Topical Outline with Specific Course Objectives
The exact topics to be covered will be determined by the three topics chosen by the instructor to cover in this course. Specific objectives are listed underneath the seven topics, with the numbers in parentheses indicating the topic(s) for which these objectives will be attained.
Three of these seven topics will be included in the course.
- Exploratory data analysis
- Sampling and decision making
- Modeling - linear, quadratic and exponential
- Financial mathematics
- History of mathematics
- Patterns, network and game theory
- Mathematics in art, nature and daily life
For each topic chosen, the instructor will develop the ideas at a level appropriate to this class, and will emphasize the following concepts and skills. Concepts with numbers in parentheses will be covered under those topics; concepts without numbers illustrate the approach of the class and may or may not be specifically addressed:
- Analyze real data sets using tools such as histograms, timelines, boxplots, tables, and descriptive statistics. (1, 2)
- Prepare a report based on an analysis of a real data set. (1,2)
- Understand basic types of sampling in opinion polls and interpret sampling error. (1,2)
- Recognize abuses and manipulations of data that occur in polling. (1,2)
- Determine whether data can be modeled by functions such as linear, quadratic, or exponential. (3)
- Assess the model to determine its usefulness. (3)
- Use exponential functions to model data such as population growth and radioactive decay. (3)
- Make informed choices in areas such as credit card and long distance carrier offers. (4)
- Make informed choices in areas such as loans, mortgages, insurance, and investment plans. (4)
- Understand simple, compound, and effective interest rates; discounts, mark-ups and markdowns. (4)
- Understand and appreciate man's evolving understanding of mathematics. (5)
- Understand other systems of numeration and modulus arithmetic. (5)
- Recognize the patterns or mathematics involved in man-made or natural occurrences: Golden ratio, Fibonacci sequence, tessellation, fractals. (6,7)
- Recognize the patterns or mathematics involved in many games and recreations; network theory, game theory, magic squares, billiards. (6,7)
- Choose appropriate methods for solving problems: tables, graphs, equations, guess-and check, and working backwards.
- Make an educated “guess” as to the reasonableness of results.
- Take basic concepts and apply them in situations that have not previously been specifically demonstrated.
- Explain the process used in solving the problem.
- Explain what the answer means in the context of the problem.
- Recognize patterns or relationships and express them in clear sentences that will be meaningful to another student.
- Solve problems and recognize the relationship among information presented numerically, algebraically, and graphically.
- Express generalizations discovered through investigations.
- Ask clarifying and extending questions related to the mathematics at hand.
The following teaching techniques, which reflect the goals of the Math Department, will be especially encouraged in this course.
- Emphasize techniques that encourage the student to become an active, involved learner: less lecture, more group and cooperative learning, interesting and challenging problems, student presentations.
- Emphasize problem solving & mathematical modeling; less emphasis on manipulation for its own sake.
- Cover fewer topics but in deeper and more interesting ways.
- Use textbooks which reflect the NCTM and AMATYC standards.
- Use appropriate technology.
Department Policies
- Comprehensive Final