Topics are chosen to appeal to a wide variety of students: primary upper-level math majors, but also a few freshmen and sophomores as well as graduate students from physics, economics, and computer science.Fakk2 wrote:Format: US version of the ROM One can then choose from chapters on map coloring, vector fields on surfaces, the fundamental group, and knot theory.Ī solid foundation in calculus is necessary, with some differential equations and basic group theory helpful in a couple of chapters. Most of the material in this and the next two chapters is esenial for the remainder of the book. 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. Exercises and open-ended projects are placed together throughout the text, making it adaptable to seminar-style classes. A primary goal is to expose students to some recent research and to get them actively involved in learning. 'īeginning 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. Nearly every one of the 112 sections in this book concludes with a set of exercises that reinforce materials already covered and prepare students for subsequent chapters. A survey of general topological spaces and mappings includes considerations of compactness, connectedness, quotient spaces, net and filter convergence, and product spaces. The following chapters offer detailed studies of metric spaces and applications to analysis. Kasriel, who taught at Georgia Tech for many years, begins with reviews of elementary set theory and Euclidean n-space. It will prove valuable to undergraduate mathematics majors as well as to graduate students and professionals pursuing mathematics research. This introductory treatment is essentially self-contained, and it features explanations and proofs that relate to every practical aspect of point-set topology. ☯ Full Synopsis : 'General topology offers a valuable tool to students of mathematics, particularly in courses involving complex, real, and functional analysis.
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