Products related to Mathematical:
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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 Logic
Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logic, using natural deduction and leading up to the completeness theorem for first-order logic.At each stage of the text, the reader is given an intuition based on standard mathematical practice, which is subsequently developed with clean formal mathematics.Alongside the practical examples, readers learn what can and can't be calculated; for example the correctness of a derivation proving a given sequent can be tested mechanically, but there is no general mechanical test for the existence of a derivation proving the given sequent.The undecidability results are proved rigorously in an optional final chapter, assuming Matiyasevich's theorem characterising the computably enumerable relations.Rigorous proofs of the adequacy and completeness proofs of the relevant logics are provided, with careful attention to the languages involved.Optional sections discuss the classification of mathematical structures by first-order theories; the required theory of cardinality is developed from scratch.Throughout the book there are notes on historical aspects of the material, and connections with linguistics and computer science, and the discussion of syntax and semantics is influenced by modern linguistic approaches.Two basic themes in recent cognitive science studies of actual human reasoning are also introduced.Including extensive exercises and selected solutions, this text is ideal for students in Logic, Mathematics, Philosophy, and Computer Science.
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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 Weaknesses
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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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Mathematical Adventures
School mathematics sometimes excite and sometimes scare, and sadly, sometimes bore.In fact, elementary school arithmetic seems to get us through most situations.So why all the rest? This book aspires to give a glimpse into how things started and evolved, and how math can help us today, from simple measurements to navigating using mathematically simplified maps.The accompanying activities (some easier and some more challenging ones) aim to engage you with what was happening at a given time.Answers and explanations are in the end of the book.
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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 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 are mathematical functions?
Mathematical functions are relationships between a set of inputs and a set of outputs, where each input is related to exactly one output. They are typically represented by an equation or a rule that describes how the input values are transformed into output values. Functions are fundamental in mathematics and are used to model various real-world phenomena, analyze data, and solve problems in a systematic way. They can take many forms, such as linear, quadratic, exponential, trigonometric, and logarithmic functions.
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What is mathematical optimization?
Mathematical optimization is the process of finding the best solution to a problem from a set of possible solutions. It involves maximizing or minimizing a certain objective function while satisfying a set of constraints. This can be applied to a wide range of fields, including engineering, economics, and computer science, to help make better decisions and improve efficiency. Optimization problems can be solved using various mathematical techniques such as linear programming, nonlinear programming, and integer programming.
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What are mathematical equations?
Mathematical equations are expressions that show the relationship between two or more quantities using mathematical symbols and operations. They typically consist of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to represent and solve various mathematical problems and are an essential tool in fields such as physics, engineering, and economics. They can be simple or complex, and their solutions provide valuable information about the relationships between different quantities.
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What is the difference between a mathematical series and a mathematical sequence?
A mathematical sequence is a list of numbers that follow a specific pattern or rule, while a mathematical series is the sum of the terms in a sequence. In other words, a sequence is a set of numbers in a specific order, while a series is the result of adding up all the terms in that sequence.
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