Math 74-114 Syllabus and Homework Assignments
Spring 2012
 Updated: May 23


There will often be last minute changes in the syllabus and homework, so check this page before doing any reading or homework.

  Jump to Week 1| Week 2|Week 3|Week 4|Week 5|Week 6|Week 7|Week 8|Week 9|Week 10|Week 11 |

Week 1
March 26
  • Topology review, surfaces, connected sum of surfaces.
  • Read: Chapter 1, Sections 1 - 5, Section 8 (lightly)
  • Homework for Week 1 can be found at Homework Week 1.
March 28
  • Cut and paste, classification of surfaces, homotopy.
March 30
  • Homotopy: retracts, deformation retracts, contractible spaces, homotopy equivalences.
  • Read: Chapter 2, pp. 43 - 46
Week 2
April 2
  • Paths in a space, the fundamental group.
  • Read: Chapter 2, Sections 1 - 4
  • Homework for Week 2 can be found at Homework Week 2.
April 4
  • Homework for Week 1 due today.
  • The fundamental group: Change of base point, the fundamental group of a product, abelian fundamental groups.
  • Read: Chapter 2, Sections 7 & 8
April 5
  • X-hour, 1:00 - 1:50
  • Free products of groups, the Seifert-van Kampen theorem.
  • Read: Class notes; Chapter 4, Sections 1 & 2 (lightly)
April 6
  • Calculation of fundamental groups.
  • Read: Chapter 4, Sections 3 - 5
Week 3
April 9
  • Covering spaces: definitions and examples.
  • Read: Chapter 5, Sections 1 & 2
  • Homework for Week 3 can be found at Homework Week 3.
April 11
  • Homework for Week 2 due today.
  • Lifting properties of covering spaces.
  • Read: Chapter 5, Sections 3 - 5
April 13
  • Applications: The degree of a map, the fundamental group of a circle, the fundamental theorem of algebra.
  • Read: Class notes
Week 4
April 16
  • Conjugate subgroups of the fundamental group, the Galois correspondence between subgroups and coverings.
  • Read: Class notes
  • Homework for Week 4 can be found at Homework Week 4.
April 18
  • Homework for Week 3 due today.
  • The Galois correspondence between subgroups and coverings, the group of deck transformations.
  • Read: Class notes; Chapter 5, Section 6
April 19
  • X-hour, 1:00 - 1:50
  • Consequences of the Galois correspondence, free groups and the fundamental group of a graph.
April 20
  • Sketch of possible future topics: groups operating properly on a space, higher homotopy groups.
  • For next class review free-abelian groups (Chapter 3, Section 3)
Week 5
April 23
  • We begin homology theory. We will follow the text more closely than before.
  • The (cubical) singular chain complex, definition of homology groups.
  • Homework for Week 4 is due today.
  • Read: Chapter 7, Sections 1 & 2
April 25
  • Connectedness and zero dimensional homology, induced homomorphisms
  • Read: Chapter 7, Sections 2 & 3
April 27
  • The homotopy theorem, homotopy type
  • Read: Chapter 7, Section 4
  • The take-home midterm is due to be handed in today.
  • Homework for Week 6 can be found at Homework Week 6.
Week 6
April 30
  • Chain complexes, the five lemma
  • Read: Chapter 10, Sections 1 & 2 (up to top of p. 258), Chapter 7, p. 184
May 2
  • Homework for Week 6 is due today.
  • Homology of a pair, the exactness theorem
  • Read: Chapter 7, Section 5
May 4
  • V-small theorem, excision theorem, Eilenberg-Steenrod axioms
  • Read: Chapter 7, Section 6 and class notes
  • Homework which covers Week 6 can be found at Homework Week 7 (revised).
Week 7
May 7
  • Homology groups of the ball and sphere, degree of a map
  • Chapter 8, Sections 1 & 2
May 9
  • Applications: The Brouwer fixed point theorem, vector fields, maps of spheres
  • Read: Chapter 8, Section 2
  • Homework Week 7 (revised) is due today.
May 11
  • Attachment of cells
  • Read Chapter 9, Sections 1 & 2
  • Homework which covers Week 7 can be found at Homework Week 8.
Week 8
May 14
  • CW-complexes
  • Read: Chapter 9, Section 3
May 16
  • Homework Week 8 is due today.
  • Homology of CW-complexes, isomorphism between singular and CW homology
  • Read: Chapter 9, Section 4
May 17
  • X-hour, Thursday, 1:00 - 1:50
  • Homology of CW-complexes continued, Euler characteristic
May 18
  • Homework which covers Week 8 can be found at Homework Week 9.
  • Computations in CW homology
Week 9
May 21
  • The Mayer-Vietoris sequence
  • Read: Chapter 8, Section 5
May 23
  • Homework Week 9 is due today.
  • Applications: The Jordan-Brouwer theorem, invariance of domain
  • Read: Chapter 8, Section 6
May 25
  • Introduction to cohomology theory
  • Read: Chapter 12, Sections 1 - 3
Week 10
May 28
  • First day of reading period - NO CLASS
May 30
  • LAST CLASS
  • Cohomology theory