Beginning Topology

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American Mathematical Soc., 2005 - Mathematics - 236 pages
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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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Contents

I
1
II
12
III
22
IV
31
V
36
VI
39
VII
41
VIII
54
XXVI
122
XXVII
131
XXVIII
133
XXIX
141
XXX
152
XXXI
153
XXXII
160
XXXIII
164

IX
56
X
57
XI
59
XII
66
XIII
67
XIV
75
XV
77
XVI
80
XVII
86
XVIII
90
XIX
91
XX
98
XXI
101
XXII
107
XXIII
113
XXIV
118
XXV
119
XXXIV
167
XXXV
171
XXXVI
173
XXXVII
179
XXXVIII
182
XXXIX
183
XL
190
XLI
191
XLII
193
XLIII
194
XLIV
202
XLV
207
XLVI
219
XLVII
230
XLVIII
234
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