Math& 107

Mathematical Models and Applications

LEARNING OUTCOMES

 

Upon successful completion of Math& 107, the student should be able to:

 

  1. Construct graphs (vertices connected by edges), Euler circuits, Hamilton circuits and minimal spanning trees to model a variety of applied situations.

 

  1. Use algorithms to find "optimal solutions" to a variety of routing problems involving Euler circuits, Hamilton circuits and minimal spanning trees.

 

  1. Construct project di-graphs from precedence data for various jobs.  Use project di-graphs and critical path analysis to determine optimal job-completion times.

 

  1. Use heuristic algorithms to construct "optimal" schedules for completing a variety of jobs.

 

  1. Use voters' preference ballots to determine the results of elections conducted by several voting methods, such as plurality, Borda count, pairwise comparison and approval.

 

  1. Describe imperfections inherent in all voting methods.

 

  1. Use two or three appropriate algorithms to distribute items among competing parties, so that each party is satisfied with the share received.  (e.g., inheritance, divorce, dissolution of business partnerships, etc.)

 

  1. Understand and describe the role of randomization in statistical investigations.

 

  1. Understand and describe the difference between surveys and statistical experiments.  Evaluate the "validity" of results obtained from surveys and statistical experiments.

 

  1. Interpret the results of statistical studies given in terms of measures of center and spread and statistical diagrams.  Use measures of center and spread, along with appropriate visual displays, to summarize numerical data sets.

 

  1. Analyze data sets.  Use the normal distribution, percentiles and standard scores to extract information from appropriate collections of data.