Mathematics 451
Applications and Modeling
(3 credit hours)

This page : [ Prerequisites | TextCatalog Description | Goal | Syllabus | Grading | Models ]
Related pages: [ Grading Rubric | Project Schedule | Project Order | Previous Projects | Abstract | Examples ]

This course will give you a chance to put your mathematical knowledge to work!  You will also be asked to practice presenting mathematical results in both written and verbal forms; to interact with others in cooperative learning activities (in and out of the classroom); and to be involved in the learning process.  You are expected to actively participate in all class meetings.

Dr. Caldwell, office 429 Holt Humanities, phone 7336. Department office 7360. Email:
Linear Algebra (310) and Multivariate Calculus (320).  (For example, we will use linear algebra to solve systems of equations and determine the ranks of matrices.  We will use multivariate calculus to both integrate and minimize functions of several variables.)
A First Course in Mathematical Modeling (4th Edition), Frank R. Giordano, William P. Fox, Steven B. Horton, Maurice D. Weir and , Brooks/Cole, 2009. 
Catalog Description:
(451, 651) Practical applications of mathematics including optimization, interpolation and best fit, simulation and dimensional analysis.  Mathematical model building including problem identification, model construction or selection, fine-tuning and validation.
To give students practice in actively applying mathematics, especially to realistic situations, and to develop their ability to present their results effectively
A copy of the department course syllabus (with course outline and objectives) can be viewed on the web at
  The grade will be a subjective mix of the following.
20 %
25 %
Large Model
30 %
Small Models
10 %
15 %
Homework (see also: extra credit)
Small Models:
Small modeling projects will be assigned and collected regularly.  These projects will roughly parallel our class work and will teach the skills necessary for the large model.  Students will often collect the data as a group, but submit work individually.
Large Models:
Part of the last part of the term will be used as a modeling practicum.  Students will work in (possibly prearranged) teams on projects of their choice (after approval by the teacher).  Each team will submit a typed proposal, abstract, draft (possibly handwritten) and a final report.  Each team will also give preliminary and final oral presentations.  The final oral and written reports will be open to the public.  Students will be involved in grading their teammates and the grade will be assigned using the grading rubric.  For an outline of the work involved, see the project schedule.
Attendance is mandatory and is enforced via the participation grade.
Homework will be assigned daily.  The homework will be collected  at the beginning of the following class period.  No late homework will be accepted.
The final will cover the large models presented by the students as well as other (possibly new) models.  It is possible that students seriously attempting both halves of the Putnam exam (first Saturday in December) will be exempted from taking the final--they will receive grade they had before the final.
Extra credit:
In support of the course goal to give students practice in actively applying mathematics, there may be bonuses offered for activities outside of the classroom such as: 
  • 2%    for each correct solution submitted to a problem in a current MAA publication.
  • 5%    for a related mathematical presentation at an approved regional or national meeting.
  • 1%    for each correct solution on the Virginia Tech. Competition (October 30th; 9 am to 11:30 am)
  • 1%    for significant progress toard a correct solution on the Putnam (always first Saturday in December, usually 9am to 3pm)
  • 8%    for each apparently correct solution on the Putnam