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Additional Math 360 Homework

3 semester credits

Catalog Description

MATH 360 ENGINEERING STATISTICS (3-0-3) Calculus-based survey of statistical techniques used in engineering. Data collection and organization, basic probability distributions, sampling, confidence intervals, hypothesis testing, process control, simple regression techniques, design of experiments. Emphasis on examples and applications to engineering, including product reliability, robust design and quality control. PREREQ: MATH 272 or MATH 275.

Prerequisites

Multivariable calculus.

Jurisdiction

The instructor has complete control over the teaching of this course, including the examinations, homework, and grading system, but works with Engineering faculty to ensure that the course meets their needs.

Learning Objectives

This course is designed to provide engineering students a sufficient background in statistics (and the requisite elements of probability theory) with emphasis on applications to, and terminology used in, the engineering field, notably design of experiments and process control. Further, a student completing the course should be able to obtain additional specific statistical tools on his/her own.

Upon completion of the course students should be able to:

  1. solve traditional problems of elementary probability and statistics
  2. choose and implement appropriate descriptive and inferential techniques in estimation, hypothesis testing, regression, experimental design, and statistical quality control, and interpret the results of the techniques employed
  3. distinguish situations in which the assumptions for use of the normal and/or binomial distributions is justified from those for which the normal or binomial theory does not apply.

Assessment of Learning Objectives

Students will be evaluated by their ability to do problems based on the learning objectives. The problems will be presented in homework sets and formal exams. Exercises will be of three types:

  • to reinforce material from the text and class
  • to extend results and ideas to new situations
  • optional exercises to allow students to investigate probability and statistical theory not covered in class.

Topics and Approximate Timeline

The following table is a rough schedule for 45 class meeting of 50 minutes each. The actual topics and the amount of time spent on each topic will vary slightly from semester to semester.

Topic

Number of Lectures

Collection and analysis of data

4

Basic definitions and properties of probability

3

Discrete probability distributions

5

Continuous probability distributions

5

Sampling distributions, confidence intervals, reliability

6

Statistical quality control

3

Tests of hypotheses

4

Design of Experiments

8

Regression analysis

4

Exams

3

Total

45

Text
Probability and Statistics for Engineers and Scientists, 6th ed., R. E. Walpole, R. H. Myers and S. L. Myers, Prentice Hall, 1998.

Probability and Statistics for Engineering and the Sciences, 5th ed., Jay L. Devore, Duxbury Press, 2000.

Format, Student Activities, and Grades

Class meetings involve a combination of lecture, questions and discussion. Homework is an important part of the course. The instructor chooses the exact grading scheme, but a typical distribution would be:

3 Exams

300

Final Exam

200

Homework

100

Total

600

Updated Spring 2002

Topics in the course will vary by semester and sometimes by section. The emphasis is on the development and application of a variety of mathematical models; the specific choice of application will certainly vary. But the tools developed in the course will include
  • The modeling process in general.
  • Discrete dynamical systems.
  • Models involving proportion and geometric similarity.
  • Graphical and analytical model-fitting; least squares.
  • Optimization problems.
  • Dimensional analysis.
  • Ordinary differential equations.
  • Autonomous systems of differential equations.

WITHDRAWAL: The last day for undergraduates to withdraw from a full-session course is Friday March 9, 2018.

GRADING: Semester grades will be assigned on the basis of 1100 points, earned as follows:

5 written projects @100 points
1 project presentation @20 points
2 one hour exams (mid-term) @100 points
1 final exam @200 points.
Homework/attendance for a total of 180 points
Your instructor will also provide a schedule of due dates and exam dates for your section.

SECTIONS AND INSTRUCTORS:

PROJECTS: Students will complete five projects during this course. Each should be considered a major assignment, and each counts as much as an hour exam. We will provide prompts and questions but your papers should be understandable to a person who does not have them and is not in the class. (You may someday soon show one of these to a prospective employer and you should write with that kind of audience in mind!) In particular the paper should have insightful introduction and conclusion sections. Each project report is to be printed on good quality paper and appropriately stapled or bound. A portion of the project grade (20 points) will be based on the quality of the writing, including grammar and spelling; neatness counts as well. More details about expectations will be provided by your instructor.

The class will be divided into groups to prepare the projects. Students are expected to investigate each of their projects in groups, but to prepare their written reports individually. Any information received from other group members should be appropriately cited. Each group will present one of the projects orally, taking one class period. Group presentations are intended to be professional, as if you were presenting to a workplace supervisor. This means, in part, that you will use some form of graphical presentation software. Additionally, because presentations will be made by groups, full group participation during the creation and preparation of the presentation, including contributing and refining plots and figures, creating slides, and taking part in the presentation.

SAMPLE EXAMS:

Spring 2011 Final Exam

Spring 2010 Final Exam

Please note that these exams are not necessarily comprehensive, and thus there are topics which were not included on these exams which may be tested on your final exam.

Your own instructor will write and grade your midterm exams and will grade your final exam.

FINAL EXAM: The final exam will be a comprehensive, departmental examination. All sections of this course will take the same final exam at the same time: Monday, May 7, 6:00-7:50 PM. The exam will probably NOT be in your regular classroom. Room assignments are usually made one to two weeks before the final exam week. They will be announced in class later on.

TECHNOLOGY: Students will be expected to use calculators and computers on a regular basis when preparing project reports and completing other assignments. if needed, a class meeting early in the semester will be held in a computer lab to introduce students to some available software tools.

Here is information about the TeX mathematical typesetting system. Students whose career aspirations include anything mathematical (research, teaching, or applications) are encouraged to learn to use TeX, and during Math 360 is a great time to try it.

TEXT:"A First Course in Mathematical Modeling", Giordano, Fox and Horton, 5th ed., publ. Cengage Learning

Some additional references:

STUDENT HANDOUTS: Please note that any information provided by your instructor supersedes these data.

Sample Project: Locating a Railway Supply Depot
Computer Orientation Material

YOUR INSTRUCTOR MAY CHOOSE FROM THESE PROJECT HANDOUTS OR DISTRIBUTE OTHERS:

Project 1
Project 2
Project 3
Project 4
Project 5

RESOURCES ON THE WEB:

Understanding Mathematics: a study guide, from the University of Utah

ACADEMIC CONDUCT: Academic honesty and mutual respect (student with student and instructor with student) are expected in this course. Mutual respect means being on time for class and not leaving early, being prepared to give full attention to class work, not reading newspapers or other material in class, not talking to other students, not using cell phones during class time, and not looking at another student's work during exams. Academic misconduct, as defined by the Student Judicial Code, will not be treated lightly.

DRC STATEMENT: If you have specific physical, psychiatric, or learning disabilities and require accommodations, please let your instructor know early in the semester so that your learning needs may be appropriately met. You will need to provide documentation of your disability to the DRC Office located in the Health Services Building, 4th floor.

ADVICE: In Math 360 you will frequently make use of SHORT topics introduced in other courses (Math 240, Math 336, Stat 350, Phys 250, ...). You are NOT expected to know this material in advance; you ARE expected to work with your instructor and your classmates to learn that material. This is deliberate --- we want you to see in advance why the ideas presented in your future courses will be useful and interesting.

You may very frequently find that the projects or the classroom discussions assume familiarity with something that you know little about --- scientific phenomena, investments, sociological patterns, etc. Don't be discouraged! Ask questions, and take the opportunity outside of class to do a little outside reading. This is a very common situation when mathematicians are working on applications. Ignorance is not a crime --- only the refusal to do something about it is criminal.

If you have difficulty with the writing of project reports (as opposed to the mathematical understanding of them), you should take advantage of the University Writing Center.

Since you will work hard on your projects you should keep clean copies of the best versions of your favorites; these projects can make a very good impression on employers who may not understand what you can offer them as a result of taking advanced mathematics courses.

Students who enjoy working on projects like these should consider participating in the Mathematical Competition in Modeling, an international contest for undergraduates held every February. NIU has had several teams do well in this competition and we hope to field one or more teams again this year. Ask your instructor for more information about this opportunity.

Last update: January 16, 2018

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