Suitable for advanced undergraduates and graduate students, this text introduces the broad scope of convexity by highlighting diverse applications. Topics include characterizations of convex sets, polytopes, duality, optimization, and convex functions. Exercises appear throughout the text, with solutions, hints, and references at the end. 1982 edition.

This informative survey chronicles the process of abstraction that ultimately led to the axiomatic formulation of the abstract notion of group. Hans Wussing, former Director of the Karl Sudhoff Institute for the History of Medicine and Science at Leipzig University, contradicts the conventional thinking that the roots of the abstract notion of group lie strictly in the theory of algebraic equations. Wussing declares their presence in the geometry and number theory of the late eighteenth and early nineteenth centuries.
This survey ranges from the works of Lagrange via Cauchy, Abel, and...

This single-volume compilation of three books centers on "Hyperbolic Functions, " an introduction to the relationship between the hyperbolic sine, cosine, and tangent, and the geometric properties of the hyperbola. The development of the hyperbolic functions, in addition to those of the trigonometric (circular) functions, appears in parallel columns for comparison. A concluding chapter introduces natural logarithms and presents analytic expressions for the hyperbolic functions.
The second book, "Configuration Theorems, " requires only the most elementary background in plane and solid...

This text for advanced undergraduates and graduate students surveys the use of Fibonacci and Lucas numbers in areas relevant to operational research, statistics, and computational mathematics. It also covers geometric topics related to the ancient principle known as the Golden Sectiona mystical expression of aesthetic harmony that bears a close connection with the Fibonacci mechanism.
The Fibonacci principle of forming a new number by an appropriate combination of previous numbers has been extended to yield sequences with surprising and sometimes mystifying properties: the Meta-Fibonacci...

Solid but concise, this account of Lie algebra emphasizes the theory's simplicity and offers new approaches to major theorems. Author David J. Winter, a Professor of Mathematics at the University of Michigan, also presents a general, extensive treatment of Cartan and related Lie subalgebras over arbitrary fields.
Preliminary material covers modules and nonassociate algebras, followed by a compact, self-contained development of the theory of Lie algebras of characteristic 0. Topics include solvable and nilpotent Lie algebras, Cartan subalgebras, and Levi's radical splitting theorem and the...

Geared toward those who have studied elementary calculus and intend to progress to more advanced mathematics, this book stresses concepts rather than techniques. It emphasizes the simplest setting of basic theorems so that students may progress from "one-space" to ""n"-space" calculus.
An introductory section by the author reviews the roles of sets, relations, and functions. Subsequent chapters explore real numbers, the limit concept, useful theorems, continuity, differentiability, and integrability. The author focuses on real-valued functions of a real variable. Considerations ofcomplex...

This elementary account of the differential geometry of curves and surfaces in space provides students with a good foundation for further study. It explores the ideas of curvature and torsion using the concept of the spin-vector, and it examines the curvature of surfaces, with particular reference to developable surfaces and ruled surfaces.
The approach is by vector methods throughout, but only the most elementary vector algebra is assumed. The text consistently appeals first to geometrical intuition, and then the treatment is made fully rigorous as far as space permits. Many special types...

This text introduces students to Hilbert space and bounded self-adjoint operators, as well as the spectrum of an operator and its spectral decomposition. The author, Emeritus Professor of Mathematics at the University of Innsbruck, Austria, has ensured that the treatment is accessible to readers with no further background than a familiarity with analysis and analytic geometry.
Starting with a definition of Hilbert space and its geometry, the text explores the general theory of bounded linear operators, the spectral analysis of compact linear operators, and unbounded self-adjoint operators....

This book features most of the important theorems and algorithms related to planar graphs. Eminently suitable as a text, it also is useful for researchers and includes an extensive reference section.
The authors, who have researched planar graphs for many years, have structured the topics in a manner relevant to graph theorists and computer scientists. The first two chapters are introductory and provide the foundations of the graph theoretic notions and algorithmic techniques used throughout the text. Succeeding chapters discuss planarity testing and embedding, drawing planar graphs,...