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Types of Masters Theses and Projec= ts

 

This list is not exhaustive; feel free to discuss your= ideas with the Mathematics faculty.

 

Thesis or Project Type

 

Application/ Adaptation of Mathematical Conc= epts

Extend definitions = and theorems to more complicated or original situation. Compare and contrast methods, evaluate why answers/adaptations  are valid, interpret results and understand how they might change, what might be significant answers/ conc= epts

Research/ Theoretical Investigation

Construct multiple = original examples, develop significant conjectures, Can replicate select proofs. D= evelop conjectures of some sophistication.  Include some original proofs or detailed understanding of complex proofs.

Implementation of Algorithm

Program algorithm o= r adapt algorithm; reframe a situation so that algorithm can be used.  Understand and explain why algor= ithm works (may need to track down proofs) specify worst-case, average-case, a= nd best-case run times. Compare with other relevant algorithms (run time, implementation pros and cons,etc)

Modeling of Data or Situation

Create or adapt mod= el to analyze data or situation.  = Choose parameters of model using physical or mathematical reason for model to fit.  Perform error analysis= .  Adapt model for non-standard sit= uation OR compare multiple models efficacy on same situation.  Analyze fit of models to data and appropriateness of models.

Survey of an area of mathematics

Master definitions, theorems and examples representing breadth of area.  Understand connections between i= deas. Develop ability to replicate select proofs. Compare and contrast methods and concepts.  Understand main p= roofs in the area.

Pedagogy/ Math in the classroom=

Develop a module/ l= esson appropriate for teaching mathematics in grades 8-12 or college.  Use two or more learning modalit= ies (when appropriate); devise multiple approaches to teaching the topic(s). = Understand where (within curriculum) the topic(s) is (are) taught in schools. Project should encompass an elaborate investigation of the background of the math= ematics taught, and connect to topics in college and/or graduate classes. Develop= er should identify and explain short-cuts for staying ahead of students, constructing good examples, etc.  Module/ lesson should be tested in a classroom.<= /p>

 

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CSUCI MS in Mathematics

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