Course Offerings Fall 2017-Summer 2018

Fall 2017

Math 551: Advanced Calculus

[MWF 9-9:50am, Prof. Clifford]

Advanced Calculus is the rigorous study of the concepts of limit, differentiation, and integration. In this course, we dig deeper into the historical developments of these concepts and deduce many principles from basic axioms. Students will practice a serious application of logic and proof techniques in the course. The basic ideas develop in this course constitute a strong foundation for any further course in mathematics. Previous experience in first-year calculus and proof methods will be helpful.

Satisfies: Core A: Analysis

Offered: Every Fall

Math 562: Mathematical Modeling

[MW 6-7:15pm, Prof. Hristova]

** Contact Prof. Hristova (yuliagh@umich.edu) for more information **

Counts toward Core C: Modeling

Offered every Fall

Math 572: Numerical Analysis

[TR 4:30-5:45, Prof. Massey]

Numerical Analysis is the study of algorithms that approximate solutions to many problems in mathematics. In this course, we study how computers approximate and store numbers and how round off error can affect computations. We develop and analyze algorithms to approximate solutions to mathematical problems including finding roots of functions, solving definite integrals, interpolating data by polynomials and splines, numerical differentiation, solving systems of linear equations, and solving differential equations. Some programming experience will be helpful.

Satisfies: Core B: Numerical Methods

Offered: every Fall

Stat 530:  Applied Regression Analysis

[TR 6-7:15pm, Prof. Pokhrel]

Topics include single variable linear regression, multiple linear regression and polynomial regression. Model checking techniques based on analysis of residuals will be emphasized. Remedies to model inadequacies such as transformations will be covered. Basic time series analysis and forecasting using moving averages and autoregressive models with prediction errors are covered. Statistical packages will be used.

Satisfies: Modeling Specialization: Stochastic Models (students admitted before Fall 16) or Modeling Specialization: Statistics Models (students admitted Fall 16 or later)

Offered: every Fall

Prerequisites: It is strongly recommended that you complete an introductory statistics course or have some computer programming experience before taking this course. Please speak with the instructor before enrolling.

Stat 590:  Nonparametric Statistics

[TR 4:30-5:15pm, Prof. Sharaf]

Nonparametric Statistics involves methods that replace parametric methods when assumptions such as normality and large samples are not met. We learn about methods that replaces parametric tests such as sample t-test and methods for two samples in both cases paired and unpaired. Additional tests for independence and tests involving more than two samples will be also discussed. Bootstrapping and Jackknife methods for creating confidence intervals will be discussed.

Satisfies: Modeling Specialization: Stochastic Models (students admitted before Fall 16) or Modeling Specialization: Statistics Models (students admitted Fall 16 or later)

Offered: Occasionally

Prerequisites: It is strongly recommended that you complete an introductory statistics course or have some computer programming experience before taking this course. Please speak with the instructor before enrolling.

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Winter 2018

Math 525: Mathematical Statistics II

[TR 2-3:15pm, Prof. Fiore]

In this class, the main goal of statistics is to infer a conclusion about a population when you only know information about a sample, and to quantify the conclusion's reliability. Statistics classes are among the most important and useful classes you can take at UM-Dearborn. In this class, we will learn the fundamentals of mathematical statistics, building on our knowledge of probability theory from last semester. We will also learn the basics of the open-source statistics language called R.

The material of this course consists of a review of fundamental notions from probability theory, the distribution function technique for finding the density of a function of a continuous random variable, the change of variable technique for continuous and discrete random variables, the change of variable technique for two continuous random variables, the bivariate normal, sample variance of a random sample from a normal distribution, Student's t-distribution, maximum likelihood estimators, confidence intervals, hypothesis testing, sufficient statistics, power of a statistical test, best critical regions, likelihood ratio tests, Chebyshev's inequality, Bayesian methods, and some non-parametric methods. 

Satisfies:  Modeling Specialization: Stochastic Models (students admitted before Fall 16) or Modeling Specialization: Statistics Models (students admitted Fall 16 or later)

Offered: every other year

Prerequisites: It is strongly recommended that you complete an introductory statistics course.

Math 573: Matrix Computations

[TR 6-7:15pm, Prof. Massey]

Matrix Computations is concerned with the solution of real world problems that involve calculations with matrices.  One aspect of the course is the translation of real world problems into matrix theoretic terms.  Another is identifying the matrix operations involved in their solution and a third is implementing matrix operations in various computer environments.  In particular, this course is concerned with computational aspects of the solution of systems of equations, optimization, eigenvalues and eigenvectors and their application to difference and differential equations, orthogonal expansions, and singular value decompositions.  It also considers the time, space, and round-off error problems that arise when the number of variables is large.  For more information: www.umd.umich.edu/~fmassey/math473/.  (Left: plot of the norm of (zI - A)-1 where A = with the complex value z = x + iy satisfying - 1 <= x <= 11 and - 5 <= y <= 5) 

Satisfies: Modeling Specialization: Stochastic Models (students admitted before Fall 16) or Modeling Specialization: Statistics Models (students admitted Fall 16 or later) 

Offered: every other Winter

Math 555: Complex Variables

[MW 4:30-5:45pm, Prof. Wiggins]

This course presents the mathematical structure that underlies many aspects in science and engineering.  One needs a broader outlook than the real number system provides to properly describe electric phenomenon, fluid flow, and thermal flow.  All these phenomena are related to potentials, and have identical basic mathematical underpinnings.  To begin, the complex number system is introduced and concepts of calculus are explored in depth as they relate to this new system.  The theory of derivatives (analytic functions) and especially integrals turns out to be a much cleaner and richer environment than with real variables.  Power Series and Laurent Series are explored, leading to residues and poles.  Towards the end of the course, applications are presented.   Conformal maps also play a significant role.

Satisfies: Core A: Analysis

Offered: every Winter

Stat 540: Design and Analysis of Experiments

[MW 12:30-1:45pm, Prof. Sharaf]

An introduction to the basic methods of designed experimentation. Fixed and random effects models together with the analysis of variance techniques will be developed. Specialized designs including randomized blocks, latin squares, nested, full and fractional factorials will be studied. A statistical computer package will be used. 

Satisfies: Modeling Specialization: Stochastic Models (students admitted before Fall 16) or Modeling Specialization: Statistics Models (students admitted Fall 16 or later) 

Offered:  Occasionally

Prerequisites: It is strongly recommended that you complete an introductory statistics course or have some computer programming experience before taking this course. Please speak with the instructor before enrolling.

Stat 550: Multivariate Statistics

[TTh 4:30-5:45, Prof Pokhrel]

An introduction to commonly encountered statistical and multivariate techniques, while assuming only a limited knowledge of higher-level mathematics. Topics include: multivariate analysis of variance, multivariate regression, principal components and factor analysis, canonical correlation, and discriminant analysis.

Satisfies: Modeling Specialization: Stochastic Models (students admitted before Fall 16) or Modeling Specialization: Statistics Models (students admitted Fall 16 or later) 

Offered:  Occasionally

Prerequisites: It is strongly recommended that you complete an introductory statistics course or have some computer programming experience before taking this course. Please speak with the instructor before enrolling.

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Summer 2018

Math 520: Stochastic Processes  

[MW 4:30-7:15pm, Prof. Kim]

Review of distribution theory. Introduction to stochastic processes, Markov chains and Markov processes, counting, and Poisson and Gaussian processes. Applications to queuing theory. 

Satisfies: Modeling Specialization: Stochastic Models (students admitted before Fall 16) or Modeling Specialization: Statistics Models (students admitted Fall 16 or later) 

Offered:  Occasionally