Format: Hardback, 412 pages, height x width: 235x155 mm, 13 Tables, color; 16 Illustrations, color;
22 Illustrations, black and white; X, 412 p. 38 illus., 16 illus. in color
Pub. Date: 17-Apr-2023
ISBN-13: 9783031237126
This textbook presents all the basics for the first two years of a course in mathematical analysis, from the natural numbers to Stokes-Cartan Theorem. The main novelty which distinguishes this book is the choice of introducing the Kurzweil-Henstock integral from the very beginning. Although this approach requires a small additional effort by the student, it will be compensated by a substantial advantage in the development of the theory, and later on when learning about more advanced topics. The text guides the reader with clarity in the discovery of the many different subjects, providing all necessary tools - no preliminaries are needed. Both students and their instructors will benefit from this book and its novel approach, turning their course in mathematical analysis into a gratifying and successful experience.
- Introduction. - Preliminaries. - Part I The Basics of Mathematical Analysis. - Sets of numbers and metric spaces. - Continuity. - Limits. - Compactness and completeness. - Exponential and circular functions. - Part II Differential and integral calculus in R. - The derivative. - The integral. - Part III Further developments. - Numerical series and series of functions. - More on the integral. - Part IV Differential and integral calculus in RN. - The differential. - The integral. - Differential forms.
Format: Paperback / softback, 468 pages, height x width: 235x155 mm, weight: 811 g, 250 Illustrations, color;
45 Illustrations, black and white; XI, 468 p. 295 illus., 250 illus. in color
Pub. Date: 02-Jan-2023
ISBN-13: 9783662664933
The volume contains a comprehensive and problem-oriented presentation of ancient Greek mathematics from Thales to Proklos Diadochos. Exemplarily, a cross-section of Greek mathematics is offered, whereby also such works of scientists are appreciated in detail, of which no German translation is available. Numerous illustrations and the inclusion of the cultural, political and literary environment provide a great spectrum of the history of mathematical science and a real treasure trove for those seeking biographical and contemporary background knowledge or suggestions for lessons or lectures. The presentation is up-to-date and realizes tendencies of recent historiography.
In the new edition, the central chapters on Plato, Aristotle and Alexandria have been updated. The explanations of Greek calculus, mathematical geography and mathematics of the early Middle Ages have been expanded and show new points of view. A completely new addition is a unique illustrated account of Roman mathematics. Also newly included are several color illustrations that successfully illustrate the book's subject matter. With more than 280 images, this volume represents a richly illustrated history book on ancient mathematics.
How Greek science began.- Thales of Miletus.- Pythagoras and the Pythagoreans.- Hippocrates of Chios.- Athens and the Academy.- Plato.- Aristotle and the Lykeion.- Alexandria.- Euclid .- Classical problems of Greek mathematics.- Archimedes of Syracuse.- Eratosthenes of Cyrene.- The conic sections.- Apollonius of Perga.- The beginnings of trigonometry.- Heron of Alexandria.- Klaudios Ptolemaios.- Nicomachus of Gerasa.- Theon of Smyrna.- Diophantos of Alexandria.- Pappos of Alexandria.- Theon of Alexandria.- Proklos Diadochos.- Roman mathematics.- The heritage of Hellenistic mathematics.
Format: Paperback / softback, 480 pages, height x width: 240x168 mm, XIV, 480 p.
Series: Frontiers in Mathematics
Pub. Date: 18-Apr-2023
ISBN-13: 9783031222917
This monograph provides an exhaustive treatment of several classes of Noetherian rings and morphisms of Noetherian local rings. Chapters carefully examine some of the most important topics in the area, including Nagata, F-finite and excellent rings, Bertini's Theorem, and Cohen factorizations. Of particular interest is the presentation of Popescu's Theorem on Neron Desingularization and the structure of regular morphisms, with a complete proof. Classes of Good Noetherian Rings will be an invaluable resource for researchers in commutative algebra, algebraic and arithmetic geometry, and number theory.
- Fibres of Noetherian Rings.- Nagata Rings and reduced morphisms.- Excellent rings and regular morphisms.- Localization and lifting theorems.- Structure of regular morphisms.- Other classes of good rings.
Format: Hardback, 210 pages, height x width: 235x155 mm, 2 Tables, color; 3 Illustrations, color; X, 210 p. 3 illus. in color.
Series: Trends in Mathematics
Pub. Date: 09-Mar-2023
ISBN-13: 9783031243103
This book collects papers related to the session "Harmonic Analysis and Partial Differential Equations" held at the 13th International ISAAC Congress in Ghent and provides an overview on recent trends and advances in the interplay between harmonic analysis and partial differential equations. The book can serve as useful source of information for mathematicians, scientists and engineers. The volume contains contributions of authors from a variety of countries on a wide range of active research areas covering different aspects of partial differential equations interacting with harmonic analysis and provides a state-of-the-art overview over ongoing research in the field. It shows original research in full detail allowing researchers as well as students to grasp new aspects and broaden their understanding of the area.
The wave resolvent for compactly supported perturbations of Minkowski space.- Smoothing effect and Strichartz estimates for some time-degenerate Schroedinger equations.- On the Cauchy problem for the nonlinear wave equation with damping and potential.- Local well-posedness for the scale-critical semilinear heat equation with a weighted gradient term.- On the Rellich type inequality for Schroedinger operators with singular potential.- Global solutions to the nonlinear Maxwell-Schroedinger system.- On the plate equation with exponentially degenerating stochastic coefficients on the torus.- Existence results for critical problems involving p-sub-Laplacians on Carnot groups.- The Wodzicki residue for pseudo-differential operators on compact Lie groups.- New characterizations of harmonic Hardy spaces.- On the solvability of the synthesis problem for optimal control systems with distributed parameters.- On the determination of a coefficient of an elliptic equation via partial boundary measurement.- Reconstruction from Boundary Measurements: complex conductivities.
Format: Hardback, 310 pages, height x width: 235x155 mm, 21 Illustrations, color;
61 Illustrations, black and white; XVI, 310 p. 82 illus., 21 illus. in color
Series: Annals of the Canadian Society for History and Philosophy of Mathematics
/ Societe canadienne d'histoire et de philosophie des mathematiques
Pub. Date: 02-Apr-2023
ISBN-13: 9783031214936
This volume contains eighteen papers that have been collected by the Canadian Society for History and Philosophy of Mathematics. It showcases rigorously-reviewed contemporary scholarship on an interesting variety of topics in the history and philosophy of mathematics, as well as the teaching of the history of mathematics. Some of the topics explored include Arabic editions of Euclid's Elements from the thirteenth century and their role in the assimilation of Euclidean geometry into the Islamic intellectual tradition Portuguese sixteenth century recreational mathematics as found in the Tratado de Pratica Darysmetica A Cambridge correspondence course in arithmetic for women in England in the late nineteenth century The mathematical interests of the famous Egyptologist Thomas Eric (T. E.) Peet The history of Zentralblatt fur Mathematik and Mathematical Reviews and their role in creating a publishing infrastructure for a global mathematical literature The use of Latin squares for agricultural crop experiments at the Rothamsted Experimental Station The many contributions of women to the advancement of computing techniques at the Cavendish Laboratory at the University of Cambridge in the 1960s The volume concludes with two short plays, one set in Ancient Mesopotamia and the other in Ancient Egypt, that are well suited for use in the mathematics classroom. Written by leading scholars in the field, these papers are accessible not only to mathematicians and students of the history and philosophy of mathematics, but also to anyone with a general interest in mathematics.
H. Amini, A 10th Century Mathematical Glossary.- G. De Young, Euclid in Maragha: The Age of the Tahrir.- J. N. Silva, P. J. Freitas, The Recreational Problems of Tratado de Pratica Darysmetica by Gaspar Nicolas, 1519.- A. Corrigan, The Mathematics of Polemic in John Napier's Plaine Discovery.- P. Blaszczyk, A. Petiurenko, Euler's Series for Sine and Cosine: An Interpretation in Nonstandard Analysis.- C. J. Huffman, Agnesi vs. Colson: Did Location Matter?- B. Larvor, The Limits of Understanding and the Understanding of Limits: David Hume's Mathematical Sources.- A. Ackerberg-Hastings, Analysis and Synthesis in Robert Simson's The Elements of Euclid.- R. Wilson, Thomas Archer Hirst: Mathematician Xtravagant.- S. L. McMurran, J. J. Tattersall, A Cambridge Correspondance Course in Arithmetic for Women.- C. D. Hollings, R. B. Parkinson; T. E. Peet, A Mathematician among Egyptologists?- M. J. Barany, Placing a Global Mathematical Literature: Geography, Infrastructure, and Information in the Mid-Century Zentralblatt fur Mathematik and Mathematical Reviews.- R. A. Bailey, Latin Squares at Rothamsted in the Time of Fisher and Yates.- R. Godard, J. de Boer, M. Lewis, Les equations differentielles ordinaires "raides" et les methodes robustes: Une approche historique.- V. Allan, The Cavendish Computors: The Women Working in Scientific Computing for Radio Astronomy.- M. Muntersbjorn, The Algebra Project, Feature Talk, and the History of Mathematics.- G. Hitchcock, Corrupt Land Inspectors: Solving Equations with Picture-Language in Ancient Mesopotamia, a Dialogue.- G. Hitchcock, Entrance into All Obscure Secrets: A Workshop on Bringing Episodes in the History of Mathematics to Life in the Classroom by Means of Theater, Incorporating a Short Play Set in an Ancient Egyptian Scribal School.