MAT 441 Introduction to Topology
Here are scanned solutions to the final exam.
I cannot send personal information (like grades) by email, and I am required to keep the finals for one year, but (i) if you'd like to see your final, come visit me over the summer or next semester, and (ii) if you email me I will reply with two numbers, encrypted in some amusing manner, which you may interpret in any way you like. Here is the distribution of final exam scores and overall course averages.
Thanks all for you hard work this semester. It was really fun teaching you guys - I hope any mysteries presented by my lectures were resolved eventually. Have an enjoyable summer break. If you are looking for something further to read, relating to the course material, my recommendations are:
Lecture Notes on Elementary Topology and Geometry, I.M. Singer and J.A. Thorpe - excellent treatment of fundamental group and covering spaces, simplicial homology, smooth manifolds and differential forms.
Topology from the Differentiable Viewpoint, J. Milnor - wonderful small paperback covering smooth manifolds and vector fields.
Algebraic Topology, An Introduction, W. Massey - fundamental group and covering spaces, classification of surfaces. I think this book may have since been incorporated into a more comprehensive algebraic topology book by Massey.
Topology, J. Munkres - a standard text for a first-year graduate course in topology. Mostly point-set, with some homotopy and fundamental group at the end.
Topology, J. Dugundji - ditto, slightly more general treatment, less fundamental group. This one I use for a general reference, since it was the one I looked at druing my first-semester graduate topology course.
Algebraic Topology, A. Hatcher - this is the current standard text for a first graduate course in algebraic topology, and is freely available from Hatcher's web page (try google).
Enjoy - and feel free to email me if you have any questions. Hasta la vista.
Syllabus (includes tentative exam dates)
Exams
.
Problem Sets
Suggested Exercises (from the text Beginning Topology, by Sue Goodman)
1.1 / 3,4,5,12,25.
1.2 / 1,12,21,22.
1.3 / 4,5,6,10,11,12,16,17,23,24,28,29,30,31,34.
2.1 / 2.
2.2 / 2,6,7.
2.3 / 1,2,3,6,9,12,13,19,22,23.
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