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Financial Engineering Prerequisite Course Descriptions |
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ACC 564
Corporate Financial Reporting
Prerequisites: A501.
I, II; 3 credits
The objective of this course is to transform students into a group of "sophisticated users" of corporate financial reports. Such training is essential to anyone who will use financial statement information as an input to economic decision-making. For example, a thorough understanding of financial statement information is crucial for doing fundamental analysis and valuation, and naturally complements. This course is a prerequisite for A318. Credit is granted for A565/A566 or A564.
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- ACC 712
Financial Statements Analysis
Prerequisites: ACC 564
I; 3 credits
This course is designed for those who expect to read, interpret, and analyze financial statements. This course adopts a modern approach to the topic of financial statements analysis. Although some attention is devoted to the mechanics of dissecting financial statements, the primary emphasis lies on development of an understanding of the market environment in which financial information is used.
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- Econ 435
Financial Economics
Prerequisites: Econ 401 and 405 or equivalent.
This course introduces the economic analysis of financial markets and financial decision-making. Topics covered include asset pricing theory (the valuation of stocks, bonds and options), net present value analysis, portfolio management, and financial market organization and behavior. The course develops the capacity to analyze investment strategies and policy issues from the standpoint of economic theory (as often opposed to conventional wisdom). Our main objectives are to understand why the financial markets work the way they do, to develop useful tools for the analysis of investment opportunities, and to use economic methods to think critically about policy issues such as government regulation of financial markets and the taxation of investment returns.
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- Econ 574
Forecasting and Modeling
Prerequisites: Econ 503.
This course investigates various economic forecasting techniques, with a primary focus on econometric modeling. A sequence of modeling topics is addressed, including model specification, data issues, model estimation and evaluation, simulation of model systems and policy simulation experiments. Special attention is given to preparing, generating, and adjusting forecasts. Alternative forecasting techniques (e.g., leading indicators, time series models, and judgment) are also briefly considered. Other topics include comparative forecasting performance, forecast services, and the current outlook. This course requires individual projects which emphasize on-line experience with modeling and forecasting techniques.
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- Econ 610
Stochastic Dynamic Optimization in Economics
Prerequisites: Econ 600 - 604, 603 and 604 can be taken concurrently, or by permission of instructor
II; 1.5 credits
This course studies stochastic dynamic optimization in discrete and continuous time. The focus is on optimal stopping and control. The discrete time theory explores discounted, positive, and negative stochastic dynamic programming, with applications to gambling, search theory, and multiarmed bandits. The continuous time portion first develops the math underlying Brownian motion, diffusions, Ito integrals, stochastic boundary value problems, and stochastic differential equations. It then investigates optimal stopping, smooth pasting, and optimal stochastic control. Applications, such as irreversible decision making in investment, exchange rate target zones, learning and R&D, and options are considered.
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- Econ 676
Applied Macroconmetrics
Prerequisites: Econ 671 and 672
The aim of this course is to equip students with a working knowledge of important econometric techniques used in monetary economics, financial economics, international economics, and econometric theory. The centerpiece of this course is the vector autoregressive model. The course is divided into six parts: (1) a review of the foundations of time series econometrics; (2) detrending methods; restricted and unrestricted estimation of stationary vector autoregressive and moving-average models; asymptotic, bootstrap and Bayesian inference; model selection and specification tests, forecasting; exogeneity and Granger causality; tests of forecast encompassing and tests of equal forecast accuracy; impulse response analysis, variance decompositions and historical decompositions; (3)estimation and inference in the presence of trends, structural change and unit roots in univariate models; (4) spurious regressions, unbalanced regressions and cointegration; (5) identification problems and the relationship between structural and reduced form models; and (6) estimation and inference for structural dynamic macroeconomic models and their relationship to vector autoregressive models
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Link to STAT 531/Econ 677 Course Outline (pdf)
- Econ 677
Statistical Analysis of Time Series
Prerequisites: Econ 674, Stat 511 or permission of instructor.
II; 3 credits
Decomposition of series; trend and regression as a special case of time series; cyclic components; smoothing techniques; representations including spectrogram, periodgram, etc., stochastic difference equations, autoregressive schemes, moving averages; large sample inference and prediction; covariance structure and spectral densities; hypothesis testing and estimation; applications and other topics.
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Electrical Engineering and Computer Science(EECS) (top)
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Link to EECS 481 Course Outline (pdf)
- EECS 481 (CS 481)
Software Engineering
Prerequisites: EECS 380
I, II; 4 credits
Pragmatic aspects of the production of software systems, dealing with structuring principles, design methodologies and informal analysis. Emphasis is given to development of large, complex software systems. A term project is usually required.
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- EECS 484 (CS 484)
Database Management Systems
Prerequisites: EECS 380 or IOE 373
I, II; 4 credits
Concepts and methods for the design, creation, query and management of large enterprise databases. Functions and characteristics of the leading database management systems. Query languages such as SQL, forms, embedded SQL, and application development tools. Database design, normalization, access methods, query optimization, transaction management and concurrency control, recovery, and integrity.
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- EECS 486 (CS 486)
Object-Oriented Software Development
Prerequisites: EECS 380
II; 4 credits
Object-based programming concepts such as data and program abstraction,
encapsulation, polymorphism, single and multiple inheritance, and reusable objects. Techniques for object-oriented system decomposition and class design. Study and use of class libraries and application frameworks. Programming projects in an objectoriented language currently standard in industry .
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Link to EECS 492 Course Outline (pdf)
- EECS 492 (CS 492)
Introduction to Artificial Intelligence
Prerequisites: EECS 380
I, II; 4credits
Fundamental concepts of AI, organized around the task of building computational agents. Core topics include search, logic, representation and reasoning, automated planning, decision making under uncertainty, and machine learning.
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- EECS 502
Stochastic Processes
Prerequisites: EECS 501
II odd years; 3 credits
Correlations and spectra. Quadratic mean calculus, including stochastic integrals and representations, wide-sense stationary processes (filtering, white noise, sampling, time averages, moving averages, auto-regression). Renewal and regenerative processes, Markov chains, random walk and run, branching processing, Markov jump processes, uniformization, reversibility, and queueing applications.
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- EECS 545 (CS 545)
Machine Learning
Prerequisites: EECS 492
II odd years; 3 credits
Survey of recent research on learning in artificial intelligence systems. Topics include learning based on examples, instructions, analogy, discovery, experimentation, observation, problem solving and explanation. The cognitive aspects of learning will also be studied.
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- EECS 547 (SI 652)
Electronic Commerce
Prerequisites: EECS 380 or SI 502 or permission of instructor.
II; 3 credits
Introduction to the design and analysis of automated commerce systems, from both a technological and social perspective. Infrastructure supporting search for commerce opportunities, negotiating terms of trade, and executing transactions. Issues of security, privacy, incentives, and strategy.
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- EECS 558
Stochastic Control
Prerequisites: EECS 501, EECS 560.
I odd years; 3 credits
Analysis and optimization of controlled stochastic systems. Models: linear and nonlinear stochastic controlled systems, controlled Markov chains. Optimization of systems described by Markov processes; dynamic programming under perfect and imperfect information, finite and infinite horizons. System identification: off-line, recursive. Stochastic adaptive control: Markov chains, self-tuning regulators, bandit problems.
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- EECS 581 (CS 581)
Software Engineering Tools
Prerequisites: EECS 481 or equivalent programming experience.
II; 3 credits
Fundamental areas of software engineering including lifecycle-paradigms,
metrics,and tools. Information hiding architecture, modular languages, design methodologies, incremental programming, and very high level languages.
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- EECS 584 (CS 584)
Advanced Database Systems
Prerequisites: EECS 484
II; 3 credits
Survey of advanced topics in database systems. Distributed databases, query processing, transaction processing. Effects of data models: object-oriented and deductive databases; architectures: main-memory and parallel repositories; distributed organizations: client-server and heterogeneous systems. Basic data management for emerging areas: internet applications, OLAP, data mining. Case studies of existing systems. Group projects.
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Link to FIN 503 Course Outline (pdf)
- FIN 503
Financial Management
I; 2.25 credits
Prerequisites:
Only MBA Day students are eligible to take this course. All Fall A core courses, or appropriate substitutes thereof, are prerequisites for this course. This course is the introductory core/course in Financial Management in the Day MBA program. The course is primarily devoted to the principles of financial valuation. We will first discuss the concept of present value in extensive detail, and then apply to the principles of valuation to value (a) real projects (or what is commonly referred to as capital budgeting) and (b) financial securities (stocks and bonds) under certainty. Since financial decision making virtually always involves risk and uncertainty, we will then introduce the concept of risk, and the relation between risk and return. We will integrate our knowledge of cash flows with our understanding of risk to modify capital budgeting techniques in the presence of risk and uncertainty. The course will end with an introductory treatment of international issues in finance, specifically the role of international parity conditions in cross-border capital budgeting decisions. Although the concepts of competitive capital markets and market efficiency will not be covered in a separate session, they will be woven in the fabric of the course. Students who take FIN 503 will not be given credit for FIN 513, 551, 552, or 553 if elected.
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| Link to FIN 513 Financial Analysis - Course Outline (pdf) |
Link to FIN 551 Course Outline 1 (pdf)
FIN 551 Course Outline 2 (pdf)
- FIN 551
Financial Management
I, II, IIIa; 3 credits
Prerequisites: Any of the following: BE 501 or BE 503, A 501, or SMS 501
This course introduces the basic concepts of finance. The first half of the course focuses on valuation techniques, the elations between risk and return and the workings of U.S. capital markets. Specific topics include Net Present Value, the Capital Asset Pricing Model, Capital Budgeting, and the Efficient Market Hypothesis. The second half of the course covers the major areas of financing decisions and internal finance.
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- FIN 565
Real Estate Feasibility Analysis
II; 3 credits
Prerequisites: RE 318 or UP 517
This course provides a practical, realistic exposure to public or private development while understanding how marketing, design, financing and environmental issues interrelate. This course is a complement to UP 613 (Architect/Planner as Developer) and to UP 517 (Real Estate Essentials). In this course, students work as a team typically composed of MBA's, Architecture or Urbhan Planner, Public Plicy, Engineering, and/or a law student to research and develop a feasibile plan for a relevant immediate development opportunity. Working on a local site and using this project as aresource for other Arch/UP courses is encouraged.
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Link to FIN 580 Course Outline (pdf)
- FIN 580
Options and Futures in Corporate Decision Making
Prerequisites: F551 or F552.
2.25 credits
This course introduces the student to options and fu-tures and illustrates their use in the context of corporate decision making. Companies increasingly issue securities with features that resemble options or futures. Options and futures also play an important role in risk management. Many corporate decisions have built-in strategic options which need to be evaluated. Credit is granted for F580/F618 OR F619.
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Link to FIN 608 Course Outline (pdf)
- FIN 608
Capital Markets and Investment Strategy
Prerequisites: F551 or F552
I, II; 2.25 credits
Elective
This course covers portfolio analysis, asset pricing models, and investment strategies. It used both the lecture and the case method if instruction to develop a practical understanding of some of the more important financial instruments and markets. Security valuation and management of investment strategies are major themes present throughout the course. A fundamental objective of the course is to enable students to gain a robust familiarity with approaches (such as security replication and arbitrage free pricing), that can be adapted to analysis of broad classes of financial assets and markets. Such skills are indispensable to investment analysis in an economic environment characterized by an unprecedented amount of financial innova-tion, both in the creation of new securities and in the development and evolution of financial institutions.
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Link to FIN 609 Course Outline (pdf)
- FIN 609
Fixed-Income Securities and Markets
Prerequisites: F551 or F552; F580 and 608
I, II; 1.5 credits
This course uses both cases and lectures to develop a practical understanding of some of the more important fixed income securities and markets. Derivatives and the management of fixed income securities are major themes present throughout the course. This course covers the term structure of interest rates, Treasury securities, strips, swaps and other fixed income derivatives.
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Link to FIN 610 Course Outline (pdf)
- FIN 610
Investments
Prerequisites: F551 or F552
3 credits
This course considers return and risk characteristics of various financial investment instruments, including common stocks, bonds, convertibles, and options, with emphasis on long-term results. Financial analysis and valuation of corporate securities are covered in some detail. Alternative portfolio management strategies in various security universes will also be covered. Concepts of modern portfolio theory are discussed and related to their implementation in the construction of portfolios for individual investors.
Credit is granted for F608/F609. Finance 610 is equivalent to taking 608 and 609.
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Link to FIN 612 Course Outline (pdf)
- FIN 612
Principles of International Finance
Prerequisites: F551/553
Ia; 1.5 credits
The purpose of this course is to provide the analytical framework required for understanding how changes in international financial conditions influence decisions faced by modern business leaders. The focus will be on interactions between cross-border trade and capital flows, inflation, interest rates, exchange rates, monetary and fiscal policy, and economic growth. Exchange rate regimes, debt and currency crises, and international financial institutions will also be explored. The course is tailored to students seeking careers in international banking and investment or with finance and strategy departments of corporations operating in work markets.
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- FIN 613
International Finance and International Financial Markets
Prerequisites: F551 or F553
3 credits
Topics covered in this course include: balance of payments analysis; the international monetary system; foreign exchange markets, including exchange rate forecasting; international capital flows and controls; international financial markets and institutions, particularly the Euromarkets; international portfolio and direct investment; and international finance and the developing countries. Guest lecturers supplement readings and case analyses of current problems. Fin 613 is equivalent to taking Fin 612 and Fin 614.
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Link to FIN 614 Course Outline (pdf)
- FIN 614
Managing International Portfolios
Prerequisites: F612
Ib; 1.5 credits
This course examines international financial markets, and the opportunities they present for achieving riskmanagement and asset allocation objectives. The principal focus will be on assets traded in liquid markets: currencies, equities, bonds, swaps, and other derivatives. Analytical tools for risk and return measurement, portfolio management, hedging, and implementing dynamic investment strategies in an international context will be examined. The course is tailored to students seeking careers in international banking and investment or with finance department of corporations operating in world markets .
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Link to FIN 615 Course Outline #1 (pdf)
FIN 615 Course Outline #2 (pdf)
- FIN 615
Valuation
Prerequisites: F551 or F553
I, II, III; 2.25credits
This course focuses on corporate asset management, in particular, on valuation. Topics include financial statement analysis, capital budgeting methods, estimating incremental cash flows, estimating cost of capital, valuation of projects, valuation of companies in takeovers, cross-border valuation, and valuation of strategic options. The course also covers working capital management.
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Link to FIN 618 Course Outline #1(pdf)
Link to FIN 618 Course Outline #2 (pdf)
Link to FIN 618 Course Outline #3 (pdf)
- FIN 618
Financial Risk Management
Prerequisites: F553 and F580
1.5 credits
Fin 618 follows 580. It develops in more detail some of the topics done in 580 such as optimal hedging with futures contracts and pricing options with dividends. It also introduces a number of new topics, such as exotic options, swaps, and the pricing of index, currency, and futures options. It does not treat interest rate derivatives, which are covered in FIN 638.
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Link to FIN 621 Course Outline (pdf)
- FIN 621
Corporate Financial Policy
Prerequisites: F551 or F553
I, II; 2.25credits
F621 is an elective course on corporate financial theory and practice with an emphasis on debt and equity management. Topics include the role of taxes, agency costs, and information asymmetries in capital structure design and financing decisions; the effects of risky debt and financial distress on corporate investment decisions; dividend policy and share repurchases; raising external capital. These topics will be covered in lectures on theoretical and conceptual issues and, depending on the instructor, the course will be either casebased or real-world example-based with discussions of large sample empirical evidence. This course is intended for those with career objectives in corporate treasury, consulting, investment banking, and general management.
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Link to FIN 622 Course Outline (pdf)
- FIN 622
Corporate Financial Engineering
Prerequisites: F580, F621
I, II; 1.5 credits
The process of creating new instruments is called financial engineering. Fin 622 is an advanced corporate finance course with an emphasis on corporate financial engineering. Topics include the costs and benefits of alternative means of going public and of raising capital; information, bargaining and misvaluation problems associate with financing new investments; how a firm should manage risk, and the role of financing in limiting conflicts of interest between managers and security holders. The course will also cover various instruments firms issue such as callable and convertible securities, warrants, and securities with other imbedded options to manage these problems. The course in intended for those with career objectives that involve corporate finance.
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Link to FIN 623 Course Outline (pdf)
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Link to FIN 629/329 Course Outline (pdf)
- FIN 629/329
Financing Research Commercialization
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Link to FIN 631 Course Outline (pdf)
- FIN 631
Banks and Financial Institutions
Prerequisites: F551 or F553
II; 1.5 credits
This course covers traditional banking activities such as lending, management of interest rate and liquidity risk and related regulatory issues. Credit is granted for F631/F632 OR F611.
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Link to FIN 632 Course Outline (pdf)
- FIN 632
Off-Balance Sheet Banking
Prerequisites: F631 and F580
II; 1.5 credits
This course covers off-balance sheet activities such as loan commitments, swaps securitization and regulatory issues. Credit is granted for F631/F632 OR F611.
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Link to FIN 640 Course Outline (pdf)
- FIN 640
Financial Trading
Prerequisites: F551
II; 1.5 credits
Fin 640 is a course about trading financial assets. The course is intended for MBA students that expect to take trading (market making) jobs, but it is also relevant for all students that expect to trade securities frequently. The course uses a combination of lectures and trading simulations/games conducted on the UMBS trading floor to make students comfortable with ideas like order type, bid-ask spread, information, and dynamic hedging. The class will also take a field trip to Chicago to visit a number of relevant sites. Students that have taken the core should be prepared for this course.
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Link to FIN 645 Course Outline (pdf)
- FIN 645
Advanced Valuation Techniques
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Link to FIN 647 Course Outline (pdf)
- FIN 647
Corporate Financial Strategy
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Link to FIN 743 Course Outline (pdf)
- FIN 743
Advanced Fundamental Equity Security Analysis
Review session at beginning of semester
IIB
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Industrial and Operations Engineering (top)
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- IOE 453 (MFG 456)
Derivative Instruments
Prerequisites: IOE 201, IOE 310, IOE 366
II; 3 credits
The main objectives of the course are first, to provide the students with a thorough understanding of the theory of pricing derivatives in the absence of arbitrage, and second, to develop the mathematical and numerical tools necessary to calculate derivative security prices. We begin by exploring the implications of the absence of static arbitrage. We study, for instance, forward and futures contracts. We proceed to develop the implications of no arbitrage in dynamic trading models; the binomial and Black-Scholes models. The theory is ap-plied to hedging and risk management. Credit not granted for both IOE 453/Mfg 456 and Math 423.
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Link to IOE 474 Course Outline (pdf)
- IOE 474
Simulation
Prerequisites: IOE 316, IOE 366, IOE 377
I, II; 4 credits
Simulation of complex discrete-event systems with applications in industrial and service organizations. Course topics include modeling and programming simulations in one or more high-level computer packages such as Pro Model or GPSS/H; input distribution modeling; generating random numbers; statistical analysis of simulation output data. The course will contain a team simulation project.
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Link to IOE 510 Course Outline (pdf)
- IOE 510
Linear Programming I
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Link to IOE 512 Course Outline (pdf)
- IOE 512
Dynamic Programming
Prerequisites: IOE 510. IOE 316
II; 3 credits
The techniques of recursive optimization and their use in solving multistage decision problems, applications to various types of problems, including an introduction to Markov decision processes.
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Link to IOE 515 Course Outline (pdf)
- IOE 515
Stochastic Processes
Prerequisites: IOE 316 or Stat 310
I; 3 credits
Introduction to nonmeasure theoretic stochastic processes. Poisson processes, renewal processes, and discrete time Markov chains. Applications in queuing systems, reliability, and inventory control.
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- IOE 552 (Math 552)
Financial Engineering I
Prerequisites: IOE 453 or Math 423
I, II; 3 credits
Theory and applications of financial engineering. Designing, structuring and pricing financial engineering products (including options, futures, swaps and other derivative securities) and their applications to financial and investment risk management. Mathematical methodology that forms the basis of financial engineering, applied stochastic processes and numerical methods in particular.
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- IOE 553 (Math 553)
Financial Engineering II
Prerequisites: IOE 453 or Math 423
I, II; 3 credits
Advanced issues in financial engineering: stochastic interest rate modeling and fixed income markets, derivative trading and arbitrage, international finance, risk management methodologies including Value-at-Risk and credit risk. Multivariate stochastic calculus methodology in finance: multivariate Ito’s lemma, Ito’s stochastic integrals, the Feynman-Kac theorem and Girsanov’s theorem.
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- IOE 565 (ME 563) (MFG 561)
Time Series Modeling, Analysis, Forecasting
Prerequisites: IOE 366 or ME 401
I; 3 credits
Time series modeling, analysis, forecasting, and control, identifying parametric time series, autovariance, spectra, Green’s function, trend and seasonality. Examples from manufacturing, quality control, ergonomics, inventory, and management.
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Link to IOE 591 Course Outline (pdf) Winter 2005
Link to IOE 591 Course Outline (pdf) Winter 2007
- IOE 591
Portfolio Risk Analysis
Prerequisites:
- Math 419 (or corresponding course)
- IOE316 (or corresponding course)
- IOE 453/Math 423
- IOE 515, or Math 526 (concurrent)
II; 3 credits
This course covers the foundations of portfolio Market Risk and Credit Risk. We model the market as a set of variables that drive prices. These variables are have a multivariate normal distribution. We derive closed form solutions for the distribution of portfolio returns in the case of linear portfolios. We then extend our domain to non-linear portfolios, and examine efficient techniques for Monte Carlo simulation of our portfolio. We examine several common measures of portfolio risk such as VaR (Value-at-Risk), marginal VaR, incremental VaR, and expected shortfall. We extend these techniques to model the credit risk of portfolios that are exposed to default risk.
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- IOE 612
Network Flow Algorithms
Prerequisites: IOE 510 (Math 561).
II; 3 credits
Flow Problems on networks. Maximum flow minimum cut theorem. Labeling algorithms. Circulation and feasibility theorems. Sensitivity analysis. Incidence matrices. Shortest routes. Minimum cost flows, out-of-kilter algorithms. Critical path networks, project cost curves. Multicommodity flow problem, biflows. Matching problems in graph theory.
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Mathematics Department (top) |
Link to Math 423 Course Outline (pdf)
- Math 423
Mathematics for Finance
Prerequisites: Math 217, Math 425 and EECS 183 or equivalents
I, II; 3 credits
Topics include risk and return theory, portfolio theory, capital asset pricing model, random walk model, stochastic processes, Black-Scholes Analysis, numerical methods and interest rate models. Alternatives: none. Subsequent Courses: none.
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- Math 506
Stochastic Analysis for Finance
I; 3 credits
The aim of this course is to teach the probabilistic techniques and concepts from the theory of stochastic processes required to understand the widely used financial models. In particular concepts such as martingales, stochastic integration/calculus, which are essential in computing the prices of derivative contracts, will be discussed. Pricing in complete/incomplete markets (in discrete/ continuous time) will be the focus of this course as well as some exposition of the mathematical tools that will be used such as Brownian motion, Levy processes and Markov processes.
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- Mathematics 521
Life Contingencies II
Prerequisites: Math 520 or permission
II; 3 credits
Topics include multiple life models--joint life, last survivor, contingent insurance; multiple decrement models---disability, withdrawal, retirement, etc.; and reserv-ing models for life insurance. Alternatives: Math 522 (Act. Theory of Pensions and Soc. Sec) is a parallel course covering mathematical models for prefunded retirement benefit programs. Subsequent Courses: None.
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Link to Math 523 Course Outline (pdf)
- Mathematics 523
Risk Theory
Prerequisites: Math 425
II; 3 credits
Topics include utility theory, application to buying general insurance to reduce risk, compound distribution models for risk portfolios, application of stochastic processes to the ruin problem and to reinsurance. Alternatives: None Subsequent Courses: None
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Link to MATH/StATS 525 Course Outline (pdf)
- Mathematics 525
Probability Theory
Prerequisites: Math 450 or, preferably, Math 451 or equivalent
I; 3 credits
This course presents a rigorous study of the mathematical theory of probability. The emphasis will be on fundamental concepts and proofs but examples and applications will also be discussed. Note: this course is intended as the first half of the 525/526 sequence which covers random processes as well. This is a core course for the Applied & Interdisciplinary Mathematics graduate program. Basic results and methods of both discrete and continuous probability theory, conditional probability and conditional expectation, discrete and continuous random variables, convergence of random variables and other topics.
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Link to MATH/StATS 526 Course Outline (pdf)
- Mathematics 526 (Stat 526)
Discr State Stoch Proc
Prerequisites: Math 525 or EECS 501
II; 3 credits
The material is divided between discrete and continuous time processes. In both, a general theory is developed and detailed study is made of some special classes of processes and their applications. Some specific topics include generating functions; recurrent events and the renewal theorem; random walks; Markov chains; branching processes; limit theorems; Markov chains in continuous time with emphasis on birth and death processes and queuing theory; an introduction to Brownian motion; stationary processes and martingales. Alternatives: This course is similar to EECS 502 and IOE 515, although the latter course tends to be somewhat more oriented to applications. It is crosslisted as Statistics 426. Subsequent Courses: The next courses in probability are Math 625 and 626, which presuppose substantial additional background (Math 597).
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Link to IOE 510 (pdf)
- Mathematics 561 (IOE 510) (SMS 518)
Linear Programming I
Prerequisites: Math 217, 417, or 419
I, II IIIa; 3 credits
Formulation of problems from the private and public sectors using the mathematical model of linear programming. Development of the simplex algorithm; duality theory and economic interpretations. Postoptimality (sensitivity) analysis; a lgorithmic complexity; the elipsoid method; scaling algorithms; applications and interpretations. Introduction to transportation and assignment problems; special purpose algorithms and advanced computational techniques. Students have opportunities to formulate and solve models developed from more complex case studies and use various computer programs. Alternatives: Cross-listed as IOE 510.
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- Mathematics 562 (IOE 511)
Cont. Optimization Math
Prerequisites: Math 217, 417 or 419
I; 3 credits
Survey of continuous optimization problems. Unconstrained optimization problems: unidirectional search techniques, gradient, conjugate direction, quasi-Newtonian methods; introduction to constrained optimization using techniques of unconstrained optimization through penalty transformation, augmented Lagrangians, and others; discussion of computer programs for various algorithms. Alternatives: Cross-listed as IOE 511. Subsequent Courses: This is not a prerequisite for any other course.
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Link to MATH 572 Course Outline (pdf)
- Mathematics 572
Meth for Sci Comput II
Prerequisites: Math 217, 419, or 513 and Math 454 or permission
II; 3 credits
Content varies somewhat with the instructor. Numerical methods for ordinary differential equations; Lax's equivalence theorem; finite difference and spectral methods for linear time dependent PDEs: diffusion equations, scalar first order hyperbolic equations, symmetric hyberbolic systems. Alternatives: There is no real alternative; Math 471 (Intro to Numerical Methods) covers a small part of the same material at a lower level. Math 571 and 572 m ay be taken in either order. Subsequent Courses: Math 671 (Analysis of Numerical Methods I) is an advanced course in numerical analysis with varying topics chosen by the instructor.
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Link to MATH 623 (pdf)
- Mathematics 623
Computational Finance
Prerequisites: Math 316 and 425 or 525
I, II; 3 credits
This is a course in computational methods in finance and financial modeling. Particular emphasis will be put on interest rate models and interest rate derivatives. Specific topics include Black-Scholes theory, noarbitrage and complete markets theory, term structure models, Hull and White models, Heath-Jarrow-Morton models, the stochastic differential equations and martingale approach, multinomial tree and Monte Carlo methods, the partial differential equations approach finite difference methods. Alternatives: None Subsequent Courses: None
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- Mathematics 663 (IOE 611)
Nonlinear Programming
Prerequisites: Math 561
Offerred alternate years ; 3 credits
Modeling, theorems of alternatives, convex sets, convex and generalized convex functions, convex inequality systems, necessary and sufficient optimality conditions, duality theory, algorithms for quadratic programming, linear complementarity problems and fixed point computing. Methods of direct search, Newton and quasi-Newton, gradient projection, feasible direction, reduced gradient; solution methods for nonlinear equations.
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Department of Statistics (top) |
Link to STAT 500 Course Outline (pdf)
- Statistics 500
Applied Statistics I
Prerequisites: Mathematics 417 and a course in statistics (Statistics 426 or permission)
FE Student Winter Only ; 3 credits
Linear models: Definition, fitting, identifiability, multicollinearity, Gauss-Markov theorem, variable selection, diagnostics, transformations, influential observations, robust procedures, ANOVA and analysis of covariance, interpretation of results, meaning of regression coefficients. Randomized block, factorial designs.
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- Statistics 508
Statistical Analysis of Financial Data
I; 3 credits
This course will cover basic topics involved in modeling and analysis of ?nancial data. These include linear and non-linear regression, nonparametric and semi-parametric regression, selected topics on the analysis of multivariate data and dimension-reduction, and time series analysis. Examples and data from ?nancial applications will be used to motivate and illustrate the methods.
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Link to MATH/StATS 526 Course Outline (pdf)
- Statistics 526 (Math 526)
Discrete State Stochastic Processes
Prerequisites: Statistics or Mathematics 525, or EECS 501, or permission.
II; 3 credits
Generating functions; recurrent events and the renewal theorem; random walks, Markov chains; branching processes; limit theorems; Markov chains in continuous time with emphasis on birth and death processes and queuing theory. An introduction to Brownian motion, stationary processes, and martingales.
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Link to STAT 531/Econ 677 Course Outline (pdf)
- Statistics 531
Statistical Analysis of Time Series
Prerequisites: Stat. 511, or permission.
I; 3 credits
Decomposition of series; trend and regression as a special case of time series, cyclic components; smoothing techniques; the variate difference method; representations including spectogram, periodogram,etc., stochastic difference equations, autoregressive schemes, moving averages; large sample inference and predictions; covariance structure and spectral densities; hypothesis testing and estimation; applications and other topics.
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- Stat 550 (IOE 560) (SMS 603)
Bayesian Decision Analysis
Prerequisites: Statistics 425 or Equivalent or permission by instructor
3 credit elective
Axiomatic foundations for personal probability and utility; interpretation and assessment of personal probability and utility; formulation of Bayesian decision problems; risk functions, admissibility; likelihood principle and properties of likelihood functions; natural conjugate prior distributions; improper and finitely additive prior distributions; examples of posterior distributions, including the general regression model and contingency tables; Bayesian credible intervals and hypothesis tests; applications to a variety of decision-making situations.
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- Statistics 560 (Biostat 685)
Elements of Nonparametric Statistics
Prerequisites: Statistics 511 or permission
I; 3 credits
Order statistics and confidence intervals for quantities; rank tests for the 1, 2, and k-sample problems; asymptotic distributions of rank statistics; asymptotic efficiency; randomization as a basis for inference; permutation tests; the sample distribution function and goodness of fit tests.
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- Statistics 630
Topics in Applied Probability
Prerequisites: Statistics 526 or Statistics 626
I; 3 credits
Advanced topics in applied probability, such as queueing theory, inventory problems, branching processes, stochastic difference and differential equations, etc. The course will study one or two advanced topics in detail.
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