HW #1:
In Section 1.1, do problems 1abcde, 2, 5, 7, 9
In Section 1.2, do problems 2, 4, 5, 16, 18, 23
Use the epsilon-delta definition of continuity to prove that the linear function f(x)= mx+b is continuous at the real number x=a.
Due: Tuesday, Sept 7.
Week 1: Chapter 1, Sections 1.1, 1.2, 1.3 Equivalence, Bijections, Continuous Functions
Week 2: Chapter 1, Sections 1.3, 1.4 Continuous Functions, Topological Equivalence
Week 3: Chapter 1, Section 1.5, 1.6 Topological Invariants, Ambient Isotopy,
Unlinking video for Dogbone Toy
Week 4: Chapter 3, Sections 3.1, 3.2, 3.3 Surfaces, Cut and Paste, Euler Characteristic
Week 5: Chapter 3, Sections 3.4 Classification of Surfaces
Week 6: Chapter 4, Sections 4.1, 4.2, 4.3 3D Manifolds, Shape of Space, Euler Characteristic, Glueing Polyhedra Solids
Week 7: Chapter 5, Sections 5.1, 5.2 Continuous Functions on Closed Bounded Intervals, Contraction Mapping Theorem EXAM 1
Week 8: Chapter 5, Section 5.3, 5.4 Sperner's Lemma, Brower's Fixed Point Theorem
Week 9: Chapter 6, Sections 6.1, 6.2, 6.3 Deformations with Singularities, Invariance of Fundamental Group
Week 10: Chapter 6, Sections 6.4, 6.5, 6.6 The Sphere and the Circle, Words & Relations, Poincare Conjecture
Spring Break
Week 11: Chapter 7, Section 7.2, 7.3 Topological Spaces, Connectedness
Week 12: Chapter 7, Sections 7.4 Compactness, EXAM 2
Week 13: Chapter 7, Section 7.5 Quotient Spaces, Simplicial & Cell Complexes
Week 14: Simplicial & Cellular Homology
Week 15: Homology Examples, review
FINAL EXAM: am
