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Peter J. Olver School of Mathematics University of Minnesota Minneapolis, MN 55455 |
Vincent Hall 302 Phone: 626-1623 e-mail: olver@umn.edu http://www.math.umn.edu/~olver |
| Office Hours: Wednesday 10:30 am–12:00 pm, Friday 11:30 am–1:00 pm, or by appointment | |
| TA: Judy Chiang |
Vincent Hall 555 e-mail: hchiang@umn.edu https://sites.google.com/view/judy-chiang/home |
| Office Hours: Tuesday 10:00 am–12:00 pm in Vincent Hall 203B | |
| Lectures: 040: M, W, F 1:25–2:15 pm Burton Hall 120 050: M, W, F 2:30–3:20 pm Burton Hall 120 |
Recitations: 040: Tuesday 1:25–2:15 pm Burton Hall 120 050: Tuesday 2:30–3:20 pm Burton Hall 120 |
Course Description: Math 4242 is a one semester course that covers the fundamentals of linear algebra and its applications. The material in this course is essential preparation for many advanced (5xxx and higher) Math and other STEM classes. Indeed, linear algebra and calculus are the two pillars supporting the entire edifice of modern mathematics. For example, a very large fraction of modern machine learning and artificial intelligence is based on the linear algebra covered in this course.
Goals and Objectives: The student will develop fluency in the methods of linear algebra, both theory and computations, geared towards its later use in advanced mathematics and applications. In addition, some familiarity with mathematical abstraction will be acquired. Key topics include vectors, matrices, solution of linear systems by Gaussian Elimination, vector spaces and subspaces, linear independence and bases, inner products and norms, orthogonality and orthonormal bases, the Gram-Schmidt process and QR factorization, eigenvalues and eigenvectors, and singular values and the singular value decomposition.
Prerequisites: Math 2243 or 2373 or 2573 or the equivalent. Familiarity with vectors, matrices, and basic linear algebra is helpful but not assumed, and single-variable calculus is the only formal prerequisite. On the other hand, the student will need to draw upon some mathematical maturity to engage with the abstraction inherent to the subject.
Text: Applied Linear Algebra, by Peter J. Olver and Chehrzad Shakiban,
Second Edition, Springer, New York, 2018, available online through the University of Minnesota Library.
• I intend to cover most of chapters 1 – 5 and 8 during the semester. Time permitting, selected topics from chapters 6, 7, and 9 may be covered. We will cover approximately one chapter every 2 weeks.
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See the text web site for corrections, a link to the students' solutions manual, and useful information.
Homework: Homework will be assigned periodically throughout the semester on the course Canvas site, where it is collected for grading. No late homework will be accepted, but the lowest score will be dropped when figuring the final grade. The assigned problems should be regarded as the minimum required for mastery of the material. Working through the homework exercises yourself, and not relying on online help and/or others is essential for success on the exams and hence the final course grade.
Python: The recitations will also include worksheets written in the Python computer programming language, designed to illustrate and reinforce the computational aspects of the subject. The Python worksheets will be run using Jupyter; students should install the Jupyter Notebook interface on their computer before the first class. See this video for an illustration.
Hour Exams: There will be two midterm exams. Students are allowed to bring one page of handwritten notes to the midterms. No calculators, phones, computers, or other electronic devices are allowed during the exams.
First Midterm:
Monday, October 20: Chapters 1 – 3.
Second Midterm:
Monday, November 17: Chapters 4 – 5.
Final Exam: Will include material from the entire semester. Students are allowed to bring three pages of handwritten notes to the final. No calculators, phones, computers, or other electronic devices are allowed during the final.
Section 040: Monday, December 15, 1:30pm – 3:30pm, location TBA.
Section 050: Saturday, December 13, 8:00am – 10:00am, location TBA.
Grading:
• Homework 15%
• Python 15%
• Hour Exams 17.5% each
• Final Exam 35%
Absence from exams: Missing an exam is permitted only for the most compelling reasons, which must be documented, and you must obtain the professor's permission in advance; otherwise you will be given a 0. If you are excused from taking an exam, you will be allowed to take a makeup exam, or, depending on the circumstances, your other exam scores will be prorated.
Incompletes: Only given in extreme circumstances, and only when the student has satisfactorily completed all but a small portion of the work in the course. Students must make prior arrangements with the professor well before the end of the semester. Incompletes will not be given solely because the student has stopped attending class or missed an exam or the final.
Student Conduct: Students are expected to be familiar with University of Minnesota Student Conduct Code, including the consequences for violatation of standards of academic honesty. Students should also read their college bulletin for the definitions and possible penalties for cheating. During the exams you must do your own work. Students suspected of cheating will be reported to the Scholastic Conduct Committee for appropriate action. According to official University of Minnesota policy, academic dishonesty in any portion of the academic work for a course shall be grounds for awarding grade of F or N for the entire course.
University of Minnesota Policies: Students are also expected to be familiar with University of Minnesota Policies as listed in the preceding link.