Dover Publications, 2012. — 416 pages. (Dover Books on Mathematics) ISBN: 0486498514 This richly detailed overview surveys the evolution of geometrical ideas and the development of the concepts of modern geometry from ancient times to the present. Topics include projective, Euclidean, and non-Euclidean geometry as well as the role of geometry in Newtonian physics, calculus, and...
Dover Publications, 2016. — 224 p. — ISBN 978-0-486-80920-5, 0-486-80920-X. This concise classic presents advanced undergraduates and graduate students in mathematics with an overview of geometric algebra. The text originated with lecture notes from a New York University course taught by Emil Artin, one of the preeminent mathematicians of the twentieth century. The Bulletin of...
Springer, 2021. — 466 p. — ISBN 978-3-030-77956-6. Machine learning and artificial intelligence increasingly use methodological tools rooted in statistical physics. Conversely, limitations and pitfalls encountered in AI question the very foundations of statistical physics. This interplay between AI and statistical physics has been attested since the birth of AI, and principles...
W. H. Freeman and Company, San Francisco, USA, 2017. — 347 p. — ISBN: 0486639622. "On the required reading list for all thoughtful students who wish to see mathematics from the 'higher standpoint.' " - American Mathematical Monthly Elegant and original, this exposition explores the foundations and development of both Euclidean and non-Euclidean geometry, particularly the...
Dover Publications, 2018. — 464 р. — ISBN: 978-0486828091. In Part One of this comprehensive and frequently cited treatment, the authors develop Euclidean and Bolyai-Lobachevskian geometry on the basis of an axiom system due, in principle, to the work of David Hilbert. Part Two develops projective geometry in much the same way. An Introduction provides background on topological...
Springer International Publishing AG, 2017. — 185 p. — (Springer INdAM Series 26). — ISBN: 3319731254. The book collects the most relevant outcomes from the INdAM Workshop "Geometric Function Theory in Higher Dimension" held in Cortona on September 5-9, 2016. The Workshop was mainly devoted to discussions of basic open problems in the area, and this volume follows the same...
3rd Edition. — Chichester, UK: Wiley, 2014. — 400 p. — ISBN: 978-1-119-94239-9. The seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions. Interest in fractal geometry continues to grow rapidly, both as a subject that is fascinating in its own right and as a concept...
Springer, 2023. — 277 p. This book focuses on the study of the volume of vector fields on Riemannian manifolds. Providing a thorough overview of research on vector fields defining minimal submanifolds, and on the existence and characterization of volume minimizers, it includes proofs of the most significant results obtained since the subject’s introduction in 1986. Aiming to...
Springer, 2019. — 569 p. — (Springer Monographs in Mathematics). — ISBN: 303003349X. Singular algebraic curves have been in the focus of study in algebraic geometry from the very beginning, and till now remain a subject of an active research related to many modern developments in algebraic geometry, symplectic geometry, and tropical geometry. The monograph suggests a unified...
Springer, 2023. — 348 p. — (Springer Undergraduate Mathematics Series). — ISBN 978-3-031-25408-6. Многообразия, векторные поля и дифференциальные формы: введение в дифференциальную геометрию This textbook serves as an introduction to modern differential geometry at a level accessible to advanced undergraduate and master's students. It places special emphasis on motivation and...
Springer, 2012. — 800 p. — (Springer Monographs in Mathematics). — ISBN: 0387847936. This self-contained text is an excellent introduction to Lie groups and their actions on manifolds. The authors start with an elementary discussion of matrix groups, followed by chapters devoted to the basic structure and representation theory of finite dimensinal Lie algebras. They then turn...
Springer, 2021. — 281 p. — (Springer Proceedings in Mathematics & Statistics, 349). — ISBN 978-3-030-68540-9. This book collects original peer-reviewed contributions to the conferences organised by the international research network “Minimal surfaces: Integrable Systems and Visualization” financed by the Leverhulme Trust. The conferences took place in Cork, Granada, Munich and...
Springer International Publishing AG, 2018. — 318 p. — ISBN: 3319753304. This book offers an essential overview of computational conformal geometry applied to fundamental problems in specific engineering fields. It introduces readers to conformal geometry theory and discusses implementation issues from an engineering perspective. The respective chapters explore fundamental...
De Gruyter, 2025. — 444 p. — ISBN-13 : 978-3111679464 Observability in Mathematics were developed by authors based on denial of infinity idea. We introduce Observers into arithmetic, and arithmetic becomes dependent on Observers. And after that the basic mathematical parts also become dependent on Observers. One of such parts is geometry. Geometry plays important role not only...
Springer, 2019. — 166 p. — ISBN: 9811339864. This introductory book offers a unique and unified overview of symplectic geometry, highlighting the differential properties of symplectic manifolds. It consists of six chapters: Some Algebra Basics, Symplectic Manifolds, Cotangent Bundles, Symplectic G-spaces, Poisson Manifolds, and A Graded Case, concluding with a discussion of the...
CRC Press, 2019. — 306 p. — (Discrete Mathematics and Its Applications). — ISBN: 978-0-367-22375-5. Volume of geometric objects plays an important role in applied and theoretical mathematics. This is particularly true in the relatively new branch of discrete geometry, where volume is often used to find new topics for research. Volumetric Discrete Geometry demonstrates the...
Birkhäuser, 2021. — 690 p. — ISBN 978-3-030-81316-1. This textbook provides a thorough introduction to the differential geometry of parametrized curves and surfaces, along with a wealth of applications to specific architectural elements. Geometric elements in architecture respond to practical, physical and aesthetic needs. Proper understanding of the mathematics underlying the...
2nd Edi. — Springer, 2018. — 447 p. — (Graduate Texts in Mathematics, 176). — ISBN: 978-3-319-91754-2. This textbook is designed for a one or two semester graduate course on Riemannian geometry for students who are familiar with topological and differentiable manifolds. The second edition has been adapted, expanded, and aptly retitled from Lee’s earlier book, Riemannian...
McGraw-Hill Education, 2019. -- 496p Dive into this book and find: • 250+ practice questions that mirror what you will find in your classwork and on exams • A bonus app with 100+ flashcards that will reinforce what you’ve learned • Extensive examples that drive home essential concepts • An easy-access setup that allows you to jump in and out of subjects • Geometry topics aligned...
Springer, 2019. — 395 p. — (Signals and Communication Technology). — ISBN: 3030025195. This book focuses on information geometry manifolds of structured data/information and their advanced applications featuring new and fruitful interactions between several branches of science: information science, mathematics and physics. It addresses interrelations between different...
Springer, 2021. — 282 p. — (Signals and Communication Technology). — ISBN 978-3-030-65458-0. This book focuses on information-geometric manifolds of structured data andmodels and related applied mathematics. It features new and fruitful interactions between several branches of science: Advanced Signal/Image/Video Processing, Complex Data Modeling and Analysis, Statistics on...
2nd edition. — CRC Press, 2022. — 1057 p. — ISBN 9781003134114. This first edition of this well-illustrated book presented a thorough introduction to the mathematics of Buckminster Fuller’s invention of the geodesic dome, which paved the way for a flood of practical applications as diverse as weather forecasting and fish farms. The author explained the principles of spherical...
Prometheus Books, 2012. — 387 p. — ISBN: 1616145870. Requiring no more than a knowledge of high school mathematics and written in clear and accessible language, this book will give all readers a new insight into some of the most enjoyable and fascinating aspects of geometry. Everyone knows what a triangle is, yet very few people appreciate that the common three-sided figure...
Springer, 2022. — 278 p. — (Moscow Lectures 08). — ISBN-13 9783030922481. This book combines the classical and contemporary approaches to differential geometry. An introduction to the Riemannian geometry of manifolds is preceded by a detailed discussion of properties of curves and surfaces. The chapter on the differential geometry of plane curves considers local and global...
Mineola, New York, USA: Dover Publications, Inc., 2010. — 480 p. — (Dover Books on Mathematics). — ISBN13: 9780486474595. Designed to inform readers about the formal development of Euclidean geometry and to prepare prospective high school mathematics instructors to teach Euclidean geometry, this text closely follows Euclid's classic, Elements. The text augments Euclid's...
Independently published, 2022. Our study of geometry begins with an examination of the historical origins of the axiomatic method in geometry. While the material in this chapter is not a mathematical prerequisite for what comes later, an appreciation of the historical roots of axiomatic thinking is essential to an understanding of why the foundations of geometry are...
2nd Edition. - Springer, 2021. — 263 p. — ISBN 978-3-030-51668-0. This textbook is perfect for a math course for non-math majors, with the goal of encouraging effective analytical thinking and exposing students to elegant mathematical ideas. It includes many topics commonly found in sampler courses, like Platonic solids, Euler’s formula, irrational numbers, countable sets,...
Уважаемые администратор, модераторы и доверенные пользователи.Я хочу предложить Вам в разделе Высшая геометрия создать новый подраздел Дифференциальная геометрия, которая является самостоятельной областью математики. Дифференциальная геометрия, раздел геометрии, в котором свойства кривых, поверхностей и других геометрических многообразий изучаются методами математического анализа, в первую очередь – дифференциального исчисленияНиже представлена некоторая часть литературы для нового подраздела. А также у меня имеется несколько десятков книг по этой теме, которые я буду постепенно добавлять....
Уважаемые: Администратор, модераторы и доверенные пользователи.Друзья, я предлагаю в разделе Высшая геометрия создать новый подраздел Алгебраическая геометрия, которая является самостоятельной областью (направлением, ветвью) математики - Высшей геометрии:Это соответствует требованиям мировых и официальных стандартов, изложенных в Википедии:1.Википедия (Алгебраическая геометрия): "Алгебраическая геометрия — раздел математики, который объединяет алгебру и геометрию".2.Википедия (Категория: Алгебраическая геометрия): "Алгебраическая геометрия — это раздел математики, где алгебра, используемая для решения систем полиномиальных уравнений от многих переменных, встречается с геометрией кривых, поверхностей и алгебраических многообразий более высокой размерности".3.Википедия (Геометрия): "Алгебраическая геометрия — изучает алгебраические многообразия (то есть множества, которые задаются полиномиальными уравнениями) с помощью методов современной общей алгебры". Вывод: Современная геометрия включает в себя следующие разделы (инструментальные подразделы, по используемым методам):Алгебраическая геометрия.Литература для переноса в новый подраздел Алгебраическая геометрия: ...С уважением, благодарностью и благословением,
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Вывод: Современная геометрия включает в себя следующие разделы (инструментальные подразделы, по используемым методам): Алгебраическая геометрия.Литература для переноса в новый подраздел Алгебраическая геометрия:
...С уважением, благодарностью и благословением,
Я благодарен Вам за добавление подраздела Алгебраическая геометрия.
С уважением,
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/file/905476/Предлагаю в разделе Геометрия создать подраздел Стереометрия, учитывая критерии создания названий разделов и подразделов .
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