This volume contains a collection of clever mathematical applications of linear algebra, mainly in combinatorics, geometry, and algorithms. Each chapter covers a single main result with motivation and full proof in at most ten pages and can be read independently of all other chapters (with minor exceptions), assuming only a modest background in linear algebra. The topics include a number of well-known mathematical gems, such as Hamming codes, the matrix-tree theorem, the Lovasz bound on the Shannon capacity, and a counterexample to Borsuk's conjecture, as well as other, perhaps less popular but similarly beautiful results, e.g., fast associativity testing, a lemma of Steinitz on ordering vectors, a monotonicity result for integer partitions, or a bound for set pairs via exterior products. The simpler results in the first part of the book provide ample material to liven up an undergraduate course of linear algebra. The more advanced parts can be used for a graduate course of linear-algebraic methods or for seminar presentations. Table of Contents: Fibonacci numbers, quickly; Fibonacci numbers, the formula; The clubs of Oddtown; Same-size intersections; Error-correcting codes; Odd distances; Are these distances Euclidean?; Packing complete bipartite graphs; Equiangular lines; Where is the triangle?; Checking matrix multiplication; Tiling a rectangle by squares; Three Petersens are not enough; Petersen, Hoffman-Singleton, and maybe 57; Only two distances; Covering a cube minus one vertex; Medium-size intersection is hard to avoid; On the difficulty of reducing the diameter; The end of the small coins; Walking in the yard; Counting spanning trees; In how many ways can a man tile a board?; More bricks--more walls?; Perfect matchings and determinants; Turning a ladder over a finite field; Counting compositions; Is it associative?; The secret agent and umbrella; Shannon capacity of the union: a tale of two fields; Equilateral sets; Cutting cheaply using eigenvectors; Rotating the cube; Set pairs and exterior products; Index. (STML/53)

The book consists of thirty lectures on diverse topics, covering much of the mathematical landscape rather than focusing on one area. The reader will learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and will discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology. The reader's effort will be rewarded in seeing the harmony of each subject. The common thread in the selected subjects is their illustration of the unity and beauty of mathematics. Most lectures contain exercises, and solutions or answers are given to selected exercises. A special feature of the book is an abundance of drawings (more than four hundred), artwork by an accomplished artist, and about a hundred portraits of mathematicians. Almost every lecture contains surprises for even the seasoned researcher.

Among other subjects explored are the Clements-Lindström extension of the Kruskal-Katona theorem to multisets and the Greene-Kleitmen result concerning k-saturated chain partitions of general partially ordered sets. Includes exercises and solutions.

Mathematics++ is a concise introduction to six selected areas of 20th century mathematics providing numerous modern mathematical tools used in contemporary research in computer science, engineering, and other fields. The areas are: measure theory, high-dimensional geometry, Fourier analysis, representations of groups, multivariate polynomials, and topology. For each of the areas, the authors introduce basic notions, examples, and results. The presentation is clear and accessible, stressing intuitive understanding, and it includes carefully selected exercises as an integral part. Theory is complemented by applications--some quite surprising--in theoretical computer science and discrete mathematics. The chapters are independent of one another and can be studied in any order. It is assumed that the reader has gone through the basic mathematics courses. Although the book was conceived while the authors were teaching Ph.D. students in theoretical computer science and discrete mathematics, it will be useful for a much wider audience, such as mathematicians specializing in other areas, mathematics students deciding what specialization to pursue, or experts in engineering or other fields.

These 35 contemporary style miniatures for organ selected by James Conely are lovely improvisatory pieces written in various styles and moods, in most major, minor and modal keys. Several pieces are marked 'con Ped.,' but since they are generally easy and most are written on two staves instead of three, they may be played on two manuals alone. Registration suggestions are included.

This is a study of the artistic and political context that led to the production of a truly exceptional Byzantine illustrated manuscript. Paris, Bibliothèque Nationale de France, codex grec 54 is one of the most ambitious and complex manuscripts produced during the Byzantine era. This thirteenth-century Greek and Latin Gospel book features full-page evangelist portraits, an extensive narrative cycle, and unique polychromatic texts. However, it has never been the subject of a comprehensive study and the circumstances of its commission are unknown. In this book Kathleen Maxwell addresses the following questions: what circumstances led to the creation of Paris 54? Who commissioned it and for what purpose? How was a deluxe manuscript such as this produced? Why was it left unfinished? How does it relate to other Byzantine illustrated Gospel books? Paris 54's innovations are a testament to the extraordinary circumstances of its commission. Maxwell's multi-disciplinary approach includes codicological and paleographical evidence together with New Testament textual criticism, artistic and historical analysis. She concludes that Paris 54 was never intended to copy any other manuscript. Rather, it was designed to eclipse its contemporaries and to physically embody a new relationship between Constantinople and the Latin West, as envisioned by its patron. Analysis of Paris 54's texts and miniature cycle indicates that it was created at the behest of a Byzantine emperor as a gift to a pope, in conjunction with imperial efforts to unify the Latin and Orthodox churches. As such, Paris 54 is a unique witness to early Palaeologan attempts to achieve church union with Rome.