Background
Croom, Frederick Hailey was born on August 6, 1941 in Lumberton, North Carolina, United States. Son of Robert DeVane and Anna Rosalyn Croom.
(This text is intended as a one semester introduction to a...)
This text is intended as a one semester introduction to algebraic topology at the undergraduate and beginning graduate levels. Basically, it covers simplicial homology theory, the fundamental group, covering spaces, the higher homotopy groups and introductory singular homology theory. The text follows a broad historical outline and uses the proofs of the discoverers of the important theorems when this is consistent with the elementary level of the course. This method of presentation is intended to reduce the abstract nature of algebraic topology to a level that is palatable for the beginning student and to provide motivation and cohesion that are often lacking in abstact treatments. The text emphasizes the geometric approach to algebraic topology and attempts to show the importance of topological concepts by applying them to problems of geometry and analysis. The prerequisites for this course are calculus at the sophomore level, a one semester introduction to the theory of groups, a one semester introduc tion to point-set topology and some familiarity with vector spaces. Outlines of the prerequisite material can be found in the appendices at the end of the text. It is suggested that the reader not spend time initially working on the appendices, but rather that he read from the beginning of the text, referring to the appendices as his memory needs refreshing. The text is designed for use by college juniors of normal intelligence and does not require "mathematical maturity" beyond the junior level.
http://www.amazon.com/gp/product/0387902880/?tag=2022091-20
(This text presents the fundamental principles of topology...)
This text presents the fundamental principles of topology rigorously but not abstractly. It emphasizes the geometric nature of the subject and the applications of topological ideas to geometry and mathematical analysis. The usual topics of point-set topology, including metric spaces, general topological spaces, continuity, topological equivalence, basis, sub-basis, connectedness , compactness, separation properties, metrization, subspaces, product spaces, and quotient spaces are treated in this text. Most of the factual information about topology presented in this text is stated in the theorems and illustrated in the accompanying examples, figures and exercises. This book contains many exercises of varying degrees of difficulty. The notation used in this text is reasonably standard; a list of symbols with definitions appears on the front end-sheets. This text is designed for a one-semester introduction to topology at the undergraduate and beginning graduate levels. It is accessible to junior mathematics majors who have studied multivariable calculus.
http://www.amazon.com/gp/product/0030128137/?tag=2022091-20
academic administrator educator mathematician
Croom, Frederick Hailey was born on August 6, 1941 in Lumberton, North Carolina, United States. Son of Robert DeVane and Anna Rosalyn Croom.
Bachelor of Science, University North Carolina, 1963. Doctor of Philosophy, University North Carolina, 1967.
Assistant professor mathematics, U. Kentucky, Lexington, 1967-1971; assistant professor mathematics, University of the South, Sewanee, Tennessee, 1971-1974; associate professor, University of the South, Sewanee, Tennessee, 1974-1981; professor, University of the South, Sewanee, Tennessee, since 1981; director Summer School, University of the South, Sewanee, Tennessee, 1980-1988; associate dean, University of the South, Sewanee, Tennessee, 1984-1988; provost, University of the South, Sewanee, Tennessee, since 1989. Board directors Regions Bank of Franklin County, Tennessee.
(Topology is a natural, geometric, and intuitively appeali...)
(This text is intended as a one semester introduction to a...)
(This text presents the fundamental principles of topology...)
President Tennessee College Association, 1999—2000. Board directors St. Andrews-Sewanee School, 1981—1986, Tennessee Foundation Indiana Colleges, 1996—1999. Trustee University of the South, 1983—1985.
Member of American Association of University Professors, Mat. Association American, American Mathematics Society, Sigma Xi.
Married Henrietta Brown, August 17, 1963 (divorced May 2000). Children: Elizabeth Bonner, Frederick Hailey. Married Nancy Mishoe Brennecke, June 1, 2002.
Children: Alexander McMillan, Augustus Brennecke.