Course Descriptions

Learner Outcome

Activity (optional)

Assessment

Evaluate theoretical properties of multiple regression models, including underlying model assumptions and model construction.

Homework and in-class exercises will ask students to work with the mathematical properties of regression models.

Graded homework exercises; final exam.

Estimate multiple regression models.

Statistical lab exercises will ask students to estimate multivariate regression models.

Graded statistical lab reports, exams.

Evaluate the appropriateness and fit of a statistical model, particularly multiple regression model, and interpret the model in context.

Lab exercises will ask students to evaluate the fit of multiple regression models and interpret the model in the context of the particular data set.

Graded statistical lab reports, exams.

Estimate ANOVA models, and interpret the results.

Lab exercises will ask students to estimate ANOVA models and interpret the model in the context of the particular data set.

Graded statistical lab reports, exams.

Propose a major statistical project, choosing appropriate questions to be answered and appropriate statistical tools.

Students will submit a proposal for a major statistical project (the project itself will be completed in Math 410B).

The project proposal will be graded in part on the appropriateness of the statistical questions and the tools proposed to be used.

Communicate statistical results clearly orally and in writing.

Students will submit written lab reports, a formal project proposal, and an oral presentation of their project proposal.

The proposal and oral presentation of the proposal will be graded in part on the quality and clarity of the writing and presentation.

Learner Outcome

Activity (optional)

Assessment

Estimate ARMA and ARIMA models for time series data.

Students will complete statistical lab assignments which require them to estimate ARMA and ARIMA models.

Written lab reports, exams, and a final project.

Evaluate the fit of time series models, and choose appropriate models for a given data set.

Students will complete statistical lab assignments which require them to choose appropriate models and evaluate the fit of their chosen models.

Written lab reports, exams, and a final project.

Assess time series data for trends and seasonality, and estimate models including these terms.

Students will complete statistical lab assignments which require them to use diagnostic checks for trends and seasonality, and fit models including trends and seasonality.

Written lab reports, exams, and a final project.

Evaluate properties of a time series model given in mathematical form, including checking stationarity and computing the autocorrelation function of a given model.

Students will complete homework problems that require them to check properties of a given model, including stationarity and computing the autocorrelation function.

Graded homework problems and exams.

Communicate statistical information professionally in writing.

Students will write lab reports for their statistical lab assignments and complete a final project where the tools from the course are applied to a time series data set of their choosing.

Written lab reports and the final project will be assessed using a rubric that includes the clarity and quality of the writing.

Learner Outcome

Activity (optional)

Assessment

Solve problems involving probabilities, conditional probabilities, and continuous and discrete random variables.

In-class and homework exercises will ask students to work with conditional probabilities, discrete and continuous random variables, and joint, marginal, and conditional distributions.

Graded in-class quizzes and exams; graded homework.

Summarize common families of discrete and continuous probability distributions.

In-class exercises will focus on identifying situations where common families of distributions apply; students will complete a chart of common families of distributions.

Graded in-class quizzes and exams; graded homework.

Apply terminology from insurance to probability questions.

In-class exercises will focus on terminology such as deductible, policy limit, and proportional insurance.

Graded in-class quizzes and exams; graded homework.

Choose appropriate tools from probability to solve problems similar to those on the actuarial Exam P.

In-class exercises and homework problems will require students to choose appropriate tools from probability theory.

Graded in-class quizzes and exams; graded homework.

Learner Outcomes

 Activity

Assessment

Students will select mathematical models to best describe the process of mathematical modeling.

Assignment or essay in which students select mathematical models to best represent steps in the modeling process, and justify their conclusions.

Essay with rubric evaluated by faculty or graded assignment

Students will predict modeling results.

Students will analyze equations for the model, understanding how each part of the equations corresponds to the modeling scenario, and will estimate the effects of what is included and excluded from the model to predict results.

Graded assignments.

This material will appear in technical reports on one or more projects with a rubric evaluated by faculty.

Students will assess mathematical models by obtaining numerical results.

Students program software and use data to obtain modeling results.

Results included in technical reports, and also included on graded assignments.

Students will appraise the requirements of a problem to make modeling decisions, they will judge what to include and what to leave out of a model, and they will defend their choices based on results and constraints.  Students will evaluate which mathematical model performs best in a modeling situation

 Students write one or more technical reports on modeling projects, defending their choices, making predictions, and judging their results.

Students may also make a presentation to the class about a chosen mathematical model.

Technical reports on one or two projects, with a rubric evaluated by faculty

Oral presentation evaluated by rubric

Learner Outcomes

Activity

Assessment

Students will describe, present and analyze numerical methods for a specific data set, and justify their conclusions.

Students will prepare technical reports of mathematical/ scientific/ technical information in a clear and concise written communication.

Report with rubric evaluated by classmates and faculty.  Rubric will measure their written communication, their process and their technical results.

Students will construct and analyze computational approximations for different data sets using interpolation and other polynomial approximations.

Students will code approximation techniques and provide a written report explaining techniques and results. Code will be documented and reviewed.

Graded assignments.

This topic will appear in technical reports on one or more projects, in class work, and homework with a rubric evaluated by faculty.  

Students will estimate numerical derivatives and numerical integrals for a given dataset.

Students will complete homework, quiz, and/or exam problems that require the application of numerical differentiation and integration.  

Graded assignments.

This topic will appear in technical reports on one or more projects with a rubric evaluated by faculty. 

Students will predict and analyze the error propagation that results from mathematical algorithms.

In classwork, homework and in the technical reports students will analyze how numerical methods compare to perfect computation, understanding how each part of the error corresponds to the numerical method, and estimate the effects. A written summary will be presented with each report submitted.

Graded assignments.

This topic will appear in technical reports on one or more projects with a rubric evaluated by faculty.

Students will evaluate other numerical approximation methods.  

Students will complete homework, quiz, and/or exam problems that require the application of Fourier Series, least squares approximation, and other numerical approximation methods.

Graded assignment using a rubric.

Learner Outcomes

Activity

Assessment

Students will describe, present and analyze numerical methods for a specific data set, and justify their conclusions.

Students will prepare technical reports of mathematical/ scientific/ technical information in a clear and concise written communication.

Report with rubric evaluated by classmates and faculty.  Rubric will measure their written communication, their process and their technical results.

Students will construct and analyze computational approximations for different data sets using interpolation and other polynomial approximations.

Students will code approximation techniques and provide a written report explaining techniques and results. Code will be documented and reviewed.

Graded assignments.

This topic will appear in technical reports on one or more projects, in class work, and homework with a rubric evaluated by faculty.  

Students will estimate numerical derivatives and numerical integrals for a given dataset.

Students will complete homework, quiz, and/or exam problems that require the application of numerical differentiation and integration.  

Graded assignments.

This topic will appear in technical reports on one or more projects with a rubric evaluated by faculty. 

Students will predict and analyze the error propagation that results from mathematical algorithms.

In classwork, homework and in the technical reports students will analyze how numerical methods compare to perfect computation, understanding how each part of the error corresponds to the numerical method, and estimate the effects. A written summary will be presented with each report submitted.

Graded assignments.

This topic will appear in technical reports on one or more projects with a rubric evaluated by faculty.

Students will evaluate other numerical approximation methods.  

Students will complete homework, quiz, and/or exam problems that require the application of Fourier Series, least squares approximation, and other numerical approximation methods.

Graded assignment using a rubric.

Learner Outcome

Activity (optional)

Assessment

Communicate mathematical and statistical ideas clearly and to an appropriate audience.

Assemble a senior portfolio that includes (in part) problem calculations, a lab report, and a project from earlier coursework, revising as necessary.

A lab report and problem write-ups from earlier courses (possibly revised) will be assessed using a rubric that looks specifically at communication and writing.

Recommend and argue for a course of action, in a situation requiring actuarial or statistical expertise.

Small project that involves conducting some analysis, then writing a formal memo recommending a course of action, aimed at an appropriate audience.

The memo will be assessed using a rubric that looks at communication to a specific audience and justifying recommendations.

Prepare documentation/annotation for a spreadsheet or computer program.

Annotate or document either a spreadsheet used in the small project above, or a computer program produced for earlier coursework.

The spreadsheet or computer program will be assessed using a rubric that looks at appropriate documentation and whether the code/spreadsheet could be used or modified by other users.

Communicate professionally in writing.

See activities above.

The elements of the portfolio will be assessed on grammar, mechanics, and clarity of style in addition to mathematical content.

Communicate technical material orally.

Students will make presentations to the class on a topic to be determined by the instructor.

Presentations will be assessed using a rubric that measures whether technical material was communicated in a clear and compelling way.

Learner Outcome

Activity (optional)

Assessment

Students will become familiar with the structure of the exam and the types of questions for each section. 

Hands-on, supervised practice tests.

Students will demonstrate their familiarity with the GRE exam structure and question types for each section by achieving improved scores on a sample GRE (post-test) taken at the end of the quarter as measured from baseline scores of a sample GRE (pre-test) taken at the start of the quarter. The students’ understanding will also be evident in their responses to quizzes and class discussions about the test structure and question types.

Students will learn proven test-taking strategies for each type of questions.

Lecture and discussion of the exam’s components.

The students’ learning of test-taking strategies for each type of question on the GRE will be reflected in their ability to complete each section of a sample GRE within the time allotted for the actual test, and in improved scores on a sample GRE taken at the end of the quarter from scores achieved on a sample GRE taken at the beginning of the quarter.

Students will learn the most common vocabulary words included in the exam. 

Drills and exercises on the exam’s content.

The students’ learning of the most common vocabulary will be evaluated on in class exercises and weekly quizzes on the vocabulary, and in improved scores on a sample GRE taken at the end of the quarter from scores achieved on a sample GRE taken at the beginning of the quarter.

Students will review arithmetic, algebra and geometry.

The students’ learning of arithmetic, algebra, and geometry will be evaluated on in class exercises and weekly quizzes on the topics, and in improved scores on a sample GRE taken at the end of the quarter from scores achieved on a sample GRE taken at the beginning of the quarter.

Students will learn to write essays that meet the standards of the highest-scoring answers on the GRE exam.

The students’ learning to write essays that meet the standards of the highest-scoring answers on the GRE exam will be evaluated on in class essay assignments and weekly essay quizzes, and in improved scores on a sample GRE taken at the end of the quarter from scores achieved on a sample GRE taken at the beginning of the quarter.

Learner Outcome

Activity (optional)

Assessment

Demonstrate lean manufacturing principles in the production of manufactured parts.

Assessed through lab work.

Produce a value stream map.

Assessed through homework, and laboratory experiments.

Identify the elements of a 5S program and demonstrate implementation.

Assessed through homework, and laboratory demonstrations.

Identify Kaizen improvements that will affect production efficiently and suggest methods in which they can be implemented.

Assessed through homework, and group kaizen activities.

Implement SPC/Quality control practices.

Assessed through written homework, lab, and examinations.

Define Lean as a business system.

Assessed through written homework and examinations.

Design a manufacturing mistake-proofing procedure.

Assessed through production application of Poka-yoke.

Identify and suggest methods for reducing or eliminating the seven wastes in manufacturing.

Assessed through laboratory applications, written and oral reports.

Identify safety hazards in a given manufacturing environment and suggest methods for mitigation.

Assessed through laboratory written reports.