Fundamentals of Economics is a concise but thorough survey of economics for instructors desiring a brief, practical text. Based on the comprehensive two-semester text by the same authors, this version of Economics "boils down" the formal economic theories and concepts into their essential parts, emphasizing domestic and international applications and policy issues.
Everyone knows some of the basics of probability, perhaps enough to play cards. Beyond the introductory ideas, there are many wonderful results that are unfamiliar to the layman, but which are well within our grasp to understand and appreciate. Some of the most remarkable results in probability are those that are related to limit theorems--statements about what happens when the trial is repeated many times. The most famous of these is the Law of Large Numbers, which mathematicians,engineers, economists, and many others use every day. In this book, Lesigne has made these limit theorems accessible by stating everything in terms of a game of tossing of a coin: heads or tails. In this way, the analysis becomes much clearer, helping establish the reader's intuition aboutprobability. Moreover, very little generality is lost, as many situations can be modelled from combinations of coin tosses. This book is suitable for anyone who would like to learn more about mathematical probability and has had a one-year undergraduate course in analysis.
Tribute to the vision and legacy of Israel Moiseevich Gel'fand Written by leading mathematicians, these invited papers reflect the unity of mathematics as a whole, with particular emphasis on the many connections among the fields of geometry, physics, and representation theory Topics include conformal field theory, K-theory, noncommutative geometry, gauge theory, representations of infinite-dimensional Lie algebras, and various aspects of the Langlands program
Presents an introduction to the conformally invariant processes that appear as scaling limits. This book covers such topics as stochastic integration, and complex Brownian motion and measures derived from Brownian motion. It is suitable for those interested in random processes and their applications in theoretical physics.
Contains new results on different aspects of Lie theory, including Lie superalgebras, quantum groups, crystal bases, representations of reductive groups in finite characteristic, and the geometric Langlands program
What a wonderful book! I strongly recommend this book to anyone, especially graduate students, interested in getting a sense of 4-manifolds. --MAA Reviews The book gives an excellent overview of 4-manifolds, with many figures and historical notes. Graduate students, nonexperts, and experts alike will enjoy browsing through it. -- Robion C. Kirby, University of California, Berkeley This book offers a panorama of the topology of simply connected smooth manifolds of dimension four. Dimension four is unlike any other dimension; it is large enough to have room for wild things to happen, but small enough so that there is no room to undo the wildness. For example, only manifolds of dimension four can exhibit infinitely many distinct smooth structures. Indeed, their topology remains the least understood today. To put things in context, the book starts with a survey of higher dimensions and of topological 4-manifolds. In the second part, the main invariant of a 4-manifold--the intersection form--and its interaction with the topology of the manifold are investigated. In the third part, as an important source of examples, complex surfaces are reviewed. In the final fourth part of the book, gauge theory is presented; this differential-geometric method has brought to light how unwieldy smooth 4-manifolds truly are, and while bringing new insights, has raised more questions than answers. The structure of the book is modular, organized into a main track of about two hundred pages, augmented by extensive notes at the end of each chapter, where many extra details, proofs and developments are presented. To help the reader, the text is peppered with over 250 illustrations and has an extensive index.
102 Top Picks makes it easy for home educators to select the right curriculum for each family situation and each child's learning style. Widely-recognized curriculum expert Cathy Duffy walks you through the curriculum selection process. This is an updated and extensively revised edition of 101 Top Picks for Homeschool Curriculum.
Ryan Collins goes from being a member of a farming commune to becoming a key player in President Eugene Gloss's twisted games. Collins must convince his team, made up of four Christian guys and girls, that he is one of President Gloss's very own private guards. There are eight teams preparing to compete against each other. The problem is that Collins is a Christian, and finds it difficult to do everything expected of him.Although he does not like it, Collins tries to the best of his ability to be a convincing guard. Unfortunately, however, his team eventually becomes suspicious of his true identity. Interestingly, Collins develops a unique relationship with Mason, one of President Gloss's guards. In order to secure his safety, Collins decides to take Mason's advice and try to play a convincing role, even though it goes against his religious teaching.
New mathematical insights and rigorous results are often gained through extensive experimentation using numerical examples or graphical images and analyzing them. Today computer experiments are an integral part of doing mathematics. This allows for a more systematic approach to conducting and replicating experiments. The authors address the role of
