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
and complete because
either concepts are used
improperly or key ideas
are missing or the
organization is unlikely
to work even if a few
more ideas were
inserted.

 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. 

 

PDF of M441 & M442 Assessment Report