Coherent treatment provides comprehensive view of basic methods and results of the combinatorial study of finite set systems. The Clements-Lindstrom extension of the Kruskal-Katona theorem to multisets is explored, as is the Greene-Kleitman result concerning k-saturated chain partitions of general partially ordered sets. Connections with Dilworth's theorem, the marriage problem, and probability are also discussed. Each chapter ends with a helpful series of exercises and outline solutions appear at the end. -An excellent text for a topics course in discrete mathematics.- -- Bulletin...
Coherent treatment provides comprehensive view of basic methods and results of the combinatorial study of finite set systems. The Clements-Lindstrom e...
This volume presents students with problems and exercises designed to illuminate the properties of functions and graphs. The 1st part of the book employs simple functions to analyze the fundamental methods of constructing graphs. The 2nd half deals with more complicated and refined questions concerning linear functions, quadratic trinomials, linear fractional functions, power functions, and rational functions. 1969 edition.
This volume presents students with problems and exercises designed to illuminate the properties of functions and graphs. The 1st part of the book empl...
Kaplansky, formerly an instructor at the University of Chicago, overviews the correlation between algebra and geometry and illustrates concepts with examples, exercises, and proofs. Coverage begins with definitions and examples of inner product spaces, and concludes with higher dimensional spaces, n
Kaplansky, formerly an instructor at the University of Chicago, overviews the correlation between algebra and geometry and illustrates concepts with e...
Originally published by Holden-Day in 1963, this textbook focuses on problem-solving skills in analysis, analytic geometry, and higher algebra. Approximately 1,200 high- level problems illustrate basic concepts and theorems; many are followed by complete answers and concise explanations. Topics incl
Originally published by Holden-Day in 1963, this textbook focuses on problem-solving skills in analysis, analytic geometry, and higher algebra. Approx...
Anyone seeking a readable and relatively brief guide to logic can do no better than this classic introduction. A treat for both the intellect and the imagination, it profiles the development of logic from ancient to modern times and compellingly examines the nature of logic and its philosophical implications. No prior knowledge of logic is necessary; readers need only an acquaintance with high school mathematics. The author emphasizes understanding, rather than technique, and focuses on such topics as the historical reasons for the formation of Aristotelian logic, the rise of mathematical...
Anyone seeking a readable and relatively brief guide to logic can do no better than this classic introduction. A treat for both the intellect and t...
Focusing on applicable rather than applied mathematics, this versatile text is appropriate for advanced undergraduates majoring in any discipline. A thorough examination of linear systems of differential equations inaugurates the text, reviewing concepts from linear algebra and basic theory. The heart of the book develops the ideas of stability and qualitative behavior. Starting with two-dimensional linear systems, the author reviews the use of polar coordinate techniques as well as Liapunov stability and elementary ideas from dynamic systems. Existence and uniqueness theorems receive a...
Focusing on applicable rather than applied mathematics, this versatile text is appropriate for advanced undergraduates majoring in any discipline. A t...
"Makes the reader feel the inspiration that comes from listening to a great mathematician." Bulletin, American Mathematical Society A distinguished mathematician and educator enlivens abstract discussions of arithmetic, algebra, and analysis by means of graphical and geometrically perceptive methods. His three-part treatment begins with topics associated with arithmetic, including calculating with natural numbers, the first extension of the notion of number, special properties of integers, and complex numbers. Algebra-related subjects constitute the second part, which examines real...
"Makes the reader feel the inspiration that comes from listening to a great mathematician." Bulletin, American Mathematical Society A disti...
This text begins with the simplest geometric manifolds, the Grassmann determinant principle for the plane and the Grassmann principle for space; and more. Also explores affine and projective transformations; higher point transformations; transformations with change of space element; and the theory of the imaginary. Concludes with a systematic discussion of geometry and its foundations. 1939 edition. 141 figures.
This text begins with the simplest geometric manifolds, the Grassmann determinant principle for the plane and the Grassmann principle for space; and m...
Written by a prominent mathematician, this text offers advanced undergraduate and graduate students a virtually self-contained treatment of the basics of Galois theory. The source of modern abstract algebra and one of abstract algebra's most concrete applications, Galois theory serves as an excellent introduction to group theory and provides a strong, historically relevant motivation for the introduction of the basics of abstract algebra. This two-part treatment begins with the elements of Galois theory, focusing on related concepts from field theory, including the structure of...
Written by a prominent mathematician, this text offers advanced undergraduate and graduate students a virtually self-contained treatment of the bas...
A century ago, Georg Cantor demonstrated the possibility of a series of transfinite infinite numbers. His methods, unorthodox for the time, enabled him to derive theorems that established a mathematical reality for a hierarchy of infinities. Cantor's innovation was opposed, and ignored, by the establishment; years later, the value of his work was recognized and appreciated as a landmark in mathematical thought, forming the beginning of set theory and the foundation for most of contemporary mathematics. As Cantor's sometime collaborator, David Hilbert, remarked, -No one will drive us from...
A century ago, Georg Cantor demonstrated the possibility of a series of transfinite infinite numbers. His methods, unorthodox for the time, enabled hi...
