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Do math more quickly and with more confidence — with less reliance on paper, apps, and calculators. For people who automatically run to the nearest calculator, Idiot's Guides: Speed Math teaches tips, tricks, and straightforward methods to doing math at a fast — and accurate — rate. Practice examples easily illustrate how even the most math-shy person can better perform calculations.

For a long time, all thought there was only one geometry — Euclidean geometry. Nevertheless, in the 19th century, many non-Euclidean geometries were discovered. It took almost two millennia to do this. This was the major mathematical discovery and advancement of the 19th century, which changed understanding of mathematics and the work of mathematicians providing innovative insights and tools for mathematical research and applications of mathematics.A similar event happened in arithmetic in the 20th century. Even longer than with geometry, all thought there was only one conventional arithmetic of natural numbers — the Diophantine arithmetic, in which 2+2=4 and 1+1=2. It is natural to call the conventional arithmetic by the name Diophantine arithmetic due to the important contributions to arithmetic by Diophantus. Nevertheless, in the 20th century, many non-Diophantine arithmetics were discovered, in some of which 2+2=5 or 1+1=3. It took more than two millennia to do this. This discovery has even more implications than the discovery of new geometries because all people use arithmetic.This book provides a detailed exposition of the theory of non-Diophantine arithmetics and its various applications. Reading this book, the reader will see that on the one hand, non-Diophantine arithmetics continue the ancient tradition of operating with numbers while on the other hand, they introduce extremely original and innovative ideas.

This book develops arithmetic without the induction principle, working in theories that are interpretable in Raphael Robinson's theory Q. Certain inductive formulas, the bounded ones, are interpretable in Q. A mathematically strong, but logically very weak, predicative arithmetic is constructed.Originally published in 1986.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Chapter 1 - Elementary Arithmetic Chapter 2 - Subtraction and Addition Chapter 3 - Multiplication Chapter 4 - Division Chapter 5 - Binary Numeral System Chapter 6 - Cube (Algebra) and Decimal Chapter 7 - Equality and Finger Binary Chapter 8 - Fraction and Negative Number Chapter 9 - Least Common Multiple and Parity of Zero

Chapter 1 - Introduction to Arithmetic Chapter 2 - Rounding Chapter 3 - Addition and Subtraction Chapter 4 - Multiplication and Division Chapter 5 - Modular Arithmetic and Fundamental Theorem of Arithmetic Chapter 6 - Introduction to Factorization Chapter 7 - Integer Factorization Chapter 8 - Greatest Common Divisor and Singular Value Decomposition Chapter 9 - Eigendecomposition of a Matrix and Cholesky Decomposition Chapter 10 - Quadratic Sieve and Shor's Algorithm

Chapter 1 - Elementary Arithmetic Chapter 2 - Subtraction and Addition Chapter 3 - Multiplication Chapter 4 - Division Chapter 5 - Binary Numeral System Chapter 6 - Cube (Algebra) and Decimal Chapter 7 - Equality and Finger Binary Chapter 8 - Elementary Algebra Chapter 9 - Quadratic Equation Chapter 10 - Linear Equation Chapter 11 - System of Linear Equations Chapter 12 - Polynomial and Simultaneous Equations

Chapter 1 - Introduction to Numbers Chapter 2 - Types of Numbers Chapter 3 - Negative and Non-negative Numbers Chapter 4 - Infinity Chapter 5 - Mathematical Constant Chapter 6 - Transcendental Number and Geometry of Numbers Chapter 7 - Transcendence Theory and Analytic Number Theory

Chapter 1 - Introduction to Arithmetic Chapter 2 - Rounding Chapter 3 - Addition and Subtraction Chapter 4 - Multiplication and Division Chapter 5 - Modular Arithmetic and Fundamental Theorem of Arithmetic Chapter 6 - Arithmetic Function Chapter 7 - Interval Arithmetic

There's an unspoken weak spot in our society most adults can't do basic math. A recent U.S. Department of Education study found that American adults are largely unable to calculate tips, understand their mortgage payments, or even figure out their weekly salary when told their hourly wage. Though we live in a world where numbers, percentages and statistics are tossed at us daily - a world that expects us to make sense of these figures - 87% of American adults are deemed non-proficient at math, according to a recent Education Department study. But there is hope. As the scope of this problem has become more publicized, community colleges have moved in to help, offering courses to help adults gain math proficiency. And programs and books have been created to address the issue, too. Still, most adults need to start their math journey is back at the beginning, and few resources have been developed to address the earliest math skills. Singing Turtle Press, publisher of the award-winning Algebra Survival Guide, is coming to the rescue, though, with a new book that helps adults master foundational math concepts. Math Basics Made Easy, a new offering in eBook format, teaches adults the four fundamental math operations: adding, subtracting, multiplying and dividing. These four skill areas are the foundation stones of mathematics, says co-author Steve Slavin. Because most Americans have never mastered these skills, they haven't gotten very far in math. And that has closed the door to many high-paying careers. Slavin should know about these problems. He has devoted his life to teaching math, and to writing books to help people grasp math. Slavin believes that no matter how far behind a person may be in math, it's never too late to learn math, even if one must go back to the very first grade. Math Basics Made Easy presents early math concepts in a format that works for adults. The book offers brief, easily understood lessons with worked-out sample problems, followed by a collection of practice problems for the reader. Answers are provided to all practice problems, so readers get instant feedback on how well they are progressing. Within each of the four content areas - adding, subtracting, multiplying and dividing - concepts are taught sequentially, easiest concepts first, most challenging topics last. The book is heavy on practice because Slavin believes that we learn math by doing math. The benefit, though, is that anyone who works his way through this book will learn the basics of math and thereby put himself in a position to move on to more challenging topics. In today's challenging economic times, Math Basics Made Easy offers a gateway to better opportunities for today's job-seeker. Slavin's co-author, Ginny Crisonino, also teaches math daily, serving as Mathematics Chair at Union County College, Cranford, NJ. The book also gives anyone who never fully understood math's basics a chance to master them, for the book's message is that it's never too late to learn. A solid self-teaching guide, Math Basics Made Easy offers solid encouragement and competent instruction to anyone with the desire to master math's basic skills.

Master math at your own pace!Does working with numbers often frustrate you? Do you need to brush up on your basic math skills? Do you feel math stands between you and your career goals, or a better grade at school?Quick Arithmetic, Third Edition is the quickest and easiest way to teach yourself the basic math skills you need to advance on the job or in school. Using cartoons and a clear writing style, this practical guide provides a fresh start for learning or reviewing how to work with whole numbers, fractions, decimals, and percentages. The book's proven self-teaching approach allows you to work at your own pace and learn only the material you need. Previews and objectives at the beginning of each section help you determine your particular needs, while self-tests, practice problems, and a final exam let you measure your progress and reinforce what you've learned.For anyone who has ever felt intimidated by a page of numbers, Quick Arithmetic, Third Edition has the answers!