric charge and baryon- and lepton quantum numbers can be only approximately conserved. |
| felix zhang ap calculus: Integral Geometry and Radon Transforms Sigurdur Helgason, 2010-11-17 In this text, integral geometry deals with Radon’s problem of representing a function on a manifold in terms of its integrals over certain submanifolds—hence the term the Radon transform. Examples and far-reaching generalizations lead to fundamental problems such as: (i) injectivity, (ii) inversion formulas, (iii) support questions, (iv) applications (e.g., to tomography, partial di erential equations and group representations). For the case of the plane, the inversion theorem and the support theorem have had major applications in medicine through tomography and CAT scanning. While containing some recent research, the book is aimed at beginning graduate students for classroom use or self-study. A number of exercises point to further results with documentation. From the reviews: “Integral Geometry is a fascinating area, where numerous branches of mathematics meet together. the contents of the book is concentrated around the duality and double vibration, which is realized through the masterful treatment of a variety of examples. the book is written by an expert, who has made fundamental contributions to the area.” —Boris Rubin, Louisiana State University |
| felix zhang ap calculus: Mathematical Reviews , 2004 |
| felix zhang ap calculus: Lectures on Contemporary Probability Gregory F. Lawler, Lester Noel Coyle, 1999 This volume is based on classes in probability for advanced undergraduates held at the IAS/Park City Mathematics Institute. It is derived from both lectures (Chapters 1-10) and computer simulations (Chapters 11-13) that were held during the program. The material is coordinated so that some of the major computer simulations relate to topics covered in the first ten chapters. The goal is to present topics that are accessible to advanced undergraduates, yet are areas of current research in probability. The combination of the lucid yet informal style of the lectures and the hands-on nature of the simulations allows readers to become familiar with some interesting and active areas of probability. The first four chapters discuss random walks and the continuous limit of random walks: Brownian motion. Chapters 5 and 6 consider the fascinating mathematics of card shuffles, including the notions of random walks on a symmetric group and the general idea of random permutations. Chapters 7 and 8 discuss Markov chains, beginning with a standard introduction to the theory. Chapter 8 addresses the recent important application of Markov chains to simulations of random systems on large finite sets: Markov Chain Monte Carlo. Random walks and electrical networks are covered in Chapter 9. Uniform spanning trees, as connected to probability and random walks, are treated in Chapter 10. The final three chapters of the book present simulations. Chapter 11 discusses simulations for random walks. Chapter 12 covers simulation topics such as sampling from continuous distributions, random permutations, and estimating the number of matrices with certain conditions using Markov Chain Monte Carlo. Chapter 13 presents simulations of stochastic differential equations for applications in finance. (The simulations do not require one particular piece of software. They can be done in symbolic computation packages or via programming languages such as $\bold C$.) The volume concludes with a number of problems ranging from routine to very difficult. Of particular note are the problems that are typical of simulation problems given to students by the authors when teaching undergraduate probability. |
| felix zhang ap calculus: Data Science for Undergraduates National Academies of Sciences, Engineering, and Medicine, Division of Behavioral and Social Sciences and Education, Board on Science Education, Division on Engineering and Physical Sciences, Committee on Applied and Theoretical Statistics, Board on Mathematical Sciences and Analytics, Computer Science and Telecommunications Board, Committee on Envisioning the Data Science Discipline: The Undergraduate Perspective, 2018-11-11 Data science is emerging as a field that is revolutionizing science and industries alike. Work across nearly all domains is becoming more data driven, affecting both the jobs that are available and the skills that are required. As more data and ways of analyzing them become available, more aspects of the economy, society, and daily life will become dependent on data. It is imperative that educators, administrators, and students begin today to consider how to best prepare for and keep pace with this data-driven era of tomorrow. Undergraduate teaching, in particular, offers a critical link in offering more data science exposure to students and expanding the supply of data science talent. Data Science for Undergraduates: Opportunities and Options offers a vision for the emerging discipline of data science at the undergraduate level. This report outlines some considerations and approaches for academic institutions and others in the broader data science communities to help guide the ongoing transformation of this field. |
| felix zhang ap calculus: Electromagnetic Wave Theory Jin Au Kong, 1990 This is a first year graduate text on electromagnetic field theory emphasizing mathematical approaches, problem solving and physical interpretation. Examples deal with guidance, propagation, radiation and scattering of electromagnetic waves, metallic and dielectric wave guides, resonators, antennas and radiating structures, Cerenkov radiation, moving media, plasmas, crystals, integrated optics, lasers and fibers, remote sensing, geophysical probing, dipole antennas and stratified media. |
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Välj bland såser, soppor, pajer, köttbullar och mycket mer. Vi på Felix väljer råvaror med omsorg och har alltid smaken i fokus, hitta dina favoriter idag!
XL Ost & Skinkpaj - Ännu större och matigare - Felix
Felix XL Ost & skinkpaj är en extra stor och matig paj med smakrik ost, svensk rökt skinka och broccoli. Den krämiga fyllningen är gjord på färsk mjölk och grädde samt svenska ägg från …
Krämig kycklinggryta med soltorkad tomat | Felix
Testa Felix krämiga kycklinggryta med soltorkad tomat, grädde och vitlök. Perfekt om du vill ha en god och snabb lunch!
Ketchup Chilisås & Senap Archives - Felix
Upptäck Felix goda sortiment av ketchup, chilisås och senap. Perfekt topping till grillkorven och hamburgaren. Älskade favoriter för hela familjen!
Green Goddess Salad med kyckling | Felix
Fräsch sallad med kyckling och Felix krämiga salladsdressing – en grön favorit som mättar och smakar fantastiskt.
Cheeseburgare med Pommes Chips och Dipp | Felix
Ett härligt recept på saftig cheeseburgare med Pommes Chips att dippa i egengjord ramslöksmajjo och Felix Vitlökssås. Mums! Receptet är framtaget av @baraenkakatill i …
Om oss - Vår historia och vår passion - Felix
I dag är Felix marknadsledande inom flera produktområden och är ett av Sveriges största varumärken inom livsmedel. Vårt produktutbud spänner sig från ketchup och dressingar till …
God mat från Sverige - Utan tillsatser eller konstigheter | Felix
Ända sen vi startade 1939 har det ofta stått FELIX på Sveriges mest omtyckta matprodukter. Och så vill vi att det ska fortsätta. Därför utvecklar vi ständigt nya smaker och produkter, förbättrar …
Fakta om ketchup – en av våra mest älskade produkter! - Felix
Felix ketchup är Sveriges mest älskade ketchup och en av våra mest populära produkter. Den tillverkas av klimatsmart odlade tomater som fått mogna under solens strålar i södra Europa. …
Mat för en - Färdigrätter till lunch och middag | Felix
Här hittar du Felix goda färdigmat för en. Bland våra enportionsrätter finns alltifrån smakrika bowls till härliga pajer! Perfekt som lunch eller middag.
Felix produkter – mat av hög kvalitet – läs mer! | Felix
Välj bland såser, soppor, pajer, köttbullar och mycket mer. Vi på Felix väljer råvaror med omsorg och har alltid smaken i fokus, hitta dina favoriter idag!
XL Ost & Skinkpaj - Ännu större och matigare - Felix
Felix XL Ost & skinkpaj är en extra stor och matig paj med smakrik ost, svensk rökt skinka och broccoli. Den krämiga fyllningen är gjord på färsk mjölk och grädde samt svenska ägg från …
Krämig kycklinggryta med soltorkad tomat | Felix
Testa Felix krämiga kycklinggryta med soltorkad tomat, grädde och vitlök. Perfekt om du vill ha en god och snabb lunch!
Ketchup Chilisås & Senap Archives - Felix
Upptäck Felix goda sortiment av ketchup, chilisås och senap. Perfekt topping till grillkorven och hamburgaren. Älskade favoriter för hela familjen!
Green Goddess Salad med kyckling | Felix
Fräsch sallad med kyckling och Felix krämiga salladsdressing – en grön favorit som mättar och smakar fantastiskt.
Cheeseburgare med Pommes Chips och Dipp | Felix
Ett härligt recept på saftig cheeseburgare med Pommes Chips att dippa i egengjord ramslöksmajjo och Felix Vitlökssås. Mums! Receptet är framtaget av @baraenkakatill i …
