University of Minnesota
CSci 5302 - Analysis of Numerical Algorithms

CSci 5302 -- Spring 2024 -- Provisional Course Syllabus

Analysis of Numerical Algorithms

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



Instructor: Prof. Daniel Boley,
Office: via Zoom (links will be posted on the Canvas page when available.)
Phone: 612-625-3887 (messages only)
Office Hours: Mondays 5:30-6:30pm
Email: boley at umn....
To avoid my e-mail spam filter, please include the string "5302" in the subject line.

Office: Zoom (links will be posted on the Canvas page when available.)
Phone: TBA
Office Hours: TBA
Email: TBA at umn....

Assignment Plan

  • 3 in-class exams: 40% of final grade
  • 4-6 homework assignments : 50% of final grade
  • Several "classroom" exercises and/or pop quizzes (up to once a week): up to 10% of final grade. You will be allowed one free omission. These quizzes will include open discussion of the questions with your neighbors during class. You get full credit for a good-faith effort to answer the questions. If your performance on the quizzes is consistently different from your performance on the homeworks and exams, we may ask for an explanation.
  • Final grade will be based on a weighted average of your scores, assuming you have reached a minimum threshold in each category.
  • Grade cut-offs: 90% for an A or A-, 80% for at least a B-, 70% for at least a C-.

General Information
This course introduces the basic numerical techniques to solve mathematical problems on a digital computer. Algorithms for several common problems encountered in computer science, 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.


  1. Scientific Computing: Goals and Fundamentals (Chap 1)
  2. Scalar non-linear equations: methods (Chap 5, secs 1-2)
    HW1 Due
  3. Linear Equations: Existence, uniqueness, conditioning (Chap 2, secs 1-4)
  4. Systems of Nonlinear Equations: gradients, Jacobians (Chap 5)
    HW2 Due
  5. Systems of Nonlinear Equations: Newton's Method, Broyden's Method (Chap 5)
    Exam I
  6. Curve fitting: Polynomial Interpolation, 1D and 2D (Chap 7)
  7. Curve fitting: Splines (Chap 7)
    HW3 Due
Spring Break
  1. Linear Least Squares: normal equations: orthogonal projections (Chap 3)
  2. Unconstrained Optimization: existence, uniqueness, optimality conditions (Chap 6, secs 1-5)
    HW4 Due
    Exam II
  3. Unconstrained Optimization Methods: Steepest Descent, Newton, BFGS (Chap 6, secs 1-5)
  4. Constrained Optimization Methods: KKT Conditions, penalty/barrier methods (Chap 6)
    HW5 Due
  5. Numerical Integration and Quadrature (Chap 8, secs 1-6)
  6. Ordinary Differential Equations: Initial Value Probs. Accuracy, stability, stiffness. (Chap 9, secs 1-3)
    ODEs (Euler's method, Runge-Kutta, multistep).
  7. Discrete Fourier Transform, FFT Algorithm. review
    Exam III
  8. (finals week) nothing

Computer Platform

Students will be expected to implement several of the algorithms on a digital computer using python with a limited set of packages (e.g., numpy, matplotlib, pdb, plus a few functions listed explicitly from other packages). 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. 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.


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 World Wide Web or any other source outside of class, you must cite it. This includes the use of ChatGPT or any Large Language Model. You may be asked to explain in person any answers you submit. In some assignments, you may be restricted on what software you can use, beyond the restrictions mentioned above.

Assignments and Grading

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. Assignments are to be done individually unless they are explicitly assigned to be done in pairs or small groups; such items should be handed in as a single item listing the names of all participants.

Electronic Submission

Unless otherwise stated, all work 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 no computer code, then just submit the single PDF file containing all your written answers. Do not use 'rar', 'tar', '7zip' or any other archiver. Submit the PDF file as a separate file, not within the ZIP file. We are not responsible if we have any problems reading it.

Late Homework Submissions

Homeworks will be accepted until answers have been posted or discussed in class and up to three working days after the due date (whichever occurs first). For regular homeworks, the late penalty will grow nonlinearly with the delay: 1% if within 12 hours ( only once during the semester), 2% if within 24 hours, 10% up to 2 days, 20% if more. If unable to complete a quiz during class, you should hand in what you can in class, and hand in your more complete answer within 24 hours. Late pop quizzes will receive only half credit. Answers could be posted any time after the due date/time without advance notice.

University Policies

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