# STATISTICS (ComBS Math of Finc/MS)

Complete 33 semester hours including the following 3 requirement(s):

1. ## STATISTICS CORE

Complete the following 18 semester hours: . If equivalent of STAT 541 has been taken previously, see department for substitution.

 STAT 541 Applied Statistics (3 hours lecture) 3 STAT 542 Statistical Theory I (3 hours lecture) 3 STAT 543 Statistical Theory II (3 hours lecture) 3 STAT 544 Statistical Computing (3 hours lecture) 3 STAT 547 Design and Analysis of Experiments (3 hours lecture) 3 STAT 548 Applied Regression Analysis (3 hours lecture) 3
2. ## STATISTICS ELECTIVES

1. Complete 3 semester hours from the following list

 STAT 640 Biostatistics I (3 hours lecture) 3 STAT 646 Multivariate Analysis (3 hours lecture) 3 STAT 648 Advanced Statistical Methods (3 hours lecture) 3
2. Complete 9 semester hours from the following list

 STAT 545 Practicum in Statistics I 3 STAT 546 Non-Parametric Statistics (3 hours lecture) 3 STAT 549 Sampling Techniques (3 hours lecture) 3 STAT 552 Intermediate Statistics Methods (3 hours lecture) 3 STAT 561 Statistical Data Mining I (3 hours lecture) 3 STAT 562 Statistical Data Mining II (3 hours lecture) 3 STAT 570 Statistical Consulting (3 hours lecture) 3 STAT 583 Fundamentals of Data Analysis (3 hours lecture) 3 STAT 595 Topics in Statistics (3 hours lecture) 3 STAT 597 Research Methods in Statistical Science (3 hours lecture) 3 STAT 640 Biostatistics I (3 hours lecture) 3 STAT 641 Biostatistics II (3 hours lecture) 3 STAT 642 Introduction to Stochastic Processes (3 hours lecture) 3 STAT 645 Advanced Topics in Statistics (3 hours lecture) 3 STAT 646 Multivariate Analysis (3 hours lecture) 3 STAT 647 Practicum in Statistics II 3 STAT 648 Advanced Statistical Methods (3 hours lecture) 3 STAT 649 Independent Study in Statistics 3 STAT 698 Master's Thesis 3 STAT 699 1
3. ## ELECTIVES AND CAPSTONE REQUIREMENT

1. ### COMP SCI, MATH and/or STAT ELECTIVES

Complete 3 semester hours hours (with Thesis option) - 6 semester hours (with Comp Exam option) from:

 CMPT 578 Introduction to Artificial Intelligence (3 hours lecture) 3 CMPT 589 Computer Simulation of Discrete Systems (3 hours lecture) 3 CMPT 593 Structured System Design and Analysis (3 hours lecture) 3 CSIT 515 Software Engineering (3 hours lecture) 3 CSIT 555 Database Systems (3 hours lecture) 3 CSIT 571 Computer Algorithms and Analysis (3 hours lecture) 3 CSIT 655 Advanced Database Systems (3 hours lecture) 3 CSIT 670 Advanced Computer Algorithms and Analysis (3 hours lecture) 3 MATH 540 Probability (3 hours lecture) 3 MATH 560 Numerical Analysis (3 hours lecture) 3 MATH 568 Applied Mathematics: Continuous (3 hours lecture) 3 MATH 569 Applied Mathematics: Discrete (3 hours lecture) 3 MATH 580 Combinatorial Mathematics (3 hours lecture) 3 MATH 584 Operations Research (3 hours lecture) 3 STAT 545 Practicum in Statistics I 3 STAT 546 Non-Parametric Statistics (3 hours lecture) 3 STAT 549 Sampling Techniques (3 hours lecture) 3 STAT 552 Intermediate Statistics Methods (3 hours lecture) 3 STAT 561 Statistical Data Mining I (3 hours lecture) 3 STAT 562 Statistical Data Mining II (3 hours lecture) 3 STAT 570 Statistical Consulting (3 hours lecture) 3 STAT 595 Topics in Statistics (3 hours lecture) 3 STAT 597 Research Methods in Statistical Science (3 hours lecture) 3 STAT 640 Biostatistics I (3 hours lecture) 3 STAT 641 Biostatistics II (3 hours lecture) 3 STAT 642 Introduction to Stochastic Processes (3 hours lecture) 3 STAT 645 Advanced Topics in Statistics (3 hours lecture) 3 STAT 646 Multivariate Analysis (3 hours lecture) 3 STAT 647 Practicum in Statistics II 3 STAT 648 Advanced Statistical Methods (3 hours lecture) 3 STAT 649 Independent Study in Statistics 3
2. ### CAPSTONE EXPERIENCE

Complete 1 of the following options:

1. #### THESIS OPTION

1. Complete for 3 semester hours.

 STAT 698 Master's Thesis 3
2. Submit the completed Thesis original and one copy to the Graduate Office. See Thesis Guidelines for details.

2. #### COMPREHENSIVE EXAMINATION

In the term that you will sit for exam, register for - which matches your major & advisor. Successfully pass exam.

## Course Descriptions:

### CMPT578: Introduction to Artificial Intelligence (3 hours lecture)

An introduction to artificial intelligence including representations of knowledge, problem solving, games, heuristics and backtracking, expert systems, theorem proving, the language LISP and PROLOG. 3 sh.

Prerequisites: CSIT 571 and departmental approval for students with Deferred or Conditional status.

### CMPT589: Computer Simulation of Discrete Systems (3 hours lecture)

Introduction to simulation and discrete simulation models. Queuing theory and stochastic processes. Simulation methodology including generation of random numbers and variates, design of simulation experiments, analysis of data generated by simulation experiments and validation of models. Survey of current simulation languages and selected applications. 3 sh.

Prerequisites: CSIT 545 and departmental approval for students with Deferred or Conditional status.

### CMPT593: Structured System Design and Analysis (3 hours lecture)

A study of the design of large scale computer systems relative to the constraints imposed by hardware, software and particular types of applications. Recent work in automated system design will be discussed. 3 sh.

Prerequisites: CSIT 555 and departmental approval for students with Deferred or Conditional status.

### CSIT515: Software Engineering (3 hours lecture)

Principles and methods for the analysis, design, implementation, testing, and verification of software systems. Topics include requirements analysis, domain analysis, implementation, testing, verification, and software management. Previous course CMPT 594 effective through Spring 2015. 3 sh.

Prerequisites: Departmental approval for students with Deferred or Conditional status.

### CSIT555: Database Systems (3 hours lecture)

Secondary storage devises. Data transfer. Primary and secondary access methods. Sequential and random access methods. File design. File organizations and corresponding processing. File maintenance. Sorting large files. Databases concepts. Required of majors. Previous course CMPT 586 effective through Spring 2015. 3 sh.

Prerequisites: Departmental approval for students with Deferred or Conditional status.

### CSIT571: Computer Algorithms and Analysis (3 hours lecture)

Algorithms: definition, design and analysis; sorting and searching techniques and introductory dynamic programming studied as algorithms with complexity theory and optimization techniques applied. Required of majors. Previous course CMPT 583 effective through Spring 2015. 3 sh.

Prerequisites: Departmental approval for students with Deferred or Conditional status.

### CSIT655: Advanced Database Systems (3 hours lecture)

To develop in-depth understanding of data base concepts and issues. The major emphasis of the course is on the conceptual (logical) organization, retrieval, and manipulation of data. Required of majors. Previous course CMPT 592 effective through Spring 2015. 3 sh.

Prerequisites: CSIS 555 and departmental approval for students with Deferred or Conditional status.

### CSIT670: Advanced Computer Algorithms and Analysis (3 hours lecture)

Dynamic programming, game trees and backtracking techniques, branch and bound, polynomial evaluation and fast Fourier transform algorithms; complexity and analysis, and optimization techniques will be applied. NP-hard problems and NP-completeness. Previous course CMPT 683 effective through Spring 2015. 3 sh.

Prerequisites: CSIT 571 and departmental approval for students with Deferred or Conditional status.

This course is a placeholder for matriculated master's students planning to take the departmental Comprehensive Examination. Successful completion of the Comprehensive Examination will result in a grade of P, unsuccessful students will receive a grade of NC. Students who do not successfully complete the Comprehensive Examination will be required to register for this placeholder course in each term for which they plan to take the examination (limited to three). 0 sh.

Prerequisites: Matriculation in Master's degree program required.

### MATH540: Probability (3 hours lecture)

Sample spaces and events, combinatorial analysis, conditional probability and stochastic independence, random variables and probability distributions, expected value and variance, probability generating functions, continuous random variables. 3 sh.

Prerequisites: MATH 340 and permission of graduate program coordinator.

### MATH560: Numerical Analysis (3 hours lecture)

Error analysis, interpolation and approximation theory, numerical solution of linear and nonlinear equations, numerical differentiation and integration, numerical solution of differential equations. 3 sh.

Prerequisites: MATH 335, and permission of graduate program coordinator.

### MATH568: Applied Mathematics: Continuous (3 hours lecture)

Formulation, manipulation and evaluation of mathematical models of continuous systems. Topics selected from: conservation principles and the classical equations of mathematical physics, applications of the qualitative and quantitative theory of ordinary and partial differential equations, optimization, calculus of variations, stability theory, stochastic models. 3 sh.

Prerequisites: MATH 335, and 340, and 420, and 425, and permission of graduate program coordinator.

### MATH569: Applied Mathematics: Discrete (3 hours lecture)

Introduction to the basic ideas of discrete mathematics and its applications. Counting principles, permutations, combinations, algorithms, complexity, graphs, trees, searching and sorting, recurrence relations, generating functions, inclusion-exclusion, the pigeonhole principle, chromatic number, eulerian chains and paths, hamiltonian chains and paths, flows in networks, finite Markov chains. 3 sh.

Prerequisites: MATH 335, and 340, and 425, and permission of graduate program coordinator.

### MATH580: Combinatorial Mathematics (3 hours lecture)

Arrangements and selections, binomial coefficients, Stirling numbers, generating functions, recurrence relations, inclusion-exclusion, Polya enumeration formula, combinatorial graph theory, combinatorial geometries. 3 sh.

Prerequisites: MATH 222 and graduate program coordinator's permission.

### MATH584: Operations Research (3 hours lecture)

An in-depth study of one or at most two topics in operations research, selected from linear programming and game theory, linear and nonlinear programming, queuing theory, inventory theory, simulation models. 3 sh.

Prerequisites: MATH 425 and STAT 440 and permission of graduate program coordinator.

### STAT541: Applied Statistics (3 hours lecture)

Review of estimation and hypothesis testing for one sample and two sample problems; introduction to non-parametric statistics and linear regression; fundamental principles of design, completely randomized design, randomized block design, latin square, and 2 factor design. 3 sh.

Prerequisites: STAT 330 or STAT 443 and permission of graduate program coordinator.

### STAT542: Statistical Theory I (3 hours lecture)

Discrete and continuous probability distributions, multivariate distributions, sampling theory, transformations, Chi-squared, 'F' and 't' distributions. Point estimation, properties of estimators, sufficiency, exponential families, interval estimation, hypothesis testing, power, Neyman-Pearson Lemma, likelihood ratio tests. The impact of the above theory on areas such as regression analysis, analysis of variance and analysis of discrete data. 3 sh.

Prerequisites: STAT 541 and permission of graduate program coordinator.

### STAT543: Statistical Theory II (3 hours lecture)

Discrete and continuous probability distributions, multivariate distributions, sampling theory, transformations, Chi-squared, 'F' and 't' distributions. Point estimation, properties of estimators, sufficiency, exponential families, interval estimation, hypothesis testing, power, Neyman-Pearson Lemma, likelihood ratio tests. The impact of the above theory on areas such as regression analysis, analysis of variance and analysis of discrete data. 3 sh.

Prerequisites: STAT 542 and permission of graduate program coordinator.

### STAT544: Statistical Computing (3 hours lecture)

Computer systems for data analysis and data graphics, and intermediate level statistical methodology are investigated. Several statistical computing packages are utilized and evaluated. 3 sh.

Prerequisites: STAT 541 or STAT 548, and CMPT 183, and permission of graduate program coordinator.

### STAT545: Practicum in Statistics I

An applied experience in which students work with practitioners in industry, government or research organizations utilizing statistical techniques in a research setting. Students will work with statisticians on projects involving experimental design and data collection as well as the analysis and interpretation of the data. May be repeated once. 3 sh.

Prerequisites: STAT 541, STAT 544, and STAT 547 or STAT 548, and permission of graduate program coordinator.

### STAT546: Non-Parametric Statistics (3 hours lecture)

Selected distribution-free tests and estimation techniques including sign, Kolmogorov-Smirnov, Wilcoxon signed rank, Mann-Whitney, Chi-square, rank correlation, Kendall's Tau, Kruskal-Wallace, Friedman, McNemar, and others. 3 sh.

Prerequisites: STAT 330 and permission of graduate program coordinator.

### STAT547: Design and Analysis of Experiments (3 hours lecture)

Fundamental principles of design; fixed, random and mixed models; factorial designs; designs with restricted randomization; split-plot design; confounding; fractional replication; experimental and sampling errors. 3 sh.

Prerequisites: STAT 541 or STAT 548, and permission of graduate program coordinator.

### STAT548: Applied Regression Analysis (3 hours lecture)

Fitting equations to data; matrices, linear regression; correlation; analysis of residuals; multiple regression; polynomial regression; partial correlation; stepwise regression; regression and model building; regression applied to analysis of variance problems; introduction to nonlinear regression. 3 sh.

Prerequisites: STAT 330 or STAT 443, and permission of graduate program coordinator.

### STAT549: Sampling Techniques (3 hours lecture)

Sampling and survey methodology; basic sampling theory; simple, stratified, random, cluster, systematic and area sampling. Sampling errors and estimation procedures. 3 sh.

Prerequisites: STAT 330 or STAT 443, and permission of graduate program coordinator.

### STAT552: Intermediate Statistics Methods (3 hours lecture)

Follow up to introductory statistical methods course. Principles of statistical inference; categorical data analysis; one and two-way anova; multiple linear regression; nonparametric methods; bootstrap methods. Examples from a wide variety of disciplines. Statistical software is used. 3 sh.

Prerequisites: STAT 330, permission of graduate program coordinator.

### STAT561: Statistical Data Mining I (3 hours lecture)

Introduction to the concepts and applications of a variety of data mining methods. Data mining is the process of selecting, exploring, and modeling large amounts of data to uncover previously unknown patterns in the data. Statistical methods covered include classification and regression trees, predictive modeling, and unsupervised learning. Hands-on applications to data sets from diverse fields. Statistical software is used. 3 sh.

Prerequisites: STAT 541 or STAT 548 or equivalent, permission of graduate program coordinator.

### STAT562: Statistical Data Mining II (3 hours lecture)

Continuation of STAT 561. An in-depth approach to the topics of STAT 561 including logistic regression, decision trees, classifier theory, predictive modeling and unsupervised learning methods. Mathematical details of these techniques as well as the computational methods for their implementation. Hands-on applications to data sets from diverse fields. Statistical software is used. 3 sh.

Prerequisites: STAT 548 and STAT 561, permission of graduate program coordinator.

### STAT570: Statistical Consulting (3 hours lecture)

An introduction to the statistical and interpersonal issues that arise in statistical consulting. Topics include communicating with scientists in other disciplines, technical writing and presentation, and statistical tools for consulting. Lectures center around real case studies presented by the instructor and invited speakers. Statistical software is used. Emphasis of the course is on the scientific, statistical, computational, and communication skills that a statistical consultant needs for interacting effectively with researchers from a wide range of disciplines. 3 sh.

Prerequisites: STAT 541 or equivalent, permission of graduate program coordinator.

### STAT583: Fundamentals of Data Analysis (3 hours lecture)

Theory and application of statistical methods for data analysis in professional industrial areas such as business, manufacturing, biomedical and marketing. Exploratory data analysis; principles of statistical inference; design and analysis of observational studies and experiments; linear regression. Additional topics based on real examples from other disciplines would include biostatistical methods, multivariate analysis, time series analysis, and data mining. Statistical software is used. 3 sh.

Prerequisites: STAT 330 and permission of the Graduate Program Coordinator.

### STAT595: Topics in Statistics (3 hours lecture)

Topics such as exploratory data analysis, statistical graphics, statistical quality control and statistical quality assurance, Bayesian methods and Markov chain Monte Carlo studies. May be repeated twice for a total of 9.0 credits. 3 sh.

Prerequisites: Permission of graduate program coordinator.

### STAT597: Research Methods in Statistical Science (3 hours lecture)

Preparation for research in statistical science. Application of mathematics and computing science to the development, modeling, validation and evaluation of statistical research methods. Identification of statistical issues in real world problems and novel applications of statistical methods to these problems. Development of research proposals in statistical science. 3 sh.

Prerequisites: STAT 552 or equivalent and departmental approval.

### STAT640: Biostatistics I (3 hours lecture)

Fundamental statistical concepts and methods used by statistical scientists in the health, biological, medical and pharmaceutical industries. Categorical data analysis, logistic regression, generalized linear models, nonparametric regression techniques. 3 sh.

Prerequisites: STAT 544, STAT 547, STAT 548, and permission of graduate program coordinator.

### STAT641: Biostatistics II (3 hours lecture)

Fundamental statistical concepts and methods used by statistical scientists in the health, biological, medical and pharmaceutical industries. Survival analysis and designs for clinical trials. 3 sh.

Prerequisites: STAT 544, STAT 547, STAT 548, and permission of graduate program coordinator.

### STAT642: Introduction to Stochastic Processes (3 hours lecture)

Generating functions, convolutions, recurrent events, random walk models, gambler's ruin problems, Markov chains and processes, time dependent stochastic processes, queuing theory and epidemic models. 3 sh.

Prerequisites: MATH 540 and permission of graduate program coordinator.

### STAT645: Advanced Topics in Statistics (3 hours lecture)

Recent developments in statistical science. Topics such as data mining, statistical genomics, computationally intensive data-analytic methods, statistical consulting, dynamic statistical graphics and visualization, applied time series analysis. May be repeated with no limit as long as the topic is different. 3 sh.

Prerequisites: Permission of graduate program coordinator.

### STAT646: Multivariate Analysis (3 hours lecture)

Analysis of multiple response variables simultaneously; covariance and the multivariate normal distribution; manova, discriminant functions; principle components and canonical correlations. 3 sh.

Prerequisites: STAT 541, STAT 548 and permission of graduate program coordinator.

### STAT647: Practicum in Statistics II

An applied experience in which students work with practitioners in industry, government or research organizations utilizing advanced statistical techniques in a research setting. Students will be expected to exhibit the ability to work independently on projects involving advanced techniques in experimental design, analysis and interpretation of data. May be repeated once. 3 sh.

Prerequisites: STAT 542, STAT 545, at least one 600-level course, and permission of graduate program coordinator.

### STAT648: Advanced Statistical Methods (3 hours lecture)

Advanced statistical concepts and methods used by statistical scientists in the analysis of designed experiments and observational studies. Response surface methodology, analysis of covariance, the general linear model, the cell means model and the analysis of variance of unbalanced or messy data. 3 sh.

Prerequisites: STAT 544, STAT 547, STAT 548, and permission of graduate program coordinator.

### STAT649: Independent Study in Statistics

Independent study under the direction of a faculty member, offering the opportunity to pursue topics in statistics which may be outside the scope of regular curricular offerings or may be an extension of an existing course or courses. Approval must be obtained from the graduate coordinator and faculty advisor. May be repeated once for a maximum of 6.0 credits during the graduate program. 3 sh.

Prerequisites: Permission of graduate program coordinator and departmental approval.

### STAT698: Master's Thesis

Independent study under faculty advisement. Students must follow the MSU Thesis Guidelines, which may be obtained from the Graduate School. Students should take STAT 699 if they do not complete STAT 698 within the semester. 3 sh.

Prerequisites: Permission of graduate program coordinator.

### STAT699:

Continuation of Master's Thesis project. Thesis extension will be graded IP (In Progress) until thesis is completed, at which time a grade of Pass or Fail will be given. Course may be repeated. 1 sh.

Prerequisites: STAT 698, permission of graduate program coordinator.