This study of basic number systems explores natural numbers, integers, rational numbers, real numbers, and complex numbers. Written by a noted expert on logic and set theory, it assumes no background in abstract mathematical thought. Undergraduates and beginning graduate students will find this treatment an ideal introduction to number systems, particularly in terms of its detailed proofs.
Starting with the basic facts and notions of logic and set theory, the text offers an axiomatic presentation of the simplest structure, the system of natural numbers. It proceeds, by set-theoretic methods, to an examination of integers that covers rings and integral domains, ordered integral domains, and natural numbers and integers of an integral domain. A look at rational numbers and ordered fields follows, along with a survey of the real number system that includes considerations of least upper bounds and greatest lower bounds, convergent and Cauchy sequences, and elementary topology. Numerous exercises and several helpful appendixes supplement the text.

Facing Tough Test Questions? Missed Lectures? Not Enough Time?

Fortunately for you, there's Schaum's.

More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Solved Problem book helps you cut study time, hone problem-solving skills, and achieve your personal best on exams! You get hundreds of examples, solved problems, and practice exercises to test your skills.

This Schaum's Solved Problems gives you

• 3,000 solved problems covering every area of calculus
• Step-by-step approach to problems
• Hundreds of clear diagrams and illustrations

Fully compatible with your classroom text, Schaum's highlights all the problem-solving skills you need to know. Use Schaum's to shorten your study time, increase your test scores, and get your best possible final grade.

Schaum's Outlines--Problem Solved

Study smarter and stay on top of your calculus course with the bestselling Schaum's Outline--now with the NEW Schaum's app and website!

Schaum's Outline of Calculus, Seventh Edition is the go-to study guide for hundreds of thousands of high school and college students enrolled in calculus courses--including Calculus, Calculus II, Calculus III, AP Calculus and Precalculus. With an outline format that facilitates quick and easy review, Schaum's Outline of Calculus, Seventh Edition helps you understand basic concepts and get the extra practice you need to excel in these courses.

Chapters include Linear Coordinate Systems, Functions, Limits, Rules for Differentiating Functions, Law of the Mean, Inverse Trigonometric Functions, The Definite Integral, Space Vectors, Directional Derivatives, and much, much more.

Features:

• NEW to this edition: the new Schaum's app and website!
• 1,105 problems solved step by step
• 30 problem-solving videos online
• Outline format supplies a concise guide to the standard college course in calculus
• Clear, concise explanations covers all course fundamentals
• Hundreds of additional practice problems
• Supports the major leading textbooks in calculus
• Appropriate for the following courses: Calculus I, Calculus II, Calculus III, AP Calculus, Precalculus

Confusing Textbooks? Missed Lectures? Not Enough Time?

Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.

This Schaum's Outline gives you

• Practice problems with full explanations that reinforce knowledge
• Coverage of the most up-to-date developments in your course field
• In-depth review of practices and applications

Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores!

Schaum's Outlines-Problem Solved.

Tough Test Questions? Missed Lectures? Not Enough Time?

Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.

This Schaum's Outline gives you:

• Practice problems with full explanations that reinforce knowledge
• Coverage of the most up-to-date developments in your course field
• In-depth review of practices and applications

Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores!

Schaum's Outlines-Problem Solved.

When you need just the essentials of calculus, this Easy Outlines book is there to help

If you are looking for a quick nuts-and-bolts overview of calculus, it's got to be Schaum's Easy Outline. This book is a pared-down, simplified, and tightly focused version of its Schaum's Outline cousin, with an emphasis on clarity and conciseness.

Graphic elements such as sidebars, reader-alert icons, and boxed highlights stress selected points from the text, illuminate keys to learning, and give you quick pointers to the essentials.

• Perfect if you have missed class or need extra review
• Gives you expert help from teachers who are authorities in their fields
• So small and light that it fits in your backpack!

Topics include: Functions, Sequences, Limits, and Continuity, Differentiation, Maxima and Minima, Differentiation of Special Functions, The Law of the Mean, Indeterminate Forms, Differentials, and Curve Sketching, Fundamental Integration Techniques and Applications, The Definite Integral, Plane Areas by Integration, Improper Integrals, Differentiation Formulas for Common Mathematical Functions, Integration Formulas for Common Mathematical Functions

This classic text, originally from the noted logician Elliot Mendelson, is intended to be an easy-to-read introduction to the basic ideas and techniques of game theory. It can be used as a class textbook or for self-study.

Introducing Game Theory and its Applications, Second Edition presents an easy-to-read introduction to the basic ideas and techniques of game theory. After a brief introduction, the authors begin with a chapter devoted to combinatorial games--a topic neglected or treated minimally in most other texts. The focus then shifts to two-person zero-sum games and their solutions.

Here the authors present the simplex method based on linear programming for solving these games and develop within this presentation the required background. The final chapter presents some of the fundamental ideas and tools of non-zero-sum games and games with more than two players, including an introduction to cooperative game theory.

The book is suitable for a first undergraduate course in game theory, or a graduate course for students with limited previous exposure. It is useful for students who need to learn some game theory for a related subject (e.g., microeconomics) and have a limited mathematical background. It also prepares its readers for more advanced study of game theory's applications in economics, business, and the physical, biological, and social sciences.

The authors hope this book breeds curiosity about the subject as its design is meant to to satisfy the readers. The book will prepare readers for deeper study of game theory applications in many fields of study.

This classic text, originally from the noted logician Elliot Mendelson, is intended to be an easy-to-read introduction to the basic ideas and techniques of game theory. It can be used as a class textbook or for self-study.

Introducing Game Theory and its Applications, Second Edition presents an easy-to-read introduction to the basic ideas and techniques of game theory. After a brief introduction, the authors begin with a chapter devoted to combinatorial games--a topic neglected or treated minimally in most other texts. The focus then shifts to two-person zero-sum games and their solutions.

Here the authors present the simplex method based on linear programming for solving these games and develop within this presentation the required background. The final chapter presents some of the fundamental ideas and tools of non-zero-sum games and games with more than two players, including an introduction to cooperative game theory.

The book is suitable for a first undergraduate course in game theory, or a graduate course for students with limited previous exposure. It is useful for students who need to learn some game theory for a related subject (e.g., microeconomics) and have a limited mathematical background. It also prepares its readers for more advanced study of game theory's applications in economics, business, and the physical, biological, and social sciences.

The authors hope this book breeds curiosity about the subject as its design is meant to to satisfy the readers. The book will prepare readers for deeper study of game theory applications in many fields of study.

The new edition of this classic textbook, Introduction to Mathematical Logic, Sixth Edition explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. The text also discusses the major results of Gödel, Church, Kleene, Rosser, and Turing.

The sixth edition incorporates recent work on Gödel's second incompleteness theorem as well as restoring an appendix on consistency proofs for first-order arithmetic. This appendix last appeared in the first edition. It is offered in the new edition for historical considerations. The text also offers historical perspectives and many new exercises of varying difficulty, which motivate and lead students to an in-depth, practical understanding of the material.

The mathematical study of games is an intriguing endeavor with implications and applications that reach far beyond tic-tac-toe, chess, and poker to economics, business, and even biology and politics. Most texts on the subject, however, are written at the graduate level for those with strong mathematics, economics, or business backgrounds. In a clear and refreshing departure from this trend, Introducing Game Theory and its Applications presents an easy-to-read introduction to the basic ideas and techniques of game theory. After a brief introduction, the author begins with a chapter devoted to combinatorial games--a topic neglected or treated minimally in most other texts. The focus then shifts to two-person zero-sum games and their solution. Here the author presents the simplex method, based on linear programming, for solving these games and develops within his presentation the required background in linear programming. The final chapter presents some of the fundamental ideas and tools of non-zero-sum games and games with more than two players, including an introduction to cooperative game theory. This book will not only satisfy the curiosity of those whose interest in the subject was piqued by the 1994 Nobel Prize awarded to Harsanyi, Nash, and Selten. It also prepares its readers for more advanced study of game theory's applications in economics, business, and the physical, biological, and social sciences.

The new edition of this classic textbook, Introduction to Mathematical Logic, Sixth Edition explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. The text also discusses the major results of Gödel, Church, Kleene, Rosser, and Turing.

The sixth edition incorporates recent work on Gödel's second incompleteness theorem as well as restoring an appendix on consistency proofs for first-order arithmetic. This appendix last appeared in the first edition. It is offered in the new edition for historical considerations. The text also offers historical perspectives and many new exercises of varying difficulty, which motivate and lead students to an in-depth, practical understanding of the material.