Week  Date  Reference  Topics 

1  Monday 1/27/2020 
Notes: Chapters 1, 2 
Euclidean geometry Cartesian coordinates Abstract vector spaces 
Wednesday 1/29/2020 
Axler: Chapters 1, 2 Notes: Chapter 3 
Abstract vector spaces Linear indepdendence Linear basis Linear maps 

2  Monday 2/3/2020 
Notes: Chapter 4 
Affine spaces Affine independence Affine basis Affine maps 
Wednesday 2/5/2020 
Notes: Chapter 6 O'Neill: Chapter 3 
Affine and vector space versions of \(\mathbb{R}^m\) Inner product on a vector space Euclidean space 

3  Monday 2/10/2020 
Notes: Chapter 7 O'Neill: Sections 2.12.3 
Curves in Euclidean space Velocity, speed, acceleration Curvature of a curve in Euclidean 2space FrenetSerret frame and equations in Euclidean 2space 
Wednesday 2/12/2020 
Notes: Chapter 7 O'Neill: Sections 2.32.4 
FrenetSerret frame and equations in Euclidean 2space  
4  Monday 2/17/2020 
No class, Presidents' Day  
Wednesday 2/19/2020 
Notes: Section 7.2 O'Neill, Chapter 4 
Curvature, torsion of a curve in Euclidean 3space FrenetSerret frame and equations in Euclidean 3space Curvature and torsion imply uniqueness up to rigid motion 

5  Monday 2/24/2020 
Notes: Chapter 8 and 9 O'Neill: Sections 4.14.2 
Definitions of a surface in \(\widetilde{\mathbb{R}}^3\) 
Wednesday 2/26/2020 
Notes: Chapter 9 O'Neill: Section 4.3 
Coordinate charts Sphere Torus Tangent space 

6  Monday 3/2/2020 
Notes: Chapter 10 O'Neill: Chapter 1 
Tangent space First fundamental form 
Wednesday 3/4/2020 
Notes: Chapter 10 O'Neill, Chapter 1 
First fundamental form 

7  Monday 3/9/2020 
Geometry of curve in surface in \(\mathbb{E}^3\) Second fundamental form Gauss map 

Wednesday 3/11/2020 
Notes: Chapter 10 
Dual vector space Dual basis Natural isomorphism \(V^{**}\simeq V\) Directional derivative Differential of function 

3/16/2020, 3/18/2020  No class, Spring Recess  
8  Monday 3/23/2020 
O'Neill, Chapter 4 

Wednesday 3/25/2020 
O'Neill, Chapter 4 


9  Monday 3/30/2020 
O'Neill, Chapter 4 

Wednesday 4/1/2020 
O'Neill, Chapters 4 


10  Monday 4/6/2020 
O'Neill: Chapters 2 and 6 

Wednesday 4/8/2020 
O'Neill: Chapter 2 


11  Monday 4/13/2020 
O'Neill: Chapter 6 

Wednesday 4/15/2020 
O'Neill: Chapter 6 


12  Monday 4/20/2020 
O'Neill: Section 3.3 

Wednesday 4/22/2020 
O'Neill: Chapter 4 


13  Monday 4/27/2020 
O'Neill: Chapter 4 

Wednesday 4/29/2020 
O'Neill: Chapters 4 and 6 


14  Monday 5/4/2020 
O'Neill: Chapters 4 and 7 

Wednesday 5/6/2020 


15  Monday 5/11/2020 
