MATH 6610-01 — Analysis of Numerical Methods I
Fall 2020
Instructor: |
Akil Narayan |
Email: |
akilsci.utah.edu |
Office phone: |
+1 801-581-8984 |
Office location: |
WEB 4666, LCB 116 |
Office hours: |
Wed 10:45-11:45am, Thu 12pm-1pm (on Zoom) |
Class meeting time: |
Monday, Wednesday, Friday 11:50am - 12:40pm |
Class meeting location: |
Zoom |
Textbook (required): |
Trefethen and Bau III. "Numerical Linear Algebra", ISBN-10 0-89871-361-7, SIAM (1997). |
Mathematical analysis of numerical methods in linear algebra, interpolation, integration, differentiation, approximation (including least squares, Fourier analysis, and wavelets), initial- and boundary-value problems of ordinary and partial differential equations
Here are some additional textbook resources (optional) that may be helpful if you're looking for more reading.- Demmel. "Applied Numerical Linear Algebra", ISBN-13 978-0898713893, SIAM (1997). This book has many similarities to the Trefethen book, but has more details on numerical linear algebra algorithms.
- Golub and Van Loan. "Matrix Computations", ISBN-13 978-0801854149, Johns Hopkins University Press, 3rd edition (1996). This book is an excellent detailed reference, but is not necessarily the best as a first learning resource. It is a fairly comprehensive book for linear algebraic algorithms.
- Strang. "Linear Algebra and its Applications", ISBN-13 978-0030105678, Brooks Cole, 4th edition (2006). This book has more worked-out explicit examples. It covers many of the topics for this course at a high level, but does not go into as much detail as some other texts.
- Lax. "Linear Algebra and Its Applications", ISBN-13 978-0471751564, Wiley, second edition (2007). This is an excellent mathematical compendium of linear algebra theory. Many computational algorithms are also treated, but at a more abstract level. This book is a "definition, theorem, proof" mathematical treatment of linear algebra.
The course syllabus is here: PDF
Graded assignments
Individual grades for each assignment will be posted to Canvas. (uNID login required.) Note that the letter grades appearing on Canvas are not representative of predicted final letter grades for the course. Final letter grades will be computed according to the rubric and policies on the syllabus.
Homework assignments
Late work will not be accepted without advance approval from the instructor.
Problem set description
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Due date
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Homework
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0 : Submission demonstration
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September 2, 2020
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PDF
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1 : Basic linear algebra and eigenvalues
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September 16, 2020
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PDF
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2 : The SVD and QR factorizations
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October 5, 2020
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PDF
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3 : LU and Cholesky factorizations
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November 6, 2020
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PDF
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4 : Approximation techniques
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December 3, 2020
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PDF
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Miscellaneous handouts
The following are various relevant handouts.
Description
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Posting date
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Download
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Homework submission instructions
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August 19, 2020
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PDF
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Sample project submission: Homework 0
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August 19, 2020
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github
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Lecture 00 slides: Linear algebra preliminaries
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August 28, 2020
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PDF
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Marked slides from class
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August 28, 2020
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PDF
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Lecture 01 slides: Projections and permutations
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September 2, 2020
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PDF
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Marked slides from class
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September 2, 2020
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PDF
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Lecture 02 slides: Eigenvalues
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September 2, 2020
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PDF
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Marked slides from class
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September 2, 2020
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PDF
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Lecture 03 slides: Hermitian matrices
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September 3, 2020
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PDF
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Marked slides from class
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September 4, 2020
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PDF
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Lecture 04 slides: The Courant-Fischer-Weyl variational theorem
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September 6, 2020
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PDF
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Marked slides from class
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September 9, 2020
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PDF
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Lecture 05 slides: Floating-point representations
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September 6, 2020
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PDF
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Marked slides from class
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September 11, 2020
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PDF
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Lecture 06 slides: Problem conditioning
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September 13, 2020
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PDF
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Marked slides from class
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September 16, 2020
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PDF
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Lecture 07 slides: Algorithm stability
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September 13, 2020
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PDF
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Marked slides from class
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September 18, 2020
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PDF
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Lecture 08 slides: The spectral theorem
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September 20, 2020
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PDF
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Marked slides from class
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September 21, 2020
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PDF
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Lecture 09 slides: The singular value decomposition
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September 20, 2020
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PDF
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Marked slides from class
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September 23, 2020
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PDF
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Lecture 10 slides: Low rank approximation
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September 20, 2020
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PDF
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Marked slides from class
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September 25, 2020
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PDF
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Lecture 11 slides: The QR decomposition
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September 25, 2020
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PDF
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Marked slides from class
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September 29, 2020
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PDF
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Lecture 12 slides: Modified Gram-Schmidt
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September 25, 2020
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PDF
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Marked slides from class
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September 30, 2020
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PDF
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Lecture 13 slides: Householder reflectors
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September 25, 2020
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PDF
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Marked slides from class
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October 2, 2020
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PDF
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Lecture 14 slides: Least-squares problems
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October 2, 2020
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PDF
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Marked slides from class
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October 9, 2020
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PDF
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Lecture 15 slides: Gaussian elimination and the LU factorization
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October 9, 2020
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PDF
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Marked slides from class
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October 12, 2020
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PDF
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Lecture 16 slides: LU and pivoting
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October 9, 2020
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PDF
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Marked slides from class
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October 14, 2020
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PDF
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Lecture 17 slides: Cholesky decompositions
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October 9, 2020
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PDF
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Marked slides from class
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October 16, 2020
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PDF
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Lecture 18 slides: Power iteration
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October 18, 2020
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PDF
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Marked slides from class
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October 21, 2020
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PDF
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Lecture 19 slides: Rayleigh iteration
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October 18, 2020
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PDF
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Marked slides from class
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October 23, 2020
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PDF
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Lecture 20 slides: The QR algorithm
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October 22, 2020
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PDF
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Marked slides from class
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October 26, 2020
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PDF
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Lecture 21 slides: The QR algorithm with shifts
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October 23, 2020
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PDF
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Marked slides from class
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November 1, 2020
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PDF
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Lecture 22 slides: Iterative methods for linear equations
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November 1, 2020
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PDF
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Lecture 23 slides: Iterative methods for nonlinear equations
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November 2, 2020
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PDF
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Lecture 24 slides: Fourier Approximation
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November 9, 2020
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PDF
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Marked slides from class
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November 11, 2020
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PDF
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Lecture 25 slides: Polynomial Approximation, I
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November 10, 2020
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PDF
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Marked slides from class
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November 13, 2020
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PDF
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Lecture 26 slides: Polynomial Approximation, II
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November 10, 2020
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PDF
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Marked slides from class
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November 16, 2020
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PDF
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Lecture 27 slides: Integration/differentiation with polynomial approximations
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November 15, 2020
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PDF
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Marked slides from class
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November 21, 2020
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PDF
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Lecture 28 slides: Rational approximation
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November 18, 2020
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PDF
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Marked slides from class
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November 25, 2020
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PDF
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