Modern Applied Mathematics I
Math 413-001 (Fall 2025)
This web page will be updated regularly and always contain the latest information on the course. It is only for general policies concerning the course, as well as for continuously updated syllabus information. For all other information on the course, including scanned lecture notes, graded homework assignments, etc. please go to Canvas.
| Instructor: | Thomas Wanner |
| Office: | Exploratory Hall 4404 |
| E-mail: | twanner@gmu.edu |
| Web Page: | https://math.cos.gmu.edu/~wanner |
| Office Hours: | MW 2-3pm, and by appointment |
| Lectures: | MW 4:30-5:45pm, Nguyen Engineering Building 1108 |
| Prerequisites: | Grade of C or better in Math 203 and 216 (or 214) |
| Textbook: | There is no required textbook for the course, I will post handwritten lecture notes on Canvas after every class. |
| While I will draw the material from a variety of sources, the following two texts can be used for supplementary reading: | |
| 📕 Mark H. Holmes: Introduction to the Foundations of Applied Mathematics, Springer, 2019. | |
| 📘 J. David Logan: Applied Mathematics, Wiley, 2013. |
Important Links
- Detailed syllabus
- Relevant official GMU policies, and required university-wide policies (or as pdf file)
- Homework assignments will be posted on Gradescope, which can be accessed via Canvas.
Syllabus
This course provides a basic introduction into important techniques of modern applied mathematics. We will discuss the interplay between discrete and continuous mathematics, as well as the role of computational mathematics. Particular focus will be put on revealing mathematical structure from equilibrium models in discrete and continuous systems. We will cover dimensional analysis, perturbation methods, stability and bifurcations, kinetics, and diffusion. A more detailed syllabus can be found here. It will be updated weekly.
Homework Assignments
Homework problems will be assigned once a week and posted on Gradescope. These assignments will be graded and count towards your homework score. The assignments have listed due dates on Gradescope, as well as late due dates. If for some reason (connectivity issues, computer issues, etc.) you cannot turn an assignment in by the due date, it is enough to turn it in before the late due date. No points will be taken off in that case. However, there will be no assignment extensions beyond the late due date. At the end of the semester, I will drop some of the lowest homework scores. More details will be announced later in the semester.
Exams
The midterm exam is Wednesday, October 8, 4:30pm-5:45pm, the final exam is Wednesday, December 10, 4:30pm-7:15pm.
Grading Policy
Your final grade in the course will be determined from your performance in the homework assignments, a midterm exam, the final exam, and your attendance and class participation. Weights for these items will be distributed approximately according to the following schedule:
| Homework | Midterm Exam | Final Exam | Participation |
|---|---|---|---|
| 50% | 20% | 20% | 10% |
The assignment of your course grade is based on the total course score. The following grading scale may serve as a guideline, although changes are possible:
| Letter Grade | A-, A, or A+ | B-, B, or B+ | C or C+ | D | F |
|---|---|---|---|---|---|
| Score above | 90% | 80% | 70% | 60% | otherwise |
Within each bracket, the top 2% give the X+ grade, and the bottom 2% give the X- grade. Also note that I do not round up the final percentage. In other words, if you receive 89.9%, you will receive a B+ in the class. Both the weight distribution and the grading scale are subject to change by announcement in class.
Important Notice
This course will be hosted on Canvas. Please ensure you are familiar with accessing and navigating this platform. Resources and support are available at https://lms.gmu.edu/getting-started-students/ to help you get started. If you have any questions, do not hesitate to reach out to me or contact the ITS Support Center for assistance.