Products related to Mathematical:
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Mathematical Logic
What is a mathematical proof? How can proofs be justified? Are there limitations to provability? To what extent can machines carry out mathe matical proofs?Only in this century has there been success in obtaining substantial and satisfactory answers.The present book contains a systematic discussion of these results.The investigations are centered around first-order logic.Our first goal is Godel's completeness theorem, which shows that the con sequence relation coincides with formal provability: By means of a calcu lus consisting of simple formal inference rules, one can obtain all conse quences of a given axiom system (and in particular, imitate all mathemat ical proofs).A short digression into model theory will help us to analyze the expres sive power of the first-order language, and it will turn out that there are certain deficiencies.For example, the first-order language does not allow the formulation of an adequate axiom system for arithmetic or analysis.On the other hand, this difficulty can be overcome--even in the framework of first-order logic-by developing mathematics in set-theoretic terms.We explain the prerequisites from set theory necessary for this purpose and then treat the subtle relation between logic and set theory in a thorough manner.
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Mathematical Physics
Mathematical Physics is an introduction to such basic mathematical structures as groups, vector spaces, topological spaces, measure spaces, and Hilbert space.Geroch uses category theory to emphasize both the interrelationships among different structures and the unity of mathematics.Perhaps the most valuable feature of the book is the illuminating intuitive discussion of the "whys" of proofs and of axioms and definitions.This book, based on Geroch's University of Chicago course, will be especially helpful to those working in theoretical physics, including such areas as relativity, particle physics, and astrophysics.
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Mathematical Meditations
Mathematical Meditations identifies, explores, and celebrates those aspects of mathematics that are good for you and your overall wellbeing.It is necessary for everyone to have a little time to think every so often: to contemplate, meditate, and try to understand where you are and what is going on around you.Mathematics can help you with all of that. The Meditations in this book are the product of thousands of years of mathematical discourse.As you read through the book and work through the various exercises, you will discover new mechanisms that allow you to contemplate and understand some complex mathematical principles.However, the focus will always be wider than a mere dry comprehension of theory, as you will be encouraged to meditate upon the deeper intrinsic beauty of mathematics and what it can reveal to us about the world around us. FeaturesAn original, engaging narrative format replete with novel exercises and examplesCould be used in a classroom setting for liberal arts students, mathematics undergraduates, or high school teachersAccessible to anyone who wants to explore a different kind of perspective on mathematics
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Mathematical Pluralism
Mathematical pluralism is the view that there is an irreducible plurality of pure mathematical structures, each with their own internal logics; and that qua pure mathematical structures they are all equally legitimate.Mathematical pluralism is a relatively new position on the philosophical landscape.This Element provides an introduction to the position.
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What is a mathematical bacterial culture?
A mathematical bacterial culture is a model that uses mathematical equations to describe the growth and behavior of bacterial populations. These models typically take into account factors such as the initial population size, growth rate, and environmental conditions to predict how the population will change over time. By using mathematical models, researchers can gain insights into the dynamics of bacterial populations and how they respond to different conditions or interventions.
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What is an example of a mathematical solution for a bacterial culture?
One example of a mathematical solution for a bacterial culture is the use of the logistic growth equation. This equation models the growth of a population over time, taking into account factors such as the carrying capacity of the environment and the growth rate of the population. By using this equation, researchers can predict the growth of a bacterial culture under different conditions and make informed decisions about how to optimize the culture for specific applications, such as biotechnology or medical research. This mathematical approach allows for a more precise and efficient management of bacterial cultures in various fields.
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What is an example of a mathematical solution to a bacterial culture?
One example of a mathematical solution to a bacterial culture is the use of the logistic growth equation. This equation models the growth of a population over time, taking into account factors such as the carrying capacity of the environment and the growth rate of the bacteria. By using this equation, researchers can predict how the population of bacteria will change over time and optimize conditions for their growth in laboratory settings. This mathematical approach helps in understanding and controlling bacterial cultures for various applications in research and industry.
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Mathematical Writing
This book teaches the art of writing mathematics, an essential -and difficult- skill for any mathematics student.The book begins with an informal introduction on basic writing principles and a review of the essential dictionary for mathematics.Writing techniques are developed gradually, from the small to the large: words, phrases, sentences, paragraphs, to end with short compositions.These may represent the introduction of a concept, the abstract of a presentation or the proof of a theorem.Along the way the student will learn how to establish a coherent notation, mix words and symbols effectively, write neat formulae, and structure a definition. Some elements of logic and all common methods of proofs are featured, including various versions of induction and existence proofs.The book concludes with advice on specific aspects of thesis writing (choosing of a title, composing an abstract, compiling a bibliography) illustrated by large number of real-life examples.Many exercises are included; over 150 of them have complete solutions, to facilitate self-study. Mathematical Writing will be of interest to all mathematics students who want to raise the quality of their coursework, reports, exams, and dissertations.
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Mathematical Cavalcade
Mathematical Cavalcade follows the very successful Amazing Mathematical Amusement Arcade and The Mathematical Funfair by the same author.It contains a further 131 puzzles to challenge people of all ages.Hints and solutions are given in a commentary at the back of the book.
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Mathematical Puzzles
Research in mathematics is much more than solving puzzles, but most people will agree that solving puzzles is not just fun: it helps focus the mind and increases one's armory of techniques for doing mathematics.Mathematical Puzzles makes this connection explicit by isolating important mathematical methods, then using them to solve puzzles and prove a theorem. Features A collection of the world’s best mathematical puzzles Each chapter features a technique for solving mathematical puzzles, examples, and finally a genuine theorem of mathematics that features that technique in its proof Puzzles that are entertaining, mystifying, paradoxical, and satisfying; they are not just exercises or contest problems.
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Mathematical Conundrums
Want to sharpen your mathematical wits? If so, then Mathematical Conundrums is for you. Daily Telegraph enigmatologist, Barry R. Clarke, presents over 120 fiendish problems that will test both your ingenuity and persistence.Between these covers are puzzles in geometry, arithmetic, and algebra (there is even a section for computer programmers). And, for the smartest readers who wish to stretch their mind to its limits, a selection of engaging logic and visual lateral puzzles is included.Although no puzzle requires a greater knowledge of mathematics than the high school curriculum, this collection will take you to the edge.But are you equal to the challenge? Features High-school level of mathematics is the only pre-requisiteVariety of algebraic, route-drawing, and geometrical conundrumsHints section for the lateral puzzlesWarm-up excercises to sharpen the witsFull solutions to every problemBarry R.Clarke has published over 1,500 puzzles in The Daily Telegraph and has contributed enigmas to New Scientist, The Sunday Times, Reader’s Digest, The Sunday Telegraph, and Prospect magazine.His book Challenging Logic Puzzles Mensa has sold over 100,000 copies.As well as a PhD in Shakespeare Studies, Barry has a master’s degree and academic publications in quantum physics.He is now working on a revised theory of the hydrogen atom.Other skills include mathematics tutor, filmmaker, comedy-sketch writer, cartoonist, computer programmer, and blues guitarist!For more information please visit http://barryispuzzled.com.
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What are mathematical prisms?
Mathematical prisms are three-dimensional shapes that have two parallel and congruent polygonal bases connected by rectangular faces. The bases can be any polygon, such as a triangle, square, or pentagon. The height of the prism is the perpendicular distance between the two bases. The volume of a prism is calculated by multiplying the area of the base by the height.
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What are mathematical terms?
Mathematical terms are words or phrases used to describe mathematical concepts, operations, or relationships. They are used to communicate specific ideas or instructions in the language of mathematics. Examples of mathematical terms include "addition," "subtraction," "equation," "variable," "function," and "theorem." Understanding mathematical terms is essential for effectively solving mathematical problems and communicating mathematical ideas.
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What are mathematical formulas?
Mathematical formulas are concise and specific representations of mathematical relationships or rules. They are used to express mathematical concepts, calculations, and relationships between variables in a clear and systematic way. Formulas often consist of symbols, numbers, and mathematical operations, and are used to solve equations, make predictions, and perform calculations in various fields of mathematics and science. They provide a standardized and efficient way to communicate mathematical concepts and principles.
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Are mathematical functions bounded?
Mathematical functions can be bounded or unbounded, depending on their behavior. A function is said to be bounded if its output values are limited within a certain range. For example, the sine function is bounded between -1 and 1. However, functions like the natural logarithm or the quadratic function are unbounded, as their output values can grow without limit. Therefore, whether a mathematical function is bounded or not depends on its specific properties and behavior.
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