This book is a well-organized text with carefully constructed examples, a full quota of exercises with solutions, and an emphasis that is algebraic rather than geometric. The book is Sage-enabled with approximately 90 examples of Sage code spread throughout. The book sections can be loaded into Sage as worksheets so that the code can be evaluated immediately; however, it is not necessary to use Sage in order to make use of this textbook.
The HTML version is a fully featured electronic text with cross references that expand in place. It works well on an iPad or any device with Internet access. The Sage examples are executed by the Sage single cell server over the Internet, and students can experiment with their own examples as they read without needing to install Sage or log into a Sage server. Most students will prefer this version over both the pdf and print versions.
As stated in the preface of the book, the dual aims are “to teach the fundamental concepts and techniques of matrix algebra and abstract vector spaces, and to teach the techniques associated with understanding the definitions and theorems forming a coherent area of mathematics.”
Verion 3.50 (spring 2016) is archived here. Online and Hardcover versions are available via the author's website.
This book, which presupposes familiarity only with the most elementary concepts of arithmetic (divisibility properties, greatest common divisor, etc.), is an expanded version of a series of lectures for graduate students on elementary number theory. Topics include: Compositions and Partitions; Arithmetic Functions; Distribution of Primes; Irrational Numbers; Congruences; Diophantine Equations; Combinatorial Number Theory; and Geometry of Numbers. Three sections of problems (which include exercises as well as unsolved problems) complete the text.
The Trillia Group accepts donations from people who are otherwise licensed to use An Introduction to the Theory of Numbers free of charge. Donations of as little as US$2 or €2 help us continue to produce and distribute quality online texts.
Presents a whole picture of China's technology progress pertain to different NEVs Summarizes the operation characteristics and charging characteristics of vehicles in different scenes in China Provides comprehensive, authoritative and systematic data of NEVs This book is open access, which means that you have free and unlimited access
Presents a whole picture of China's technology progress pertain to different NEVs Summarizes the operation characteristics and charging characteristics of vehicles in different scenes in China Provides comprehensive, authoritative and systematic data of NEVs This book is open access, which means that you have free and unlimited access
This book helps the student complete the transition from purely manipulative to rigorous mathematics. The clear exposition covers many topics that are assumed by later courses but are often not covered with any depth or organization: basic set theory, induction, quantifiers, functions and relations, equivalence relations, properties of the real numbers (including consequences of the completeness axiom), fields, and basic properties of n-dimensional Euclidean spaces.
The many exercises and optional topics (isomorphism of complete ordered fields, construction of the real numbers through Dedekind cuts, introduction to normed linear spaces, etc.) allow the instructor to adapt this book to many environments and levels of students. Extensive hypertextual cross-references and hyperlinked indexes of terms and notation add truly interactive elements to the text.
There is a list of errata that records changes made to the text since the version of October 29, 2001. Other formats available at trillia.com
On 7 March 2014 at 16:42,1 Malaysian Airlines flight MH370 departed from Kuala Lumpur (KL) International Airport bound for Beijing. There was a total of 239 persons on board (227 passengers and 12 crew). The aircraft lost contact with Air Traffic Control (ATC) during a transition between Malaysian and Vietnamese airspace. Over the following days, an intensive air and sea rescue search was made around the last reported position of the aircraft in the Gulf of Thailand without success. It then became clear that satellite communication messages between the aircraft and one member of Inmarsat’s constellation of geosynchronous satellites were crucial to defining the search zone for the aircraft.
Inmarsat conducted a rapid and innovative analysis of the data which placed the aircraft in the Australian search and rescue zone on an arc in the Southern part of the Indian Ocean. On 17 March 2014, the Australian Maritime Safety Authority took responsibility of the search and rescue operation. Subsequently the Joint Agency Coordination Centre (JACC) was established on 30 March 2014 to coordinate the Australian Government’s support for the search and over the following weeks an intensive aerial and surface search was conducted by an international team.
In this book we detail the statistical approach adopted by the DST Group team to analyse the available data and produce a probability density function (pdf) of the accident aircraft’s final location. Being statistical in nature, this book seeks to identify aircraft paths that are most likely, given models which incorporate sensor measurements, commonly observed commercial aircraft motion, and air transport safety investigator and manufacturer expert advice and assessments. The goal is not to identify the complete and exhaustive set of all possible aircraft paths, but rather the subset of those trajectories that are most probable. The area covered by the set of end-points of all possible paths is prohibitively large and the overwhelming majority of this area contains vanishingly small probability. In determining how to allocate finite search resources, priority is directed to the area containing the highest probability trajectories. The proposed method incorporates a rich variety of possible paths, and calculates a probability distribution based on the well-established, rigorous Bayesian toolkit, which automatically trades the complexity of the model against the match to the observed measurements.
On 7 March 2014 at 16:42,1 Malaysian Airlines flight MH370 departed from Kuala Lumpur (KL) International Airport bound for Beijing. There was a total of 239 persons on board (227 passengers and 12 crew). The aircraft lost contact with Air Traffic Control (ATC) during a transition between Malaysian and Vietnamese airspace. Over the following days, an intensive air and sea rescue search was made around the last reported position of the aircraft in the Gulf of Thailand without success. It then became clear that satellite communication messages between the aircraft and one member of Inmarsat’s constellation of geosynchronous satellites were crucial to defining the search zone for the aircraft.
Inmarsat conducted a rapid and innovative analysis of the data which placed the aircraft in the Australian search and rescue zone on an arc in the Southern part of the Indian Ocean. On 17 March 2014, the Australian Maritime Safety Authority took responsibility of the search and rescue operation. Subsequently the Joint Agency Coordination Centre (JACC) was established on 30 March 2014 to coordinate the Australian Government’s support for the search and over the following weeks an intensive aerial and surface search was conducted by an international team.
In this book we detail the statistical approach adopted by the DST Group team to analyse the available data and produce a probability density function (pdf) of the accident aircraft’s final location. Being statistical in nature, this book seeks to identify aircraft paths that are most likely, given models which incorporate sensor measurements, commonly observed commercial aircraft motion, and air transport safety investigator and manufacturer expert advice and assessments. The goal is not to identify the complete and exhaustive set of all possible aircraft paths, but rather the subset of those trajectories that are most probable. The area covered by the set of end-points of all possible paths is prohibitively large and the overwhelming majority of this area contains vanishingly small probability. In determining how to allocate finite search resources, priority is directed to the area containing the highest probability trajectories. The proposed method incorporates a rich variety of possible paths, and calculates a probability distribution based on the well-established, rigorous Bayesian toolkit, which automatically trades the complexity of the model against the match to the observed measurements.
This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.
Print editions available via the author's website.
Derivatives tell how a function is changing. Integrals construct the function from its changes. Calculus is the starting point for science and engineering and economics and understanding.
Published in 1991 by Wellesley-Cambridge Press, (hard copies are available for purchase) the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. There is also an online Instructor's Manual and a student Study Guide at MIT Open Courseware.
Category theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within mathematics. This book shows that category theory can be useful outside of mathematics as a rigorous, flexible, and coherent modeling language throughout the sciences. Information is inherently dynamic; the same ideas can be organized and reorganized in countless ways, and the ability to translate between such organizational structures is becoming increasingly important in the sciences. Category theory offers a unifying framework for information modeling that can facilitate the translation of knowledge between disciplines.
Written in an engaging and straightforward style, and assuming little background in mathematics, the book is rigorous but accessible to non-mathematicians. Using databases as an entry to category theory, it begins with sets and functions, then introduces the reader to notions that are fundamental in mathematics: monoids, groups, orders, and graphs—categories in disguise. After explaining the “big three” concepts of category theory—categories, functors, and natural transformations—the book covers other topics, including limits, colimits, functor categories, sheaves, monads, and operads. The book explains category theory by examples and exercises rather than focusing on theorems and proofs. It includes more than 300 exercises, with solutions.
Category Theory for the Sciences is intended to create a bridge between the vast array of mathematical concepts used by mathematicians and the models and frameworks of such scientific disciplines as computation, neuroscience, and physics.
Print and online edition available from MIT Press.
In the light of better and more detailed administrative databases, this open access book provides statistical tools for evaluating the effects of public policies advocated by governments and public institutions. Experts from academia, national statistics offices and various research centers present modern econometric methods for an efficient data-driven policy evaluation and monitoring, assess the causal effects of policy measures and report on best practices of successful data management and usage. Topics include data confidentiality, data linkage, and national practices in policy areas such as public health, education and employment. It offers scholars as well as practitioners from public administrations, consultancy firms and nongovernmental organizations insights into counterfactual impact evaluation methods and the potential of data-based policy and program evaluation.
In the light of better and more detailed administrative databases, this open access book provides statistical tools for evaluating the effects of public policies advocated by governments and public institutions. Experts from academia, national statistics offices and various research centers present modern econometric methods for an efficient data-driven policy evaluation and monitoring, assess the causal effects of policy measures and report on best practices of successful data management and usage. Topics include data confidentiality, data linkage, and national practices in policy areas such as public health, education and employment. It offers scholars as well as practitioners from public administrations, consultancy firms and nongovernmental organizations insights into counterfactual impact evaluation methods and the potential of data-based policy and program evaluation.
Dieses Open Access Buch befasst sich mit praktischen Fragestellungen datenreicher internationaler Verbund-Forschung. Die datenreiche Medizin spielt in Diagnostik und Therapie eine immer größere Rolle – gerade angesichts immer leistungsfähigerer algorithmischer Mustererkennung. Mithilfe wachsender Datenbestände sind diese Algorithmen zunehmend in der Lage, Krankheitssymptome zu erkennen, diese mit anderen Daten in Beziehung zu setzen und so entweder bei der Suche nach Krankheitsursachen zu helfen oder Therapien zu optimieren. Vor dem Hintergrund dieser Entwicklungen vereint der Sammelband multidisziplinäre Perspektiven auf die datengetriebene medizinische Forschung mit besonderem Blick auf die Frage der Einwilligung in die Sekundärnutzung medizinischer Daten. Dabei werden zum einen ethische Überlegungen in den Bereichen Patientenautonomie und -wohlergehen, Privatheit und Datensicherheit, sowie Verantwortungsdiffusion aufgeworfen, als auch konkrete rechtliche Fragen hinsichtlich der DSGVO-Konformität erörtert. Sozialwissenschaftliche Studien zur Art und Form der Einwilligung sowie dem Patientenverhalten runden den Band ab.
Dieses Open Access Buch befasst sich mit praktischen Fragestellungen datenreicher internationaler Verbund-Forschung. Die datenreiche Medizin spielt in Diagnostik und Therapie eine immer größere Rolle – gerade angesichts immer leistungsfähigerer algorithmischer Mustererkennung. Mithilfe wachsender Datenbestände sind diese Algorithmen zunehmend in der Lage, Krankheitssymptome zu erkennen, diese mit anderen Daten in Beziehung zu setzen und so entweder bei der Suche nach Krankheitsursachen zu helfen oder Therapien zu optimieren. Vor dem Hintergrund dieser Entwicklungen vereint der Sammelband multidisziplinäre Perspektiven auf die datengetriebene medizinische Forschung mit besonderem Blick auf die Frage der Einwilligung in die Sekundärnutzung medizinischer Daten. Dabei werden zum einen ethische Überlegungen in den Bereichen Patientenautonomie und -wohlergehen, Privatheit und Datensicherheit, sowie Verantwortungsdiffusion aufgeworfen, als auch konkrete rechtliche Fragen hinsichtlich der DSGVO-Konformität erörtert. Sozialwissenschaftliche Studien zur Art und Form der Einwilligung sowie dem Patientenverhalten runden den Band ab.
Arnold Scholz (1906-1941) war einer der vielversprechendsten jungen Zahlentheoretiker in den 1930er Jahren, einer der besten Kenner der Klassenkörpertheorie. Als Doktorand von Issai Schur war er auch mit gruppentheoretischen Methoden vertraut. Da er während des Dritten Reichs als politisch nicht zuverlässig galt (er war ein enger Freund des ebenfalls „suspekten“ Ernst Zermelo), konnte er keine sichere Stelle finden. Trotzdem gelang es ihm, eine Reihe wichtiger Resultate zu erhalten, u.a. bei der Realisierung von Galoisgruppen und in der Theorie der Normenreste. Der zu einem klaren Verständnis dieser Ergebnisse notwendige kohomologische Apparat war damals noch nicht entwickelt, und daher konnten zunächst nur Wenige mit den Scholzschen Ideen etwas anfangen. Eine Reihe seiner Resultate wurden später wiederentdeckt. Schafarewitsch konnte mit Hilfe der Scholzschen Methoden zeigen, dass jede endliche auflösbare Gruppe als Galoisgruppe einer Erweiterung der rationalen Zahlen vorkommt. Das vorliegende Buch, das als erster Schritt zu einem besseren Verständnis des Werks von Arnold Scholz anzusehen ist, enthält die Korrespondenz zwischen Arnold Scholz und Helmut Hasse einerseits und Olga Taussky andererseits, soweit sie in den Archiven der Universität Göttingen und des California Institute of Technology in Pasadena erhalten sind. Auch die Korrespondenz zwischen Hasse und Taussky bis zum frühen Tod von Arnold Scholz wurde aufgenommen.
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