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Theorems Of The 21st Century

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Theorems Of The 21st Century

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Author : Bogdan Grechuk
language : en
Publisher: Springer
Release Date : 2019-06-15

Theorems Of The 21st Century written by Bogdan Grechuk and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-15 with Mathematics categories.

This book consists of short descriptions of 106 mathematical theorems, which belong to the great achievements of 21st century mathematics but require relatively little mathematical background to understand their formulation and appreciate their importance. The selected theorems of this volume, chosen from the famous Annals of Mathematics journal, cover a broad range of topics from across mathematics. Each theorem description is essentially self-contained, can be read independently of the others, and requires as little preliminary knowledge as possible. Although the sections often start with an informal discussion and toy examples, all the necessary definitions are included and each description culminates in the precise formulation of the corresponding theorem. Filling the gap between surveys written for mathematicians and popular mathematics, this book is intended for readers with a keen interest in contemporary mathematics.

Theorems Of The 21st Century

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Author : Bogdan Grechuk
language : en
Publisher:
Release Date : 2019

Theorems Of The 21st Century written by Bogdan Grechuk and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Induction (Mathematics) categories.

Landscape Of 21st Century Mathematics

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Author : Bogdan Grechuk
language : en
Publisher: Springer Nature
Release Date : 2021-09-21

Landscape Of 21st Century Mathematics written by Bogdan Grechuk and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-21 with Mathematics categories.

Landscape of 21st Century Mathematics offers a detailed cross section of contemporary mathematics. Important results of the 21st century are motivated and formulated, providing an overview of recent progress in the discipline. The theorems presented in this book have been selected among recent achievements whose statements can be fully appreciated without extensive background. Grouped by subject, the selected theorems represent all major areas of mathematics: number theory, combinatorics, analysis, algebra, geometry and topology, probability and statistics, algorithms and complexity, and logic and set theory. The presentation is self-contained with context, background and necessary definitions provided for each theorem, all without sacrificing mathematical rigour. Where feasible, brief indications of the main ideas of a proof are given. Rigorous yet accessible, this book presents an array of breathtaking recent advances in mathematics. It is written for everyone with a background in mathematics, from inquisitive university students to mathematicians curious about recent achievements in areas beyond their own.

Model And Mathematics From The 19th To The 21st Century

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Author : Michael Friedman
language : en
Publisher: Springer Nature
Release Date : 2022-08-08

Model And Mathematics From The 19th To The 21st Century written by Michael Friedman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-08 with Mathematics categories.

This open access book collects the historical and medial perspectives of a systematic and epistemological analysis of the complicated, multifaceted relationship between model and mathematics, ranging from, for example, the physical mathematical models of the 19th century to the simulation and digital modelling of the 21st century. The aim of this anthology is to showcase the status of the mathematical model between abstraction and realization, presentation and representation, what is modeled and what models. This book is open access under a CC BY 4.0 license.

Theorems On The Prevalence Threshold And The Geometry Of Screening Curves

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Author : Jacques Balayla
language : en
Publisher: Springer Nature
Release Date : 2024-11-09

Theorems On The Prevalence Threshold And The Geometry Of Screening Curves written by Jacques Balayla and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-09 with Medical categories.

In Theorems on the Prevalence Threshold and the Geometry of Screening Curves, the author explores the mathematical underpinnings of screening and diagnostic testing, offering a unique and novel perspective which employs classical differential geometry and Bayesian theory to elucidate critical aspects of clinical decision-making. Taking the reader on a mathematical journey which bridges these seemingly unrelated worlds, the author presents a quantifiable framework on clinical judgement by introducing the “prevalence threshold” – a novel statistical parameter derived from Bayesian principles by means of the study of the geometry of screening curves. As the prevalence threshold demarcates the pretest probability level beyond which additional information ceases to significantly enhance the yield and reliability of a clinical assessment, it may serve as a benchmark for confidence in clinical decision-making. Given the theorems herein described, readers will find comprehensive analyses and insightful explorations of how these geometric concepts apply to real-world diagnostic scenarios, allowing the clinician to navigate clinical care more effectively at both the individual and public health levels.

A Mathematical Space Odyssey

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Author : Claudi Alsina
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-12-31

A Mathematical Space Odyssey written by Claudi Alsina and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-31 with Mathematics categories.

Solid geometry is the traditional name for what we call today the geometry of three-dimensional Euclidean space. This book presents techniques for proving a variety of geometric results in three dimensions. Special attention is given to prisms, pyramids, platonic solids, cones, cylinders and spheres, as well as many new and classical results. A chapter is devoted to each of the following basic techniques for exploring space and proving theorems: enumeration, representation, dissection, plane sections, intersection, iteration, motion, projection, and folding and unfolding. The book includes a selection of Challenges for each chapter with solutions, references and a complete index. The text is aimed at secondary school and college and university teachers as an introduction to solid geometry, as a supplement in problem solving sessions, as enrichment material in a course on proofs and mathematical reasoning, or in a mathematics course for liberal arts students.--

A Conversation On Professional Norms In Mathematics

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Author : Pamela E. Harris
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-10-19

A Conversation On Professional Norms In Mathematics written by Pamela E. Harris and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-19 with Education categories.

The articles in this volume grew out of a 2019 workshop, held at Johns Hopkins University, that was inspired by a belief that when mathematicians take time to reflect on the social forces involved in the production of mathematics, actionable insights result. Topics range from mechanisms that lead to an inclusion-exclusion dichotomy within mathematics to common pitfalls and better alternatives to how mathematicians approach teaching, mentoring and communicating mathematical ideas. This collection will be of interest to students, faculty and administrators wishing to gain a snapshot of the current state of professional norms within mathematics and possible steps toward improvements.

Perspectives On The Teaching Of Geometry For The 21st Century

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Author : C. Mammana
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Perspectives On The Teaching Of Geometry For The 21st Century written by C. Mammana and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Education categories.

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.

Automated Theorem Proving

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Author : Monty Newborn
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Automated Theorem Proving written by Monty Newborn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

As the 21st century begins, the power of our magical new tool and partner, the computer, is increasing at an astonishing rate. Computers that perform billions of operations per second are now commonplace. Multiprocessors with thousands of little computers - relatively little! -can now carry out parallel computations and solve problems in seconds that only a few years ago took days or months. Chess-playing programs are on an even footing with the world's best players. IBM's Deep Blue defeated world champion Garry Kasparov in a match several years ago. Increasingly computers are expected to be more intelligent, to reason, to be able to draw conclusions from given facts, or abstractly, to prove theorems-the subject of this book. Specifically, this book is about two theorem-proving programs, THEO and HERBY. The first four chapters contain introductory material about automated theorem proving and the two programs. This includes material on the language used to express theorems, predicate calculus, and the rules of inference. This also includes a description of a third program included with this package, called COMPILE. As described in Chapter 3, COMPILE transforms predicate calculus expressions into clause form as required by HERBY and THEO. Chapter 5 presents the theoretical foundations of seman tic tree theorem proving as performed by HERBY. Chapter 6 presents the theoretical foundations of resolution-refutation theorem proving as per formed by THEO. Chapters 7 and 8 describe HERBY and how to use it.

Novikov Conjectures Index Theorems And Rigidity Volume 1

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Author : Steven C. Ferry
language : en
Publisher: Cambridge University Press
Release Date : 1995-11-23

Novikov Conjectures Index Theorems And Rigidity Volume 1 written by Steven C. Ferry and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-11-23 with Mathematics categories.

These volumes are the outgrowth of a conference held at the Mathematisches Forschungsinstitut Oberwolfach (Germany) on the subject of 'Novikov Conjectures, Index Theorems and Rigidity'.

Theorems Of The 21st Century

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