Week 1
Date 
Class Topics 
Reading (due next class) 
Problems 
Fri., Jan. 4 
What's a manifold? Geometry/Topology (sphere theorem and Hadamard's Theorem) A little topology (open, closed, connected, compact, etc.) Vector Fields & Integral Curves 
Chpt. 13 
HW 1 DUE January 11 
Sat., Jan. 5 
WE'RE NOT MEETING FOR THE SPECIAL DAY OF CLASSES 


Week 2
Date 
Class Topics 
Reading (due next class) 
Problems 
Mon., Jan. 7 
Vector Fields & Integral Curves 
Chp. 4 

Tues. Jan 8 
Integral Curves Tangent Spaces 
Chp. 5 

Wed., Jan 9 
Tangent Spaces Implicit Function Thm. Surfaces 
chp. 6 

Fri., Jan 11 
Functions on Surfaces & The method of Lagrange Multipliers HW 1 DUE TODAY 
Chp. 16 
HW 2 Due Jan 18 
Week 3
Date 
Class Topics 
Reading (due next class) 
Problems 
Mon., Jan. 14 
Lagrange Multipliers Vector Fields & Integral Curves on Surfaces 
Chp. 8 

Wed., Jan. 16 
Orientation Möbius Strip & Real Projective Space Covariant Differentiation 
Chp. 7 

Fri., Jan. 18 
Geodesics HW 2 Due Today 
Chp. 6 and Review 

Week 4
Date 
Class Topics 
Reading (due next class) 
Problems 
Mon., Jan. 21 
MLK Day (Class Moved to Xhour) 


Tues., Jan 22 
Geodesics 
Chp 9 

Wed., Jan. 23 
Parallelism on nsurfaces 
Chp. 9 

Fri., Jan, 25 
Parallel Transport More on Differentiating vector fields 
Chp. 10 & 12 

Week 5
Date 
Class Topics 
Reading (due next class) 
Problems 
Mon., Jan. 28 
No Class 


Wed., Jan. 30 
Covariant Differentiation The Shape Operator (a.k.a. Weingarten Map) Guest Lecturer: Prof. Chernov 
Chp. 11 

Fri., Feb. 1 
Curvature of plane Curves HW 3 Due Today 
Chp. 112 
HW 4 Due Feb. 6 
Week 6
Date 
Class Topics 
Reading (due next class) 
Problems 
Mon., Feb. 4 
Curvature of Surfaces: Quadratic Forms, First & Second Fundamental Form, Normal Curvature 
Chp. 112 

Tues., Feb. 5 
GaussKronecker Curvature, Mean Curvature Interpreting/Calculating Gaussian curvature 
Chp. 1 12 

Wed., Feb. 6 
Interpreting/Calculating GaussKronecker Curvature HW 4 Due Today 
Review & Chp. 14 
Revisions Due Monday 
Fri., Feb. 8 
Winter Carnival  No Class 
Review & Chp. 14 
Revisions Due Monday 
Week 7
Date 
Class Topics 
Reading (due next class) 
Problems 
Mon., Feb. 11 
Comments on Exercises 2.10 (Flows) and 8.7 (Holonomy) Revisions Due Today 


Tues. Feb. 12 
Review Session 


Wed., Feb. 13 
Parametrized Surfaces 
Chp. 15 

Th., Feb. 14 
Valentine's Day 


Fri., Feb. 15 
More on Parametrized Surfaces Midterm 46pm 104 Bradley 
Chp. 17 

Week 8
Date 
Class Topics 
Reading (due next class) 
Problems 
Mon., Feb. 18 
locally nsurfaces are parametrized nsurfaces. Coordinate Charts and Atlases 


Tues. Feb. 19 
Stereographic Projection Locally param. nsurfaces are nsurfaces Revisiting smooth functions on nsurfaces 
Chp. 22 
HW 5 due Feb. 25 Oral Exam Topic Due March 4 
Wed., Feb. 20 
Inverse Func. Thm. for Surfaces Smooth Structures on nsurfaces. 


Fri., Feb. 22 
New definition of Smooth functions using local param. (a.k.a., coordinate charts) Final Call for rewrites of HW 3 & 4* 
Chp. 23 

Week 9
Date 
Class Topics 
Reading (due next class) 
Problems 
Mon., Feb. 25 
Rigid Motions HW 5 due today 


Tues. Feb. 26 
Congruence preserves geometric properties 
Chp. 23 
HW 6 Due March 5 
Wed., Feb. 27 
More on Congruence Isometries 


Fri., March 1 
Isometries 
Chp. 24 

Week 10
Date 
Class Topics 
Reading (due next class) 
Problems 
Mon., March 4 
Isometries Riemannian metrics Oral Exam/Presentation Today 


Tues. March 5 
Riemannian Metrics HW 6 Due Today 


Wed., March 6 
Riemannian metrics & Summing up the quarter 





