Syllabus for Mathematical Modeling & Decision Analysis
This course is an effort to meet students’ need for an applied mathematics course that will prepare them for a successful transition to a four year university program requiring calculus-based quantitative skills (e.g. math, science, engineering, economics, management). In addition to expanding math skills in modeling-related areas, this project-based course will allow students to obtain…
- an integrated understanding of their math skills;
- an understanding of when and how math models will be useful to decision makers;
- practice in articulating (oral and written) a quantitative understanding of real-world problems; and
- enhanced ability to organize analytic work in a team setting.
FAQs for the Prospective Student
Will this course help me get a job?
Being able to report that you took a course in which you did applied mathematics for a “real client” is a great conversation starter for any technical job interview, whether it is permanent employment, summer job, or an internship.
How will this course help me transfer to a competitive 4-year public or private college?
Although IVC’s guaranteed transfer agreements assure many students of the opportunity to obtain a 4-year degree from a few California schools, successfully applying to transfer to a college outside this system means you need something in addition to “good grades.” The Math Modeling & Decision Analysis course offers you that “something extra” – a real-world applied math project, a potential recommendation from a project sponsor or IVC instructor, opportunity to compete in a national math modeling competition, and an opportunity to present your project results at the 2009 National Joint Meeting of the American Mathematical Society and the Mathematical Association of America.
Will this course help me decide on a major for my BS degree?
By exposing yourself to understanding the wide range of practical problems that can be solved with advanced math, you are will gain greater insight into many other educational programs and potential careers.
How is this course going to help me obtain a 4-year degree?
This course will prepare you to excel in a number of different upper-division courses in math engineering, science and economics. The following upper division CS and UC courses are a sample of the many courses for which Math Modeling and Decision Analysis will prepare you:
UC San Diego, Math 111, Mathematical Modeling
UC San Diego, Math 126, Mathematical Control Theory
UC San Diego, Electrical and Computer Engineering 171, Linear Control System Theory
UC San Diego, Applied Math 210, Mathematical Models
UC Los Angeles, Applied Math 142, Mathematical Modeling
UC Los Angeles, Management 140, Elements of Production and Operations Research
UC Los Angeles, Management 212, Decision Analysis
UC Irvine, Math 115, Mathematical Modeling
Cal Poly Pomona, Math 371 Math Modeling Seminar
Cal Poly Pomona, Math 372, Mathematical Community Service Projects
CSU Fullerton, Math 370, Mathematical Model Building
CSU Long Beach, Math 479, Mathematical Modeling
Why doesn’t this course articulate to a specific UC or CS course?
Although many private and public universities offer math modeling and applied projects in upper division and graduate programs, almost no one in California opens these courses exclusively to Freshmen and Sophomores or requires these as prerequisites to enroll in an upper division major. Consequently, taking IVC’s Math Modeling course will not yet substitute for taking a specific math or engineering course at a UC or CS, but IVC is in the process of obtaining approval for the transferability and articulation of this course. Such approval is expected on or before Fall 2008 and when it is received students who have taken the course during its “experimental” phase will become eligible to transfer the units.
How did you select the textbook for this course?
In this class, the textbook, “A Course in Mathematical Modeling” by Doug Mooney, is not an outline of the course, it is an educational reference. We looked for a modeling textbook that was targeted at undergrads with calculus background and there are not many in this category. Mooney was selected because it has the appropriate range of math topics presented at the right level of difficulty, and it is an inexpensive paperback. The principal limitation of the textbook is that most of its modeling examples are taken from environmental science. Consequently, we have assembled a large number of handouts and lecture materials that will illustrate the use of math modeling in many other disciplines.
1) Decision Analysis
a) Decision Criteria and Utility Theory
b) Games as Decision-making Under Uncertainty
c) Extensive and Normal Forms of Description
d) Two-Person Games
i) Zero Sum
ii) Non-Zero Sum
iii) Cooperative Games
e) Equilibrium Outcomes
f) Minimax Theorem
g) Geometrical Interpretations
h) Linear Programming Interpretation of Two-Person Games
i) Differential Equation representation of Symmetric Games
j) Arrow Paradox and Theorem
2) Optimization Models (Template 1)
a) Derivative and Integral Representations
b) Matrix Algebra and Systems of Equations
c) Linear Programming Techniques
d) Interpretation of Linear Programming Representations
e) Non-Linear and Integer Programming
3) Modeling Discrete Processes (Template 2)
a) Difference Equations
b) Stochastic Processes
i) Markov Processes
ii) Noise and Uncertainty
4) Probabilistic Models (Template 3)
a) Queuing Theory
i) Poisson Distribution
ii) Single Server System
b) Bayes’ Theorem
i) Sampling Methods and Likelihood Measures
ii) Monte Carlo Estimation
c) Regression Models
i) Least-squares Estimation
ii) Systems of Regression Equations
iii) Linearization Procedures
5) Modeling Continuous Processes (Template 4)
a) Differential Equations
i) Linear, Homogeneous
ii) Non-linear, Non-Homogeneous
b) Systems of Differential Equations
i) First order stock and flow models
ii) Logistic processes
iii) Describing Chaotic Behavior
6) Validating and Qualifying Models
a) Sensitivity Analysis
b) Scenario Analysis
d) Experimental/Historical Validation