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Presents short rhymes about numbers of objects from one through fourteen and provides information about the Ohio natural history and social studies topics that the objects represent. Also includes a set of open-ended counting problems.
Aimed at the beginner who has no prior knowledge of Arabic, this work begins with the first letter of the alphabet, and gradually builds up the learner's skills to a level where he or she would be able to read a passage of vocalised Arabic text. It also includes numerous copying exercises that enable students to develop a clear handwritten style.
DIVDIVFrom the author of Inner Tube and Odditorium, a book of strikingly original, convention-defying short stories/div Cardinal Numbers is a posthumous collection of brilliantly enigmatic short fiction by Hob Broun, written with the aid of a respirator when the author was paralyzed from the neck down. Witty and full of minimalist surprise, these stories flirt with fragment, fabulism, and collage. In “Rosella, in Stages,” an old woman’s experience is movingly charted through the voice of her writing in six different life stages—and in six pages, no less. “Highspeed Linear Main Street,” a standout tale and an artistic credo of sorts, centers on a photographer’s fixation on highway life, while the surreal “Finding Florida” features a Che Guevara who becomes struck with longing for a librarian and receives some unwelcome news from a fortune teller.DIV Powerfully felt as well as mordantly funny, Cardinal Numbers is a freshly singular contribution to the American short story./divDIV/div/div
Following the success of Logic for Mathematicians, Dr Hamilton has written a text for mathematicians and students of mathematics that contains a description and discussion of the fundamental conceptual and formal apparatus upon which modern pure mathematics relies. The author's intention is to remove some of the mystery that surrounds the foundations of mathematics. He emphasises the intuitive basis of mathematics; the basic notions are numbers and sets and they are considered both informally and formally. The role of axiom systems is part of the discussion but their limitations are pointed out. Formal set theory has its place in the book but Dr Hamilton recognises that this is a part of mathematics and not the basis on which it rests. Throughout, the abstract ideas are liberally illustrated by examples so this account should be well-suited, both specifically as a course text and, more broadly, as background reading. The reader is presumed to have some mathematical experience but no knowledge of mathematical logic is required.
Set Theory
Nearly everyone has heard about the little piggy that went to the market and the one that stayed home-but there's a lot more to the story! 20 Hungry Piggies completes the tale while, unbeknownst to the reader, teaching an important math concept at the same time. There are many counting books that deal with cardinal numbers (1,2,3,etc), but this book teaches ordinal numbers as well-an important part of the kindergarten math curriculum. As an added bonus, children will have a great time trying to find the hidden wolf and hidden numbers in each spread.
In preparing this monograph I had three objectives. First, I wanted to introduce the reader to some topics in mathematics that seldom receive coverage in typical high school and college math programs. The topics include axioms, sets, logic, truth tables and plausible reasoning. In the sections on logic and plausible reasoning, I wanted the reader to see how to transition from formal (mathematical) logic to plausible logic when analyzing the reliability of a source and the credibility of its information content. Readers whose formal education did not cover these topics were not given the opportunity to develop the skills necessary to compete successfully in the world of finance, business and management. These readers will find the information on sets, logic, truth tables and plausible reasoning especially useful. Included are examples that show how the new analysis skills can help analysts draw conclusions and make important decisions from subjective information supplied by less than reliable sources. Second, I wanted the reader to see how subjects in the foundations area of mathematics are used to develop the real number system and its extension through transfinite cardinal numbers. The development of the number system starts with a description of the history of numbers. Readers will find the history both interesting and understandable. The real number continuum is identified as consisting of seven sets of numbers. Each set of numbers can stand alone. The number sets include the simple to understand natural numbers to the more abstract transcendental numbers. Each set is defined and included in a vocabulary consisting of the natural numbers N, integers Z, the rational numbers F, the algebraic numbers A, transcendental numbers T, irrational numbers I, and real numbers R. Venn diagrams are used to explain the relationships existing among the seven sets. The relationships allow the reader to understand the role played by sets and logic in the development of the number system. Included In the development of the real number system are examples of base2 numbers and the algorithms used to convert between base 2 and base 10 numbers. Power Sets are introduced to show how the size of sets can be increased exponentially beyond the cardinal numbers N0 and c. Finally, through exponentiation, cardinal numbers are generated beyond the N0
An introduction to modern cardinal arithmetic is presented in this volume, in addition to a survey of results. A discussion of classical theory is included, paired with investigations in pcf theory, which answers questions left open since the 1970’s.
An entertaining and informative anthology of popular math writing from the Renaissance to cyberspace Despite what we may sometimes imagine, popular mathematics writing didn't begin with Martin Gardner. In fact, it has a rich tradition stretching back hundreds of years. This entertaining and enlightening antholog—the first of its kind—gathers nearly one hundred fascinating selections from the past 500 years of popular math writing, bringing to life a little-known side of math history. Ranging from the late fifteenth to the late twentieth century, and drawing from books, newspapers, magazines, and websites, A Wealth of Numbers includes recreational, classroom, and work mathematics; mathematical histories and biographies; accounts of higher mathematics; explanations of mathematical instruments; discussions of how math should be taught and learned; reflections on the place of math in the world; and math in fiction and humor. Featuring many tricks, games, problems, and puzzles, as well as much history and trivia, the selections include a sixteenth-century guide to making a horizontal sundial; "Newton for the Ladies" (1739); Leonhard Euler on the idea of velocity (1760); "Mathematical Toys" (1785); a poetic version of the rule of three (1792); "Lotteries and Mountebanks" (1801); Lewis Carroll on the game of logic (1887); "Maps and Mazes" (1892); "Einstein's Real Achievement" (1921); "Riddles in Mathematics" (1945); "New Math for Parents" (1966); and "PC Astronomy" (1997). Organized by thematic chapters, each selection is placed in context by a brief introduction. A unique window into the hidden history of popular mathematics, A Wealth of Numbers will provide many hours of fun and learning to anyone who loves popular mathematics and science.