Week 0 (January 17): Introduction Reading for Week 1 : 1-6 Homework Assigned: 2.4, 2.5, 2.7, 2.12, 3.4, 4.12, 4.14,
5.5, 5.7, 6.4, 6.9 Week 1 (January 24): Introduction: Level Sets
through Gauss Map Chapters Discussed on Week 1 : 1-3 Homework Problems Discussed in the class : 2.4, 2.5, 2.7, 2.12, 3.4 Reading for Week 2: Chap. 7 HW Problems for Week 2 : 7.7, 7.9 Week 2 (January 31): Geodesics Chapters Discussed on Week 2: 4-7 Homework Problems Discussed in the class : 4.12, 4.14, 5.5,
5.7, 6.4, 6.9 Reading for Week 3: Chapters 7 and 8 HW Problems for Week 3 : 7.7, 7.9, 8.2, 8.4, 8.7 Week 3 (Feb 7): Homework Problems from
Chapters 4-7. Chapters Discussed on Week 3: 4-7 Homework Problems Discussed in the class : 7.7, 7.9 Reading for Week 4: Chapters 8,9 and 10 Homework Assignments for Week 4: 8.2, 8.4, 8.7, 9.2, 9.6, 9.12, 9.15 Week 4 (Feb 14): Parallel Transport
and Wiengarten Map Chapters Discussed on Week 4: Parallel Transport
and Wiengarten Map (Chapter 8 and 9) Homework Problems Discussed in the class :
Proof (Alberto), 8.2 (Ross K.) ,
8.4 (Ross H.), 8.7 (Amir), 9.2, 9.6, 9.12, 9.15 Reading for Week 5: Chapters 9 and 10 Week 5 (Feb 21): Wiengarten Map Chapters Discussed on Week 5: Weingarten Map ( Chapter 9) Homework Problems Discussed in the class : 9.2, 9.6, 9.12, 9.15 Reading for Week 6: Chapters 10, 11, and 12. Homework Assignments for Week 6: 10.7, 11.11, 11.16, 11.17, 12.1, 12.4, 12.13, 12.14 Typos in Thorpe: 11.17. The end of the second line should read "\phi_u : [a,b] \rightarrow R^2-{0}" Week 6a (Feb 28) and Week 6b(March 13):
Curvature of Plane curves, Arc length and Line Integrals. Chapters Discussed on Week 6: Curvature of Plane Curves, Arc
Length and Line Integrals( Chapter 10 and 11) Homework Problems Discussed in the class : 10.7, 11.11, 11.16, 11.17 Reading Assignment for Week 7: Chapters 12 and 13. Homework Assignments for Week 7: 12.1, 12.4, 12.13, 12.14 Week 7(March 20,21): Curvature of Surfaces Chapters Discussed on Week 7: Curvature of Surfaces( Chapter 12) Homework Problems discussed in the class : 12.1, 12.4, 12.13, 12.14 Reading Assignment for Week 8: Chapters 13, 14 Homework Assignments for Week 8: 13.5 Week 8 (March 28): Curvature of Surfaces,
Convex Surfaces Chapters Discussed on Week 8: Curvature of Surfaces,
Convex Surfaces (Chapter 13) Homework Problems Discussed : 12.14, 13.5 Reading Assignment for Week 9: Chapter 14. Homework Assignments for Week 9: 14.7, 14.13, 14.14, 14.16 Week 9 (April 4): Convex Surfaces,
Parameterized Surfaces. Chapters Discussed on Week 9 : Convex Surfaces,
Parameterized Surfaces (Chapters 13 and 14) Homework Problems Discussed in the class: -- Reading Assignment for Week 10: Chapter 15. Homework Assignments for Week 10: 15.2, 15.7, 15.9, 15.13 Week 10 (April 11): Clarification of
doubts from previous chapters, Local Equivalence of Surfaces
and Parameterized Surfaces (beginning). Chapters Discussed on Week 10: Doubts from Chapters 12,
13 and 14. Beginning of Chapter 15. Local Equivalence of Surfaces and Parameterized
Surfaces and (Chapter 15). Homework Problems Discussed in the class: 12.13 (redo),
14.7, 14.13, 14.16 Reading Assignment for Week 10: Chapter 15 --
Local Equivalence of Surfaces and Parameterized Surfaces. Homework Assignments for Week 11: 15.2, 15.7, 15.9, 15.13 Week 11(April 18): Local Equivalence of
Surfaces and Parameterized Surfaces. Chapters discussed on Week 11 : Local Equivalence of Surfaces
and Parameterized Surfaces (Chapter 15) Homework Problems discussed in the class : 14.14 Reading Assignment for Week 12: Chapter 15 Homework Assignments for Week 12: -- Week 12(April 25): Local Equivalence
of Surfaces and Parameterized Surfaces. Chapters discussed on Week 12 : Local Equivalence
of Surfaces and Parameterized Surfaces (Chapter 15) Homework Problems discussed in the class : 15.2, 15.7, 15.9, 15.13 Reading Assignment for Week 13: Surface Area and Volume (Chapter 17). Homework Assignments for Week 13: 17.6, 17.9, 17.13, 17.18 Week 13(May 25): Surface Area and Volume. Chapters to be discussed on Week 13: Surface Area and Volume
(Chapter 17). Homework Problems discussed in the class : 17.6, 17.9 Reading Assignment for Week 14: Minimal Surfaces (skipped),
The Exponential Map. Homework Assignments for Week 13b+14: 17.10, 17.13,
17.18, 19.2, 19.3, 19.5, 19.6 Week 13b: Surface Area and Volume. Chapters to be discussed on Week 13: Surface Area
and Volume (Chapter 17). Homework Problems discussed in the class: 17.10, 17.13, 17.18 Reading Assignment for Week 14: Minimal Surfaces (skipped),
The Exponential Map. Homework Assignments for Week 14: 19.2, 19.3, 19.5, 19.6 Week 14: The Exponential Map. Chapters to be discussed on Week 14: The Exponential Map (Chapter 19)
Homework Problems discussed in the class :--- Reading Assignment for Week 15: Surfaces with boundary. Homework Assignments for Week 15: 20.2, 20.5, 20.9, 20.10 Week 15: The Exponential Map (discussion),
Problems from Chapters 17 and 19. Chapters discussed on Week 15: The Exponential Map (Chapter 19). Homework Problems to be discussed in the class : 19.2, 19.3. Reading Assignment for Week 16: Surfaces with boundary
(brief discussion). Homework Assignments for Week 16: 20.2, 20.5, 20.9, 20.10 Week 16: Surfaces with Boundary Chapters discussed on Week 16: Surfaces with Boundary. Week 17: Surfaces with Boundary Chapters discussed on Week 17: Surfaces with Boundary. Homework Problems discussed in the class : 20.2, 20.5, 20.9, 20.10 Reading Assignment for Week 18: The Gauss-bonnet Theorem. Homework Assignments for Week 18: 21.1, 21.2, 21.4, 21.5 |
Week 0 (September 12): Introduction: Level
Sets through Vector Fields
Chapters Discussed on Week 1 : 1-5
Homework Problems Discussed in the class : -
Reading for next week: Chaps.1-7
HW Problems for Next Week : Uma 2.5, Matt 2.7 a,b ,Sidd 3.4,Uma 4.12,
Matt 5.7, Sidd 6.4, Uma 6.9, Matt 7.7, Sidd 7.9
Week 1 (Sep 19) NSH 4201: Level Sets through
Geodesics
Chapters Discussed this Week : 1-7
Homework Problems Discussed in the class : Uma 2.5, Matt 2.7 a,b,
Sidd 3.4,Uma 4.12, Matt 5.7, Sidd 6.4, Uma 6.9, Matt 7.7, Sidd 7.9
Reading for week 2: Chaps. 8-10
HW Problems for next week: Sidd 7.9 (from last week) and 8.2,
Matt 8.4, Uma 8.7, Sidd 9.2, Matt 9.6, Uma 9.12, Sidd 9.15, Matt 10.7
Week 2 (Sep 26) NSH 4201: Finish Geodesics,
Parallel Transport, Weingarten Map, and Curvature
of Plane Curves
Chapters Discussed on Week 2: 8-10
Homework Problems Discussed in the class : Sidd 7.9 (from last week)
and 8.2, Matt 8.4, Uma 8.7, Sidd 9.2, Matt 9.6, Uma 9.12, Sidd 9.15,
Matt 10.7
Reading for Week 3: Chapters 11-13
HW Problems for next week :11.11, 11.16, 11.17, 12.1, 12.4,
12.13, 12.14, 13.5
Week 3-5 (Oct) Smith 100: Arc length
and line integrals, Curvature of surfaces,
Convex surfaces
Chapters Discussed on Weeks 3-5: 11-13
Homework Problems Discussed in the class : 11.11, 11.16, 11.17,
12.1, 12.4, 12.13, 12.14, 13.5
Reading for next week: Chapters 14
HW Problems for next week :14.7, 14.13, 14.14, 14.16
Week 6 (Nov 14) Parametrized Surfaces
Chapters Discussed on Weeks 6: 14
Homework Problems Discussed in the class : 14.7, 14.13, 14.14
Reading for next meeting (11/28): Chapters 15
HW Problems for next week :15.2 Matt, 15.7 Sidd, 15.9 Matt,
15.13 Sidd
Week 7 (Nov 28): Local Equivalence
of Surfaces and Parameterized Surfaces.
Chapters discussed this week : Local Equivalence
of Surfaces and Parameterized Surfaces (Chapter 15)
Homework problems discussed in class : 15.2, 15.7, 15.9,
part of 15.13
Reading assignment for next week: Surface Area and Volume
(Chapter 17).
Homework assignments for next week: 15.13 Sidd, 17.6 Sidd,
17.9 Matt, 17.13 Sidd, 17.18 Matt
Week 8,9 (Dec): Surface Area and Volume
Chapters discussed this week : Surface Area and Volume (Chapter 17)
Homework problems discussed in class : 17.6 Sidd, 17.9 Matt,
17.13 Sidd - only a, 17.18 Matt - only first part
Reading assignment for next week:
Homework assignments for next meeting: 17.13b Sidd,
17.18 second part Matt
-----------Spring 2008------------- Week 1 (Jan 24): The Exponential Map
Chapters discussed this week : The Exponential Map (Chapter 19)
Homework problems discussed in class : 17.13b Sidd,
17.18 second part Matt,
Reading assignment for next week: Surfaces with boundary (Chap 20)
Homework assignments for next meeting: 19.2 (Amir), 19.3(Ross),
19.5 (Alberto), 19.6 (Matt)
Week 2 (Jan 31, Feb 14): The Exponential Map
Chapters discussed this week : The Exponential Map (Chapter 19)
Homework problems discussed in class : 19.2 (Amir), 19.3(Ross),
19.5 (Alberto), 19.6 (Matt)
Reading assignment for next week: Surfaces with boundary (Chap 20)
Homework assignments for next meeting: 20.2, 20.5, 20.9, 20.10
Week 3 (Feb 21): Surfaces with boundary
Chapters discussed this week : Surfaces with boundary (Chapter 20)
Homework problems discussed in class :
Reading assignment for next week:
Homework assignments for next meeting:
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