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.
Jump to Week: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Instructors
Joe Rabinoff
jdr@math.duke.eduMath & Physics 243
Office Hours:
| M | 12 | –1:30pm | Math & Physics 243 |
| Tu | 10 | –11:30am | Math & Physics 243 |
Suzanne Crifo
suzanne.crifo@duke.eduOffice Hours:
| M | 10 | –11am | Math & Physics 274J |
| Th | 10 | –11am | Math & Physics 274J |
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.
Rabinoff's Reliable Row Reducer
For practicing row reduction when you're allergic to fractions.
Interactive Linear Algebra
A complement to Strang's book written by Joe.
Textbook
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
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. |
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| Vectors and Matrices (Ch. 1, 2.4, 2.7) |
Joe's Notes Recorded: Watch on WarpWire (on Canvas) before the second lecture. |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
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| Projection Matrices (4.2) | Joe's Notes | ||||||
| Friday, 10/4: MIDTERM 1 |
Practice Midterm
and Solutions |
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| Week 7: 10/7 | Least Squares (4.3) |
Homework #7 Due 10/16 11:59pm |
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| Gram–Schmidt and QR (4.4) | |||||||
| Problem Session | |||||||
| Week 8: 10/14 | FALL BREAK |
Homework #8 Due 10/23 11:59pm |
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| Determinants I (5.1, 5.3) | |||||||
| Problem Session | |||||||
| Week 9: 10/21 | Determinants II (5.2) |
Homework #9 Due 10/30 11:59pm |
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| Eigenvalues and Eigenvectors (6.1) | |||||||
| Problem Session | |||||||
| Week 10: 10/28 | Diagonalization: Vector Form (6.2) |
Homework #10 Due 11/6 11:59pm |
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| 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 |
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| 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 |
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| LDLT; Quadratic Optimization (2.7, 6.5) | |||||||
| Problem Session | |||||||
| Week 13: 11/18 | Quadratic Optimization II (6.5) |
Homework #13 Due 11/27 11:59pm |
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| 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 |
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| THANKSGIVING | |||||||
| Problem Session | |||||||
| Week 15: 12/2 | PCA I (7.3, 7.4) |
Homework #15 (Not collected) |
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| PCA II (7.3) | |||||||
| Problem Session | |||||||
Final exams:
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