University of Minnesota
CSci 5302 - Analysis of Numerical Algorithms
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CSci 5302 -- Spring 2020 -- Course Syllabus

Analysis of Numerical Algorithms

Preliminary: Subject to changes and corrections

Class Hours
Lecture: Monday Wednesday 4:00-5:15pm in Keller 3-115

Textbook
Scientific Computing: An Introductory Survey; by Michael T. Heath (2nd edition) McGraw Hill, 2002

Instructor: Prof. Daniel Boley,
Office: Keller bldg, room 6-209 (Office may move during semester)
Phone: 612-625-3887
Office Hours: TBA (or after class)
To avoid my e-mail spam filter, please include the string "5302" in the subject line.

TA: Zhimeng Yin
Office: Keller bldg, room 2-209 (during office hour -- office may move during semester)
Phone: 612-626-7512 (during office hour)
Office Hours: TTh 4-5pm
Email: yinxx283 at umn....

Assignment Plan (not in order)

  • Several classroom exercises and/or pop quizzes: up to 10% of final grade.
  • 3 midterms: 45% of final grade.
  • 4-6 assignments: 45% of final grade.
  If the number of exams and/or assignments changes, the relative weights will be adjusted.

General Information
This course introduces the basic numerical techniques to solve mathematical problems on a digital computer. Algorithms for several common problems encountered in mathematics, science and engineering are introduced. The pitfalls and errors that can arise when solving mathematical problems with methods taking finite time and in finite precision arithmetic are discussed, and measures to predict when such pitfalls are encountered will be introduced.

TOPICS

  • Scientific Computing - Goals and Fundamentals (Chap 1)
  • Linear Equations (a review - Chap 2, secs 1-4)
  • Nonlinear Equations (Chap 5)
  • Polynomial Interpolation, Splines (Chap 7)
  • Linear Least Squares (Chap 3)
  • Optimization Problems (Chap 6)
  • Numerical Integration and Quadrature (Chap 8, secs 1-6)
  • Ordinary Differential Equations: Initial Value Probs. (Chap 9)
... time and interest permitting ....
  • Fast Fourier Transform (Chap 12)
  • Boundary Val. Probs. for Ord. Diff. Equs (Chap 10)
  • Matrix eigenvalues and singular values (Chap 4, secs 1, 2, 3, 5)
  • Random Number Generation (Chap 13)

Computer Platform

Students will be expected to implement several of the algorithms on a digital computer in MATLAB. In the cases where another equivalent interactive programming environment is allowed, you will be responsible for implementing the equivalent features and may find only limited help from the instructional staff. Students should be familiar with basic programming techniques, as well as being able use the help system in MATLAB. Students should also be acquainted with the basic concepts of the more elementary mathematical and numerical methods (e.g. solving simple linear equations, root-finding, computing averages, using derivatives to find the minimum of a scalar function, etc.) though some of this will be reviewed during the course.

Ethics

All items handed in to be graded must represent the individual effort of whoever's name(s) appears on the item. At a minimum, violators of this policy may fail the course and/or may have their names recorded at appropriate University or Departmental offices. Mutual discussion of each individual's results in the homeworks is encouraged, as long as the results themselves represent individual efforts. If you use or submit any material or software you obtained from the WWW or any other source outside of class, you must cite it. In some assignments, you may be restricted on what software you can use.

Assignments and Grading

Some assignments may be assigned to be done by pairs of students; such items should be handed in as a single item listing the names of all participants. To pass the course, you will have to achieve a passing grade on the exams alone, and do satisfactorily on the homeworks. Any questions about the grading of any item must be asked within a week of when items are first handed back to students. After one week has passed, the scores become final.

Electronic Submission

Unless otherwise stated, homeworks must be submitted electronically through canvas. We are not responsible if we cannot read your handwriting, or if electronic scans of written material are unreadable. Even if late, all submissions should be submitted as a single unit directly to canvas (no parts submitted separately at a later time).

Electronic homework submissions should consist of at most 2 files: a zip file containing all computer code (if any), and a separate PDF file containing everything else, including the answers. If there is not computer code, then just submit the single PDF file containing all your written answers. Do not use 'rar', 'tar', '7zip' or any other archiver. We are not responsible if we have any problems reading it.

Late Homework Submissions

Homeworks will be accepted until answers have been posted and up to two working days after the due date (whichever occurs first) with a deduction of 5% of the total grade per day or fraction. Answers could be posted any time after the due date/time without advance notice.

Classroom Exercises

Classroom exercises are given during class on an irregular basis. These are informal exercises to review and use some methods just discussed in lecture. Students will be encouraged and expected to discuss the methods among themselves during the exercise (unlike during formal exams). Classroom exercises handed in at the end of class will receive full credit, as long as they show any attempt to answer the questions. Classroom exercises submitted outside of class will be accepted only up to the following morning. Exercises handed in outside of class by the following morning receive only half credit (full credit for UNITE students). The exercise questions are posted online right after class, so even if you miss class you may hand in an exercise answer sheet electronically. UNITE students should scan and submit their classroom exercises (by e-mail to boley@umn.edu) the same day, or by the following morning. Be sure to include the string "5302" in the subject line of the message. You can miss up to one classroom exercise during the semester with no penalty. These deadlines may be extended for excused unanticipated absences on a case-by-case basis.

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