Welcome to Math 218D! I will post almost all course materials on this page. Please check back for information about homework assignments, exams, and additional resources. You should probably read the syllabus.
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M  12  –1:30pm  Math & Physics 243 
Tu  10  –11:30am  Math & Physics 243 
M  10  –11am  Math & Physics 274J 
Th  10  –11am  Math & Physics 274J 
Lecture  Instructor  Location  Time 

218D1 (001)  Joe Rabinoff  Gross Hall 103  TTh 11:45am–1:00pm 
218D1 (002)  Suzanne Crifo  Math & Physics 235  MW 8:30–9:45am 
Problem Session  Instructor  Location  Time 
218D1 (01D)  Soham Karwa  Math & Physics 047  F 10:05–11:20am 
218D1 (02D)  Soham Karwa  Math & Physics 259  F 11:45am–1:00pm 
218D1 (03D)  Soham Karwa  Math & Physics 047  F 1:25pm–2:40pm 
218D1 (04D)  Soham Karwa  Math & Physics 235  F 3:05–4:20pm 
Access Gradescope by clicking on the tab in Canvas.
For practicing row reduction when you're allergic to fractions.
A complement to Strang's book written by Joe.
Topic and Section  Materials  Homework  

Week 1: 8/26  Introduction 
Joe's Notes Demo: Best fit ellipse Demo: Rabbit population Demo: A Plane Demo: Two Planes 
Homework #1 Due 9/4 11:59pm Solutions Note: HW#1 also covers the recorded lecture. 

Vectors and Matrices (Ch. 1, 2.4, 2.7) 
Joe's Notes Recorded: Watch on WarpWire (on Canvas) before the second lecture. 

Solving Equations: Elimination (2.2)  Joe's Notes  
Problem Session  
Week 2: 9/2  Gauss–Jordan Algorithm (2.2, 2.5) 
Joe's Notes Gauss–Jordan Slideshow Rabinoff's Reliable Row Reducer 
Homework #2 Due 9/11 11:59pm Solutions 

LU Decomposition (2.3, 2.6)  Joe's Notes  
Problem Session  
Week 3: 9/9  Parametric Form 
Joe's Notes Demo: Parameterized Line Demo: Parameterized Plane 
Homework #3 Due 9/18 11:59pm Solutions 

Spans (3.2, 3.3) 
Joe's Notes Demo: A vector Demo: Scalar multiplication Demo: Vector addition Demo: Vector subtraction Demo: Linear combinations of two vectors in R^{2} Demo: Linear combinations of two vectors in R^{3} Demo: Linear combinations of three vectors in R^{3} Demo: Span of 1 vector in R^{2} Demo: Span of 2 vectors in R^{2} Demo: Span of 1 vector in R^{3} Demo: Span of 2 vectors in R^{3} Demo: Span of 3 vectors in R^{3} Demo: Column Picture for Consistency: Consistent Demo: Column Picture for Consistency: Inconsistent Demo: Row/column picture: parallel lines 

Problem Session  
Week 4: 9/16  Subspaces (3.1, 3.2) 
Joe's Notes Demo: Column and Null Space 
Homework #4 Due 9/25 11:59pm Solutions 

Linear Independence and Basis (3.4, 3.5) 
Joe's Notes Demo: Coplanar vectors Demo: Redundant parameterization Demo: Linearly dependent vectors Demo: Linearly independent vectors Demo: Linear (In)dependence of 1 vector Demo: Linear (In)dependence of 2 vectors Demo: Linear (In)dependence of 3 vectors Demo: Linear Dependence of 3 vectors in R^{2} 

Problem Session  
Week 5: 9/23  Fundamental Subspaces (3.4, 3.5) 
Joe's Notes Demo: Ranknullity: n=3, r=0 Demo: Ranknullity: n=3, r=1 Demo: Ranknullity: n=3, r=2 Demo: Ranknullity: n=3, r=3 
Homework #5 Due 10/2 11:59pm 

Orthogonal Complements (3.5, 4.1) 
Joe's Notes Demo: Closest vector to b Demo: Orthogonal complement of one vector Demo: Orthogonal complement of two vectors Demo: Orthogonal complements in R^{2} 

Problem Session  
Week 6: 9/30  Orthogonal Projections (4.2) 
Joe's Notes Demo: Decomposition relative a line in R^{2} Demo: Decomposition relative a line in R^{3} Demo: Decomposition relative a plane in R^{3} Demo: Projection onto a plane Demo: Projection onto a line Demo: Projection onto a plane 
Homework #6 Due 10/9 11:59pm 

Projection Matrices (4.2)  Joe's Notes  
Friday, 10/4: MIDTERM 1 
Practice Midterm
and Solutions 

Week 7: 10/7  Least Squares (4.3) 
Homework #7 Due 10/16 11:59pm 

Gram–Schmidt and QR (4.4)  
Problem Session  
Week 8: 10/14  FALL BREAK 
Homework #8 Due 10/23 11:59pm 

Determinants I (5.1, 5.3)  
Problem Session  
Week 9: 10/21  Determinants II (5.2) 
Homework #9 Due 10/30 11:59pm 

Eigenvalues and Eigenvectors (6.1)  
Problem Session  
Week 10: 10/28  Diagonalization: Vector Form (6.2) 
Homework #10 Due 11/6 11:59pm 

Diagonalization: Geometry (6.2)  
Problem Session  
Week 11: 11/4  Complex Numbers; Euler's Formula (9.1) 
Joe's Notes Recorded: Watch on WarpWire (on Canvas) before Tuesday's lecture. 
Homework #11 Due 11/13 11:59pm 

AM/GM and Diagonalizability (6.2)  
Stochastic Processes and PageRank  
Friday, 11/8: MIDTERM 2  
Week 12: 11/11  Spectral Theorem (6.4) 
Homework #12 Due 11/20 11:59pm 

LDL^{T}; Quadratic Optimization (2.7, 6.5)  
Problem Session  
Week 13: 11/18  Quadratic Optimization II (6.5) 
Homework #13 Due 11/27 11:59pm 

SVD: Outer Product Form (7.1, 7.2)  
Problem Session  
Week 14: 11/25  SVD: Matrix Form (7.3) 
Homework #14 Due 12/4 11:59pm 

THANKSGIVING  
Problem Session  
Week 15: 12/2  PCA I (7.3, 7.4) 
Homework #15 (Not collected) 

PCA II (7.3)  
Problem Session  
Final exams:
