M441/M442: Assessment Report
M 441-Numerical Linear Algebra and Optimization
Assessment Coordinator: Tianyu Zhang
This report summarizes an assessment of M441 with regard to the Applied Mathematics Option. The learning outcome and rubric are listed below.
Outcome 1
Use rigorous mathematical reasoning or computations to establish fundamental applied mathematics concepts.
Evaluation
There were 17 students in the fall 2015 M441 section 1 class that finished and received
a letter grade. Out of
these 9 students were Applied Math or Mathematics majors. Forthe assessment two problems
of the final exam were used. More specifically, problem 1 was designed to test the
comprehensive understanding of some fundamental concepts in numerical linear algebra
such as vector and matrix norm, orthogonal projection, condition number and inverse
matrix. Problem 7 was designed to test the computational skills by calculating the
LU factorization of a matrix with partial pivoting.
Results
The overall outcome of the assessment was positive. In the future, more emphasis should be place on rigorous mathematical reasoning and establishing fundamental applied mathematics concepts.
| Assessed | Exceptional | Acceptable | Marginal | Unacceptable |
|---|---|---|---|---|
| Computational skills | 6 | 1 | 1 | 1 |
| Mathematical reasoning | 1 | 4 | 3 | 1 |
| Overall | 4 | 3 | 1 | 1 |
M 442- Numerical Solution and Differential Equations
Assessment Coordinator: Tianyu Zhang
This report summarizes an assessment of M441 with regard to the Applied Mathematics Option. The learning outcome and rubric are listed below.
Outcome 4
Demonstrate a working knowledge of the technological tools needed to solve problems from applied mathematics.
Evaluation
Therewere 18 studentsin the spring 2016 M442 class that finished and received a letter grade. Out of these 14 students were Applied Math or Mathematics majors. For the assessment two problems of the final exam were used. More specifically, problem 1 was designed to test the understanding of some fundamental concepts in numerical solution to differential equations such as convergence, consistency, stability, stiff problems and linear multistep methods. Problem 2 was designed to test the computational skills by calculating the general and particular solutions of a linear difference equation.
Results
The overall outcome of the assessment was positive. In the future, more emphasis should be placed on rigorous mathematical reasoning and establishing fundamental applied mathematics concepts.
| Assessed | Exceptional | Acceptable | Marginal | Unacceptable |
|---|---|---|---|---|
| Computational skills | 9 | 4 | 1 | 0 |
| Mathematical reasoning | 4 | 7 | 1 | 2 |
| Overall | 5 | 6 | 2 | 1 |
Program Learning Outcomes
| LO# | Students should demonstrate the ability to: |
|---|---|
| 1. | Use rigorous mathematical reasoning or computations to establish fundamental applied mathematics concepts. |
| 2. | Set up mathematical models and critically interpret their results |
| 3. | Select and implement an appropriate mathematical technique needed to analyze and validate a mathematical model. |
| 4. | Demonstrate a working knowledge of the technological tools needed to solve problems from applied mathematics. |
Curriculum Map and Assessment Schedule
| Course | LO 1 | LO 2 | LO 3 | LO 4 | Assessment Schedule |
|---|---|---|---|---|---|
| M386 | X | X | Odd spring semesters | ||
| M430 | X | Odd spring semesters | |||
| M441 | X | X | Odd fall semesters | ||
| M442 | X | Even spring semesters | |||
| M450 | X | X | Every 4th fall begins F13 | ||
| M451 | X | X | Every 4th fall begins F14 | ||
| M454 | X | Every 4th fall begins F14 | |||
| M455 | X | Every 4th spring begins S15 |
Rubric
| LO | Unacceptable | Marginal | Acceptable | Excellent |
|---|---|---|---|---|
| 1 |
The work is not correct |
The work is not correct and complete because one or two significant ideas are missing, but the terms are properly defined and the work shows a type of organization that might well work if the right ideas were inserted in the proper places. Also, the work is "marginal" if most of the work is leading toward a correct argument, but a false statement is inserted. |
The work is almost correct with relevant concepts used and ideas that could work, but not well‐ organized, for example, with some steps out of order, or with something relatively minor incomplete. |
The work is fully correct and complete, with the relevant concepts properly employed and ideas that work, and the steps well‐organized into a proper sequence |
| 2 | If the work is not correct and complete because either there are fundamental gaps in understanding of the underlying scientific principles or in the understanding of the appropriate technique and its implementation. |
The work is not correct and complete because one or two significant ideas are missing, but the majority of the ingredients are present. |
The work is almost correct with relevant scientific concepts and mathematical techniques that could work, but not well‐organized, with a minor omission, misunderstanding, or inadequate choice of mathematical technique. |
The work is fully correct and complete, with the complete understanding of the scientific principles of the modeled problem and with employment of the appropriate mathematical techniques. |
| 3 | The work is not correct and complete because either there are fundamental gaps in understanding of the underlying mathematical assumptions or in the understanding of the appropriate technique and its implementation. |
The work is not correct and complete because one or two significant components of the analysis or of the implementation are missing, but the majority of the ingredients are present. |
The work is almost correct with relevant assumptions addressed and the correct algorithm chosen with an implementation that could work, but is implemented with a minor misunderstanding of a technique or a minor error in other elements of the computations. |
The work is fully correct and complete, with a full under- standing of the under- lying mathematical assumptions that deem a particular mathematical technique applicable to a given model and with an appropriate knowledge of the main principles and techniques related to the implementation of a particular form of analysis, mathematical or numerical. |
| 4 | If less than half of the criteria are completed. |
If at least half of the criteria are completed. |
If three of the above are adequately addressed. |
If all four criteria are adequately addressed |
Threshold
At least half of the majors in each of the courses are assessed as "excellent" or "acceptable" for all the learning outcomes.