Probabilistic Methods in Engineering

Course ID: SH17020210248EUC01
Discipline: Economics/Applied Statistics
Registration recommendations: Domestic and international undergraduate and graduate students in engineering
Prerequisites: Calculus IV,Honors Mathematics III,Honors Mathematics III
Lecture Hours & Credits: 60 leture hours/4 credits
Project year: 2016

上海交通大学
UM-SJTU Joint Institute

Horst Hohberger

Prof. Horst Hohberger Professor Horst Hohberger received his Ph.D. in Mathematics in 2006 at the University of Potsdam, Germany. He joined the University of Michigan – Shanghai Jiao Tong University Joint Institute in March 2007. Prof. Hohberger teaches in English for domestic and international undergraduate and graduate students..

Objectives

Focusing on the ability of using math and science knowledge to solve real engineering problems, this course aims to provide basic knowledge of mathematics and its application to engineering problems, to provide knowledge of computer algebra systems (e.g., Mathematica) and their use in modeling engineering problems and solving complex mathematical questions, to provide experience in team work (division of labor and allocation of tasks among team members, integration of diverse contributions into a unified whole), and to provide experience in creating written technical reports.

Contents

This course covers combinatorics and counting, basic concepts in probability, discrete and continuous probability distributions, joint distributions, descriptive statistics, estimation, hypothesis testing, non-parametric methods, analysis of categorical data, simple and multiple regression analysis, model selection, introduction to analysis of variance and experimental design. The first part of the course introduces some basic elements of probability theory and combinatorics, with proofs of theorems demonstrated as far as practical within the time constraints of the course. Students are expected to have a good knowledge of the standard calculus material of the first three terms, including, but not limited to, polar coordinates in higher dimensions, integration of single- and multiple-variable functions, the theory of convergence of series and sequences of functions, the theory of matrices and linear maps as well as systems of ordinary differential equations. The second part of the course discusses some basic statistical methods for testing statistical hypotheses and analyzing means, variances and proportions. The results of the first part are applied to practical problems. Students are required to comprehend and interpret formulations of real-life situations, use their judgment and apply the correct procedure to find a suitable solution to a given problem. In this respect, the required skill sets are closer to a physics or engineering course than a mathematics course. The third part of the course touches upon categorical data analysis, simple and multiple linear regression and analysis of variance (ANOVA). For regression problems in particular, familiarity with matrix calculus is required. The course makes use of the Mathematica software, for which all JI students have a free license. The commands necessary for implementing statistical methods are given in the lecture at regular intervals. A term project will be completed by groups of 4-5 students. The project includes analyses of quality control in China, the rate of homicides in London between 2004 and 2010 as well as performance data for sports teams.

Textbooks and Reference Books

J. S. Milton and J. C. Arnold, Introduction to Probability and Statistics, 4th Edition, McGraw Hill, International Edition 2004 Hines, Montgomery, Goldsman and Borror, Probability and Statistics in Engineering, 4th Edition, J. Wiley & Sons, 2003.

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