Math 218D-1 Fall 2024


Welcome

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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Instructors

Joe Rabinoff
Joe Rabinoff

Joe Rabinoff

jdr@math.duke.edu
Math & Physics 243
Office Hours:
M12–1:30pmMath & Physics 243
Tu10–11:30amMath & Physics 243
Suzanne Crifo
Suzanne Crifo

Suzanne Crifo

suzanne.crifo@duke.edu
Office Hours:
M10–11amMath & Physics 274J
Th10–11amMath & Physics 274J
Soham Karwa
Soham Karwa

Soham Karwa

soham.karwa@duke.edu
Office Hours:
Tu6–8pmMath & Physics 259

Classes

Lecture Instructor Location Time
218D-1 (001) Joe Rabinoff Gross Hall 103 TTh 11:45am–1:00pm
218D-1 (002) Suzanne Crifo Math & Physics 235 MW 8:30–9:45am
Problem Session Instructor Location Time
218D-1 (01D) Soham Karwa Math & Physics 047 F 10:05–11:20am
218D-1 (02D) Soham Karwa Math & Physics 259 F 11:45am–1:00pm
218D-1 (03D) Soham Karwa Math & Physics 047 F 1:25pm–2:40pm
218D-1 (04D) Soham Karwa Math & Physics 235 F 3:05–4:20pm

Resources


Access Gradescope by clicking on the tab in Canvas.


Textbook

Strang
Strang, Introduction to Linear Algebra
The official text for the course is Introduction to Linear Algebra (6th Ed) by Gilbert Strang, Wellesley–Cambridge Press/SIAM (2016). However, we will follow Strang only loosely. Another good reference is the online text Interactive Linear Algebra, by Dan Margalit and Joe Rabinoff.

Help

Office Hours
Your first stop for help should be office hours! Joe, Suzanne, and Soham will be holding plenty (times listed above), and you should not hesitate to show up with questions and chat with the other students there. If you can't make the scheduled office hours, send us an email and we'll set up a meeting.
Ed Discussion
Ask questions on Ed Discussion. Your instructors and fellow students are happy to post answers for everyone to see, and usually do so much more quickly than someone can respond to an email message.
Help Rooms
Help Rooms
The Math Department operates several Help Rooms to provide assistance to students in lower-level courses. Students are invited to drop by the Help Rooms whenever they are open. No appointment is necessary. Please check the MVLA + Probability HR Schedule to find the times dedicated to Math 218D-1.
The Academic Resource Center
The Academic Resource Center (ARC) offers free services to all students during their undergraduate careers at Duke. Services include Learning Consultations, Peer Tutoring, Learning Communities, ADHD/LD Coaching, Outreach Workshops, GRE/MCAT Prep, Study Connect, and more. Because learning is a process unique to every individual, we work with each student to discover and develop their own academic strategy for success at Duke. Contact the ARC to schedule an appointment. Undergraduates in any year, studying any discipline can benefit!

Schedule

  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 R2
Demo: Linear combinations of two vectors in R3
Demo: Linear combinations of three vectors in R3
Demo: Span of 1 vector in R2
Demo: Span of 2 vectors in R2
Demo: Span of 1 vector in R3
Demo: Span of 2 vectors in R3
Demo: Span of 3 vectors in R3
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 R2
Problem Session
Week 5: 9/23 Fundamental Subspaces (3.4, 3.5) Joe's Notes
Demo: Rank-nullity: n=3, r=0
Demo: Rank-nullity: n=3, r=1
Demo: Rank-nullity: n=3, r=2
Demo: Rank-nullity: n=3, r=3
Homework #5
Due 10/2
11:59pm

Solutions
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 R2
Problem Session
Week 6: 9/30 Orthogonal Projections (4.2) Joe's Notes
Demo: Decomposition relative a line in R2
Demo: Decomposition relative a line in R3
Demo: Decomposition relative a plane in R3
Demo: Projection onto a plane
Demo: Projection onto a line
Demo: Projection onto a plane
Homework #6
Due 10/9
11:59pm

Solutions
Projection Matrices (4.2) Joe's Notes
Friday, 10/4: MIDTERM 1 Practice Midterm and Solutions
Midterm and Solutions
Week 7: 10/7 Least Squares (4.3) Joe's Notes
Demo: Least-Squares
Demo: Best-fit line
Demo: Best-fit parabola
Demo: Best-fit trigonometric function
Demo: Best-fit ellipse
Demo: Best-fit ellipse: what is minimized?
Homework #7
Due 10/16
11:59pm

Solutions
Gram–Schmidt and QR (4.4) Joe's Notes
Demo: Projection formula
Problem Session
Week 8: 10/14 FALL BREAK Homework #8
Due 10/23
11:59pm

Solutions
Determinants I (5.1, 5.3) Joe's Notes
Problem Session
Week 9: 10/21 Determinants II (5.2) Joe's Notes
Supplement: cofactor matrix
Homework #9
Due 10/30
11:59pm

Solutions
Eigenvalues and Eigenvectors (6.1) Joe's Notes
Demo: Rabbits Multiply
Demo: Eigenspaces of a flip
Demo: Eigenspaces of a shear
Demo: Eigenspaces of a rotation
Demo: Eigenspaces of the rabbit matrix
Demo: Eigenspaces of a 3x3 matrix
Demo: Eigenspaces of a projection matrix
Problem Session
Week 10: 10/28 Diagonalization: Vector Form (6.2) Joe's Notes Homework #10
Due 11/6
11:59pm

Solutions
Diagonalization: Geometry (6.2) Joe's Notes
Dynamics demos:
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

Solutions
AM/GM and Diagonalizability (6.2) Joe's Notes
Supplement: Proof of the AM≥GM theorem

AM/GM demos:
Dynamics with a Complex Eigenvalue
Stochastic Processes and PageRank Joe's Notes
Friday, 11/8: MIDTERM 2 Practice Midterm and Solutions
Midterm and Solutions
Week 12: 11/11 Spectral Theorem (6.4) Joe's Notes
Demo: Eigenspaces of a 3x3 symmetric matrix
Demo: Eigenspaces of a 3x3 symmetric matrix (GM=2)
Demo: Dynamics of a 2x2 symmetric matrix
Homework #12
Due 11/20
11:59pm

Solutions
LDLT; Quadratic Optimization (2.7, 6.5) Joe's Notes
Supplement: LDLT and Cholesky
Problem Session
Week 13: 11/18 Quadratic Optimization II (6.5) Joe's Notes Homework #13
Due 11/27
11:59pm

Solutions
SVD: Outer Product Form (7.1, 7.2) Joe's Notes
Problem Session
Week 14: 11/25 SVD: Matrix Form (7.3) Joe's Notes Homework #14
Due 12/6
11:59pm

Solutions
THANKSGIVING
Week 15: 12/2 PCA I (7.3, 7.4) Joe's Notes Homework #15
(Not collected)

Solutions
PCA II (7.3) Joe's Notes
Problem Session
 
Final exams:
218D-1 (001):Thursday, 12/12, 9am–noon
218D-1 (002):Monday, 12/16, 2–5pm
Practice Final and Solutions