Products related to Mathematical:
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Symmetry : A Mathematical Exploration
This textbook invites readers to explore the properties of objects that we effortlessly recognize as symmetrical.From the human body, to elaborate artworks and abstract networks, symmetry is ubiquitous in the world around us; it is essential to function and beauty across the built and natural world.By developing mathematical language to describe symmetry, this textbook equips readers to explore symmetries with precision, illuminating commonalities across art and science. Beginning with an exploration of intuitive notions of symmetry, the author introduces the algebraic structure of groups by examining rotations and reflections.Topics that follow include the classification of two-dimensional patterns, the Platonic solids, and a study of real and prime numbers.This second edition features numerous new examples and exercises, “Elements of Mathematics” sections that more closely examine mathematical tools, and optional content that offers opportunities for extension.Figures are woven into the presentation throughout, with many illustrations now offered in motion as integrated video content. Symmetry suits a wide audience, demanding no mathematical training past high school basics, yet stretching the imagination of math and non-math majors alike.Its engaging yet rigorous style offers a window into mathematicians’ ways of thinking.By developing mathematical reasoning skills in a spatial context, this text is ideal for a course that meets quantitative requirements for non-STEM majors.Instructors will appreciate the author’s comprehensive online resources, which include a full set of animated lecture slides; all readers will delight in watching the book’s content come alive using the multimedia app.
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Mathematical Analysis II
This secondEnglish edition of a very popular two-volume work presents a thorough firstcourse in analysis, leading from real numbers to such advanced topics asdifferential forms on manifolds; asymptotic methods; Fourier, Laplace, andLegendre transforms; elliptic functions; and distributions.Especially notablein this course are the clearly expressed orientation toward the naturalsciences and the informal exploration of the essence and the roots of the basicconcepts and theorems of calculus.Clarity of exposition is matched by a wealthof instructive exercises, problems, and fresh applications to areas seldomtouched on in textbooks on real analysis. The maindifference between the second and first English editions is the addition of aseries of appendices to each volume.There are six of them in the first volumeand five in the second.The subjects of these appendices are diverse. They aremeant to be useful to both students (in mathematics and physics) and teachers,who may be motivated by different goals.Some of the appendices are surveys,both prospective and retrospective.The final survey establishes importantconceptual connections between analysis and other parts of mathematics. This second volumepresents classical analysis in its current form as part of a unifiedmathematics.It shows how analysis interacts with other modern fields ofmathematics such as algebra, differential geometry, differential equations,complex analysis, and functional analysis.This book provides a firm foundationfor advanced work in any of these directions.
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Sharpening Mathematical Analysis Skills
This book gathers together a novel collection of problems in mathematical analysis that are challenging and worth studying.They cover most of the classical topics of a course in mathematical analysis, and include challenges presented with an increasing level of difficulty.Problems are designed to encourage creativity, and some of them were especially crafted to lead to open problems which might be of interest for students seeking motivation to get a start in research. The sets of problems are comprised in Part I. The exercises are arranged on topics, many of them being preceded by supporting theory.Content starts with limits, series of real numbers and power series, extending to derivatives and their applications, partial derivatives and implicit functions.Difficult problems have been structured in parts, helping the reader to find a solution.Challenges and open problems are scattered throughout the text, being an invitation to discover new original methodsfor proving known results and establishing new ones.The final two chapters offer ambitious readers splendid problems and two new proofs of a famous quadratic series involving harmonic numbers.In Part II, the reader will find solutions to the proposed exercises.Undergraduate students in mathematics, physics and engineering, seeking to strengthen their skills in analysis, will most benefit from this work, along with instructors involved in math contests, individuals who want to enrich and test their knowledge in analysis, and anyone willing to explore the standard topics of mathematical analysis in ways that aren’t commonly seen in regular textbooks.
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Mathematical Models In Science
Mathematical Models in Science treats General Relativity and Quantum Mechanics in a non-commutative Algebraic Geometric framework.Based on ideas first published in Geometry of Time-Spaces: Non-commutative Algebraic Geometry Applied to Quantum Theory (World Scientific, 2011), Olav Arnfinn Laudal proposes a Toy Model as a Theory of Everything, starting with the notion of the Big Bang in Cosmology, modeled as the non-commutative deformation of a thick point.From this point, the author shows how to extract reasonable models for both General Relativity and Quantum Theory.This book concludes that the universe turns out to be the 6-dimensional Hilbert scheme of pairs of points in affine 3-space.With this in place, one may develop within the model much of the physics known to the reader.In particular, this theory is applicable to the concept of Dark Matter and its effects on our visual universe.Hence, Mathematical Models in Science proves the dependency of deformation theory in Mathematical Physics and summarizes the development of physical applications of pure mathematics developed in the twentieth century.
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What is the connection between computer science and mathematical research?
Computer science and mathematical research are closely connected because computer science often relies on mathematical principles and techniques. Many algorithms and data structures used in computer science are based on mathematical concepts such as calculus, linear algebra, and discrete mathematics. Additionally, mathematical research often involves the use of computer simulations and modeling to test and validate theories. The two fields also share a common focus on problem-solving and logical reasoning, making them complementary and interdependent.
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What is a mathematical random experiment?
A mathematical random experiment is a process or procedure that leads to one of several possible outcomes, each with a certain probability of occurring. It is a way to model real-world situations where the outcome is uncertain or unpredictable. In mathematical terms, a random experiment can be described by a sample space, which is the set of all possible outcomes, and a probability measure that assigns a likelihood to each outcome. By studying random experiments, mathematicians can analyze and predict the likelihood of different outcomes occurring.
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Is computer science very mathematical?
Yes, computer science is very mathematical. It involves the study of algorithms, data structures, and problem-solving techniques, all of which require a strong foundation in mathematics. Additionally, computer science often involves complex mathematical concepts such as discrete mathematics, calculus, and linear algebra, which are essential for understanding and developing computer programs and systems. Therefore, a solid understanding of mathematical principles is crucial for success in the field of computer science.
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What mathematical problems could I research?
There are countless mathematical problems that you could research, depending on your interests and expertise. Some potential areas of research could include number theory, cryptography, optimization, graph theory, differential equations, mathematical modeling, or even the application of mathematics in other fields such as physics, biology, or economics. You could also explore open problems in specific branches of mathematics, such as the Riemann hypothesis in number theory or the P vs NP problem in computer science. Ultimately, the possibilities are vast, and you could choose to delve into any area of mathematics that piques your curiosity.
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Mathematical Analysis of Infectious Diseases
Mathematical Analysis of Infectious Diseases updates on the mathematical and epidemiological analysis of infectious diseases.Epidemic mathematical modeling and analysis is important, not only to understand disease progression, but also to provide predictions about the evolution of disease.One of the main focuses of the book is the transmission dynamics of the infectious diseases like COVID-19 and the intervention strategies.It also discusses optimal control strategies like vaccination and plasma transfusion and their potential effectiveness on infections using compartmental and mathematical models in epidemiology like SI, SIR, SICA, and SEIR. The book also covers topics like: biodynamic hypothesis and its application for the mathematical modeling of biological growth and the analysis of infectious diseases, mathematical modeling and analysis of diagnosis rate effects and prediction of viruses, data-driven graphical analysis of epidemic trends, dynamic simulation and scenario analysis of the spread of diseases, and the systematic review of the mathematical modeling of infectious disease like coronaviruses.
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Mathematical Analysis and its Applications
This book covers contemporary topics in mathematical analysis and its applications and relevance in other areas of research.It provides a better understanding of methods, problems, and applications in mathematical analysis.It also covers applications and uses of operator theory, approximation theory, optimization, variable exponent analysis, inequalities, special functions, functional equations, statistical convergence and some function spaces, and presents various associated problems and ways to solve such problems.The book provides readers a better understanding of discussed research problems by presenting related developments in reasonable details.It strives to bring scientists, researchers and scholars together on a common platform.
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Mathematical Analysis : Theory and Applications
Mathematical Analysis: Theory and Applications provides an overview of the most up-to-date developments in the field, presenting original contributions and surveys from a spectrum of respected academics.Readers will discover numerous valuable tools and techniques to enhance their understanding of recent advancements in mathematical analysis and its applications.Each chapter highlights new research directions, making this book suitable for graduate students, faculty, and researchers with an active interest in the development of mathematical analysis and its practical implementation.Minimal prerequisites in analysis, topology, and functional analysis are required for readers to fully benefit from the content. Features? Showcases the latest advancements in these areas by featuring contributions from distinguished scientists and mathematicians from around the world?Suitable as a reference for postgraduate students and researchers?Explores future research directions
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Mathematical Foundations for Data Analysis
This textbook, suitable for an early undergraduate up to a graduate course, provides an overview of many basic principles and techniques needed for modern data analysis.In particular, this book was designed and written as preparation for students planning to take rigorous Machine Learning and Data Mining courses.It introduces key conceptual tools necessary for data analysis, including concentration of measure and PAC bounds, cross validation, gradient descent, and principal component analysis.It also surveys basic techniques in supervised (regression and classification) and unsupervised learning (dimensionality reduction and clustering) through an accessible, simplified presentation.Students are recommended to have some background in calculus, probability, and linear algebra. Some familiarity with programming and algorithms is useful to understand advanced topics on computational techniques.
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I urgently need help in Mathematical Analysis.
If you urgently need help in Mathematical Analysis, I recommend reaching out to a tutor or professor for one-on-one assistance. You can also try looking for online resources, such as video tutorials or practice problems, to help clarify any concepts you are struggling with. Additionally, forming a study group with classmates can be beneficial for discussing difficult topics and working through problems together.
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Can you help me with mathematical analysis?
Yes, I can help you with mathematical analysis. I can assist you with understanding and solving problems related to calculus, differential equations, linear algebra, and other mathematical topics. Just let me know what specific concepts or problems you need help with, and I will do my best to provide clear explanations and guidance.
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What is the problem in mathematical analysis?
The problem in mathematical analysis is to rigorously study and understand the behavior of functions, sequences, and series. This involves investigating concepts such as continuity, differentiability, integrability, and convergence. The challenge lies in developing precise definitions and theorems to describe and analyze these mathematical objects, as well as proving these results using logical reasoning and mathematical techniques. Additionally, mathematical analysis often deals with infinite processes, which can introduce complexities and subtleties that require careful consideration.
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What is a mathematical question about analysis?
A mathematical question about analysis could be: "What is the limit of the sequence (1/n) as n approaches infinity?" This question involves the concept of limits in analysis, which is concerned with the behavior of functions and sequences as their inputs approach certain values. By studying the limit of this sequence, one can gain insight into the behavior of functions and sequences as they approach certain values, which is a fundamental concept in mathematical analysis.
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