| dartmouth mathematical data science: Introduction to Probability David F. Anderson, Timo Seppäläinen, Benedek Valkó, 2017-11-02 This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work. |
| dartmouth mathematical data science: Digital Humanities in the Library Arianne Hartsell-Gundy, Laura Braunstein, Liorah Golomb, 2015 In the past decade there has been an intense growth in the number of library publishing services supporting faculty and students. Unified by a commitment to both access and service, library publishing programs have grown from an early focus on backlist digitization to encompass publication of student works, textbooks, research data, as well as books and journals. This growing engagement with publishing is a natural extensions of the academic library's commitment to support the creation of and access to scholarship.--Back cover. |
| dartmouth mathematical data science: What Are the Arts and Sciences? Dan Rockmore, 2017-06-06 What constitutes the study of philosophy or physics? What exactly does an anthropologist do, or a geologist or historian? In short, what are the arts and sciences? While many of us have been to college and many aspire to go, we may still wonder just what the various disciplines represent and how they interact. What are their origins, methods, applications, and unique challenges? What kind of people elect to go into each of these fields, and what are the big issues that motivate them? Curious to explore these questions himself, Dartmouth College professor and mathematician Dan Rockmore asked his colleagues to explain their fields and what it is that they do. The result is an accessible, entertaining, and enlightening survey of the ideas and subjects that contribute to a liberal education. The book offers a doorway to the arts and sciences for anyone intrigued by the vast world of ideas. |
| dartmouth mathematical data science: Representations and Characters of Groups Gordon James, Martin Liebeck, 2001-10-18 This book provides a modern introduction to the representation theory of finite groups. Now in its second edition, the authors have revised the text and added much new material. The theory is developed in terms of modules, since this is appropriate for more advanced work, but considerable emphasis is placed upon constructing characters. Included here are the character tables of all groups of order less than 32, and all simple groups of order less than 1000. Applications covered include Burnside's paqb theorem, the use of character theory in studying subgroup structure and permutation groups, and how to use representation theory to investigate molecular vibration. Each chapter features a variety of exercises, with full solutions provided at the end of the book. This will be ideal as a course text in representation theory, and in view of the applications, will be of interest to chemists and physicists as well as mathematicians. |
| dartmouth mathematical data science: Digital Signal Processing Using MATLAB for Students and Researchers John W. Leis, 2011-10-14 Quickly Engages in Applying Algorithmic Techniques to Solve Practical Signal Processing Problems With its active, hands-on learning approach, this text enables readers to master the underlying principles of digital signal processing and its many applications in industries such as digital television, mobile and broadband communications, and medical/scientific devices. Carefully developed MATLAB® examples throughout the text illustrate the mathematical concepts and use of digital signal processing algorithms. Readers will develop a deeper understanding of how to apply the algorithms by manipulating the codes in the examples to see their effect. Moreover, plenty of exercises help to put knowledge into practice solving real-world signal processing challenges. Following an introductory chapter, the text explores: Sampled signals and digital processing Random signals Representing signals and systems Temporal and spatial signal processing Frequency analysis of signals Discrete-time filters and recursive filters Each chapter begins with chapter objectives and an introduction. A summary at the end of each chapter ensures that one has mastered all the key concepts and techniques before progressing in the text. Lastly, appendices listing selected web resources, research papers, and related textbooks enable the investigation of individual topics in greater depth. Upon completion of this text, readers will understand how to apply key algorithmic techniques to address practical signal processing problems as well as develop their own signal processing algorithms. Moreover, the text provides a solid foundation for evaluating and applying new digital processing signal techniques as they are developed. |
| dartmouth mathematical data science: 99 Variations on a Proof Philip Ording, 2021-10-19 An exploration of mathematical style through 99 different proofs of the same theorem This book offers a multifaceted perspective on mathematics by demonstrating 99 different proofs of the same theorem. Each chapter solves an otherwise unremarkable equation in distinct historical, formal, and imaginative styles that range from Medieval, Topological, and Doggerel to Chromatic, Electrostatic, and Psychedelic. With a rare blend of humor and scholarly aplomb, Philip Ording weaves these variations into an accessible and wide-ranging narrative on the nature and practice of mathematics. Inspired by the experiments of the Paris-based writing group known as the Oulipo—whose members included Raymond Queneau, Italo Calvino, and Marcel Duchamp—Ording explores new ways to examine the aesthetic possibilities of mathematical activity. 99 Variations on a Proof is a mathematical take on Queneau’s Exercises in Style, a collection of 99 retellings of the same story, and it draws unexpected connections to everything from mysticism and technology to architecture and sign language. Through diagrams, found material, and other imagery, Ording illustrates the flexibility and creative potential of mathematics despite its reputation for precision and rigor. Readers will gain not only a bird’s-eye view of the discipline and its major branches but also new insights into its historical, philosophical, and cultural nuances. Readers, no matter their level of expertise, will discover in these proofs and accompanying commentary surprising new aspects of the mathematical landscape. |
| dartmouth mathematical data science: Mathematical Puzzles Peter Winkler, 2021-01-21 Research in mathematics is much more than solving puzzles, but most people will agree that solving puzzles is not just fun: it helps focus the mind and increases one's armory of techniques for doing mathematics. Mathematical Puzzles makes this connection explicit by isolating important mathematical methods, then using them to solve puzzles and prove a theorem. Features A collection of the world’s best mathematical puzzles Each chapter features a technique for solving mathematical puzzles, examples, and finally a genuine theorem of mathematics that features that technique in its proof Puzzles that are entertaining, mystifying, paradoxical, and satisfying; they are not just exercises or contest problems. |
| dartmouth mathematical data science: Calculus with Analytic Geometry Richard H. Crowell, William E. Slesnick, 1968 This book introduces and develops the differential and integral calculus of functions of one variable. |
| dartmouth mathematical data science: An Introduction to Knot Theory W.B.Raymond Lickorish, 2012-12-06 A selection of topics which graduate students have found to be a successful introduction to the field, employing three distinct techniques: geometric topology manoeuvres, combinatorics, and algebraic topology. Each topic is developed until significant results are achieved and each chapter ends with exercises and brief accounts of the latest research. What may reasonably be referred to as knot theory has expanded enormously over the last decade and, while the author describes important discoveries throughout the twentieth century, the latest discoveries such as quantum invariants of 3-manifolds as well as generalisations and applications of the Jones polynomial are also included, presented in an easily intelligible style. Readers are assumed to have knowledge of the basic ideas of the fundamental group and simple homology theory, although explanations throughout the text are numerous and well-done. Written by an internationally known expert in the field, this will appeal to graduate students, mathematicians and physicists with a mathematical background wishing to gain new insights in this area. |
| dartmouth mathematical data science: Optimization Modeling with Spreadsheets Kenneth R. Baker, 2012-01-10 Reflects the latest applied research and features state-of-the-art software for building and solving spreadsheet optimization models Thoroughly updated to reflect the latest topical and technical advances in the field, Optimization Modeling with Spreadsheets, Second Edition continues to focus on solving real-world optimization problems through the creation of mathematical models and the use of spreadsheets to represent and analyze those models. Developed and extensively classroom-tested by the author, the book features a systematic approach that equips readers with the skills to apply optimization tools effectively without the need to rely on specialized algorithms. This new edition uses the powerful software package Risk Solver Platform (RSP) for optimization, including its Evolutionary Solver, which employs many recently developed ideas for heuristic programming. The author provides expanded coverage of integer programming and discusses linear and nonlinear programming using a systematic approach that emphasizes the use of spreadsheet-based optimization tools. The Second Edition also features: Classifications for the various problem types, providing the reader with a broad framework for building and recognizing optimization models Network models that allow for a more general form of mass balance A systematic introduction to Data Envelopment Analysis (DEA) The identification of qualitative patterns in order to meaningfully interpret linear programming solutions An introduction to stochastic programming and the use of RSP to solve problems of this type Additional examples, exercises, and cases have been included throughout, allowing readers to test their comprehension of the material. In addition, a related website features Microsoft Office® Excel files to accompany the figures and data sets in the book. With its accessible and comprehensive presentation, Optimization Modeling with Spreadsheets, Second Edition is an excellent book for courses on deterministic models, optimization, and spreadsheet modeling at the upper-undergraduate and graduate levels. The book can also serve as a reference for researchers, practitioners, and consultants working in business, engineering, operations research, and management science. |
| dartmouth mathematical data science: Women in Mathematics Claudia Henrion, 1997-10-22 ... a wonderful addition to any mathematics teacher's professional bookshelf. -- The Mathematics Teacher The individual biographies themselves make for enthralling, often inspiring, reading... this volume should be compelling reading for women mathematics students and professionals. A fine addition to the literature on women in science... Highly recommended. -- Choice ... it makes an important contribution to scholarship on the interrelations of gender, mathematics, and culture in the U.S. in the second half of the twentieth century. -- Notices of the AMS Who is the audience for this book? Certainly women who are interested in studying mathematics and women already in mathematics who have become discouraged will find much to interest and help them. Faculty who teach such women would put it to good use. But it would be a loss to relegate the book to a shelf for occasional reference to an interested student or beginning mathematician. Everyone in the mathematics community in which each of Henrion's subjects struggled so hard to find a place could benefit by a thoughtful reading. -- Society for Industrial and Applied Mathematics (SIAM) News Mathematics is often described as the purest of the sciences, the least tainted by subjective or cultural influences. Theoretically, the only requirement for a life of mathematics is mathematical ability. And yet we see very few women mathematicians. Why? Based upon a series of ten intensive interviews with prominent women mathematicians throughout the United States, this book investigates the role of gender in the complex relationship between mathematician, the mathematical community, and mathematics itself. |
| dartmouth mathematical data science: Elementary Algebraic Geometry Klaus Hulek, 2003 This book is a true introduction to the basic concepts and techniques of algebraic geometry. The language is purposefully kept on an elementary level, avoiding sheaf theory and cohomology theory. The introduction of new algebraic concepts is always motivated by a discussion of the corresponding geometric ideas. The main point of the book is to illustrate the interplay between abstract theory and specific examples. The book contains numerous problems that illustrate the general theory. The text is suitable for advanced undergraduates and beginning graduate students. It contains sufficient material for a one-semester course. The reader should be familiar with the basic concepts of modern algebra. A course in one complex variable would be helpful, but is not necessary. |
| dartmouth mathematical data science: Financial Management Jack Alexander, 2024-01-31 A comprehensive and insightful approach enabling finance mangers to contribute to business performance and valuation In Financial Management: Partner in Driving Performance and Value, experienced financial executive and consultant Jack Alexander delivers a fresh, new take on improving performance and creating shareholder value for CFOs, controllers, C-suite executives, and FP&A professionals. In the book, you’ll learn about best practices in operational and strategic planning, forecasting, enterprise performance management, business valuation, capital investment, mergers and acquisitions, developing finance talent, supporting growth, and more. Frameworks for dealing with the pace of change and level of uncertainty in today’s environment are also provided, including scenario planning, business agility and monitoring external forces. The book provides actionable insights and practical tools for finance professionals to contribute as trusted advisors and business partners. The author offers free access to financial models in Microsoft Excel and PowerPoint templates on the accompanying website, as well as: Expanded and enhanced content from the author’s widely read previous works Models, illustrations, examples, and dashboards Anecdotes and stories drawn from the author’s 45-year-long career in financial leadership Perfect for CFOs, controllers, financial executives, financial planning and analysis professionals, and accounting managers, Financial Management is also the ideal desk reference for treasurers, strategic planners, Certified Public Accountants, and equity research analysts. It’s an essential and timely resource for financial leaders everywhere. |
| dartmouth mathematical data science: Knots and Links Dale Rolfsen, 2003 Rolfsen's beautiful book on knots and links can be read by anyone, from beginner to expert, who wants to learn about knot theory. Beginners find an inviting introduction to the elements of topology, emphasizing the tools needed for understanding knots, the fundamental group and van Kampen's theorem, for example, which are then applied to concrete problems, such as computing knot groups. For experts, Rolfsen explains advanced topics, such as the connections between knot theory and surgery and how they are useful to understanding three-manifolds. Besides providing a guide to understanding knot theory, the book offers 'practical' training. After reading it, you will be able to do many things: compute presentations of knot groups, Alexander polynomials, and other invariants; perform surgery on three-manifolds; and visualize knots and their complements.It is characterized by its hands-on approach and emphasis on a visual, geometric understanding. Rolfsen offers invaluable insight and strikes a perfect balance between giving technical details and offering informal explanations. The illustrations are superb, and a wealth of examples are included. Now back in print by the AMS, the book is still a standard reference in knot theory. It is written in a remarkable style that makes it useful for both beginners and researchers. Particularly noteworthy is the table of knots and links at the end. This volume is an excellent introduction to the topic and is suitable as a textbook for a course in knot theory or 3-manifolds. Other key books of interest on this topic available from the AMS are The Shoelace Book: A Mathematical Guide to the Best (and Worst) Ways to Lace your Shoes and The Knot Book. |
| dartmouth mathematical data science: Essential Mathematics for Games and Interactive Applications James M. Van Verth, Lars M. Bishop, 2008-05-19 Essential Mathematics for Games and Interactive Applications, 2nd edition presents the core mathematics necessary for sophisticated 3D graphics and interactive physical simulations. The book begins with linear algebra and matrix multiplication and expands on this foundation to cover such topics as color and lighting, interpolation, animation and basic game physics. Essential Mathematics focuses on the issues of 3D game development important to programmers and includes optimization guidance throughout. The new edition Windows code will now use Visual Studio.NET. There will also be DirectX support provided, along with OpenGL - due to its cross-platform nature. Programmers will find more concrete examples included in this edition, as well as additional information on tuning, optimization and robustness. The book has a companion CD-ROM with exercises and a test bank for the academic secondary market, and for main market: code examples built around a shared code base, including a math library covering all the topics presented in the book, a core vector/matrix math engine, and libraries to support basic 3D rendering and interaction. |
| dartmouth mathematical data science: 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. |
| dartmouth mathematical data science: Quantitative Social Science Scott, Jacqueline L. Scott, Yu Xie, 2012 |
| dartmouth mathematical data science: Research in Collegiate Mathematics Education III James J. Kaput, Ed Dubinsky, Alan H. Schoenfeld, Thomas P. Dick, 1998 Volume 3 of Research in Collegiate Mathematics Education (RCME) presents state-of-the-art research on understanding, teaching and learning mathematics at the post-secondary level. This volume contains information on methodology and research concentrating on these areas of student learning: Problem Solving; Understanding Concepts; and Understanding Proofs. |
| dartmouth mathematical data science: Didactics of Mathematics as a Scientific Discipline Rolf Biehler, Roland W. Scholz, Rudolf Sträßer, Bernard Winkelmann, 2006-04-11 Didactics of Mathematics as a Scientific Discipline describes the state of the art in a new branch of science. Starting from a general perspective on the didactics of mathematics, the 30 original contributions to the book, drawn from 10 different countries, go on to identify certain subdisciplines and suggest an overall structure or `topology' of the field. The book is divided into eight sections: (1) Preparing Mathematics for Students; (2) Teacher Education and Research on Teaching; (3) Interaction in the Classroom; (4) Technology and Mathematics Education; (5) Psychology of Mathematical Thinking; (6) Differential Didactics; (7) History and Epistemology of Mathematics and Mathematics Education; (8) Cultural Framing of Teaching and Learning Mathematics. Didactics of Mathematics as a Scientific Discipline is required reading for all researchers into the didactics of mathematics, and contains surveys and a variety of stimulating reflections which make it extremely useful for mathematics educators and teacher trainers interested in the theory of their practice. Future and practising teachers of mathematics will find much to interest them in relation to their daily work, especially as it relates to the teaching of different age groups and ability ranges. The book is also recommended to researchers in neighbouring disciplines, such as mathematics itself, general education, educational psychology and cognitive science. |
| dartmouth mathematical data science: Introduction to Computation and Programming Using Python, second edition John V. Guttag, 2016-08-12 The new edition of an introductory text that teaches students the art of computational problem solving, covering topics ranging from simple algorithms to information visualization. This book introduces students with little or no prior programming experience to the art of computational problem solving using Python and various Python libraries, including PyLab. It provides students with skills that will enable them to make productive use of computational techniques, including some of the tools and techniques of data science for using computation to model and interpret data. The book is based on an MIT course (which became the most popular course offered through MIT's OpenCourseWare) and was developed for use not only in a conventional classroom but in in a massive open online course (MOOC). This new edition has been updated for Python 3, reorganized to make it easier to use for courses that cover only a subset of the material, and offers additional material including five new chapters. Students are introduced to Python and the basics of programming in the context of such computational concepts and techniques as exhaustive enumeration, bisection search, and efficient approximation algorithms. Although it covers such traditional topics as computational complexity and simple algorithms, the book focuses on a wide range of topics not found in most introductory texts, including information visualization, simulations to model randomness, computational techniques to understand data, and statistical techniques that inform (and misinform) as well as two related but relatively advanced topics: optimization problems and dynamic programming. This edition offers expanded material on statistics and machine learning and new chapters on Frequentist and Bayesian statistics. |
| dartmouth mathematical data science: Connections in Discrete Mathematics Steve Butler, Joshua Cooper, Glenn Hurlbert, 2018-06-14 Many of the best researchers and writers in discrete mathematics come together in a volume inspired by Ron Graham. |
| dartmouth mathematical data science: Naive Lie Theory John Stillwell, 2008-12-15 In this new textbook, acclaimed author John Stillwell presents a lucid introduction to Lie theory suitable for junior and senior level undergraduates. In order to achieve this, he focuses on the so-called classical groups'' that capture the symmetries of real, complex, and quaternion spaces. These symmetry groups may be represented by matrices, which allows them to be studied by elementary methods from calculus and linear algebra. This naive approach to Lie theory is originally due to von Neumann, and it is now possible to streamline it by using standard results of undergraduate mathematics. To compensate for the limitations of the naive approach, end of chapter discussions introduce important results beyond those proved in the book, as part of an informal sketch of Lie theory and its history. John Stillwell is Professor of Mathematics at the University of San Francisco. He is the author of several highly regarded books published by Springer, including The Four Pillars of Geometry (2005), Elements of Number Theory (2003), Mathematics and Its History (Second Edition, 2002), Numbers and Geometry (1998) and Elements of Algebra (1994). |
| dartmouth mathematical data science: Ethics and Mathematics Education Paul Ernest, 2024 This edited volume is an inquiry into the ethics of mathematics education, and to a lesser extent, the ethics of mathematics. The imposition of mathematics for all raises questions of ethics. What are the ethics of teaching school mathematics? What are the costs as well as the benefits? What are the ethical issues raised by the official aims of mathematics teaching, the planned curriculum, the pedagogies employed in school and college mathematics and the assessment systems? These questions are addressed in the book as well as what systems of ethics we might use. The volume ventures into a burgeoning new field. It offers a unique set of investigations, both theoretical and in terms of practices. It announces the ethics of mathematics education as a new subfield of research and includes valuable contributions from many of the best-known researchers in mathematics education; additionally, it is a valuable resource for students, teachers and researchers in the field. This is an enduring and classic source book in the field. From the wisdom of leading scholars to the little heard voices of students, this collection offers the reader many striking new insights into the ethics of mathematics and education. |
| dartmouth mathematical data science: Computing the Continuous Discretely Matthias Beck, Sinai Robins, 2015-11-14 This richly illustrated textbook explores the amazing interaction between combinatorics, geometry, number theory, and analysis which arises in the interplay between polyhedra and lattices. Highly accessible to advanced undergraduates, as well as beginning graduate students, this second edition is perfect for a capstone course, and adds two new chapters, many new exercises, and updated open problems. For scientists, this text can be utilized as a self-contained tooling device. The topics include a friendly invitation to Ehrhart’s theory of counting lattice points in polytopes, finite Fourier analysis, the Frobenius coin-exchange problem, Dedekind sums, solid angles, Euler–Maclaurin summation for polytopes, computational geometry, magic squares, zonotopes, and more. With more than 300 exercises and open research problems, the reader is an active participant, carried through diverse but tightly woven mathematical fields that are inspired by an innocently elementary question: What are the relationships between the continuous volume of a polytope and its discrete volume? Reviews of the first edition: “You owe it to yourself to pick up a copy of Computing the Continuous Discretely to read about a number of interesting problems in geometry, number theory, and combinatorics.” — MAA Reviews “The book is written as an accessible and engaging textbook, with many examples, historical notes, pithy quotes, commentary integrating the mate rial, exercises, open problems and an extensive bibliography.” — Zentralblatt MATH “This beautiful book presents, at a level suitable for advanced undergraduates, a fairly complete introduction to the problem of counting lattice points inside a convex polyhedron.” — Mathematical Reviews “Many departments recognize the need for capstone courses in which graduating students can see the tools they have acquired come together in some satisfying way. Beck and Robins have written the perfect text for such a course.” — CHOICE |
| dartmouth mathematical data science: Data Science in Context Alfred Z. Spector, Peter Norvig, Chris Wiggins, Jeannette M. Wing, 2022-10-20 Data science is the foundation of our modern world. It underlies applications used by billions of people every day, providing new tools, forms of entertainment, economic growth, and potential solutions to difficult, complex problems. These opportunities come with significant societal consequences, raising fundamental questions about issues such as data quality, fairness, privacy, and causation. In this book, four leading experts convey the excitement and promise of data science and examine the major challenges in gaining its benefits and mitigating its harms. They offer frameworks for critically evaluating the ingredients and the ethical considerations needed to apply data science productively, illustrated by extensive application examples. The authors' far-ranging exploration of these complex issues will stimulate data science practitioners and students, as well as humanists, social scientists, scientists, and policy makers, to study and debate how data science can be used more effectively and more ethically to better our world. |
| dartmouth mathematical data science: Lectures on the Curry-Howard Isomorphism Morten Heine Sørensen, Pawel Urzyczyn, 2006-07-04 The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance,minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, sequent calculus is related to explicit substitution, etc.The isomorphism has many aspects, even at the syntactic level:formulas correspond to types, proofs correspond to terms, provability corresponds to inhabitation, proof normalization corresponds to term reduction, etc.But there is more to the isomorphism than this. For instance, it is an old idea---due to Brouwer, Kolmogorov, and Heyting---that a constructive proof of an implication is a procedure that transformsproofs of the antecedent into proofs of the succedent; the Curry-Howard isomorphism gives syntactic representations of such procedures. The Curry-Howard isomorphism also provides theoretical foundations for many modern proof-assistant systems (e.g. Coq).This book give an introduction to parts of proof theory and related aspects of type theory relevant for the Curry-Howard isomorphism. It can serve as an introduction to any or both of typed lambda-calculus and intuitionistic logic.Key features- The Curry-Howard Isomorphism treated as common theme- Reader-friendly introduction to two complementary subjects: Lambda-calculus and constructive logics- Thorough study of the connection between calculi and logics- Elaborate study of classical logics and control operators- Account of dialogue games for classical and intuitionistic logic- Theoretical foundations of computer-assisted reasoning· The Curry-Howard Isomorphism treated as the common theme.· Reader-friendly introduction to two complementary subjects: lambda-calculus and constructive logics · Thorough study of the connection between calculi and logics.· Elaborate study of classical logics and control operators.· Account of dialogue games for classical and intuitionistic logic.· Theoretical foundations of computer-assisted reasoning |
| dartmouth mathematical data science: Mathematical Theories of Machine Learning - Theory and Applications Bin Shi, S. S. Iyengar, 2019-06-12 This book studies mathematical theories of machine learning. The first part of the book explores the optimality and adaptivity of choosing step sizes of gradient descent for escaping strict saddle points in non-convex optimization problems. In the second part, the authors propose algorithms to find local minima in nonconvex optimization and to obtain global minima in some degree from the Newton Second Law without friction. In the third part, the authors study the problem of subspace clustering with noisy and missing data, which is a problem well-motivated by practical applications data subject to stochastic Gaussian noise and/or incomplete data with uniformly missing entries. In the last part, the authors introduce an novel VAR model with Elastic-Net regularization and its equivalent Bayesian model allowing for both a stable sparsity and a group selection. |
| dartmouth mathematical data science: Developing Quantitative Literacy Skills in History and the Social Sciences Kathleen W. Craver, 2014-07-22 History and social sciences educators have been charged with ensuring that our students are quantitatively literate. Being able to integrate research data in the form of graphs, charts, and tables and deconstruct quantitative evidence to address questions and solve problems is no longer the domain of mathematicians. Being quantitatively literate is considered an educational imperative in a data-drenched world that holds so many employment challenges. The internet contains a treasure trove of valid and reliable sources of quantitative data that history and social sciences teachers can easily use to satisfy the quantitative literacy requirements of the National Common Core Standards. This book features 85 interesting and exciting multi-century and multicultural web sites that are accompanied by numerical critical thinking questions and activities. Teachers can pose the questions to their entire class or individually assign them. It also contains lists of best practices and examples for interpreting, visualizing, and displaying quantitative data. History and social sciences educators will find this book an indispensable tool for incorporating numerical literacy skills into their class activities and assignments. |
| dartmouth mathematical data science: Illustrating Mathematics Diana Davis, 2020-10-16 This book is for anyone who wishes to illustrate their mathematical ideas, which in our experience means everyone. It is organized by material, rather than by subject area, and purposefully emphasizes the process of creating things, including discussions of failures that occurred along the way. As a result, the reader can learn from the experiences of those who came before, and will be inspired to create their own illustrations. Topics illustrated within include prime numbers, fractals, the Klein bottle, Borromean rings, tilings, space-filling curves, knot theory, billiards, complex dynamics, algebraic surfaces, groups and prime ideals, the Riemann zeta function, quadratic fields, hyperbolic space, and hyperbolic 3-manifolds. Everyone who opens this book should find a type of mathematics with which they identify. Each contributor explains the mathematics behind their illustration at an accessible level, so that all readers can appreciate the beauty of both the object itself and the mathematics behind it. |
| dartmouth mathematical data science: Introduction To Algorithms Thomas H Cormen, Charles E Leiserson, Ronald L Rivest, Clifford Stein, 2001 An extensively revised edition of a mathematically rigorous yet accessible introduction to algorithms. |
| dartmouth mathematical data science: International Congress and Workshop on Industrial AI 2021 Ramin Karim, Alireza Ahmadi, Iman Soleimanmeigouni, Ravdeep Kour, Raj Rao, 2022-02-07 This proceedings of the International Congress and Workshop on Industrial AI 2021 encompasses and integrates the themes and topics of three conferences, eMaintenance, Condition Monitoring and Diagnostic Engineering management (COMADEM), and Advances in Reliability, Maintainability and Supportability (ARMS) into a single resource. The 21st century is witnessing the emerging extensive applications of Artificial Intelligence (AI) and Information Technologies (IT) in industry. Industrial Artificial Intelligence (IAI) integrates IT with Operational Technologies (OT) and Engineering Technologies (ET) to achieve operational excellence through enhanced analytics in operation and maintenance of industrial assets. This volume provides insight into opportunities and challenges caused by the implementation of AI in industries apart from future developments with special reference to operation and maintenance of industrial assets. Industry practitioners in the maintenance field as well as academics seeking applied research in maintenance will find this text useful. |
| dartmouth mathematical data science: Serial Holdings CDC Library (U.S.), 1979 |
| dartmouth mathematical data science: Naked Statistics: Stripping the Dread from the Data Charles Wheelan, 2013-01-07 A New York Times bestseller Brilliant, funny…the best math teacher you never had. —San Francisco Chronicle Once considered tedious, the field of statistics is rapidly evolving into a discipline Hal Varian, chief economist at Google, has actually called sexy. From batting averages and political polls to game shows and medical research, the real-world application of statistics continues to grow by leaps and bounds. How can we catch schools that cheat on standardized tests? How does Netflix know which movies you’ll like? What is causing the rising incidence of autism? As best-selling author Charles Wheelan shows us in Naked Statistics, the right data and a few well-chosen statistical tools can help us answer these questions and more. For those who slept through Stats 101, this book is a lifesaver. Wheelan strips away the arcane and technical details and focuses on the underlying intuition that drives statistical analysis. He clarifies key concepts such as inference, correlation, and regression analysis, reveals how biased or careless parties can manipulate or misrepresent data, and shows us how brilliant and creative researchers are exploiting the valuable data from natural experiments to tackle thorny questions. And in Wheelan’s trademark style, there’s not a dull page in sight. You’ll encounter clever Schlitz Beer marketers leveraging basic probability, an International Sausage Festival illuminating the tenets of the central limit theorem, and a head-scratching choice from the famous game show Let’s Make a Deal—and you’ll come away with insights each time. With the wit, accessibility, and sheer fun that turned Naked Economics into a bestseller, Wheelan defies the odds yet again by bringing another essential, formerly unglamorous discipline to life. |
| dartmouth mathematical data science: Data-ism Steve Lohr, 2015-03-10 By one estimate, 90 percent of all of the data in history was created in the last two years. In 2014, International Data Corporation calculated the data universe at 4.4 zettabytes, or 4.4 trillion gigabytes. That much information, in volume, could fill enough slender iPad Air tablets to create a stack two-thirds of the way to the moon. Now, that's Big Data. Coal, iron ore, and oil were the key productive assets that fueled the Industrial Revolution. The vital raw material of today's information economy is data. In Data-ism, New York Times reporter Steve Lohr explains how big-data technology is ushering in a revolution in proportions that promise to be the basis of the next wave of efficiency and innovation across the economy. But more is at work here than technology. Big data is also the vehicle for a point of view, or philosophy, about how decisions will be—and perhaps should be—made in the future. Lohr investigates the benefits of data while also examining its dark side. Data-ism is about this next phase, in which vast Internet-scale data sets are used for discovery and prediction in virtually every field. It shows how this new revolution will change decision making—by relying more on data and analysis, and less on intuition and experience—and transform the nature of leadership and management. Focusing on young entrepreneurs at the forefront of data science as well as on giant companies such as IBM that are making big bets on data science for the future of their businesses, Data-ism is a field guide to what is ahead, explaining how individuals and institutions will need to exploit, protect, and manage data to stay competitive in the coming years. With rich examples of how the rise of big data is affecting everyday life, Data-ism also raises provocative questions about policy and practice that have wide implications for everyone. The age of data-ism is here. But are we ready to handle its consequences, good and bad? |
| dartmouth mathematical data science: Advanced Statistics with Applications in R Eugene Demidenko, 2019-11-12 Advanced Statistics with Applications in R fills the gap between several excellent theoretical statistics textbooks and many applied statistics books where teaching reduces to using existing packages. This book looks at what is under the hood. Many statistics issues including the recent crisis with p-value are caused by misunderstanding of statistical concepts due to poor theoretical background of practitioners and applied statisticians. This book is the product of a forty-year experience in teaching of probability and statistics and their applications for solving real-life problems. There are more than 442 examples in the book: basically every probability or statistics concept is illustrated with an example accompanied with an R code. Many examples, such as Who said π? What team is better? The fall of the Roman empire, James Bond chase problem, Black Friday shopping, Free fall equation: Aristotle or Galilei, and many others are intriguing. These examples cover biostatistics, finance, physics and engineering, text and image analysis, epidemiology, spatial statistics, sociology, etc. Advanced Statistics with Applications in R teaches students to use theory for solving real-life problems through computations: there are about 500 R codes and 100 datasets. These data can be freely downloaded from the author's website dartmouth.edu/~eugened. This book is suitable as a text for senior undergraduate students with major in statistics or data science or graduate students. Many researchers who apply statistics on the regular basis find explanation of many fundamental concepts from the theoretical perspective illustrated by concrete real-world applications. |
| dartmouth mathematical data science: Probability Models , 2024-10-24 Probability Models, Volume 51 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters on Stein's methods, Probabilities and thermodynamics third law, Random Matrix Theory, General tools for understanding fluctuations of random variables, An approximation scheme to compute the Fisher-Rao distance between multivariate normal distributions, Probability Models Applied to Reliability and Availability Engineering, Backward stochastic differential equation– Stochastic optimization theory and viscous solution of HJB equation, and much more.Additional chapters cover Probability Models in Machine Learning, The recursive stochastic algorithm, randomized urn models and response-adaptive randomization in clinical trials, Random matrix theory: local laws and applications, KOO methods and their high-dimensional consistencies in some multivariate models, Fourteen Lectures on Inference for Stochastic Processes, and A multivariate cumulative damage model and some applications. - Provides the latest information on probability models - Offers outstanding and original reviews on a range of probability models research topics - Serves as an indispensable reference for researchers and students alike |
| dartmouth mathematical data science: Tools of American Mathematics Teaching, 1800–2000 Peggy Aldrich Kidwell, Amy Ackerberg-Hastings, David Lindsay Roberts, 2008-08-11 From the blackboard to the graphing calculator, the tools developed to teach mathematics in America have a rich history shaped by educational reform, technological innovation, and spirited entrepreneurship. In Tools of American Mathematics Teaching, 1800–2000, Peggy Aldrich Kidwell, Amy Ackerberg-Hastings, and David Lindsay Roberts present the first systematic historical study of the objects used in the American mathematics classroom. They discuss broad tools of presentation and pedagogy (not only blackboards and textbooks, but early twentieth-century standardized tests, teaching machines, and the overhead projector), tools for calculation, and tools for representation and measurement. Engaging and accessible, this volume tells the stories of how specific objects such as protractors, geometric models, slide rules, electronic calculators, and computers came to be used in classrooms, and how some disappeared. |
| dartmouth mathematical data science: Management Science Powell, Kenneth R. Baker, 2013-10-07 Now in its fourth edition, Powell and Baker’s Management Science: The Art of Modeling with Spreadsheets, 4th Edition provides students and business analysts with the technical knowledge and skill needed to develop real expertise in business modeling. In this book, the authors cover spreadsheet engineering, management science, and the modeling craft. Management Science, 4th Edition provides students and business analysts with the technical knowledge and skill needed to develop real expertise in business modeling. The authors cover spreadsheet engineering, management science, and the modeling craft. The text is designed to improve modeling efficiency and modeling effectiveness by focusing on the most important tasks and tools. |
| dartmouth mathematical data science: R Programming for Data Science Dr. Sanjoy Mitra , Dr. Parijata Majumdar , 2024-09-10 Introduction to R Programming for Data Science is a comprehensive guide designed for beginners and intermediate learners interested in using R for data science. The book covers the fundamentals of R programming, including data manipulation, visualization, and statistical analysis. It provides practical examples and exercises to help readers apply R in real-world data science projects. Through step-by-step instructions, the book emphasizes developing the skills necessary to clean, analyze, and visualize data using R, making it an essential resource for anyone aiming to harness the power of R in data science. |
| dartmouth mathematical data science: Discrete Mathematics for Computer Scientists Clifford Stein, Robert L. Drysdale, Kenneth P. Bogart, 2011 Stein/Drysdale/Bogart's Discrete Mathematics for Computer Scientists is ideal for computer science students taking the discrete math course. Written specifically for computer science students, this unique textbook directly addresses their needs by providing a foundation in discrete math while using motivating, relevant CS applications. This text takes an active-learning approach where activities are presented as exercises and the material is then fleshed out through explanations and extensions of the exercises. |
为什么Dartmouth College作为藤校，世界排名在200位之后？ - 知乎
为什么Dartmouth College作为藤校，世界排名在200位之后？ Dartmouth作为Ivy League之一，每年福布斯榜单，U.S news等排行榜都能到前10，前20，但是为什么上海交大世界大学学术排 …
RPA是什么技术？ - 知乎
注释：AI（Artificial Intelligence），人工智能：1956年于Dartmouth学会上提出，一种旨在以类似人类反应的方式对刺激做出反应并从中学习的技术，是对人的意识、思维的信息过程的模拟。 …
为什么莱斯大学（Rice University）的美国排名和世界排名相差如此 …
所有北美小型学校都有这种问题，莱斯， 范德堡 ， 罗彻斯特 这几个学校都是这样，因为世界排名里面很多是看整个学校的科研产出的，对小学校天然不利，而 US news 更侧重本科教学质 …
常春藤、25所新常春藤、公立常春藤都是哪些学校？ - 知乎
知乎，中文互联网高质量的问答社区和创作者聚集的原创内容平台，于 2011 年 1 月正式上线，以「让人们更好的分享知识、经验和见解，找到自己的解答」为品牌使命。知乎凭借认真、专业 …
为什么Dartmouth College作为藤校，世界排名在200位之后？ - 知乎
为什么Dartmouth College作为藤校，世界排名在200位之后？ Dartmouth作为Ivy League之一，每年福布斯榜单，U.S news等排行榜都能到前10，前20，但是为什么上海交大世界大学学术排 …
RPA是什么技术？ - 知乎
注释：AI（Artificial Intelligence），人工智能：1956年于Dartmouth学会上提出，一种旨在以类似人类反应的方式对刺激做出反应并从中学习的技术，是对人的意识、思维的信息过程的模拟。 …
为什么莱斯大学（Rice University）的美国排名和世界排名相差如此 …
所有北美小型学校都有这种问题，莱斯， 范德堡 ， 罗彻斯特 这几个学校都是这样，因为世界排名里面很多是看整个学校的科研产出的，对小学校天然不利，而 US news 更侧重本科教学质 …
常春藤、25所新常春藤、公立常春藤都是哪些学校？ - 知乎
知乎，中文互联网高质量的问答社区和创作者聚集的原创内容平台，于 2011 年 1 月正式上线，以「让人们更好的分享知识、经验和见解，找到自己的解答」为品牌使命。知乎凭借认真、专业 …
