Note: The syllabus given here is the one I wrote in 1998, at Chapman University. The revision of this syllabus, as it is now used at the University of Northern Colorado is available through my web site (see hopper.unco.edu/hauk/mat120/mat120syllabus.html).
The two semester mathematics requirement for the Liberal Studies major for prospective elementary teachers included one semester of algebra-based descriptive and inferential statistics and the course below. Thus, neither statistics nor probability are included in this Mathematical Modeling syllabus (from 1998)
Title: Mathematical Modeling Credits: 3
Catalog Description: Prerequisite: Math 99 (intermediate algebra) or equivalent. Topics covered: basic number theory; sets and logic; linear programming; linear, quadratic, exponential and logarithmic models; interest theory, loans, annuities. Two additional topics are chosen from: Euclidean and non-Euclidean geometries; introduction to calculus; introduction to rate equations modeling infectious diseases; trigonometry.
Course Objectives: The primary objective of this course is to develop understanding of the techniques involved in the construction of mathematical models using problem solving strategies from mathematics and computer science. Given a situation to be modeled with mathematics, presented in the form of a real life problem or in the more structured format of a word problem, students will be able to evaluate the posited situation and propose a solution method for the problem. Students should also have the ability, by the end of the course, to analyze solution(s) and discuss restrictions on their accuracy and applicability.
Major Study Units : All of topics 1-4 and at least two of 5-8.
|1. Numbers, Numerals and Words||5. Geometry and Art|
|Ancient Systems||Euclidean and Non-Euclidean Models|
|Basic Number Theory||Tiling and Tessellation|
|2. Sets and Logic||Modeling Nature with Fractals|
|Sets, Venn Diagram Models||6. Calculus|
|Symbolic Logic||Functional Difference Quotients|
|Inductive and Deductive Reasoning||Derivatives; Modeling Rate of Change|
|Flowchart Modeling||Basic Integration|
|3. Algebraic and Exponential Models||7. Trigonometry|
|Function notation||Sine, Cosine, Tangent|
|Linear Models ; Linear Programming||Modeling with Right Triangles|
|Quadratic Models; Polynomial Models||The Laws of Sine and Cosine|
|Exponential and Logarithmic Models||Modeling with Acute Triangles|
|4. Finance||Circular functions|
|Interest Theory||8. Modeling Infectious Disease|
|Annuities||Rate Equations; Difference Equations|
|Loans||Programming the Equations|
|Present Value||Predicting Trends; Effect of Quarantine|
Instructional Strategies: There are three major instructional strategies in teaching the course:
an emphasis on effective writing about
mathematics, the effective use of technology and the rule of three.
Written assignments in the course:
- a project that includes an essay of at least 1000 words,
- homework assignments which include all of the short essay answer Explain questions in addition to some Apply and Explore exercises,
- exam questions that require explanation and/or justification (in full sentences) of solutions.
Technology, in particular a graphing calculator along with its manual (or an equivalent computer program with manual), are used to help each student think about and analyze mathematics. In addition to the traditional use as a simple calculational tool, students are expected to master the graphing and basic programming capabilities of their calculators in order to better visualize models and estimate solutions.
The ``rule of three'' means that concept, symbols, and words are presented for
each topic. The most common interpretation of the rule of three in
mathematics is to offer students the geometric, numeric and algebraic views for every topic.
Methods of Evaluation: Assessment of student learning is accomplished via at
least two in-class examinations, two projects (at least one of which is
an individual research project whose outcome is either a written report or an oral report
accompanied by a written abstract; the other project
culminates in an essay of at least 1000 words involving a draft step - the preferred topic for
this essay is the student's mathematical autobiography)
and a comprehensive final exam. Lab sessions on a computer
(or using graphing calculators) which illustrate the topics discussed in class are
necessary and are to include assessment of technological mastery through either
quizzes or short essay assignments.
Required Text: Staszkow, R. and R. Bradshaw, The Mathematical Palette, 2nd ed.,
Saunders College Publishing, 1995.
COMAP project, For all practical purposes: introduction to contemporary mathematics, Freeman and Co., New York, 1994.
Giordano, F. and M. Weir, A First Course in Mathematical Modeling, 2nd ed. Brooks Cole, 1997.
Giordano,F. and M. Weir, Mathematical Modeling with Minitab, Brooks Cole, 1987.
Hauk, S., Modeling Infectious Disease, Unpublished, 1996 (contact S. Hauk at: email@example.com)
Mesterton-Gibbons, Michael, A Concrete Approach to Mathematical Modeling, Addison Wesley, 1989.
Staszkow, R. and R. Bradshaw, Student Study Guide to Accompany the Mathematical Palette, 2nd ed., Saunders College Publishing, 1995.