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Excursions in Modern Mathematics: A Journey into the Beautiful and Unexpected
Are you fascinated by the elegance of mathematical proofs, the power of algorithms, or the mind-bending implications of infinity? Do you crave a deeper understanding of the mathematical landscape that shapes our modern world? Then join us on an exciting excursions in modern mathematics! This post will guide you through some of the most captivating and influential areas of modern mathematical research, offering a glimpse into their beauty, their practical applications, and the ongoing questions that continue to challenge and inspire mathematicians worldwide. We’ll navigate beyond the familiar arithmetic and algebra of school days, venturing into realms that are both intellectually stimulating and surprisingly relevant to everyday life.
H2: The Allure of Number Theory: Beyond Prime Numbers
Number theory, the study of integers and their properties, often serves as a gateway to the deeper mysteries of mathematics. While seemingly simple, it harbors profound complexities. We're all familiar with prime numbers – those divisible only by 1 and themselves. But modern number theory delves far beyond this basic concept.
H3: Cryptography and the Power of Primes: The security of online transactions and confidential communications relies heavily on number theory. Specifically, the difficulty of factoring extremely large numbers into their prime components forms the bedrock of RSA encryption, one of the most widely used cryptographic systems. The hunt for ever-larger prime numbers is a crucial ongoing endeavor in this field.
H3: The Riemann Hypothesis: An Unsolved Enigma: This famous unsolved problem poses a question about the distribution of prime numbers. Its solution would have profound implications for our understanding of prime number distribution and related areas of mathematics. The Riemann Hypothesis remains one of the most significant unsolved problems in mathematics, driving ongoing research and attracting significant attention.
H2: The Elegance of Geometry: Beyond Euclid
Geometry, once confined to the study of shapes and figures, has blossomed into vastly richer and more abstract fields. Modern geometry extends far beyond the familiar theorems of Euclid.
H3: Fractal Geometry: The Beauty of Infinity: Fractals are intricate geometric shapes that exhibit self-similarity at different scales. Think of a fern leaf: each smaller branch resembles the overall shape of the leaf. Fractals appear everywhere in nature, from coastlines to snowflakes, and their study reveals surprising patterns and mathematical relationships.
H3: Topology: Shapes that Can Be Bent and Stretched: Topology is the study of shapes and spaces that are invariant under continuous deformations – like stretching, bending, or twisting, but not tearing or gluing. This seemingly abstract field has practical applications in fields like data analysis and network design.
H2: The Power of Algorithms: Computation and Complexity
The development and analysis of algorithms are central to modern mathematics and computer science. Algorithms are step-by-step procedures for solving problems, and their efficiency is a key consideration.
H3: Computational Complexity Theory: The Limits of Computation: This field explores the inherent difficulty of computational problems. Some problems are simply too complex to solve efficiently, regardless of the algorithm used. Understanding these limits is crucial for developing efficient solutions to practical problems.
H3: Machine Learning and Artificial Intelligence: These rapidly evolving fields rely heavily on sophisticated algorithms. Modern machine learning algorithms often leverage advanced mathematical techniques, including linear algebra, calculus, and probability theory, to analyze massive datasets and make predictions.
H2: The Abstract World of Abstract Algebra: Groups, Rings, and Fields
Abstract algebra deals with abstract algebraic structures like groups, rings, and fields, defined by axioms rather than specific numerical values. This level of abstraction allows mathematicians to explore fundamental relationships across various mathematical domains.
H3: Group Theory and its Applications: Group theory, the study of groups, finds surprising applications in areas as diverse as physics (especially in particle physics and quantum mechanics), cryptography, and chemistry (understanding molecular symmetry).
H3: Ring Theory and Polynomial Equations: Ring theory focuses on rings, algebraic structures extending the concept of integers. This is crucial in solving polynomial equations and understanding algebraic number theory.
Conclusion:
This excursions in modern mathematics has only scratched the surface of the rich and diverse landscape of contemporary mathematical research. From the elegant patterns of number theory to the abstract structures of algebra, and the powerful tools of algorithms, mathematics continues to surprise, challenge, and inspire us. By understanding the fundamental principles and applications of these various branches, we can better grasp the mathematical underpinnings of our technological world and appreciate the enduring beauty and power of mathematical thought.
FAQs:
1. What are some good resources to learn more about modern mathematics? Excellent resources include introductory textbooks on number theory, abstract algebra, and topology, as well as online courses offered by platforms like Coursera and edX.
2. Is a strong background in mathematics required to understand these concepts? While a solid foundation in high school mathematics is helpful, many introductory texts and courses are designed to be accessible to those with a strong interest but limited prior formal training.
3. How are these mathematical concepts applied in real-world scenarios? Modern mathematical concepts are fundamental to various fields, including cryptography, computer science, engineering, finance, and even the arts.
4. What are some current unsolved problems in mathematics that are actively being researched? Besides the Riemann Hypothesis, the Birch and Swinnerton-Dyer conjecture, the Navier-Stokes existence and smoothness problem, and the Poincaré conjecture (now proven) represent significant challenges in modern mathematics.
5. Where can I find communities of people interested in discussing modern mathematics? Online forums, mathematical societies, and university mathematics departments often host discussions and events for those interested in exploring modern mathematics further.
| excursions in modern mathematics: Excursions in Modern Mathematics Peter Tannenbaum, 2014 Disability and Academic Exclusion interrogates obstacles the disabled have encountered in education, from a historical perspective that begins with the denial of literacy to minorities in the colonial era to the later centuries' subsequent intolerance of writing, orality, and literacy mastered by former slaves, women, and the disabled. The text then questions where we stand today in regards to the university-wide rhetoric on promoting diversity and accommodating disability in the classroom. Amazon.com viewed 6/2/2020. |
| excursions in modern mathematics: Excursions in Modern Mathematics Peter Tannenbaum, Anne Kelly, 2014 |
| excursions in modern mathematics: Excursions in Modern Mathematics Peter Tannenbaum, 2014 |
| excursions in modern mathematics: Excursions in Modern Mathematics Peter Tannenbaum, Robert Arnold, 2000-10-01 For undergraduate courses in Liberal Arts Mathematics, Quantitative Literacy, and General Education.This very successful liberal arts mathematics textbook is a collection of excursions into the real-world applications of modern mathematics. The excursions are organized into four independent parts: 1) The Mathematics of Social Choice, 2) Management Science, 3) Growth and Symmetry, and 4) Statistics. Each part consists of four chapters plus a mini-excursion (new feature in 6/e). The book is written in an informal, very readable style, with pedagogical features that make the material both interesting and clear. The presentation is centered on an assortment of real-world examples and applications specifically chosen to illustrate the usefulness, relevance, and beauty of liberal arts mathematics. |
| excursions in modern mathematics: Excursions in Modern Mathematics Peter Tannenbaum, 2010-01-01 |
| excursions in modern mathematics: Excursions in Modern Mathematics, Books a la Carte Edition Peter Tannenbaum, 2009-07-01 |
| excursions in modern mathematics: Excursions in Modern Mathematics -- Print Offer Peter Tannenbaum, 2017-01-01 |
| excursions in modern mathematics: Excursions in Modern Math Tannenbaum, 1997-08-01 |
| excursions in modern mathematics: Excursions in Modern Mathematics Pearson Custom Publishing, 1998-09-01 |
| excursions in modern mathematics: Mathematical Excursions to the World's Great Buildings Alexander J. Hahn, 2012-07-22 How mathematics helped build the world's most important buildings from early Egypt to the present From the pyramids and the Parthenon to the Sydney Opera House and the Bilbao Guggenheim, this book takes readers on an eye-opening tour of the mathematics behind some of the world's most spectacular buildings. Beautifully illustrated, the book explores the milestones in elementary mathematics that enliven the understanding of these buildings and combines this with an in-depth look at their aesthetics, history, and structure. Whether using trigonometry and vectors to explain why Gothic arches are structurally superior to Roman arches, or showing how simple ruler and compass constructions can produce sophisticated architectural details, Alexander Hahn describes the points at which elementary mathematics and architecture intersect. Beginning in prehistoric times, Hahn proceeds to guide readers through the Greek, Roman, Islamic, Romanesque, Gothic, Renaissance, and modern styles. He explores the unique features of the Pantheon, the Hagia Sophia, the Great Mosque of Cordoba, the Duomo in Florence, Palladio's villas, and Saint Peter's Basilica, as well as the U.S. Capitol Building. Hahn celebrates the forms and structures of architecture made possible by mathematical achievements from Greek geometry, the Hindu-Arabic number system, two- and three-dimensional coordinate geometry, and calculus. Along the way, Hahn introduces groundbreaking architects, including Brunelleschi, Alberti, da Vinci, Bramante, Michelangelo, della Porta, Wren, Gaudí, Saarinen, Utzon, and Gehry. Rich in detail, this book takes readers on an expedition around the globe, providing a deeper understanding of the mathematical forces at play in the world's most elegant buildings. |
| excursions in modern mathematics: Excursions in Modern Math Tannenbaum, Robert Arnold, 1997-11 |
| excursions in modern mathematics: Excursions Modern Math Tannenbaum, 1995-01-01 |
| excursions in modern mathematics: Excursions in Modern Mathematics -Nasta Edition Tannenbaum, 2009 |
| excursions in modern mathematics: Excursions in Number Theory Charles Stanley Ogilvy, John Timothy Anderson, 1988-01-01 Challenging, accessible mathematical adventures involving prime numbers, number patterns, irrationals and iterations, calculating prodigies, and more. No special training is needed, just high school mathematics and an inquisitive mind. A splendidly written, well selected and presented collection. I recommend the book unreservedly to all readers. — Martin Gardner. |
| excursions in modern mathematics: Excursions in Geometry Charles Stanley Ogilvy, 1990-01-01 A straightedge, compass, and a little thought are all that's needed to discover the intellectual excitement of geometry. Harmonic division and Apollonian circles, inversive geometry, hexlet, Golden Section, more. 132 illustrations. |
| excursions in modern mathematics: Excursions in Modern Mathematics with Mini-Excursions a la Carte Plus Peter Tannenbaum, 2008-08-10 |
| excursions in modern mathematics: Insider's Guide to Teaching with Excursions in Modern Mathematics Peter Tannenbaum, |
| excursions in modern mathematics: Excursions in Classical Analysis Hongwei Chen, 2010-12-31 Excursions in Classical Analysis will introduce students to advanced problem solving and undergraduate research in two ways: it will provide a tour of classical analysis, showcasing a wide variety of problems that are placed in historical context, and it will help students gain mastery of mathematical discovery and proof. The [Author]; presents a variety of solutions for the problems in the book. Some solutions reach back to the work of mathematicians like Leonhard Euler while others connect to other beautiful parts of mathematics. Readers will frequently see problems solved by using an idea that, at first glance, might not even seem to apply to that problem. Other solutions employ a specific technique that can be used to solve many different kinds of problems. Excursions emphasizes the rich and elegant interplay between continuous and discrete mathematics by applying induction, recursion, and combinatorics to traditional problems in classical analysis. The book will be useful in students' preparations for mathematics competitions, in undergraduate reading courses and seminars, and in analysis courses as a supplement. The book is also ideal for self study, since the chapters are independent of one another and may be read in any order. |
| excursions in modern mathematics: Excursions in Modern Mathematics Plus MyMathLab Student Access Kit Peter Tannenbaum, 2009-03-17 |
| excursions in modern mathematics: Excursions in Modern Mathematics Peter Tannenbaum, 2013-08-27 Excursions in Modern Mathematics introduces non-math majors to the power of math by exploring applications like social choice and management science, showing that math is more than a set of formulas. Ideal for an applied liberal arts math course, Tannenbaum’s text is known for its clear, accessible writing style and its unique exercise sets that build in complexity from basic to more challenging. The Eighth Edition offers more real data and applications to connect with today’s students, expanded coverage of applications like growth, and revised exercise sets. MyMathLab exercise sets are expanded and the new Ready To Go MyMathLab course makes course set-up even easier. |
| excursions in modern mathematics: Mathematical Excursions Richard N. Aufmann, Richard D. Nation, Joanne Lockwood, Daniel K. Clegg, 2003-03-01 Developed for the liberal arts math course by a seasoned author team,Mathematical Excursions,is uniquely designed to help students see math at work in the contemporary world. Using the proven Aufmann Interactive Method, students learn to master problem-solving in meaningful contexts. In addition, multi-partExcursionexercises emphasize collaborative learning. The text's extensive topical coverage offers instructors flexibility in designing a course that meets their students' needs and curriculum requirements. TheExcursionsactivity and correspondingExcursion Exercises,denoted by an icon, conclude each section, providing opportunities for in-class cooperative work, hands-on learning, and development of critical-thinking skills. These activities are also ideal for projects or extra credit assignments. TheExcursionsare designed to reinforce the material that has just been covered in the section in a fun and engaging manner that will enhance a student's journey and discovery of mathematics. The proven Aufmann Interactive Method ensures that students try concepts and manipulate real-life data as they progress through the material. Every objective contains at least one set of matched-pair examples. The method begins with a worked-out example with a solution in numerical and verbal formats to address different learning styles. The matched problem, calledCheck Your Progress,is left for the student to try. Each problem includes a reference to a fully worked out solution in an appendix to which the student can refer for immediate feedback, concept reinforcement, identification of problem areas, and prevention of frustration. Eduspace, powered by Blackboard, for the Aufmann/Lockwood/Nation/CleggMath Excursionscourse features algorithmic exercises and test bank content in question pools. |
| excursions in modern mathematics: Guide to Competitive Programming Antti Laaksonen, 2018-01-02 This invaluable textbook presents a comprehensive introduction to modern competitive programming. The text highlights how competitive programming has proven to be an excellent way to learn algorithms, by encouraging the design of algorithms that actually work, stimulating the improvement of programming and debugging skills, and reinforcing the type of thinking required to solve problems in a competitive setting. The book contains many “folklore” algorithm design tricks that are known by experienced competitive programmers, yet which have previously only been formally discussed in online forums and blog posts. Topics and features: reviews the features of the C++ programming language, and describes how to create efficient algorithms that can quickly process large data sets; discusses sorting algorithms and binary search, and examines a selection of data structures of the C++ standard library; introduces the algorithm design technique of dynamic programming, and investigates elementary graph algorithms; covers such advanced algorithm design topics as bit-parallelism and amortized analysis, and presents a focus on efficiently processing array range queries; surveys specialized algorithms for trees, and discusses the mathematical topics that are relevant in competitive programming; examines advanced graph techniques, geometric algorithms, and string techniques; describes a selection of more advanced topics, including square root algorithms and dynamic programming optimization. This easy-to-follow guide is an ideal reference for all students wishing to learn algorithms, and practice for programming contests. Knowledge of the basics of programming is assumed, but previous background in algorithm design or programming contests is not necessary. Due to the broad range of topics covered at various levels of difficulty, this book is suitable for both beginners and more experienced readers. |
| excursions in modern mathematics: A Book of Abstract Algebra Charles C Pinter, 2010-01-14 Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition. |
| excursions in modern mathematics: Excursions into Combinatorial Geometry Vladimir Boltyanski, Horst Martini, P.S. Soltan, 2012-12-06 siehe Werbetext. |
| excursions in modern mathematics: The Unimaginable Mathematics of Borges' Library of Babel William Goldbloom Bloch, 2008-08-25 Combinatorics -- Topology and cosmology -- Information theory -- Geometry and Graph Theory -- Real Analysis -- More Combinatorics -- A Homomorphism |
| excursions in modern mathematics: Foundations of Modern Probability Olav Kallenberg, 2002-01-08 The first edition of this single volume on the theory of probability has become a highly-praised standard reference for many areas of probability theory. Chapters from the first edition have been revised and corrected, and this edition contains four new chapters. New material covered includes multivariate and ratio ergodic theorems, shift coupling, Palm distributions, Harris recurrence, invariant measures, and strong and weak ergodicity. |
| excursions in modern mathematics: Prelude to Mathematics W. W. Sawyer, 2012-04-19 This lively, stimulating account of non-Euclidean geometry by a noted mathematician covers matrices, determinants, group theory, and many other related topics, with an emphasis on the subject's novel, striking aspects. 1955 edition. |
| excursions in modern mathematics: Introduction to Mathematical Thinking Keith J. Devlin, 2012 Mathematical thinking is not the same as 'doing math'--unless you are a professional mathematician. For most people, 'doing math' means the application of procedures and symbolic manipulations. Mathematical thinking, in contrast, is what the name reflects, a way of thinking about things in the world that humans have developed over three thousand years. It does not have to be about mathematics at all, which means that many people can benefit from learning this powerful way of thinking, not just mathematicians and scientists.--Back cover. |
| excursions in modern mathematics: A Concrete Approach to Classical Analysis Marian Muresan, 2015-09-16 Mathematical analysis offers a solid basis for many achievements in applied mathematics and discrete mathematics. This new textbook is focused on differential and integral calculus, and includes a wealth of useful and relevant examples, exercises, and results enlightening the reader to the power of mathematical tools. The intended audience consists of advanced undergraduates studying mathematics or computer science. The author provides excursions from the standard topics to modern and exciting topics, to illustrate the fact that even first or second year students can understand certain research problems. The text has been divided into ten chapters and covers topics on sets and numbers, linear spaces and metric spaces, sequences and series of numbers and of functions, limits and continuity, differential and integral calculus of functions of one or several variables, constants (mainly pi) and algorithms for finding them, the W - Z method of summation, estimates of algorithms and of certain combinatorial problems. Many challenging exercises accompany the text. Most of them have been used to prepare for different mathematical competitions during the past few years. In this respect, the author has maintained a healthy balance of theory and exercises. |
| excursions in modern mathematics: Mathematics and Computation Avi Wigderson, 2019-10-29 From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography |
| excursions in modern mathematics: Playing with Infinity Rozsa Peter, 1986-01 Popular account ranges from counting to mathematical logic and covers many concepts related to infinity: graphic representation of functions; pairings, other combinations; prime numbers; logarithms, circular functions; more. 216 illustrations. |
| excursions in modern mathematics: An Invitation to Abstract Mathematics Béla Bajnok, 2020-10-27 This undergraduate textbook promotes an active transition to higher mathematics. Problem solving is the heart and soul of this book: each problem is carefully chosen to demonstrate, elucidate, or extend a concept. More than 300 exercises engage the reader in extensive arguments and creative approaches, while exploring connections between fundamental mathematical topics. Divided into four parts, this book begins with a playful exploration of the building blocks of mathematics, such as definitions, axioms, and proofs. A study of the fundamental concepts of logic, sets, and functions follows, before focus turns to methods of proof. Having covered the core of a transition course, the author goes on to present a selection of advanced topics that offer opportunities for extension or further study. Throughout, appendices touch on historical perspectives, current trends, and open questions, showing mathematics as a vibrant and dynamic human enterprise. This second edition has been reorganized to better reflect the layout and curriculum of standard transition courses. It also features recent developments and improved appendices. An Invitation to Abstract Mathematics is ideal for those seeking a challenging and engaging transition to advanced mathematics, and will appeal to both undergraduates majoring in mathematics, as well as non-math majors interested in exploring higher-level concepts. From reviews of the first edition: Bajnok’s new book truly invites students to enjoy the beauty, power, and challenge of abstract mathematics. ... The book can be used as a text for traditional transition or structure courses ... but since Bajnok invites all students, not just mathematics majors, to enjoy the subject, he assumes very little background knowledge. Jill Dietz, MAA Reviews The style of writing is careful, but joyously enthusiastic.... The author’s clear attitude is that mathematics consists of problem solving, and that writing a proof falls into this category. Students of mathematics are, therefore, engaged in problem solving, and should be given problems to solve, rather than problems to imitate. The author attributes this approach to his Hungarian background ... and encourages students to embrace the challenge in the same way an athlete engages in vigorous practice. John Perry, zbMATH |
| excursions in modern mathematics: Naming Infinity Loren Graham, Jean-Michel Kantor, 2009-03-31 In 1913, Russian imperial marines stormed an Orthodox monastery at Mt. Athos, Greece, to haul off monks engaged in a dangerously heretical practice known as Name Worshipping. Exiled to remote Russian outposts, the monks and their mystical movement went underground. Ultimately, they came across Russian intellectuals who embraced Name Worshipping—and who would achieve one of the biggest mathematical breakthroughs of the twentieth century, going beyond recent French achievements. Loren Graham and Jean-Michel Kantor take us on an exciting mathematical mystery tour as they unravel a bizarre tale of political struggles, psychological crises, sexual complexities, and ethical dilemmas. At the core of this book is the contest between French and Russian mathematicians who sought new answers to one of the oldest puzzles in math: the nature of infinity. The French school chased rationalist solutions. The Russian mathematicians, notably Dmitri Egorov and Nikolai Luzin—who founded the famous Moscow School of Mathematics—were inspired by mystical insights attained during Name Worshipping. Their religious practice appears to have opened to them visions into the infinite—and led to the founding of descriptive set theory. The men and women of the leading French and Russian mathematical schools are central characters in this absorbing tale that could not be told until now. Naming Infinity is a poignant human interest story that raises provocative questions about science and religion, intuition and creativity. |
| excursions in modern mathematics: The Mathematics of Diffusion John Crank, 1979 Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained. |
| excursions in modern mathematics: In Pursuit of the Traveling Salesman William J. Cook, 2014-11-09 The story of one of the greatest unsolved problems in mathematics What is the shortest possible route for a traveling salesman seeking to visit each city on a list exactly once and return to his city of origin? It sounds simple enough, yet the traveling salesman problem is one of the most intensely studied puzzles in applied mathematics—and it has defied solution to this day. In this book, William Cook takes readers on a mathematical excursion, picking up the salesman's trail in the 1800s when Irish mathematician W. R. Hamilton first defined the problem, and venturing to the furthest limits of today’s state-of-the-art attempts to solve it. He also explores its many important applications, from genome sequencing and designing computer processors to arranging music and hunting for planets. In Pursuit of the Traveling Salesman travels to the very threshold of our understanding about the nature of complexity, and challenges you yourself to discover the solution to this captivating mathematical problem. |
| excursions in modern mathematics: When Einstein Walked with Gödel Jim Holt, 2018-05-15 From Jim Holt, the New York Times bestselling author of Why Does the World Exist?, comes an entertaining and accessible guide to the most profound scientific and mathematical ideas of recent centuries in When Einstein Walked with Gödel: Excursions to the Edge of Thought. Does time exist? What is infinity? Why do mirrors reverse left and right but not up and down? In this scintillating collection, Holt explores the human mind, the cosmos, and the thinkers who’ve tried to encompass the latter with the former. With his trademark clarity and humor, Holt probes the mysteries of quantum mechanics, the quest for the foundations of mathematics, and the nature of logic and truth. Along the way, he offers intimate biographical sketches of celebrated and neglected thinkers, from the physicist Emmy Noether to the computing pioneer Alan Turing and the discoverer of fractals, Benoit Mandelbrot. Holt offers a painless and playful introduction to many of our most beautiful but least understood ideas, from Einsteinian relativity to string theory, and also invites us to consider why the greatest logician of the twentieth century believed the U.S. Constitution contained a terrible contradiction—and whether the universe truly has a future. |
| excursions in modern mathematics: Mirror Symmetry Kentaro Hori, 2003 This thorough and detailed exposition is the result of an intensive month-long course on mirror symmetry sponsored by the Clay Mathematics Institute. It develops mirror symmetry from both mathematical and physical perspectives with the aim of furthering interaction between the two fields. The material will be particularly useful for mathematicians and physicists who wish to advance their understanding across both disciplines. Mirror symmetry is a phenomenon arising in string theory in which two very different manifolds give rise to equivalent physics. Such a correspondence has significant mathematical consequences, the most familiar of which involves the enumeration of holomorphic curves inside complex manifolds by solving differential equations obtained from a ``mirror'' geometry. The inclusion of D-brane states in the equivalence has led to further conjectures involving calibrated submanifolds of the mirror pairs and new (conjectural) invariants of complex manifolds: the Gopakumar-Vafa invariants. This book gives a single, cohesive treatment of mirror symmetry. Parts 1 and 2 develop the necessary mathematical and physical background from ``scratch''. The treatment is focused, developing only the material most necessary for the task. In Parts 3 and 4 the physical and mathematical proofs of mirror symmetry are given. From the physics side, this means demonstrating that two different physical theories give isomorphic physics. Each physical theory can be described geometrically, and thus mirror symmetry gives rise to a ``pairing'' of geometries. The proof involves applying $R\leftrightarrow 1/R$ circle duality to the phases of the fields in the gauged linear sigma model. The mathematics proof develops Gromov-Witten theory in the algebraic setting, beginning with the moduli spaces of curves and maps, and uses localization techniques to show that certain hypergeometric functions encode the Gromov-Witten invariants in genus zero, as is predicted by mirror symmetry. Part 5 is devoted to advanced topi This one-of-a-kind book is suitable for graduate students and research mathematicians interested in mathematics and mathematical and theoretical physics. |
| excursions in modern mathematics: A Tour of the Calculus David Berlinski, 2011-04-27 Were it not for the calculus, mathematicians would have no way to describe the acceleration of a motorcycle or the effect of gravity on thrown balls and distant planets, or to prove that a man could cross a room and eventually touch the opposite wall. Just how calculus makes these things possible and in doing so finds a correspondence between real numbers and the real world is the subject of this dazzling book by a writer of extraordinary clarity and stylistic brio. Even as he initiates us into the mysteries of real numbers, functions, and limits, Berlinski explores the furthest implications of his subject, revealing how the calculus reconciles the precision of numbers with the fluidity of the changing universe. An odd and tantalizing book by a writer who takes immense pleasure in this great mathematical tool, and tries to create it in others.--New York Times Book Review |
| excursions in modern mathematics: Infinitesimal Amir Alexander, 2014-07-03 On August 10, 1632, five leading Jesuits convened in a sombre Roman palazzo to pass judgment on a simple idea: that a continuous line is composed of distinct and limitlessly tiny parts. The doctrine would become the foundation of calculus, but on that fateful day the judges ruled that it was forbidden. With the stroke of a pen they set off a war for the soul of the modern world. Amir Alexander takes us from the bloody religious strife of the sixteenth century to the battlefields of the English civil war and the fierce confrontations between leading thinkers like Galileo and Hobbes. The legitimacy of popes and kings, as well as our modern beliefs in human liberty and progressive science, hung in the balance; the answer hinged on the infinitesimal. Pulsing with drama and excitement, Infinitesimal will forever change the way you look at a simple line. |
| excursions in modern mathematics: Differential Geometry of Curves and Surfaces Kristopher Tapp, 2016-09-30 This is a textbook on differential geometry well-suited to a variety of courses on this topic. For readers seeking an elementary text, the prerequisites are minimal and include plenty of examples and intermediate steps within proofs, while providing an invitation to more excursive applications and advanced topics. For readers bound for graduate school in math or physics, this is a clear, concise, rigorous development of the topic including the deep global theorems. For the benefit of all readers, the author employs various techniques to render the difficult abstract ideas herein more understandable and engaging. Over 300 color illustrations bring the mathematics to life, instantly clarifying concepts in ways that grayscale could not. Green-boxed definitions and purple-boxed theorems help to visually organize the mathematical content. Color is even used within the text to highlight logical relationships. Applications abound! The study of conformal and equiareal functions is grounded in its application to cartography. Evolutes, involutes and cycloids are introduced through Christiaan Huygens' fascinating story: in attempting to solve the famous longitude problem with a mathematically-improved pendulum clock, he invented mathematics that would later be applied to optics and gears. Clairaut’s Theorem is presented as a conservation law for angular momentum. Green’s Theorem makes possible a drafting tool called a planimeter. Foucault’s Pendulum helps one visualize a parallel vector field along a latitude of the earth. Even better, a south-pointing chariot helps one visualize a parallel vector field along any curve in any surface. In truth, the most profound application of differential geometry is to modern physics, which is beyond the scope of this book. The GPS in any car wouldn’t work without general relativity, formalized through the language of differential geometry. Throughout this book, applications, metaphors and visualizations are tools that motivate and clarify the rigorous mathematical content, but never replace it. |
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Apr 25, 2018 · Department of Mathematics Syllabus Math 01.115-Contemporary Mathematics CATALOG DESCRIPTION: Math 01.115 - Contemporary Mathematics 3 S.H. Prerequisites: Basic Algebra II ... Excursions in Modern Mathematics, Peter Tannenbaum, Pearson, 9th edition Updated: 4.25.18 .
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Excursions in Modern Mathematics, Tannenbaum, 10th edition. Calculators You should have a scientific calculator. You will not need a graphing calculator, though you are welcome to use one. You are expected to bring your calculator to class each day. You may not use a phone or any device with internet access as a calculator on quizzes or tests.
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Excursions in Modern Mathematics Peter Tannenbaum,2007 For undergraduate courses in Liberal Arts Mathematics, Quantitative Literacy, and General Education. This very successful liberal arts mathematics textbook is a collection of excursions into the real-world applications of modern mathematics. The excursions are organized into four independent
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Text: Excursions in Modern Mathematics, 6th edition, by Tannenbaum. The actual content of the course varies from instructor to instructor and from semester to semester. Most instructors choose topics from the chapters in the text that are listed here. Part 1: The Mathematics of Social Choice
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Excursions in Modern Mathematics, Books a la Carte Edition Excursions in Modern Mathematics -Nasta Edition Tannenbaum 2009 An Invitation to Abstract Mathematics Béla Bajnok 2020-10-27 This undergraduate textbook promotes an active transition to higher mathematics. Problem solving is the heart and soul of this
Excursions in Modern Mathematics, Sixth Edition,
Textbook: Excursions in Modern Mathematics, Sixth Edition, by Peter Tannenbaum. Course Objectives: The goal of this course is for you to gain a basic ... In particular, you should leave this course with a sense that mathematics is more than just working with numbers, and that it can be used in a variety of applications. Grades: Grades will be ...
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Excursions in Modern Mathematics Peter Tannenbaum,Anne Kelly,2014 Excursions in Modern Mathematics Peter Tannenbaum,2014 Disability and Academic Exclusion interrogates obstacles the disabled have encountered in education from a historical perspective that begins with the denial of literacy to minorities in the colonial era to the later ...
Excursions In Modern Mathematics (book) - mx.up.edu.ph
Excursions In Modern Mathematics: Bestsellers in 2023 The year 2023 has witnessed a remarkable surge in literary brilliance, with numerous captivating novels enthralling the hearts of readers worldwide. Lets delve into the realm of top-
Excursions In Modern Mathematics 7th Edition(1)
Excursions in Modern Mathematics Peter Tannenbaum,2007 For undergraduate courses in Liberal Arts Mathematics, Quantitative Literacy, and General Education. This very successful liberal arts mathematics textbook is a collection of excursions into the real-world applications of modern mathematics. The excursions are organized into four independent
Excursions In Modern Mathematics 7th Edition(1)
Excursions in Modern Mathematics Peter Tannenbaum,2007 For undergraduate courses in Liberal Arts Mathematics, Quantitative Literacy, and General Education. This very successful liberal arts mathematics textbook is a collection of excursions into the real-world applications of modern mathematics. The excursions are organized into four independent
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10/21/2013 3 Copyright © 2014 Pearson Education. All rights reseCopyright © 2010 Pearson Education, Inc. rved. Excursions in Modern Mathematics, 7e: 1.1 -5.1-1313 A ...
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Excursions In Modern Mathematics Test Answers WCaty. The mj.unc.edu 1 / 85. Original Black Cultures of Eastern Europe and Asia. LEARN NC has been archived soe unc edu. Strong ... in Modern English mj.unc.edu 10 / 85. Ambleside Online. Brain Blast Quiz Final Fantasy XIII 2 Wiki Guide IGN WCaty May 11th, 2018 - Continuing mj.unc.edu 11 / 85 ...
Math 1001, Excursions in Mathematics, Spring 2003 Semester
Math 1001, Excursions in Mathematics, Spring 2003 Semester Lecturer: Jonathan Rogness O ce: Vincent Hall 358 ... some di erent areas of modern mathematics, particularly those which are not covered in the standard \algebra, geometry, trigonometry, calculus" sequence of courses. The course aims to expose you to mathematical thinking,
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Text: Peter Tannenbaum, Excursions in Modern Mathematics, second custom edition for the University of Kentucky, Pearson. Course Website: http:
Excursions In Modern Mathematics 5th Edition Teacher ? ; …
Excursions in Modern Mathematics, Books a la Carte Edition Peter Tannenbaum 2012-12-21 This edition features the exact same content as the traditional text in a convenient, three-hole- punched, loose-leaf version. Books a la Carte also offer a great value- …
Excursions In Modern Mathematics (book) - bihon.up.edu.ph
Excursions in Modern Mathematics Peter Tannenbaum,2003-03-01 Contains worked out solutions to odd numbered problems from the text Also contains a glossary of terms for each chapter Excursions in Modern Mathematics with Mini-Excursions Peter Tannenbaum,2006-10 For undergraduate courses in Liberal Arts
Excursions In Modern Mathematics 7th Edition Solutions Pdf …
excursions-in-modern-mathematics-7th-edition-solutions-pdf 2 Downloaded from g3.pymnts.com on 2019-04-27 by guest 2012-09-07 David Lippman Math in Society is a survey of contemporary mathematical topics, appropriate for a college-level topics course for liberal arts major, or as a general quantitative reasoning course.This book is
Excursions In Modern Mathematics 5th Edition Teacher …
Excursions in Modern Mathematics: With Mini-Excursions Peter Tannenbaum,2006-12-01 Student Resource Guide Dale R. Buske,Peter Tannenbaum,2006-08 Student Resource Guide contains full worked out solutions to odd-numbered exercises from the text, selected hints that point the reader in one of many directions leading to a
Excursions In Modern Math (PDF) - cie-advances.asme.org
5. Are there any misconceptions about modern mathematics that you'd like to address? A common misconception is that modern mathematics is purely theoretical and irrelevant to real-world problems. As this post demonstrates, modern mathematical concepts find applications in a wide range of fields, impacting our daily lives in countless ways.
3 The Mathematics of Sharing - University of Kentucky
Copyright © 2010 Pearson Education, Inc. Excursions in Modern Mathematics, 7e: 3.2 - 8 This example illustrates that it is better to be . Author: Paul Koester ...
Excursions In Modern Mathematics (book)
Excursions Modern Math Tannenbaum,1995-01-01 Excursions in Modern Mathematics Plus MyMathLab Student Access Kit Peter Tannenbaum,2009-03-17 Student Resource Guide for Excursions in Modern Mathematics Dale R.
