Since its publication in 1908, it has been a classic work to which successive generations of budding mathematicians have turned at the beginning of their undergraduate courses. In its pages, Hardy combines the enthusiasm of a missionary with the rigor of a purist in his exposition of the fundamental ideas of the differential and integral calculus, of the properties of infinite series and of other topics involving the notion of limit.

    This is a very old science and its gems have lost their charm for us through everyday use. We have tried in this book to refresh them for you. The main part of the book is made up of problems. The best way to deal with them is: Solve the problem by yourself - compare your solution with the solution in the book (if it exists) - go to the next problem. However, if you have difficulties solving a problem (and some of them are quite difficult), you may read the hint or start to read the solution. If there is no solution in the book for some problem, you may skip it (it is not heavily used in the sequel) and return to it later. The book is divided into sections devoted to different topics. Some of them are very short, others are rather long. Of course, you know arithmetic pretty well. However, we shall go through it once more, starting with easy things. 2 Exchange of terms in addition Let's add 3 and 5: 3+5=8. And now change the order: 5+3=8. We get the same result. Adding three apples to five apples is the same as adding five apples to three - apples do not disappear and we get eight of them in both cases. 3 Exchange of terms in multiplication Multiplication has a similar property. But let us first agree on notation.

    It reveals the attraction that has drawn leading mathematicians and amateurs alike to number theory over the course of history.

    In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simplicity of the proofs for many theorems.Among the topics covered in this accessible, carefully designed introduction are multiplicativity-divisibility, including the fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots and prime numbers. Later chapters offer lucid treatments of quadratic congruences, additivity (including partition theory) and geometric number theory.Of particular importance in this text is the author's emphasis on the value of numerical examples in number theory and the role of computers in obtaining such examples. Exercises provide opportunities for constructing numerical tables with or without a computer. Students can then derive conjectures from such numerical tables, after which relevant theorems will seem natural and well-motivated..

    Clear, comprehensive coverage of utility theory, 2-person zero-sum games, 2-person non-zero-sum games, n-person games, individual and group decision-making, more. Bibliography.

    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.

    This book considers many of those ideas and presents a new solution why three is the magic number.

    Russell's classic The Principles of Mathematics sets forth his landmark thesis that mathematics and logic are identical―that what is commonly called mathematics is simply later deductions from logical premises.His ideas have had a profound influence on twentieth-century work on logic and the foundations of mathematics.

    Yet geometry is so much more than shapes and numbers; indeed, it governs much of our lives—from architecture and microchips to car design, animated movies, the molecules of food, even our own body chemistry. And as Siobhan Roberts elegantly conveys in The King of Infinite Space, there can be no better guide to the majesty of geometry than Donald Coxeter, perhaps the greatest geometer of the twentieth century.Many of the greatest names in intellectual history—Pythagoras, Plato, Archimedes, Euclid— were geometers, and their creativity and achievements illuminate those of Coxeter, revealing geometry to be a living, ever-evolving endeavor, an intellectual adventure that has always been a building block of civilization. Coxeter's special contributions—his famed Coxeter groups and Coxeter diagrams—have been called by other mathematicians "tools as essential as numbers themselves," but his greatest achievement was to almost single-handedly preserve the tradition of classical geometry when it was under attack in a mathematical era that valued all things austere and rational.Coxeter also inspired many outside the field of mathematics. Artist M. C. Escher credited Coxeter with triggering his legendary Circle Limit patterns, while futurist/inventor Buckminster Fuller acknowledged that his famed geodesic dome owed much to Coxeter's vision. The King of Infinite Space is an elegant portal into the fascinating, arcane world of geometry.

    This text introduces students to proof techniques and writing proofs of their own. As such, it is an introduction to the mathematics enterprise, providing solid introductions to relations, functions, and cardinalities of sets.

    This title enables students to grasp key sociological concepts and learn the useful lesson that there is much that goes on in the social world that escapes the sociologically untrained eye.

    Fundamentals of Biostatistics with CD-Rom.

    The authors help students learn key sociological concepts through real research examples related to the dynamic interplay of race, class, gender, and other social variables.

    This well-respected text offers an accessible introduction to functional programming concepts and techniques for students of mathematics and computer science. The treatment is as nontechnical as possible, and it assumes no prior knowledge of mathematics or functional programming. Cogent examples illuminate the central ideas, and numerous exercises appear throughout the text, offering reinforcement of key concepts. All problems feature complete solutions.

    This book is about making those encounters as compelling as we can make them." -Harvey "Smokey" Daniels and Steven ZemelmanWe are specialists to the bone-in science, math, social studies, art, music, business, and foreign language. But now, the Common Core and state standards require us to help our students better understand the distinctive texts in our subject areas. "Nobody's making us into reading teachers," write Smokey Daniels and Steve Zemelman, "but we must become teachers of disciplinary thinking through our students' reading."If this shift sounds like a tough one, Subjects Matter, Second Edition is your solution. Smokey and Steve, two of America's most popular educators, share exactly what you need to help students read your nonfiction content closely and strategically: 27 proven teaching strategies that help meet-and exceed-the standards how-to suggestions for engaging kids with content through wide, real-world reading a lively look at using "boring" textbooks motivating instruction that's powered by student collaboration specifics for helping struggling readers succeed.Subjects Matter, Second Edition enables deep, thoughtful learning for your students, while keeping the irreverent, inspiring heart that's made the first edition indispensable. You'll discover fresh and re-energized lessons, completely updated research, and vibrant vignettes from new colleagues and old friends who have as much passion for their subjects as you do."We'll be using methods particular to our fields as well as engaging reading materials that help students understand and remember our content better," write Smokey and Steve. "We can realize that vision of the light going on in kids' heads and maybe fill them with enthusiasm about the amazing subject matter that we have to offer. Sound good? Let's get to work." Read a sample chapter from Subjects Matter, Second Edition.