{"title":"Number systems Books","description":"","products":[{"product_id":"problem-based-journey-from-elementary-number-theory-to-an-introduction-to-matrix-theory-a-the-president-problems-9789811234873","title":"Problem Based Journey From Elementary Number","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe book is based on lecture notes of a course 'from elementary number theory to an introduction to matrix theory' given at the Technion to gifted high school students. It is problem based, and covers topics in undergraduate mathematics that can be introduced in high school through solving challenging problems. These topics include Number theory, Set Theory, Group Theory, Matrix Theory, and applications to cryptography and search engines.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48743279558999,"sku":"9789811234873","price":33.25,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811234873.jpg?v=1720064898"},{"product_id":"trilogy-of-numbers-and-arithmetic-book-1-history-of-numbers-and-arithmetic-an-information-perspective-9789811236839","title":"Trilogy Of Numbers And Arithmetic - Book 1:","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe book is the first in the trilogy which will bring you to the fascinating world of numbers and operations with them. Numbers provide information about myriads of things. Together with operations, numbers constitute arithmetic forming in basic intellectual instruments of theoretical and practical activity of people and offering powerful tools for representation, acquisition, transmission, processing, storage, and management of information about the world.The history of numbers and arithmetic is the topic of a variety of books and at the same time, it is extensively presented in many books on the history of mathematics. However, all of them, at best, bring the reader to the end of the 19th century without including the developments in these areas in the 20th century and later. Besides, such books consider and describe only the most popular classes of numbers, such as whole numbers or real numbers. At the same time, a diversity of new classes of numbers and arithmetic were introduced in the 20th century.This book looks into the chronicle of numbers and arithmetic from ancient times all the way to 21st century. It also includes the developments in these areas in the 20th century and later. A unique aspect of this book is its information orientation of the exposition of the history of numbers and arithmetic.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48743279984983,"sku":"9789811236839","price":112.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811236839.jpg?v=1720064899"},{"product_id":"level-up-maths-homework-book-level-46-9780435537395","title":"Level Up Maths Homework Book Level 46","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Pearson Education","offers":[{"title":"Default Title","offer_id":48884130578775,"sku":"9780435537395","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780435537395.jpg?v=1722530582"},{"product_id":"single-digits-9780691175690","title":"Single Digits","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Fascinating... Chamberland offers enticing explanations that will leave readers hungry to know more. This wonderful book never loses its focus or momentum.\"--Publishers Weekly \"[B]oth amateur and professional mathematicians alike will find new items of interest here... [A] welcome, splendid, fruitful addition to my math bookshelf.\"--Math Tango blog \"The collection is outright delightful. It will agitate the minds of students and shake the sense of know-all off many a professional and most of the amateurs.\"--Alexander Bogomolny, Cut the Knot blog \"Boring deep into the innocuous-looking number one, Chamberland opens an unexpected entry point into a dizzying maze of infinities... A bracing mathematical adventure.\"--Booklist \"The exotics like pi and e have gotten their share of attention in the world of popular mathematical writing. Now it's time to give proper attention to the integers 1 through 9... [Single Digits] is consistently entertaining and well-written.\"--MAA Reviews \"Chamberland takes readers on a fascinating exploration of small numbers, from one to nine, looking at their history, applications, and connections to various areas of mathematics, including number theory, geometry, chaos theory, numerical analysis, and mathematical physics... Appealing to high-school and college students, professional mathematicians, and those mesmerized by patterns, this book shows that single digits offer a plethora of possibilities that readers can count on.\"--DVD, Lunar and Planetary Information Bulletin \"Chamberland makes this an entertaining and historical exposition, using wit and humor throughout.\"--Math Horizons \"To put it simply, this book is a delight. Chamberland has assembled a fascinating collection of vignettes, each tied to a digit from one to nine, that inform, entertain, and intrigue... This wide spectrum of ideas is consistently interesting, and the author's skill in mining each nugget is worthy of great respect.\"--Choice \"The range of topics included virtually guarantees that any reader will find new and unfamiliar material to enjoy... [Single Digits] is a very enjoyable book which, at many points, makes some very deep mathematics quite accessible. Highly recommended.\"--Keith Johnson, CMS Notes \"For instructors of math courses of all levels, the vignettes in Single Digits can provide a very readable introduction or jumping-off point for discussions and projects... In an introductory group theory course, it would be a good exercise for students to consider perfect riffle shuffles in decks of size other than 52. Finally, a statistics class collecting and analyzing real-world data sets could consider whether Benford's Law applies in their situation.\"--Matthew Welz, MAA Focus \"I highly recommend Single Digits: In Praise of Small Numbers. It would be a fine addition to any high school or math department library. As a carefully curated set of interesting topics, it would serve as a good place to start exploring the ocean of ideas in mathematics.\"--Bruce Cohen, NCTM\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e*Frontmatter, pg. i*Contents, pg. v*Preface, pg. xi*Chapter 1. The Number One, pg. 1*Chapter 2. The Number Two, pg. 24*Chapter 3. The Number Three, pg. 69*Chapter 4. The Number Four, pg. 111*Chapter 5. The Number Five, pg. 132*Chapter 6. The Number Six, pg. 156*Chapter 7. The Number Seven, pg. 170*Chapter 8. The Number Eight, pg. 191*Chapter 9. The Number Nine, pg. 205*Chapter 10. Solutions, pg. 216*Further reading, pg. 219*Credits for illustrations, pg. 223*Index, pg. 225","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403845542231,"sku":"9780691175690","price":16.14,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691175690.jpg?v=1730484700"},{"product_id":"numbers-to-infinity-and-beyond-9781952178221","title":"Numbers: To Infinity and Beyond","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Wooden Books","offers":[{"title":"Default Title","offer_id":49414951469399,"sku":"9781952178221","price":7.55,"currency_code":"GBP","in_stock":true}]},{"product_id":"wissenschaftliches-rechnen-9783540784944","title":"Wissenschaftliches Rechnen","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eDas Ziel des nun auch in deutscher Übersetzung erhältlichen Buches ist es, angewandte Mathematik und Ingenieurmathematik so darzustellen, wie sie heutzutage Anwendung findet. Das Buch basiert auf dem Kurs „Wissenschaftliches Rechnen\" des Massachusetts Institute of Technology und versucht, Konzepte und Algorithmen zusammenzuführen. Beginnend mit der angewandten linearen Algebra entwickeln die Autoren die Methoden der finiten Differenzen und finiten Elemente – stets in Verbindung mit Anwendungen in zahlreichen Wissensgebieten.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“... Der in jeder Hinsicht hervorragende Text von Strang wird für lange Zeit eine Standardreferenz in der Literatur zur Ausbildung im wissenschaftlichen Rechnen sein. Es gibt viele gute Gründe, ihn zu besitzen ...” (H.R. Schneebeli, in: Elemente der Mathematik, jg. 67, S. 200 f. 2012)\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e“... Das Buch enthält zahlreiche Aufgaben in unterschiedlichen Schwierigkeitsgraden und drei Anhänge und ist, wenn man es nicht als Begleitbuch zu einer Vorlesung gebraucht, hervorragend zum Stöbern geeignet. ... ist das Buch äußerst empfehlenswert nicht nur für Ingenieure. Teile des Buches sind sicher auch schon für begabte und interessierte Schülerinnen und Schüler geeignet und von Pseudoanwendungen in Schulbüchern genervte Lehrkräfte an unseren Gymnasien können hier realistische Anwendungen finden, die man mit Mathematik bearbeiten kann.“ (in: Mathematische Semesterberichte, 2012, Issue 1)\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e“... in diesem umfangreichen, ursprünglich in englisch erschienenem Werk mit mathematischer Exaktheit und anwendungsorientierter Zielrichtung ... Angesprochen sind vorwiegend Studierende der Mathematik und der Ingenieurwissenschaften. ... Der kurze Anhang ist allenfalls geeignet, Erinnerungslücken zu schließen.“ (Wolfgang Grölz, in: ekz-Informationsdienst, 2010, Vol. 2010\/34)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eAngewandte lineare Algebra.- Ein Grundmuster der angewandten Mathematik.- Randwertprobleme.- Fourier-Reihen und Fourier-Integrale.- Analytische Funktionen.- Anfangswertprobleme.- Große Systeme.- Optimierung und Minimumprinzip.","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":49419505697111,"sku":"9783540784944","price":42.74,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783540784944.jpg?v=1730538565"},{"product_id":"numerische-mathematik-eine-einfuhrung-anhand-von-differentialgleichungsproblemen-band-1-stationare-probleme-9783764384265","title":"Numerische Mathematik: Eine Einführung anhand von","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\"Numerik\", in zwei Bänden, ist eine Einführung in die Numerische Mathematik anhand von Differenzialgleichungsproblemen. Gegliedert nach elliptischen, parabolischen und hyperbolischen Differenzialgleichungen, erläutert sie zunächst jeweils die Diskretisierung solcher Probleme. Als Diskretisierungstechniken stehen Finite-Elemente-Methoden im Raum und (partitionierte) Runge-Kutta-Methoden in der Zeit im Vordergrund. Die diskretisierten Gleichungen motivieren die Diskussion von Methoden für endlichdimensionale (nicht)lineare Gleichungen, die anschließend als eigenständige Themen behandelt werden. Ein in sich geschlossenes Bild.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1 Einleitung.- 2 Ein erstes Beispiel einer Variationsformulierung.- 3 Der Satz von Lax-Milgram.- 4 Die Galerkin-Methode.- 4.1 Ein Beispiel einer Finite-Elemente-Methode.- 4.2 Der Diskretisierungsfehler.- 5 Lineare Gleichungssysteme.- 5.1 Kondition des Problems.- 5.2 Konditionszahl der Steifigkeitsmatrix.- 6 Das Gaußsche Eliminationsverfahren.- 6.1 Der Algorithmus.- 6.2 Numerische Stabilität des Algorithmus.- 7 Erweiterung auf lineare mehrdimensionale Randwertprobleme.- 8 Iterative Verfahren für lineare Gleichungssysteme.- 8.1 Das Richardson-Verfahren.- 8.2 Das Gradientenverfahren.- 8.3 Das Verfahren der konjugierten Gradienten.- 8.4 Präkonditionierung.- 9 Erweiterung auf nichtlineare Randwertprobleme.- 10 Das Newton-Verfahren.","brand":"Birkhauser Verlag AG","offers":[{"title":"Default Title","offer_id":49421515456855,"sku":"9783764384265","price":17.09,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783764384265.jpg?v=1730545508"},{"product_id":"algorithmische-methoden-zahlen-vektoren-polynome-9783764384340","title":"Algorithmische Methoden: Zahlen, Vektoren,","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eDas Lehrbuch diskutiert gängige Fragen der Analysis und linearen Algebra und verwendet für die rechnergestützten Antworten die Software Matlab und Mathematica. Es stellt mathematische Standard-Algorithmen im Detail vor und zeigt deren Umsetzung in die Programme. Zusätzlich erläutert es, wie deren Funktionen Probleme lösen. Die Inhalte sind nach Datentypen (Polynome, reelle Funktionen, Matrizen) gegliedert. Im Vordergrund: die Objekte am Rechner, Grundoperationen an diesen Objekten und typische Fragen. Mit Algorithmen in Pseudocode. Plus zum Download: Programme für Mathematica und Matlab, alle Beispiele, Grafiken, interaktive Elemente.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e“Algorithmic methods are useful tools for solving technical, scientific, or industrial problems. … This book for students in the first or second year presents the basic knowledge necessary for applying the methods to different problems. … The presentation is given in mathematical rigorous style and no further reading … to be required to read the text or design a course. … underlying course was designed for students of technical mathematics, but is as well suited for computer science students in the area of scientific computing.” (Thomas Rauber, Zentralblatt MATH, Vol. 1181, 2010)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eEinleitung.- I. Grundbegriffe und Grundfragen einer algorithmischen Mathematik:1. Probleme, Lösungen und Algorithmen.- 2 Einführende Beispiele zur algorithmischen Lösung am Computer.- 3. Kondition eines Problems.- 4. Eigenschaften von Algorithmen.- II. Zahlbereiche: 5. Natürliche und ganze Zahlen.- 6. Kongruenzklassen modulo m.- 7. Rationale Zahlen.- 8. Reelle Zahlen.- III. Vektoren: 9. Mathematische Grundlagen.- 10. Vektoren am Computer.- 11. Euklidsches Skalarprodukt in Rm.- 12. Orthonormalisierung in Rm.- IV. Univariate Polynome: 13. Mathematische Grundlagen.- 14. Polynome am Computer.- 15. Polynomdivision und größter gemeinsamer Teiler.- 16. Polynomauswertung in R.- 17. Polynominterpolation in R.","brand":"Birkhauser Verlag AG","offers":[{"title":"Default Title","offer_id":49421515555159,"sku":"9783764384340","price":17.09,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783764384340.jpg?v=1730545509"},{"product_id":"everyday-chaos-the-mathematics-of-unpredictability-from-the-weather-to-the-stock-market-9780262539692","title":"Everyday Chaos The Mathematics of","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cb\u003eChaos and complexity explained, with illuminating examples ranging from unpredictable pendulums to London''s wobbly Millennium Bridge.\u003c\/b\u003e\u003cp\u003eThe math we are taught in school is precise and only deals with simple situations. Reality is far more complex. Trying to understand a system with multiple interacting components—the weather, for example, or the human body, or the stock market—means dealing with two factors: chaos and complexity. If we don''t understand these two essential subjects, we can''t understand the real world. In \u003ci\u003eEveryday Chaos\u003c\/i\u003e, Brian Clegg explains chaos and complexity for the general reader, with an accessible, engaging text and striking full-color illustrations.\u003c\/p\u003e\u003cp\u003eBy chaos, Clegg means a system where complex interactions make predicting long-term outcomes nearly impossible; complexity means complex interacting systems that have new emergent properties that make them more than the sum of their parts. Clegg illustrates these phenomena with discu\u003c\/p\u003e","brand":"MIT Press Ltd","offers":[{"title":"Default Title","offer_id":49524684882263,"sku":"9780262539692","price":22.95,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780262539692.jpg?v=1731857742"},{"product_id":"parallel-programming-for-modern-high-performance-computing-systems-9781138305953","title":"Parallel Programming for Modern High Performance","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eIn view of the growing presence and popularity of multicore and manycore processors, accelerators, and coprocessors, as well as clusters using such computing devices, the development of efficient parallel applications has become a key challenge to be able to exploit the performance of such systems. This book covers the scope of parallel programming for modern high performance computing systems.\u003cb\u003e \u003c\/b\u003e\u003c\/p\u003e\u003cp\u003eIt first discusses selected and popular state-of-the-art computing devices and systems available today, These include multicore CPUs, manycore (co)processors, such as Intel Xeon Phi, accelerators, such as GPUs, and clusters, as well as programming models supported on these platforms.\u003c\/p\u003e\u003cp\u003eIt next introduces parallelization through important programming paradigms, such as master-slave, geometric Single Program Multiple Data (SPMD) and divide-and-conquer.\u003c\/p\u003e\u003cp\u003eThe practical and useful elements of the most popular and important APIs for programming parallel HPC systems are\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e1. Understanding the Need for Parallel Computing 2. Overview of Selected Parallel and Distributed Systems for High Performance Computing 3. Typical Paradigms for Parallel Applications 4. Selected APIs for Parallel Programming 5. Programming Parallel Paradigms Using Selected APIS 6. Optimization Techniques and Best Practices for Parallel Codes Appendix A. Resources Appendix B. Further reading \u003c\/p\u003e","brand":"Taylor \u0026 Francis Ltd","offers":[{"title":"Default Title","offer_id":50577816650071,"sku":"9781138305953","price":90.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781138305953.jpg?v=1746096809"},{"product_id":"hidden-order-9780201442304","title":"Hidden Order","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cdiv\u003eExplains how scientists who study complexity are convinced that certain constant processes are at work in all kinds of unrelated complex systems.\u003c\/div\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e* Basic Elements  * Adaptive Agents  * Echoing Emergence  * Simulating Echo  * Toward Theory","brand":"Hachette Book Group USA","offers":[{"title":"Default Title","offer_id":51017643163991,"sku":"9780201442304","price":20.42,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780201442304.jpg?v=1750774205"},{"product_id":"irrationality-and-transcendence-in-number-theory-9780367628758","title":"Irrationality and Transcendence in Number Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003e\u003ci\u003eIrrationality and Transcendence in Number Theory \u003c\/i\u003e\u003c\/b\u003etells the story of irrational numbers from their discovery in the days of Pythagoras to the ideas behind the work of Baker and Mahler on transcendence in the 20th century. It focuses on themes of irrationality, algebraic and transcendental numbers, continued fractions, approximation of real numbers by rationals, and relations between automata and transcendence. This book serves as a guide and introduction to number theory for advanced undergraduates and early postgraduates. Readers are led through the developments in number theory from ancient to modern times. The book includes a wide range of exercises, from routine problems to surprising and thought-provoking extension material.\u003c\/p\u003e\u003cp\u003e\u003cb\u003eFeatures\u003c\/b\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eUses techniques from widely diverse areas of mathematics, including number theory, calculus, set theory, complex analysis, linear algebra, and the theory of computation\u003c\/li\u003e\n\u003cli\u003eSuitable as a primary textbook for\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\"Exceptionally informative, impressively organized and presented, \u003cem\u003eIrrationality and Transcendence in Number Theory\u003c\/em\u003e is an ideal selection as a curriculum textbook.\"\u003cbr\u003e\u003cstrong\u003e- \u003cem\u003eMidwest Books Review\u003c\/em\u003e\u003c\/strong\u003e\u003cbr\u003e\"This excellent book not only helps fill a substantial gap in the undergraduate mathematics literature, but it does so in a way that most students will, I think, find interesting, inviting and accessible. \u003cbr\u003e[. . .] This material is, of course, very nontrivial, but Angell goes to great lengths to make it accessible. He writes slowly and clearly and spends a lot of time motivating results. As previously noted, he also includes background Appendices in each chapter.\u003cbr\u003eThere are other useful pedagogical features. Each chapter ends with an extensive collection of exercises, most of them non-routine; a 20-page section at the end of the book offers hints to these. The book also contains a five-page bibliography (one that, surprisingly, omits the Burger\/Tubbs book mentioned earlier) that directs a reader to useful sources. \u003cbr\u003eThe subject matter of this book is interesting and beautiful and deserves to be made accessible to well-prepared senior undergraduates. Angell has done an excellent job in helping to do so.\"\u003cbr\u003e\u003cstrong\u003e- \u003c\/strong\u003e\u003cem\u003e\u003cstrong\u003eMAA Reviews\u003c\/strong\u003e\u003c\/em\u003e \u003c\/p\u003e\n\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cstrong\u003e1. Introduction.\u003c\/strong\u003e 1.1. Irrational Surds. 1.2. Irrational Decimals. 1.3. Irrationality of the Exponential Constant. 1.4. Other Results, and Some Open Questions. Exercises. Appendix: Some Elementary Number Theory. \u003cstrong\u003e2. Hermite’s Method.\u003c\/strong\u003e 2.1. Irrationality of \u003ci\u003eer. \u003c\/i\u003e2.2. Irrationality of \u003ci\u003eπ. \u003c\/i\u003e2.3. Irrational values of trigonometric functions. Exercises. Appendix: Some Results of Elementary Calculus.\u003cstrong\u003e 3. Algebraic \u0026amp; Transcendental Numbers.\u003c\/strong\u003e 3.1. Definitions and Basic Properties. 3.2. Existence of Transcendental Numbers. 3.3. Approximation of Real Numbers by Rationals. 3.4. Irrationality of (3) : a sketch. Exercises. Appendix 1: Countable and Uncountable Sets. Appendix 2: The Mean Value Theorem. Appendix 3: The Prime Number Theorem. \u003cstrong\u003e4. Continued Fractions.\u003c\/strong\u003e Definition and Basic Properties. 4.2. Continued Fractions of Irrational Numbers. 4.3. Approximation Properties of Convergents. 4.4. Two important Approximation Problems. 4.5. A \"Computational\" Test for Rationality. 4.6. Further Approximation Properties of Convergents. 4.7. Computing the Continued Fraction of an Algebraic Irrational. 4.8. The Continued Fraction of \u003ci\u003ee. \u003c\/i\u003eExercises. Appendix 1: A Property of Positive Fractions. Appendix 2: Simultaneous Equations with Integral Coefficients. Appendix 3: Cardinality of Sets of Sequences. Appendix 4: Basic Musical Terminology. \u003cstrong\u003e5. Hermite’s Method for Transcendence.\u003c\/strong\u003e 5.1. Transcendence of \u003ci\u003ee.\u003c\/i\u003e 5.2. Transcendence of \u003ci\u003eπ. 5.3. \u003c\/i\u003eSome more Irrationality Proofs. 5.4. Transcendence of ea .5.5. Other Results. Exercises. Appendix 1: Roots and Coefficients of Polynomials. Appendix 2: Some Real and Complex Analysis. Appendix 3: Ordering Complex Numbers. \u003cstrong\u003e6. Automata and Transcendence.\u003c\/strong\u003e 6.1. Deterministic Finite Automata. 6.2 Mahler’s Transcendence Proof. 6.3 A More General Transcendence Result. 6.4. A Transcendence Proof for the Thue Sequence. 6.5. Automata and Functional Equations. 6.6. Conclusion. Exercises. Appendix 1: Alphabets, Languages and DFAs. Appendix 2: Some Results of Complex Analysis. Appendix 3: A Result on Linear Equations.\u003cstrong\u003e 7. Lambert’s Irrationality Proofs.\u003c\/strong\u003e 7.1. Generalised Continued Fractions. 7.2. Further Continued Fractions. Exercises. Appendix: Some Results from Elementary Algebra and Calculus. Hints for Exercises. Bibliography. Index. \u003c\/p\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"Taylor \u0026 Francis Ltd","offers":[{"title":"Default Title","offer_id":51017989521751,"sku":"9780367628758","price":45.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780367628758.jpg?v=1750775283"},{"product_id":"quantitative-aptitude-volume-i-9781925823868","title":"Quantitative Aptitude: Volume I","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Central West Publishing","offers":[{"title":"Default Title","offer_id":51020908659031,"sku":"9781925823868","price":84.79,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781925823868.jpg?v=1750784714"},{"product_id":"theorie-und-numerik-restringierter-optimierungsaufgaben-9783540427902","title":"Theorie und Numerik restringierter","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eAufbauend auf Vorlesungen an den Universitäten Hamburg und Trier stellen die Autoren die „Theorie und Numerik restringierter Optimierungsaufgaben\" umfassend dar. Ausführlich behandelt werden lineare Programme, Simplex-Verfahren und Innere-Punkte-Methoden, Optimalitätsbedingungen, nichtlineare restringierte Programme, nichtglatte Optimierung sowie Variationsungleichungen. Mit ca. 140 Aufgaben unterschiedlichen Schwierigkeitsgrades.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eIch habe das Buch mit großem Interesse gelesen. Es enthält alle für Vorlesungen auf diesem Gebiet der nichtlinearen endlichdimensionalen Optimierung notwendigen Aussagen. Ausgehend von ihm können die Gebiete der linearen Optimierung, der Theorie nichtlinearer Optimierungsaufgaben, der Numerik nichtlinearer Optimierung und der Variationsaufgaben studiert werden. Es unterscheidet sich positiv von vielen weiteren auf dem Markt befindlichen Lehrbüchern dadurch, dass es sowohl eine umfangreiche Diskussion von Lösungsalgorithmen für Optimierungsaufgaben als auch die theoretischen Aussagen zu Optimalitäts- und Regularitätsbedingungen in hinreichender Breite und Tiefe enthält. Die Aussagen sind durchweg bewiesen, was für Vorlesungen für mathematische Studiengänge notwendig ist. Hervorheben möchte ich auch die Aufnahme von Übungsaufgaben. Zusammenfassend kann ich sagen: Das Buch ist das beste Lehrbuch zu Theorie und Lösungsverfahren der mathematischen Optimierung. Ich kann es sowohl Studierenden (mathematischer und auch anderer) Fachrichtungen als auch den Lehrenden auf dem Gebiet der mathematischen Optimierung sehr empfehlen. 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