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AMATH 352 A: Applied Linear Algebra And Numerical Analysis

Summer Term: 
Full-term
Meeting Time: 
MWF 10:50am - 11:50am
Location: 
EEB 125
SLN: 
10064
Instructor:
Saumya Sinha
Saumya Sinha

Syllabus Description:

Lectures: MWF 10:50-11:50 am, EEB 125

Website: https://canvas.uw.edu/courses/1204820

Instructor: Saumya Sinha (Email: saumya@uw.edu)

Office Hours: Mon 1:30-2:30 pm, LEW 129; Wed 1:30-2:30 pm, LEW 128.

Teaching Assistant: Yu-Chen Cheng (Email: yuchench@uw.edu)

TA Office Hours: Thursday, 3-5pm, LEW 129

Prerequisites: MATH 126 or MATH 136.

Course description: Linear algebra plays a fundamental role in a wide range of applications from physical and social sciences, statistics, engineering, finance, computer graphics, big data and machine learning. This course covers basic concepts of linear algebra, with an emphasis on computational techniques. We will study vectors, vector spaces, linear transformations, solving linear systems, least squares problems, matrix decompositions (e.g. LU, QR, SVD), and eigenvalue problems. The emphasis will be on practical aspects of linear algebra and numerical methods for solving these problems.

Course materials: There is no textbook for this class. Instead, we will follow reference notes written by R. LeVeque and Ulrich Hetmaniuk (available under the 'Files' tab as '352Book.pdf').

The following texts are freely available online and can be used to supplement the course notes.

Additional reference texts are:

  • G. Strang, Introduction to Linear Algebra, Wellesley Cambridge Press, 2009.
  • R.L. Burden and J.D. Faires, Numerical Analysis.

Computing: We will use Matlab for computation, and you must obtain access to Matlab or Octave (a free alternative) for your use.

  • You may obtain a Matlab license through the University for $30 (UW Matlab). Note that these will only be available from July 1st. 
  • You may purchase a student license for Matlab here. (The unbundled version ($50) will be sufficient for this class, but the $100 version has other useful packages.)
  • Matlab is also available at several labs on campus, including the ICL (Communications, B022). Remote access is available through the College of Engineering.
  • You may also download Octave, an open-source Matlab-like program, here. We will, however, not be available to provide support for this.

Grading:

  • Homework: There will be a total of six graded homeworks worth 40% of the course grade. (Homework 0 will not be graded.) I strongly urge you to type up the homework using LATEX or another typesetting software. Typesetting the first homework will be worth 5 bonus points, and typesetting subsequent homeworks will each be worth 2 bonus points. Typed homeworks may be submitted through Canvas, while handwritten ones must not be submitted online.
    Each homework will also consist of a programming portion and you will be asked to submit your Matlab scripts online via Scorelator where they will be graded automatically. Written answers must be submitted for the remaining problems.
    Late policy: Late homework will not be accepted under any circumstances except certified medical reasons.
    You are encouraged to discuss and collaborate with your peers on the homework, but solutions must be written up individually and not shared with others. Questions may be brought to class, office hours and the Canvas discussion board. Please note that homework-related questions will not be answered via email.
  • Exams: The midterm will be in class on Monday, July 16. The final exam will be in class on Friday, August 17.

Your course grade will be a weighted sum of your score in the homeworks, midterm and final, added in the proportions 40%, 30% and 30% respectively. The grade for this class will not be curved.

Date Class Topic
06/18/18 Lecture 1 n-dimensional vectors.
06/20/18 Lecture 2 Norms in R^n.
06/22/18 Lecture 3 Inner products in R^n, linear spaces.
06/25/18 Lecture 4 Subspaces of linear spaces.
06/27/18 Lecture 5 Linear independence and span of vectors, basis of a linear space.
06/29/18 Lecture 6 Basis and dimension of a linear space.
07/02/18 Lecture 7 Linear functions, matrices.
07/04/18 No class. 4th of July holiday.
07/06/18 Lecture 8 Multiplication of matrices, range and rank.
07/09/18 Lecture 9 Matrices - range, null space, rank and nullity.
07/11/18 Lecture 10 Matrices - rank and nullity, determinants. Midterm review.
07/13/18 Lecture 11 Revisiting inverses, eigenvalues and eigenvectors.
07/16/18 Midterm In-class midterm.
07/18/18 Lecture 12 Matrix norms.
07/20/18 Lecture 13 Inner products, solutions of linear systems. Numerical errors.
07/23/18 Lecture 14 Conditioning, computer arithmetic, operations counts and complexity.
07/25/18 Lecture 15 QR factorization, Gram-Schmidt orthogonalization.
07/27/18 Lecture 16 Gram-Schmidt: examples and modifications.
07/30/18 Lecture 17 LU decomposition without pivoting.
08/01/18 Lecture 18 LU decomposition with pivoting.
08/03/18 Lecture 19 LU decomposition with pivoting. Least squares.
08/06/18 Lecture 20 Least squares and function approximation, interpolation. 
08/08/18 Lecture 21 Interpolation and curve fitting, regression.
08/10/18 Lecture 22 Eigenvalue decomposition.
08/13/18 Lecture 23 Singular Value Decomposition, Principal Component Analysis.
08/15/18 Lecture 24 Iterative solvers. Final Review.
08/17/18 Final Exam In-class final.

 

Catalog Description: 
Analysis and application of numerical methods and algorithms to problems in the applied sciences and engineering. Applied linear algebra, including eigenvalue problems. Emphasis on use of conceptual methods in engineering, mathematics, and science. Extensive use of MATLAB package for programming and solution techniques. Prerequisite: MATH 126 or MATH 136. Offered: AWSpS.
GE Requirements: 
Natural World (NW)
Credits: 
3.0
Status: 
Active
Last updated: 
June 14, 2018 - 3:20pm
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