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Length (Math Counts)

Length (Math Counts) Lowest new price: $3.96
Lowest used price: $0.94
List price: $4.95
Author: Henry Pluckrose
Brand: Childrens Pr

Children can become mathematical problem solvers, learning to communicate and reason mathematically, by using the Math Counts series.

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Category Theory in Context (Aurora: Dover Modern Math Originals)

Category Theory in Context (Aurora: Dover Modern Math Originals) Lowest new price: $16.36
Lowest used price: $17.16
List price: $29.95
Author: Emily Riehl
Brand: Riehl Emily

Category theory has provided the foundations for many of the twentieth century's greatest advances in pure mathematics. This concise, original text for a one-semester introduction to the subject is derived from courses that author Emily Riehl taught at Harvard and Johns Hopkins Universities. The treatment introduces the essential concepts of category theory: categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads, Kan extensions, and other topics.

Suitable for advanced undergraduates and graduate students in mathematics, the text provides tools for understanding and attacking difficult problems in algebra, number theory, algebraic geometry, and algebraic topology. Drawing upon a broad range of mathematical examples from the categorical perspective, the author illustrates how the concepts and constructions of category theory arise from and illuminate more basic mathematical ideas. While the reader will be rewarded for familiarity with these background mathematical contexts, essential prerequisites are limited to basic set theory and logic.


  • Category Theory in Context

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Crossing the River with Dogs: Problem Solving for College Students

Crossing the River with Dogs: Problem Solving for College Students Lowest new price: $55.32
Lowest used price: $52.27
Author: Ken Johnson

Crossing the River with Dogs: Problem Solving for College Students has been adapted from the popular high school text to provide an accessible and coherent college-level course in mathematical problem solving for adults.  Focusing entirely on problem solving and using issues relevant to college students for examples, the authors continue their approach of explaining classic as well as non-traditional strategies through dialogs among fictitious students.  This text is appropriate for a problem solving, liberal arts mathematics, mathematics for elementary teachers, or developmental mathematics course.

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Computational Complexity: A Modern Approach

Computational Complexity: A Modern Approach Lowest new price: $52.70
Lowest used price: $43.50
List price: $62.00
Author: Sanjeev Arora
Brand: Brand: Cambridge University Press

This beginning graduate textbook describes both recent achievements and classical results of computational complexity theory. Requiring essentially no background apart from mathematical maturity, the book can be used as a reference for self-study for anyone interested in complexity, including physicists, mathematicians, and other scientists, as well as a textbook for a variety of courses and seminars. More than 300 exercises are included with a selected hint set.


  • Used Book in Good Condition

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Logic: Propositional Logic (Quickstudy: Academic)

Logic: Propositional Logic (Quickstudy: Academic) Lowest new price: $2.97
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Author: Inc. BarCharts
Brand: Brand: BarCharts

This 4-page study guide contains fundamental logic definitions and analysis which is specifically designed to aid science students.


  • Used Book in Good Condition

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Logic For Dummies

Logic For Dummies Lowest new price: $11.16
Lowest used price: $3.02
List price: $19.99
Author: Mark Zegarelli
Brand: Mark Zegarelli

Logic concepts are more mainstream than you may realize. There’s logic every place you look and in almost everything you do, from deciding which shirt to buy to asking your boss for a raise, and even to watching television, where themes of such shows as CSI and Numbers incorporate a variety of logistical studies. Logic For Dummies explains a vast array of logical concepts and processes in easy-to-understand language that make everything clear to you, whether you’re a college student of a student of life. You’ll find out about:

  • Formal Logic
  • Syllogisms
  • Constructing proofs and refutations
  • Propositional and predicate logic
  • Modal and fuzzy logic
  • Symbolic logic
  • Deductive and inductive reasoning

Logic For Dummies tracks an introductory logic course at the college level. Concrete, real-world examples help you understand each concept you encounter, while fully worked out proofs and fun logic problems encourage you students to apply what you’ve learned.


  • Logic For Dummies

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The Foundations of Mathematics

The Foundations of Mathematics Lowest new price: $16.86
Lowest used price: $18.61
List price: $24.95
Author: Ian Stewart
Brand: Oxford University Press USA

The transition from school mathematics to university mathematics is seldom straightforward. Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory.

The authors have many years' experience of the potential difficulties involved, through teaching first-year undergraduates and researching the ways in which students and mathematicians think. The book explains the motivation behind abstract foundational material based on students' experiences of school mathematics, and explicitly suggests ways students can make sense of formal ideas.

This second edition takes a significant step forward by not only making the transition from intuitive to formal methods, but also by reversing the process- using structure theorems to prove that formal systems have visual and symbolic interpretations that enhance mathematical thinking. This is exemplified by a new chapter on the theory of groups.

While the first edition extended counting to infinite cardinal numbers, the second also extends the real numbers rigorously to larger ordered fields. This links intuitive ideas in calculus to the formal epsilon-delta methods of analysis. The approach here is not the conventional one of 'nonstandard analysis', but a simpler, graphically based treatment which makes the notion of an infinitesimal natural and straightforward.

This allows a further vision of the wider world of mathematical thinking in which formal definitions and proof lead to amazing new ways of defining, proving, visualising and symbolising mathematics beyond previous expectations.


  • Oxford University Press USA

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The Art and Craft of Problem Solving

The Art and Craft of Problem Solving Lowest new price: $59.36
Lowest used price: $54.21
Author: Paul Zeitz

The newly revised Second Edtion of this distinctive text uniquely blends interesting problems with strategies, tools, and techniques to develop mathematical skill and intuition necessary for problem solving. Readers are encouraged to do math rather than just study it. The author draws upon his experience as a coach for the International Mathematics Olympiad to give students an enhanced sense of mathematics and the ability to investigate and solve problems.

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Introduction to Logic: and to the Methodology of Deductive Sciences (Dover Books on Mathematics)

Introduction to Logic: and to the Methodology of Deductive Sciences (Dover Books on Mathematics) Lowest new price: $8.95
Lowest used price: $4.35
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Author: Alfred Tarski
Brand: Alfred Tarski

First published in Polish in 1936, this classic work was originally written as a popular scientific book — one that would present to the educated lay reader a clear picture of certain powerful trends of thought in modern logic. According to the author, these trends sought to create a unified conceptual apparatus as a common basis for the whole of human knowledge.
Because these new developments in logical thought tended to perfect and sharpen the deductive method, an indispensable tool in many fields for deriving conclusions from accepted assumptions, the author decided to widen the scope of the work. In subsequent editions he revised the book to make it also a text on which to base an elementary college course in logic and the methodology of deductive sciences. It is this revised edition that is reprinted here.
Part One deals with elements of logic and the deductive method, including the use of variables, sentential calculus, theory of identity, theory of classes, theory of relations and the deductive method. The Second Part covers applications of logic and methodology in constructing mathematical theories, including laws of order for numbers, laws of addition and subtraction, methodological considerations on the constructed theory, foundations of arithmetic of real numbers, and more. The author has provided numerous exercises to help students assimilate the material, which not only provides a stimulating and thought-provoking introduction to the fundamentals of logical thought, but is the perfect adjunct to courses in logic and the foundation of mathematics.


  • Introduction to Logic

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How to Read and Do Proofs: An Introduction to Mathematical Thought Processes

How to Read and Do Proofs: An Introduction to Mathematical Thought Processes Lowest new price: $62.09
Lowest used price: $57.79
Author: Daniel Solow

This text makes a great supplement and provides a systematic approach for teaching undergraduate and graduate students how to read, understand, think about, and do proofs. The approach is to categorize, identify, and explain (at the student's level) the various techniques that are used repeatedly in all proofs, regardless of the subject in which the proofs arise. How to Read and Do Proofs also explains when each technique is likely to be used, based on certain key words that appear in the problem under consideration. Doing so enables students to choose a technique consciously, based on the form of the problem.

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