Beginning Topology is designed to give undergraduate students a broad notion of the scope of topology in areas of point-set, geometric, combinatorial, differential, and algebraic topology, including an introduction to knot theory. A primary goal is to expose students to some recent research and to get them actively involved in learning. Exercises and open-ended projects are placed throughout the text, making it adaptable to seminar-style classes. The book starts with a chapter introducing the basic concepts of point-set topology, with examples chosen to captivate students' imaginations while illustrating the need for rigor. Most of the material in this and the next two chapters is essential for the remainder of the book. One can then choose from chapters on map coloring, vector fields on surfaces, the fundamental group, and knot theory. A solid foundation in calculus is necessary, with some differential equations and basic group theory helpful in a couple of chapters. Topics are chosen to appeal to a wide variety of students: primarily upper-level math majors, but also a few freshmen and sophomores as well as graduate students from physics, economics, and computer science. All students will benefit from seeing the interaction of topology with other fields of mathematics and science; some will be motivated to continue with a more in-depth, rigorous study of topology.
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Sue Goodman is Professor of Mathematics at the University of North Carolina at Chapel Hill. Her research is in the area of foliations and dynamical systems, particularly on low dimensional manifolds. Dr. Goodman studies the relationship between dynamical and topological properties of the foliations and their ambient manifolds. She is an exceptional teacher. At UNC-CH, Dr. Goodman received the Graduate Math Association Award for graduate teaching in 1978 and the UNC-CH Tanner Award for undergraduate teaching a few years later in 1981. In 1991-94, she held the post of Bowman Gordon Gray Professor in honor of her undergraduate teaching. In March 2003, she received the SE MAA Distinguished College or University Teaching Award.
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