MTH 118W - Mathematical Explorations

Credits: 4

Provides a course for students majoring in fields that do not have a specific mathematics requirement. Emphasizes practical applications of mathematics, problem solving, and the communication of mathematics. Includes core topics in Finance, Probability, Statistics, and Geometry. Integrates measurement in the geometry topic, and infuses algebra throughout all topics. A minimum of 4 additional topics will be selected from Economics, Calculus, Graph Theory, Set Theory, Game Theory, Number Theory, Logic, Voting, Apportionment, Combinatorics, Linear Programming, or other approved topics. A GRAPHING CALCULATOR IS REQUIRED.

Prerequisite(s): MATH LEVEL 4
Corequisite(s): None
Lecture Hours: 60 Lab Hours: 0
Meets MTA Requirement: Natural Science
Pass/NoCredit: Yes

Outcomes and Objectives

Students will apply the basic concepts and formulas of mathematical finance.
1. Apply the concepts and formulas of compound interest, simple interest and future value and present value annuities.
2. Model a scenario for wealth accumulation.
3. Work with amortization tables.
4. Explore the brilliant human invention of compound interest and exponential growth.
Students will apply the basic concepts of statistics.
1. Present data using statistical graphs: stem and leaf plots, bar graphs, histograms, line graphs, circle graphs, and box and whisker plots.
2. Interpret several types of graphs.
3. Summarize data using the following measures of central tendency: mode, median, and mean.
4. Summarize data using the following measures of dispersion: standard deviation, variance and range.
5. Apply and interpret percentiles.
6. Describe features of a normal distribution.
Students will apply the basic concepts of elementary probability.
1. Use sample spaces to show possible outcomes and calculate probabilities.
2. Use a tree diagram to represent the outcomes in a sample space and calculate probabilities.
3. Compute probabilities in a binomial experiment.
4. Determine the odds in favor of or against an event occurring.
5. Compute the expected value of an event.
6. Determine whether two events, A and B, are dependent or independent.
7. Determine whether two events, A and B, are mutually exclusive.
8. Compute compound probabilities, that is P(A and B) or P(A or B).
Students will investigate and apply several concepts in geometry.
1. Find the area of rectangles, squares, parallelograms, triangles, and circles.
2. Find the perimeter of any given polygon and the circumference of any given circle.
3. Find the volume of rectangular solids, cylinders, cones, and spheres.
4. Find the surface area of rectangular solids and cylinders.
5. Explore and describe the numerical and geometric patterns that occur in art and nature.
6. Perform conversions in various systems of measurement.
7. Work with English and Metric systems of measurement.
8. Convert between Celsius and Fahrenheit.
Students will communicate effectively about mathematics.
1. Provide complete written solutions to problems using appropriate terminology.
2. Articulate important ideas and conclusions in writing.
Students will use technology (graphing calculator) appropriately as a tool to assist in mathematical problem solving, sketching statistical graphs, and simplifying tedious calculations.
1. Use the Finance menu of the graphing calculator to simplify complicated mathematical calculations.
2. Use the binomial probability distribution function of the calculator to simplify binomial probability calculations.
3. Use the Stat Plot feature of the graphing calculator to assist in generating statistical graphs.
4. Use the Stat menu of the graphing calculator to assist in calculating complicated statistics such as the standard deviation.
Note: Faculty members will choose at least 4 outcomes from the following list (outcomes 7 - 17). Students will investigate and apply the mathematics of economics.
1. Use and apply growth models such as population growth, Ponzi schemes, and chain letters.
2. Use and apply decay models such as population decline, radioactive decay, half-life and carbon-14 dating.
3. Use and apply logistic models.
4. Describe the mathematics behind the Consumer Price Index.
5. Model biological populations with chaos theory.
Students will investigate and apply the elementary concepts of calculus.
1. Define a derivative and provide several of examples of its use.
2. Define an integral and provide several of examples of its use.
3. Explain the relationship between a derivative and a rate of change.
4. Explain the relationship between and integral and an area.
5. Solve elementary problems in differential calculus.
6. Solve elementary problems in integral calculus.
Students will use graph theory to solve problem