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  • Mathematical Physics
    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
    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
    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 Logic
    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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  • How do you investigate local extrema in a mathematical function?

    To investigate local extrema in a mathematical function, you first find the critical points by setting the derivative of the function equal to zero and solving for the variable. Then, you use the second derivative test to determine whether each critical point corresponds to a local maximum, local minimum, or neither. If the second derivative is positive at a critical point, the function has a local minimum at that point; if the second derivative is negative, the function has a local maximum at that point. If the second derivative is zero or undefined, the test is inconclusive and you may need to use other methods to determine the nature of the critical point.

  • How do you calculate the local slope of this mathematical problem?

    To calculate the local slope of a mathematical problem, you can use calculus. Specifically, you would find the derivative of the function at the point of interest. The derivative gives you the rate of change of the function at that point, which represents the local slope. By evaluating the derivative at the specific point, you can determine the slope of the function at that point.

  • What mathematical skills are required to work in emergency medical services?

    Mathematical skills required to work in emergency medical services include the ability to calculate medication dosages based on patient weight and condition, interpret vital signs and lab results, and perform basic arithmetic for tasks such as calculating IV drip rates or determining the appropriate amount of fluid to administer. Additionally, EMS professionals need to be able to quickly and accurately perform mental math in high-pressure situations to make critical decisions about patient care. Strong mathematical skills are essential for providing safe and effective medical treatment in emergency situations.

  • What is the function of price in mathematical business calculations?

    Price plays a crucial role in mathematical business calculations as it helps determine the total revenue, profit, and cost of goods sold. By multiplying the price per unit by the quantity sold, businesses can calculate their total revenue. Price is also used in calculating profit margins by subtracting the cost per unit from the selling price. Additionally, price elasticity is considered when analyzing consumer behavior and making pricing decisions to maximize profits.

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  • Mathematical Conundrums
    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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  • Mathematical Meditations
    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 examples. Could be used in a classroom setting for liberal arts students, mathematics undergraduates, or high school teachers. Accessible to anyone who wants to explore a different kind of perspective on mathematics.

    Price: 22.99 £ | Shipping*: 3.99 £
  • Mathematical Meditations
    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 examples. Could be used in a classroom setting for liberal arts students, mathematics undergraduates, or high school teachers. Accessible to anyone who wants to explore a different kind of perspective on mathematics.

    Price: 150.00 £ | Shipping*: 0.00 £
  • Mathematical Adventures
    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.

    Price: 9.99 £ | Shipping*: 3.99 £
  • Is it possible to study Business Law with average mathematical skills?

    Yes, it is possible to study Business Law with average mathematical skills. While some aspects of Business Law may involve mathematical concepts such as calculating damages or analyzing financial statements, the focus of the field is primarily on legal principles and regulations. As long as you are willing to put in the effort to understand and apply the mathematical aspects of the subject, you can still succeed in studying Business Law with average mathematical skills. Additionally, there are resources available such as tutors or study groups that can help you improve your mathematical skills if needed.

  • 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.

  • 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.

  • 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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