University at Buffalo · Department of Mathematics
MTH 537: Numerical Analysis I
Fall 2026 · Course Syllabus
Course Information
- Instructor
- Sergey A. Dyachenko
- sergeydy@buffalo.edu
- Class meetings
- Monday, Wednesday, and Friday, 11:00–11:50 a.m.
- Classroom
- Math 205
- Office hours
- Wednesday, 3:00–4:00 p.m., and by appointment
- Office
- Math 312
- Course materials
- Homework assignments and tentative weekly schedule
Course Description
Numerical analysis studies the mathematical foundations of algorithms for solving problems on a computer. This course introduces floating-point arithmetic, approximation, convergence, conditioning, stability, and computational cost. Students will analyze numerical algorithms, implement selected methods, and assess their performance through computational experiments. Applications will include problems arising in mathematics, science, and engineering.
Previous programming experience is not required. A brief introduction to MATLAB or GNU Octave will be provided.
Recommended Textbook
Timothy Sauer, Numerical Analysis, 2nd ed., Pearson. The textbook is recommended but not required. Additional course materials will be provided.
Tentative Course Topics
- Floating-point arithmetic; errors, conditioning, and stability.
- Nonlinear equations and root-finding methods.
- Direct methods for linear systems.
- Least-squares problems and QR factorization.
- Eigenvalue problems.
- Polynomial interpolation, Chebyshev nodes, and splines.
- Numerical differentiation and integration.
- Numerical methods for ordinary differential equations.
- Introduction to finite-difference methods.
The sequence and extent of topics are tentative and may be adjusted as the course progresses.
Grading
| Component | Weight |
|---|---|
| Homework | 20% |
| Midterm examination | 40% |
| Cumulative final examination | 40% |
Written solutions must be legible and include supporting reasoning. Answers without adequate supporting work may receive no credit. Missing assignments and examinations receive a score of zero unless an exception is approved.
Examinations
Midterm examination: Date to be announced.
Final examination: Wednesday, December 9, 2026, 11:45 a.m.–2:45 p.m., Math 205.
The final examination is cumulative and also serves as the Numerical Analysis qualifying examination for eligible graduate students. Satisfaction of the qualifying-examination requirement is determined separately under the policies of the graduate program.
Homework and Academic Integrity
Homework assignments and due dates will be posted on the course schedule. One lowest homework score will be dropped. Assignments are due on the announced due date; late homework will not be accepted unless an exception is approved in advance.
Students may discuss homework problems with one another, but each student must independently prepare and understand all submitted solutions. Solutions copied from another person or another source will not receive credit. Computational assignments should include the relevant code, numerical results, figures, and an explanation of the results.
Guidelines for the Use of Artificial Intelligence
AI tools may be used to clarify course material, explore examples, and assist with programming. However, students must develop their own solutions to assigned problems and must be able to explain all submitted reasoning and code. AI may not be used to generate mathematical solutions that are submitted as the student's own work.
Make-up Examinations
A make-up examination will be considered only for a documented university-approved absence, illness, family emergency, or comparable circumstance. Notify the instructor in advance whenever possible.