! ROCHESTER INSTITUTE OF TECHNOLOGY COURSE OUTLINE FORM COLLEGE OF SCIENCE School of Mathematical Sciences New Revised COURSE: COS-MATH-421 Mathematical Modeling 1.0 Course designations and approvals: Required Course Approvals: Approval Approval Request Date Grant Date Academic Unit Curriculum Committee 4-08-10 4-15-10 College Curriculum Committee 11-01-10 12-17-10 Optional Course Designations: Yes No General Education Writing Intensive Honors Approval Request Date Approval Grant Date 2.0 Course information: Course Title: Mathematical Modeling Credit Hours: 3 Prerequisite(s): COS-MATH-221, -231, -241, and -251 Co-requisite(s): None Course proposed by: School of Mathematical Sciences Effective date: Fall 2013 Contact Hours Maximum Students/section Classroom 3 20 Lab Workshop Other (specify) 2.1 Course conversion designation: (Please check which applies to this course) Semester Equivalent (SE) to: 1016-461 Semester Replacement (SR) to: New 2.2 Semester(s) offered: Fall Spring Summer Offered every other year only Other Page 1 of 5
2.3 Student requirements: Students required to take this course: (by program and year, as appropriate) Fourth-year Applied Mathematics and Computational Mathematics majors Students who might elect to take the course: Applied Statistics majors and Mathematics minors 3.0 Goals of the course: (including rationale for the course, when appropriate) 3.1 To survey the types of mathematical models one frequently encounters such as deterministic models, stochastic models, axiomatic models, and simulation models. 3.2 To describe the generic modeling process including a discussion of modeling assumptions, reliability of data, testing of a model against data, and the necessity of criticizing the model. 3.3 To apply the modeling process to three or four substantial examples drawn from among the physical sciences, engineering, and the social sciences. 3.4 To provide an opportunity to produce a substantial modeling project. 4.0 Course description: (as it will appear in the RIT Catalog, including pre- and co-requisites, semesters offered) COS-MATH-421 Mathematical Modeling This course explores problem solving, formulation of the mathematical model from physical considerations, solution of the mathematical problem, testing the model, and interpretation of results. Problems are selected from the physical sciences, engineering, and economics. (COS-MATH-221, -231, -241, and -251) Class 3, Credit 3 (F) 5.0 Possible resources: (texts, references, computer packages, etc.) 5.1 Richard Haberman, Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow, Prentice Hall, Upper Saddle River, NJ. 5.2 Walter J. Meyer, Concepts of Mathematical Modeling, McGraw-Hill, Columbus, OH. 5.3 TEAM Learning Modules, Mathematical Association of America, Washington, DC. 6.0 Topics: (outline) Topics with an asterisk(*) are at the instructor s discretion, as time permits 6.1 Description of the Generic Modeling Process 6.1.1 The necessity of simplifying assumptions 6.1.2 Modeling as problem solving 6.1.3 Types of data 6.1.4 Continuous versus stochastic models 6.1.5 Testing and criticism of a model 6.2 Review of Model Types with Brief Examples 6.2.1 Deterministic models 6.2.2 Stochastic models Page 2 of 5
6.2.3 Axiomatic models 6.2.4 Simulation models 6.3 Three or four example models such as 6.3.1 Differential equations and phase plane analysis for the damped and undamped pendulum 6.3.2 Richardson s model for an arms race 6.3.3 Regular and absorbing Markov chains such as gambler s ruin 6.3.4 Leontief model for an open economy 6.4 6.4.1 Discussion of stylistic elements in a technical report 6.4.2 Selection of topic in consultation with the instructor 6.4.3 Proposal approved by instructor 6.4.4 Draft of written report 6.4.5 Final written report 7.0 Intended learning outcomes and associated assessment methods of those outcomes: Assessment Methods Learning Outcomes 7.1 Students will recognize the various types of mathematical models such as deterministic models, stochastic models, axiomatic models, and simulation models 7.2 Students will describe the generic modeling process including validation of modeling assumptions, determining the reliability of data, testing of a model against data, and the necessity of criticizing the model 7.3 Students will apply the modeling process to several examples drawn from among the physical sciences, engineering, and the social sciences, and produce a brief written analysis of the models 7.4 Students will produce a substantial mathematical model, and write a high-quality, thorough report detailing the model s scope, and analyzing the conclusions that can be drawn from it 8.0 Program goals supported by this course: 8.1 To develop an understanding of the mathematical framework that supports engineering, science, and mathematics. 8.2 To develop critical and analytical thinking. Page 3 of 5
8.3 To develop an appropriate level of mathematical literacy and competency. 8.4 To provide an acquaintance with mathematical notation used to express physical and natural laws. 8.5 To produce graduates who can effectively use mathematics and/or statistics to model, analyze, and solve problems arising in science, engineering, business, and other disciplines. 9.0 General education learning outcomes and/or goals supported by this course: Assessment Methods General Education Learning Outcomes 9.1 Communication Express themselves effectively in common college-level written forms using standard American English Revise and improve written and visual content Express themselves effectively in presentations, either in spoken standard American English or sign language (American Sign Language or English-based Signing) Comprehend information accessed through reading and discussion 9.2 Intellectual Inquiry Review, assess, and draw conclusions about hypotheses and theories Analyze arguments, in relation to their premises, assumptions, contexts, and conclusions Construct logical and reasonable arguments that include anticipation of counterarguments Use relevant evidence gathered through accepted scholarly methods and properly acknowledge sources of information 9.3 Ethical, Social and Global Awareness Analyze similarities and differences in human experiences and consequent perspectives Examine connections among the world s populations Identify contemporary ethical questions and relevant stakeholder positions 9.4 Scientific, Mathematical and Technological Literacy Explain basic principles and concepts of one of the natural sciences Page 4 of 5
Assessment Methods General Education Learning Outcomes Apply methods of scientific inquiry and problem solving to contemporary issues Comprehend and evaluate mathematical and statistical information Perform college-level mathematical operations on quantitative data Describe the potential and the limitations of technology Use appropriate technology to achieve desired outcomes 9.5 Creativity, Innovation and Artistic Literacy Demonstrate creative/innovative approaches to coursebased assignments or projects Interpret and evaluate artistic expression considering the cultural context in which it was created 10.0 Other relevant information: (such as special classroom, studio, or lab needs, special scheduling, media requirements, etc.) The in this class (see Topic 6.4) will constitute at least 20% of the overall grade (the portion of the overall grade determined by the project has varied from 30 50% in previous terms) Students will receive written feedback from the instructor regarding the rough draft of their final report (see Topic 6.4), and are expected to implement revisions accordingly. Page 5 of 5