Reed College

MWF 10:00-10:50 in Library 389

Office Hours: M 15:00-16:30, W 13:30-15:00 in Library 390; also by appointment

Syllabus

*Week 1*- W 1/25: ch. 2 the definition of a topology, the Euclidean topology, metric spaces
- F 1/27: ch. 2 closure, interior, exterior, continuous maps [HW due: exercises 2.4(a)-(c)]

*Week 2*- M 1/30: ch. 2 continuous maps and homeomorphisms [HW due: prove Prop 2.8(h), exercises 2.10, 2.13, 2.33, problems 2-1(a)(d)(e)]
- W 2/1: ch. 2 Hausdorff spaces, bases
- F 2/3: ch. 2 countability conditions, manifolds [HW due: exercises 2.38, 2.42, problems 2-7, 2-8]

*Week 3*- M 2/6: ch. 2, ch. 3 manifolds, operations on manifolds, the subspace topology
- W 2/8: interlude on category theory [see the handout on categories and functors]
- F 2/10: interlude on category theory

*Week 4*- M 2/13: interlude on category theory [HW due: problems 2-10, 2-22, 2-24, exercise 3.7]
- W 2/15: interlude on category theory
- F 2/17: interlude on category theory [HW due: exercises 1.6, 1.14, 1.16 from the handout on categories and functors]

*Week 5*- M 2/20: ch. 3 product spaces
- W 2/22: ch. 3 disjoint union spaces and quotient spaces
- F 2/24: [[CLASS CANCELLED]]

*Week 6*- M 2/27: ch. 3 quotient spaces [HW due: exercises 3.26, 3.45 problems 3-3, 3-6, 3-9, 3-17]
- W 3/1: ch. 3 quotient spaces and group actions
- F 3/3: ch. 4 connectedness [HW due: problems 3-18, 3-24]

*Week 7*- M 3/6: ch. 4 connectedness and path-connectedness
- W 3/8: ch. 4 compactness
- F 3/10: ch. 4 compactness
**TAKE-HOME MIDTERM EXAM DUE**

*Spring Break*

*Week 8*- M 3/20: ch. 4 the closed map lemma
- W 3/22: ch. 5 real projective spaces, CW complexes (skim ch. 5)
- F 3/24: ch. 5 the classification of 1-manifolds [HW due: exercises 4.3, 4.29, 6.3]
*Week 9*- M 3/27: ch. 5 the classification of 1-manifolds, simplicial complexes [HW due: problems 4-10(a)(b), 4-11(a)]
- W 3/29: ch. 6 polygonal presentations of surfaces
- F 3/31: ch. 6 the classification of surfaces
*Week 10*- M 4/3: ch. 6 the classification of surfaces, continued [HW: decompose T^2 as a CW complex; how many cells does your decomposition have? Is it regular? Does it arise from a simplicial complex?]
- W 4/5: ch. 6 the classification of surfaces, orientability, and the Euler characteristic [HW due: 4-15, 4-23(a)(b)(d), 4-25]
- F 4/7: ch. 7 the homotopy relation and the fundamental group
*Week 11*- M 4/10: ch. 7 the fundamental group [HW due: 6-2, 6-6]
- W 4/12: ch. 7 retracts and homotopy equivalences
- F 4/14: ch. 8 the fundamental group of S^1 [HW due: exercises 7.6, 7.14, 7.42, problem 7-13]
*Week 12*- M 4/17: ch. 7, 10 calculating fundamental groups
- W 4/19: ch. 10 coproducts and pushouts
- F 4/21: ch. 10 the Van-Kampen theorem [HW due: problems 8-6, 8-10 (for (c), replace "the index of V around the loop \omega" with "the winding number of V around the loop \omega"), 8-11, 9-6(d), 7-19, 9-9(c) (Hint: you already did this earlier in the term!)]
*Week 13*- M 4/24: ch. 11 covering spaces
- W 4/26: ch. 11 covering spaces
- F 4/28: course evaluations [HW due: problems 10-1, 10-2, 10-13, 11-4, 11-17]