MATH 307 Applied Linear Algebra
MATH 307 Applied Linear Algebra
Course Outline 2021S1
Linear systems of equations, orthogonality, least squares approximation, eigenvalue problems, ma-trix decompositions LU, QR and SVD, discrete Fourier transform. Applications: interpolation, finite difference method, data fitting, principal component analysis, Markov chains, PageRank, image deblurring, computed tomography, digital signal processing. Matrix computations with mathematical software Python, SciPy and Jupyter.
Learning Goals
• Summarize properties and constructions of matrix decompositions LU, QR and SVD
• Perform matrix computations using mathematical software Python, SciPy and Jupyter
• Compute solutions of large systems of linear equations using matrix decompositions
• Compute least squares approximations of large linear systems using matrix decompositions
• Compute eigenvalues of large matrices using iterative methods
• Analyze digital signals using the discrete Fourier transform
• Create and analyze mathematical models of real-world phenomenon
Instructor Information
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Patrick Walls
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Instructor
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–
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Teaching Assistant
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–
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Online Learning
All communications, course materials, lectures and assessments are deployed via canvas.ubc.ca. Please visit keeplearning.ubc.ca for resources to help you set up, learn effectively online, understand the technologies used at UBC and get support.
Online Lectures
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Tuesday
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Wednesday
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Thursday
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2–4pm
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2–4pm
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2–4pm
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• First lecture is Monday May 10 2-3pm
• All lectures delivered on Canvas via Zoom
• All lectures to be recorded and posted on Canvas
Schedule
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Lectures
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Topics
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9
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Linear systems of equations. Gaussian elimination, elementary matrices, LU
and Cholesky decompositions, vector and matrix norms, condition number. Appli-
cations: interpolation, finite difference method.
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9
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Subspaces, orthogonality and least squares approximation. Orthogonal sub-
spaces, fundamental subspaces of a matrix, orthogonal projection, Gram-Schmidt
orthogonalization, QR decomposition. Applications: fitting models to data.
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10
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Eigenvalue problems. Spectral theorem, power method, singular value decom-
position, pseudoinverse, SVD expansion. Applications: Markov chains, PageRank,
principal component analysis, image deblurring, computed tomography.
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8
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Discrete Fourier transform. Complex vector spaces, discrete Fourier transform,
amplitude and phase, fast Fourier transform, convolution theorem. Applications:
digital signal processing
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36
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Assessments
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Quizzes
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5 × 10% each = 50% |
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Python Assignments
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4 × 5% each = 20%
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Final Exam
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30%
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• Weekly quizzes scheduled Monday 2-3pm (except Quiz 2 Tuesday May 25 2-3pm)
• Alternate quiz time to be announced (for students in different time zones)
• Python assignments do not require prior programming experience
• Final Exam delivered on Canvas during the exam period June 21–25
Textbooks and Resources
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MATH 307 Course Notes
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Mathematical Python
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Linear Algebra with Applications
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Syzygy
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Scientific Computing
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Prerequisites
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Linear Algebra
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One of MATH 152, MATH 221, MATH 223
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Multivariable Calculus
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One of MATH 200, MATH 217, MATH 226, MATH 253, MATH 254
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• See the UBC Course Schedule
Important Dates
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Monday May 10
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First day of class
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Monday May 24
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Victoria Day (no lecture or quiz)
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Thursday June 17
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Last day of class
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June 21–25
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Final exam period
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• See the UBC Academic Calendar 2020/2021
Student Resources
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Science Advising
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Health and Wellbeing
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Centre for Accessibility
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Academic Concession
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Academic Integrity
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Counselling Services
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University Policies
UBC provides resources to support student learning and to maintain healthy lifestyles but recog-nizes that sometimes crises arise and so there are additional resources to access including those for survivors of sexual violence. UBC values respect for the person and ideas of all members of the academic community. Harassment and discrimination are not tolerated nor is suppression of academic freedom. UBC provides appropriate accommodation for students with disabilities and for religious observances. UBC values academic honesty and students are expected to acknowledge the ideas generated by others and to uphold the highest academic standards in all of their actions. Details of the policies and how to access support are available on the UBC Senate website.
2021-05-13