Twin Cities campus
 
Twin Cities Campus

Economics M.A.

Economics
College of Liberal Arts
Link to a list of faculty for this program.
Contact Information
Department of Economics, 4-101 Hanson Hall, 1925 4th Street South, Minneapolis MN 55455 (612-625-6833; fax: 612-624-0209)
  • Program Type: Master's
  • Requirements for this program are current for Fall 2020
  • Length of program in credits: 30
  • This program does not require summer semesters for timely completion.
  • Degree: Master of Arts
Along with the program-specific requirements listed below, please read the General Information section of this website for requirements that apply to all major fields.
Note: Students are admitted only for the PhD in economics; the MA is an optional part of the PhD program. The economics graduate program offers degree work in both theoretical and applied fields of economics with an emphasis on quantitative economic analysis. The strong quantitative component in this degree emphasizes multivariate calculus, linear algebra, and econometrics (statistical methods of economic data). Economics coursework consists of microeconomic theory, macroeconomic theory, economic growth, price theory, cost-benefit analysis, econometrics, economic modelling and forecasting, industrial organization, economic development, game theory, optimization theory, and financial, computational, international, mathematical, monetary, public, and labor economics. Fields of specialization and written preliminary examinations include microeconomic theory, macroeconomic theory, econometrics, economic growth and development, financial economics, game theory, computational economics, industrial organization, labor economics, international economics, mathematical economics, monetary economics, and public economics.
Program Delivery
  • via classroom (the majority of instruction is face-to-face)
Prerequisites for Admission
Special Application Requirements:
Note: The Economics graduate program does not accept applications directly to the MA; rather, the MA is an additional or alternative credential for students admitted to the Economics PhD program.
For an online application or for more information about graduate education admissions, see the General Information section of this website.
Program Requirements
Plan B: Plan B requires 24 major credits and 6 credits outside the major. The final exam is written. A capstone project is required.
Capstone Project:Two Plan B projects consisting of research papers or literature reviews are required; the PhD written preliminary exams required in two fields outside of economic theory ("field exams") may be used to satisfy either or both of the Plan B projects.
This program may be completed with a minor.
Use of 4xxx courses towards program requirements is not permitted.
A minimum GPA of 3.00 is required for students to remain in good standing.
Coursework offered on both the A/F and S/N grade basis must be taken A/F, with a minimum grade of C+ earned for each.
Required Core Courses (16 Credits)
Take the following courses for 16 credits:
ECON 8101 - Microeconomic Theory (2.0 cr)
ECON 8102 - Microeconomic Theory (2.0 cr)
ECON 8103 - Microeconomic Theory (2.0 cr)
ECON 8104 - Microeconomic Theory (2.0 cr)
ECON 8105 - Macroeconomic Theory (2.0 cr)
ECON 8106 - Macroeconomic Theory (2.0 cr)
ECON 8107 - Macroeconomic Theory (2.0 cr)
ECON 8108 - Macroeconomic Theory (2.0 cr)
Economics Electives (8 Credits)
Select at least 8 credits of electives in consultation with the director of graduate studies.
ECON 8117 - Noncooperative Game Theory (2.0 cr)
ECON 8118 - Noncooperative Game Theory (2.0 cr)
ECON 8181 - Advanced Topics in Microeconomics (2.0 cr)
ECON 8182 - Advanced Topics in Microeconomics (2.0 cr)
ECON 8185 - Advanced Topics in Macroeconomics (2.0 cr)
ECON 8186 - Advanced Topics in Macroeconomics (2.0 cr)
ECON 8205 - Applied Econometrics (2.0 cr)
ECON 8206 - Applied Econometrics (2.0 cr)
ECON 8207 - Applied Econometrics (2.0 cr)
ECON 8208 - Applied Econometrics (2.0 cr)
ECON 8311 - Economic Growth and Development (2.0 cr)
ECON 8312 - Economic Growth and Development (2.0 cr)
ECON 8401 - International Trade and Payments Theory (2.0 cr)
ECON 8402 - International Trade and Payments Theory (2.0 cr)
ECON 8403 - International Trade and Payments Theory (2.0 cr)
ECON 8501 - Wages and Employment (2.0 cr)
ECON 8502 - Wages and Employment (2.0 cr)
ECON 8503 - Wages and Employment (2.0 cr)
ECON 8581 - Advanced Topics in Labor Economics (2.0 cr)
ECON 8582 - Advanced Topics in Labor Economics (2.0 cr)
ECON 8601 - Industrial Organization and Government Regulation (2.0 cr)
ECON 8602 - Industrial Organization and Government Regulation (2.0 cr)
ECON 8603 - Industrial Organization and Government Regulation (2.0 cr)
ECON 8701 - Monetary Economics (2.0 cr)
ECON 8702 - Monetary Economics (2.0 cr)
ECON 8703 - Monetary Economics (2.0 cr)
ECON 8704 - Financial Economics (2.0 cr)
ECON 8705 - Financial Economics (2.0 cr)
ECON 8801 - Public Economics (2.0 cr)
ECON 8802 - Public Economics (2.0 cr)
ECON 8803 - Public Economics (2.0 cr)
Outside Coursework (6 Credits)
Take at least 6 credits outside the major. Courses are selected in consultation with the director of graduate studies.
CSCI 5302 - Analysis of Numerical Algorithms (3.0 cr)
CSCI 5512 - Artificial Intelligence II (3.0 cr)
CSCI 5521 - Introduction to Machine Learning (3.0 cr)
CSCI 5523 - Introduction to Data Mining (3.0 cr)
CSCI 5525 - Machine Learning (3.0 cr)
CSCI 5715 - From GPS and Virtual Globes to Spatial Computing (3.0 cr)
CSCI 5801 - Software Engineering I (3.0 cr)
CSCI 8115 - Human-Computer Interaction and User Interface Technology (3.0 cr)
FINA 8802 - Theory of Capital Markets I: Discrete Time (2.0 cr)
FINA 8803 - Theory of Capital Markets II: Continuous Time (2.0 cr)
FINA 8810 - Topics in Asset Pricing (2.0 cr)
FINA 8812 - Corporate Finance I (2.0 cr)
FINA 8820 - Topics in Corporate Finance (2.0 cr)
IE 8534 - Advanced Topics in Operations Research (4.0 cr)
MATH 5485 - Introduction to Numerical Methods I (4.0 cr)
MATH 5486 - Introduction To Numerical Methods II (4.0 cr)
MATH 5615H - Honors: Introduction to Analysis I (4.0 cr)
MATH 5616H - Honors: Introduction to Analysis II (4.0 cr)
MATH 5651 - Basic Theory of Probability and Statistics (4.0 cr)
MATH 5652 - Introduction to Stochastic Processes (4.0 cr)
MATH 8201 - General Algebra (3.0 cr)
MATH 8271 - Lie Groups and Lie Algebras (3.0 cr)
MATH 8301 - Manifolds and Topology (3.0 cr)
MATH 8302 - Manifolds and Topology (3.0 cr)
MATH 8306 - Algebraic Topology (3.0 cr)
MATH 8441 - Numerical Analysis and Scientific Computing (3.0 cr)
MATH 8442 - Numerical Analysis and Scientific Computing (3.0 cr)
MATH 8445 - Numerical Analysis of Differential Equations (3.0 cr)
MATH 8501 - Differential Equations and Dynamical Systems I (3.0 cr)
MATH 8502 - Differential Equations and Dynamical Systems II (3.0 cr)
MATH 8520 - Topics in Dynamical Systems (1.0-3.0 cr)
MATH 8571 - Theory of Evolutionary Equations (3.0 cr)
MATH 8572 - Theory of Evolutionary Equations (3.0 cr)
MATH 8583 - Theory of Partial Differential Equations (3.0 cr)
MATH 8590 - Topics in Partial Differential Equations (1.0-3.0 cr)
MATH 8601 - Real Analysis (3.0 cr)
MATH 8602 - Real Analysis (3.0 cr)
MATH 8651 - Theory of Probability Including Measure Theory (3.0 cr)
MATH 8652 - Theory of Probability Including Measure Theory (3.0 cr)
MATH 8659 - Stochastic Processes (3.0 cr)
NSCI 5101 - Neurobiology I: Molecules, Cells, and Systems (3.0 cr)
PSY 5015 - Cognition, Computation, and Brain (3.0 cr)
PSY 5018H - Mathematical Models of Human Behavior (3.0 cr)
PSY 5062 - Cognitive Neuropsychology (3.0 cr)
PSY 5064 - Brain and Emotion (3.0 cr)
PSY 5065 - Functional Imaging: Hands-on Training (3.0 cr)
PSY 5137 - Introduction to Behavioral Genetics (3.0 cr)
STAT 5101 - Theory of Statistics I (4.0 cr)
STAT 8054 - Statistical Methods 4: Advanced Statistical Computing (3.0 cr)
STAT 8056 - Statistical Learning and Data Mining (3.0 cr)
STAT 8101 - Theory of Statistics 1 (3.0 cr)
STAT 8102 - Theory of Statistics 2 (3.0 cr)
STAT 8501 - Introduction to Stochastic Processes with Applications (3.0 cr)
 
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ECON 8101 - Microeconomic Theory
Credits: 2.0 [max 2.0]
Typically offered: Every Fall
Decision problems faced by the household and firm; theories of choice under conditions of certainty and uncertainty. Partial equilibrium analysis of competition and monopoly. General equilibrium analysis. Welfare economics: economic efficiency of alternative market structures, social welfare functions. Dynamics: stability of markets, capital theory. Seven-week course. prereq: 5151 or equiv, Math 2243 or equiv, concurrent registration is required (or allowed) in Math 5615 or concurrent registration in Math 8601, grad econ major or instr consent
ECON 8102 - Microeconomic Theory
Credits: 2.0 [max 2.0]
Typically offered: Every Fall
Decision problems faced by the household and firm; theories of choice under conditions of certainty and uncertainty. Partial equilibrium analysis of competition and monopoly. General equilibrium analysis. Welfare economics: economic efficiency of alternative market structures, social welfare functions. Dynamics: stability of markets, capital theory. Seven-week course. prereq: 8101, concurrent registration is required (or allowed) in Math 5615 or concurrent registration is required (or allowed) in Math 8601, grad econ major or instr consent
ECON 8103 - Microeconomic Theory
Credits: 2.0 [max 2.0]
Typically offered: Every Spring
Decision problems faced by the household and firm; theories of choice under conditions of certainty and uncertainty. Partial equilibrium analysis of competition and monopoly. General equilibrium analysis. Welfare economics: economic efficiency of alternative market structures, social welfare functions. Dynamics: stability of markets, capital theory. Seven-week course. prereq: 8102, concurrent registration is required (or allowed) in Math 5616 or concurrent registration is required (or allowed) in Math 8602 or comparable abstract math course, grad econ major or instr consent
ECON 8104 - Microeconomic Theory
Credits: 2.0 [max 2.0]
Typically offered: Every Spring
Decision problems faced by the household and firm; theories of choice under conditions of certainty and uncertainty. Partial equilibrium analysis of competition and monopoly. General equilibrium analysis. Welfare economics: economic efficiency of alternative market structures, social welfare functions. Dynamics: stability of markets, capital theory. Seven-week course. prereq: 8103, concurrent registration is required (or allowed) in Math 5616 or concurrent registration is required (or allowed) in Math 8602 or comparable abstract math course, grad econ major or instr consent
ECON 8105 - Macroeconomic Theory
Credits: 2.0 [max 2.0]
Typically offered: Every Fall
Dynamic general equilibrium models: solving for paths of interest rates, consumption, investment, prices. Models with uncertainty, search, matching, indivisibilities, private information. Implications for measurement and data reporting. Overlapping generations and dynasty models. Variational and recursive methods. This seven-week course meets with 4165. prereq: 5152 or equiv, Math 2243, Math 2263 or equiv or instr consent
ECON 8106 - Macroeconomic Theory
Credits: 2.0 [max 2.0]
Typically offered: Every Fall
Dynamic general equilibrium models: solving for paths of interest rates, consumption, investment, prices. Models with uncertainty, search, matching, indivisibilities, private information. Implications for measurement and data reporting. Overlapping generations and dynasty models. Variational and recursive methods. This seven-week course meets with 4166. prereq: 8105
ECON 8107 - Macroeconomic Theory
Credits: 2.0 [max 2.0]
Typically offered: Every Spring
Dynamic general equilibrium models: solving for paths of interest rates, consumption, investment, prices. Models with uncertainty, search, matching, indivisibilities, private information. Implications for measurement and data reporting. Overlapping generations and dynasty models. Variational and recursive methods. This seven-week course meets with 4167. prereq: 8106
ECON 8108 - Macroeconomic Theory
Credits: 2.0 [max 2.0]
Typically offered: Every Spring
Dynamic general equilibrium models: solving for paths of interest rates, consumption, investment, prices. Models with uncertainty, search, matching, indivisibilities, private information. Implications for measurement and data reporting. Overlapping generations and dynasty models. Variational and recursive methods. This seven-week course meets with 4168. prereq: 8107
ECON 8117 - Noncooperative Game Theory
Credits: 2.0 [max 2.0]
Typically offered: Every Fall
Solution concepts for noncooperative games in normal form, including Nash and perfect equilibrium and stable sets of equilibria. Extensive form games of perfect and incomplete information, sequential equilibrium, and consequences of stability for extensive form. Applications including bargaining and auctions. Seven-week course. prereq: Math 5616 or equiv or instr consent
ECON 8118 - Noncooperative Game Theory
Credits: 2.0 [max 2.0]
Typically offered: Every Fall & Spring
Solution concepts for noncooperative games in normal form, including Nash and perfect equilibrium and stable sets of equilibria. Extensive form games of perfect and incomplete information, sequential equilibrium, and consequences of stability for extensive form. Applications including bargaining and auctions. Seven-week course. prereq: 8117
ECON 8181 - Advanced Topics in Microeconomics
Credits: 2.0 [max 4.0]
Typically offered: Every Fall
Faculty and student presentations based on recent literature. Seven-week course. prereq: 8104 or instr consent
ECON 8182 - Advanced Topics in Microeconomics
Credits: 2.0 [max 4.0]
Typically offered: Every Spring
Faculty and student presentations based on recent literature. Seven-week course. prereq: 8104 or instr consent
ECON 8185 - Advanced Topics in Macroeconomics
Credits: 2.0 [max 4.0]
Typically offered: Every Fall & Spring
Faculty and student presentations based on recent literature. Seven-week course. prereq: 8108 or instr consent
ECON 8186 - Advanced Topics in Macroeconomics
Credits: 2.0 [max 4.0]
Typically offered: Periodic Spring
Faculty and student presentations based on recent literature. Seven-week course. prereq: 8108 or instr consent
ECON 8205 - Applied Econometrics
Credits: 2.0 [max 2.0]
Typically offered: Every Fall
Application in research, including classical and Bayesian approaches; formulation, comparison, and use of models and hypotheses; inference and prediction in structural models; simulation methods. Seven-week course. prereq: Math 4242 or equiv, concurrent registration is required (or allowed) in Econ 8101, concurrent registration is required (or allowed) in Econ 8105, concurrent registration is required (or allowed) in Stat 5101 or instr consent
ECON 8206 - Applied Econometrics
Credits: 2.0 [max 2.0]
Typically offered: Every Fall
Application in research, including classical and Bayesian approaches; formulation, comparison, and use of models and hypotheses; inference and prediction in structural models; simulation methods. Seven-week course. prereq: 8205, concurrent registration is required (or allowed) in 8102, concurrent registration is required (or allowed) in 8106, concurrent registration is required (or allowed) in Stat 5101 or instr consent
ECON 8207 - Applied Econometrics
Credits: 2.0 [max 2.0]
Typically offered: Every Spring
Application in research, including classical and Bayesian approaches; formulation, comparison, and use of models and hypotheses; inference and prediction in structural models; simulation methods. Seven-week course. prereq: 8206, concurrent registration is required (or allowed) in 8103, concurrent registration is required (or allowed) in 8107, concurrent registration is required (or allowed) in Stat 5102 or instr consent
ECON 8208 - Applied Econometrics
Credits: 2.0 [max 2.0]
Typically offered: Periodic Spring
Application in research, including classical and Bayesian approaches; formulation, comparison, and use of models and hypotheses; inference and prediction in structural models; simulation methods. Seven-week course. prereq: 8207, concurrent registration is required (or allowed) in 8104, concurrent registration is required (or allowed) in 8108, concurrent registration is required (or allowed) in Stat 5102 or instr consent
ECON 8311 - Economic Growth and Development
Credits: 2.0 [max 2.0]
Typically offered: Every Fall
Methods of analyzing dynamical systems; applying methods to new models of growth and development; deriving and evaluating models' quantitative implications in light of growth and development in a number of countries. Seven-week course. prereq: 8104, 8106 or instr consent
ECON 8312 - Economic Growth and Development
Credits: 2.0 [max 2.0]
Typically offered: Every Fall & Spring
Methods of analyzing dynamical systems; applying methods to new models of growth and development; deriving and evaluating models' quantitative implications in light of growth and development in a number of countries. Seven-week course. prereq: 8311 or instr consent
ECON 8401 - International Trade and Payments Theory
Credits: 2.0 [max 2.0]
Typically offered: Every Fall
Impact of trade on factor rentals. Stolper-Samuelson, Rybczynski, and factor price equalization theorems. Heckscher-Ohlin theorem. Derivation of offer curves and general international equilibrium. Transfer problem. Seven-week course. prereq: 8103, 8105 or instr consent
ECON 8402 - International Trade and Payments Theory
Credits: 2.0 [max 2.0]
Typically offered: Every Fall & Spring
Tariffs, quotas, and other barriers to trade; gains from trade; trading blocs; increasing returns; growth. This is a seven-week course. prereq: 8401 or instr consent
ECON 8403 - International Trade and Payments Theory
Credits: 2.0 [max 2.0]
Typically offered: Every Spring
International business cycles; exchange rates; capital movements; international liquidity. This is a 7-week course. prereq: 8402 or instr consent
ECON 8501 - Wages and Employment
Credits: 2.0 [max 4.0]
Typically offered: Every Fall
Economic analysis of labor markets and their operation under conditions of both individual and collective bargaining. Implications of labor market operations for resource allocation, wage and price stability, income and employment growth. Wage structures and wage levels. Wage and employment theories and practices. Economic impacts of unions. Seven-week course. prereq: 8102, 8106 or instr consent
ECON 8502 - Wages and Employment
Credits: 2.0 [max 4.0]
Typically offered: Every Fall & Spring
Economic analysis of labor markets and their operation under conditions of both individual and collective bargaining. Implications of labor market operations for resource allocation, wage and price stability, income and employment growth. Wage structures and wage levels. Wage and employment theories and practices. Economic impacts of unions. Seven-week course. prereq: 8501 or instr consent
ECON 8503 - Wages and Employment
Credits: 2.0 [max 4.0]
Typically offered: Every Spring
Economic analysis of labor markets and their operation under conditions of individual/collective bargaining. Implications of labor market operations for resource allocation, wage/price stability, income/employment growth. Wage structures and wage levels. Wage/employment theories/practices. Economic impacts of unions. Seven-week course. prereq: 8502 or instr consent
ECON 8581 - Advanced Topics in Labor Economics
Credits: 2.0 [max 4.0]
Typically offered: Every Fall & Spring
Faculty and student presentations based on recent literature. Seven-week course. prereq: 8502 or instr consent
ECON 8582 - Advanced Topics in Labor Economics
Credits: 2.0 [max 4.0]
Typically offered: Every Fall & Spring
Faculty and student presentations based on recent literature. Seven-week course. prereq: 8502 or instr consent
ECON 8601 - Industrial Organization and Government Regulation
Credits: 2.0 [max 2.0]
Typically offered: Every Fall
Behavior of businesses and industries: productivity, firm size distributions, exit-entry dynamics, etc. Theories of the firm, industry structure and performance, invention and innovation, and technology adoption. Positive and normative theories of regulation. Seven-week course. prereq: 8102 or instr consent
ECON 8602 - Industrial Organization and Government Regulation
Credits: 2.0 [max 2.0]
Typically offered: Every Fall
Behavior of businesses and industries: productivity, firm size distributions, exit-entry dynamics, etc. Theories of the firm, industry structure and performance, invention and innovation, and technology adoption. Positive and normative theories of regulation. Seven-week course. prereq: 8601 or instr consent
ECON 8603 - Industrial Organization and Government Regulation
Credits: 2.0 [max 2.0]
Typically offered: Every Spring
Behavior of businesses and industries: productivity, firm size distributions, exit-entry dynamics, etc. Theories of the firm, industry structure and performance, invention and innovation, and technology adoption. Positive and normative theories of regulation. Seven-week course. prereq: 8602 or instr consent
ECON 8701 - Monetary Economics
Credits: 2.0 [max 2.0]
Typically offered: Every Fall
Economic role of principal financial institutions. Determinants of value of money. Principal problems of monetary policy. Seven-week course. prereq: 8103, 8106 or instr consent
ECON 8702 - Monetary Economics
Credits: 2.0 [max 2.0]
Typically offered: Every Fall & Spring
Economic role of principal financial institutions. Determinants of value of money. Principal problems of monetary policy. Seven-week course. prereq: 8701 or instr consent
ECON 8703 - Monetary Economics
Credits: 2.0 [max 4.0]
Typically offered: Every Spring
Economic role of principal financial institutions. Determinants of value of money. Principal problems of monetary policy. Seven-week course. prereq: 8702 or instr consent
ECON 8704 - Financial Economics
Credits: 2.0 [max 2.0]
Typically offered: Every Fall
Role of financial institutions in efficient allocation of risk; multiperiod and continuous-time securities markets; theory of firm under uncertainty; financial intermediation; derivation of empirical asset-pricing relationships; tests concerning alternative market structures. Seven-week course. prereq: 8103, 8106 or instr consent
ECON 8705 - Financial Economics
Credits: 2.0 [max 2.0]
Typically offered: Every Fall & Spring
Role of financial institutions in efficient allocation of risk; multiperiod and continuous-time securities markets; theory of firm under uncertainty; financial intermediation; derivation of empirical asset-pricing relationships; tests concerning alternative market structures. Seven-week course. prereq: 8704 or instr consent
ECON 8801 - Public Economics
Credits: 2.0 [max 4.0]
Typically offered: Every Fall & Spring
Theories of public choice and role of government in economy. Economic effects of taxes, public debt, and public expenditure. Current problems in economics of public sector, including political economy. Seven-week course. prereq: 8103, 8106 or instr consent
ECON 8802 - Public Economics
Credits: 2.0 [max 2.0]
Typically offered: Every Fall & Spring
Theories of public choice and role of government in economy. Economic effects of taxes, public debt, and public expenditure. Current problems in economics of public sector, including political economy. Seven-week course. prereq: 8801 or instr consent
ECON 8803 - Public Economics
Credits: 2.0 [max 2.0]
Typically offered: Periodic Spring
Theories of public choice and role of government in economy. Economic effects of taxes, public debt, and public expenditure. Current problems in economics of public sector, including political economy. Seven-week course. prereq: 8802 or instr consent
CSCI 5302 - Analysis of Numerical Algorithms
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Additional topics in numerical analysis. Interpolation, approximation, extrapolation, numerical integration/differentiation, numerical solutions of ordinary differential equations. Introduction to optimization techniques. prereq: 2031 or 2033 or instr consent
CSCI 5512 - Artificial Intelligence II
Credits: 3.0 [max 3.0]
Course Equivalencies: CSci 5512W/5512
Typically offered: Every Spring
Uncertainty in artificial intelligence. Probability as a model of uncertainty, methods for reasoning/learning under uncertainty, utility theory, decision-theoretic methods. prereq: [STAT 3021, 4041] or instr consent
CSCI 5521 - Introduction to Machine Learning
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall
Problems of pattern recognition, feature selection, measurement techniques. Statistical decision theory, nonstatistical techniques. Automatic feature selection/data clustering. Syntactic pattern recognition. Mathematical pattern recognition/artificial intelligence. prereq: [[2031 or 2033], STAT 3021] or instr consent
CSCI 5523 - Introduction to Data Mining
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall & Spring
Data pre-processing techniques, data types, similarity measures, data visualization/exploration. Predictive models (e.g., decision trees, SVM, Bayes, K-nearest neighbors, bagging, boosting). Model evaluation techniques, Clustering (hierarchical, partitional, density-based), association analysis, anomaly detection. Case studies from areas such as earth science, the Web, network intrusion, and genomics. Hands-on projects. prereq: 4041 or equiv or instr consent
CSCI 5525 - Machine Learning
Credits: 3.0 [max 3.0]
Typically offered: Fall Even Year
Models of learning. Supervised algorithms such as perceptrons, logistic regression, and large margin methods (SVMs, boosting). Hypothesis evaluation. Learning theory. Online algorithms such as winnow and weighted majority. Unsupervised algorithms, dimensionality reduction, spectral methods. Graphical models. prereq: Grad student or instr consent
CSCI 5715 - From GPS and Virtual Globes to Spatial Computing
Credits: 3.0 [max 3.0]
Typically offered: Spring Even Year
Mathematical concepts, geo-information, representations, algorithms, data-structures/access methods, analysis, architectures, interfaces, reasoning, time. prereq: Familiarity with Java, C++, or Python
CSCI 5801 - Software Engineering I
Credits: 3.0 [max 3.0]
Prerequisites: 2041 or #
Typically offered: Every Fall
Advanced introduction to software engineering. Software life cycle, development models, software requirements analysis, software design, coding, maintenance. prereq: 2041 or instr consent
CSCI 8115 - Human-Computer Interaction and User Interface Technology
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall & Spring
Current research issues in human-computer interaction, user interface toolkits and frameworks, and related areas. Research techniques, model-based development, gesture-based interfaces, constraint-based programming, event processing models, innovative systems, HCI in multimedia systems. prereq: 5115 or instr consent
FINA 8802 - Theory of Capital Markets I: Discrete Time
Credits: 2.0 [max 2.0]
Typically offered: Every Spring
Modern asset pricing theory. Static/discrete time frameworks. Fundamental asset pricing equation. Classical finance models: CAPM, consumption-based CAPM, APT. Complete markets, representative agent, Pareto optimality. Challenges to theories. Approaches such as habit formation, heterogeneous agents (incomplete markets) model. prereq: [Econ 8101, Econ 8102, business admin PhD student] or instr consent
FINA 8803 - Theory of Capital Markets II: Continuous Time
Credits: 2.0 [max 2.0]
Typically offered: Every Spring
Continuous-time financial economics. Emphasizes mathematical/statistical tools. Ito processes, Girsanov?s theorem, risk-neutral pricing. How to formulate/analyze continuous-time models. prereq: [Econ 8101, Econ 8102, Bbsiness admin PhD student] or instr consent
FINA 8810 - Topics in Asset Pricing
Credits: 2.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Fall Even Year
Current topics in asset pricing literature. Students read papers on these topics, rederive the main results, identify the main assumptions and thus identify ideas on how to improve upon the current literature. prereq: Business admin PhD student or instr consent
FINA 8812 - Corporate Finance I
Credits: 2.0 [max 2.0]
Typically offered: Every Fall & Spring
Corporate control, managerial incentives, corporate governance, capital structure. What assets are collected within firm. What determines boundaries of firm. Empirical evidence in support of theoretical models. Modern theories of firm, based on incomplete contracts. How corporate finance decisions expand/limit scope of firm. prereq: [Econ 8103, Econ 8104, business admin PhD student] or instr consent
FINA 8820 - Topics in Corporate Finance
Credits: 2.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Fall Odd Year
Current topics in corporate finance literature. Students read current papers, rederive the main results, identify the main assumptions and thus identify ideas on how to improve on the current literature. prereq: Business admin PhD student or instr consent
IE 8534 - Advanced Topics in Operations Research
Credits: 4.0 [max 8.0]
Typically offered: Every Fall & Spring
Special topics determined by instructor. Examples include Markov decision processes, stochastic programming, integer/combinatorial optimization, and queueing networks. prereq: 5531, 8532
MATH 5485 - Introduction to Numerical Methods I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Solution of nonlinear equations in one variable. Interpolation, polynomial approximation. Methods for solving linear systems, eigenvalue problems, systems of nonlinear equations. prereq: [2243 or 2373 or 2573], familiarity with some programming language
MATH 5486 - Introduction To Numerical Methods II
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Numerical integration/differentiation. Numerical solution of initial-value problems, boundary value problems for ordinary differential equations, partial differential equations. prereq: 5485
MATH 5615H - Honors: Introduction to Analysis I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Axiomatic treatment of real/complex number systems. Introduction to metric spaces: convergence, connectedness, compactness. Convergence of sequences/series of real/complex numbers, Cauchy criterion, root/ratio tests. Continuity in metric spaces. Rigorous treatment of differentiation of single-variable functions, Taylor's Theorem. prereq: [[2243 or 2373], [2263 or 2374], [2283 or 3283]] or 2574
MATH 5616H - Honors: Introduction to Analysis II
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Rigorous treatment of Riemann-Stieltjes integration. Sequences/series of functions, uniform convergence, equicontinuous families, Stone-Weierstrass Theorem, power series. Rigorous treatment of differentiation/integration of multivariable functions, Implicit Function Theorem, Stokes' Theorem. Additional topics as time permits. prereq: 5615
MATH 5651 - Basic Theory of Probability and Statistics
Credits: 4.0 [max 4.0]
Course Equivalencies: 00259 - MATH 4653/Math 5651/Stat 5101
Typically offered: Every Fall & Spring
Logical development of probability, basic issues in statistics. Probability spaces, random variables, their distributions/expected values. Law of large numbers, central limit theorem, generating functions, sampling, sufficiency, estimation. prereq: [2263 or 2374 or 2573], [2243 or 2373]; [2283 or 2574 or 3283] recommended.
MATH 5652 - Introduction to Stochastic Processes
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Random walks, Markov chains, branching processes, martingales, queuing theory, Brownian motion. prereq: 5651 or Stat 5101
MATH 8201 - General Algebra
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall
Groups through Sylow, Jordan-H[o]lder theorems, structure of finitely generated Abelian groups. Rings and algebras, including Gauss theory of factorization. Modules, including projective and injective modules, chain conditions, Hilbert basis theorem, and structure of modules over principal ideal domains. prereq: 4xxx algebra or equiv or instr consent
MATH 8271 - Lie Groups and Lie Algebras
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Periodic Fall
Definitions and basic properties of Lie groups and Lie algebras; classical matrix Lie groups; Lie subgroups and their corresponding Lie subalgebras; covering groups; Maurer-Cartan forms; exponential map; correspondence between Lie algebras and simply connected Lie groups; Baker-Campbell-Hausdorff formula; homogeneous spaces. prereq: 8302 or instr consent
MATH 8301 - Manifolds and Topology
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall
Classification of compact surfaces, fundamental group/covering spaces. Homology group, basic cohomology. Application to degree of a map, invariance of domain/dimension. prereq: [Some point-set topology, algebra] or instr consent
MATH 8302 - Manifolds and Topology
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Spring
Smooth manifolds, tangent spaces, embedding/immersion, Sard's theorem, Frobenius theorem. Differential forms, integration. Curvature, Gauss-Bonnet theorem. Time permitting: de Rham, duality in manifolds. prereq: 8301 or instr consent
MATH 8306 - Algebraic Topology
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Periodic Fall
Singular homology, cohomology theory with coefficients. Eilenberg-Stenrod axioms, Mayer-Vietoris theorem. prereq: 8301 or instr consent
MATH 8441 - Numerical Analysis and Scientific Computing
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Approximation of functions, numerical integration. Numerical methods for elliptic partial differential equations, including finite element methods, finite difference methods, and spectral methods. Grid generation. prereq: [4xxx analysis, 4xxx applied linear algebra] or instr consent
MATH 8442 - Numerical Analysis and Scientific Computing
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Numerical methods for integral equations, parabolic partial differential equations, hyperbolic partial differential equations. Monte Carlo methods. prereq: 8441 or instr consent; 5477-5478 recommended for engineering and science grad students
MATH 8445 - Numerical Analysis of Differential Equations
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall
Finite element and finite difference methods for elliptic boundary value problems (e.g., Laplace's equation) and solution of resulting linear systems by direct and iterative methods. prereq: 4xxx numerical analysis, 4xxx partial differential equations or instr consent
MATH 8501 - Differential Equations and Dynamical Systems I
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall
Existence, uniqueness, continuity, and differentiability of solutions. Linear theory and hyperbolicity. Basics of dynamical systems. Local behavior near a fixed point, a periodic orbit, and a homoclinic or heteroclinic orbit. Perturbation theory. prereq: 4xxx ODE or instr consent
MATH 8502 - Differential Equations and Dynamical Systems II
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Spring
Stable, unstable, and center manifolds. Normal hyperbolicity. Nonautonomous dynamics and skew product flows. Invariant manifolds and quasiperiodicity. Transversality and Melnikov method. Approximation dynamics. Morse-Smale systems. Coupled oscillators and network dynamics. prereq: 8501 or instr consent
MATH 8520 - Topics in Dynamical Systems
Credits: 1.0 -3.0 [max 12.0]
Grading Basis: A-F or Aud
Typically offered: Periodic Fall & Spring
Current research. prereq: 8502
MATH 8571 - Theory of Evolutionary Equations
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall
Infinite dimensional dynamical systems, global attractors, existence and robustness. Linear semigroups, analytic semigroups. Linear and nonlinear reaction diffusion equations, strong and weak solutions, well-posedness of solutions. prereq: 8502 or instr consent
MATH 8572 - Theory of Evolutionary Equations
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Periodic Spring
Dynamics of Navier-Stokes equations, strong/weak solutions, global attractors. Chemically reacting fluid flows. Dynamics in infinite dimensions, unstable manifolds, center manifolds perturbation theory. Inertial manifolds, finite dimensional structures. Dynamical theories of turbulence. prereq: 8571 or instr consent
MATH 8583 - Theory of Partial Differential Equations
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall
Classification of partial differential equations/characteristics. Laplace, wave, heat equations. Some mixed problems. prereq: [Some 5xxx PDE, 8601] or instr consent
MATH 8590 - Topics in Partial Differential Equations
Credits: 1.0 -3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall & Spring
Research topics. prereq: 8602; offered for one yr or one sem as circumstances warrant
MATH 8601 - Real Analysis
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall
Set theory/fundamentals. Axiom of choice, measures, measure spaces, Borel/Lebesgue measure, integration, fundamental convergence theorems, Riesz representation. prereq: 5616 or instr consent
MATH 8602 - Real Analysis
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Spring
Radon-Nikodym, Fubini theorems. C(X). Lp spaces (introduction to metric, Banach, Hilbert spaces). Stone-Weierstrass theorem. Basic Fourier analysis. Theory of differentiation. prereq: 8601 or instr consent
MATH 8651 - Theory of Probability Including Measure Theory
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Probability spaces. Distributions/expectations of random variables. Basic theorems of Lebesque theory. Stochastic independence, sums of independent random variables, random walks, filtrations. Probability, moment generating functions, characteristic functions. Laws of large numbers. prereq: 5616 or instr consent
MATH 8652 - Theory of Probability Including Measure Theory
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Conditional distributions and expectations, convergence of sequences of distributions on real line and on Polish spaces, central limit theorem and related limit theorems, Brownian motion, martingales and introduction to other stochastic sequences. prereq: 8651 or instr consent
MATH 8659 - Stochastic Processes
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
In-depth coverage of various stochastic processes and related concepts, such as Markov sequences and processes, renewal sequences, exchangeable sequences, stationary sequences, Poisson point processes, Levy processes, interacting particle systems, diffusions, and stochastic integrals. prereq: 8652 or instr consent
NSCI 5101 - Neurobiology I: Molecules, Cells, and Systems
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall & Spring
This course discusses the basic principles of cellular and molecular neurobiology and nervous systems. The main topics include: Organization of simple networks, neural systems and behavior; how the brain develops and the physiology and communication of neurons and glia; the molecular and genetic basis of cell organization; ion channel structure and function; the molecular basis of synaptic receptors; transduction mechanisms and second messengers; intracellular regulation of calcium; neurotransmitter systems, including excitation and inhibition, neuromodulation, system regulation and the cellular basis of learning, memory and cognition. The course is intended for students majoring in neuroscience, but is open to all students with the required prerequisites.
PSY 5015 - Cognition, Computation, and Brain
Credits: 3.0 [max 3.0]
Typically offered: Spring Even Year
Human cognitive abilities (perception, memory, attention) from different perspectives (e.g., cognitive psychological approach, cognitive neuroscience approach). prereq: [Honors or grad] or [[jr or sr], [3011 or 3031 or 3051 or 3061]] or instr consent
PSY 5018H - Mathematical Models of Human Behavior
Credits: 3.0 [max 3.0]
Grading Basis: A-F only
Typically offered: Periodic Fall
Mathematical models of complex human behavior, including individual/group decision making, information processing, learning, perception, and overt action. Specific computational techniques drawn from decision theory, information theory, probability theory, machine learning, and elements of data analysis. prereq: Math 1271 or instr consent
PSY 5062 - Cognitive Neuropsychology
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Consequences of different types of brain damage on human perception/cognition. Neural mechanisms of normal perceptual/cognitive functions. Vision/attention disorders, split brain, language deficits, memory disorders, central planning deficits. Emphasizes function/phenomenology. Minimal amount of brain anatomy. prereq: Grad or [[jr or sr], [3011 or 3031 or 3051 or 3061]] or instr consent
PSY 5064 - Brain and Emotion
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Spring Odd Year
Introduction to affective neuroscience. How brain promotes emotional/motivated behavior in animals/humans. Biological theories of emotion in historical/current theoretical contexts. Fundamental brain motivational systems, including fear, pleasure, attachment, stress, and regulation of motivated behavior. Implications for emotional development, vulnerability to psychiatric disorders. prereq: 3061 or 5061 or instr consent
PSY 5065 - Functional Imaging: Hands-on Training
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Basic neuroimaging techniques/functional magnetic resonance imaging (fMRI). First half of semester covers basic physical principles. Second half students design/execute fMRI experiment on Siemens 3 Tesla scanner. prereq: [3801 or equiv], [3061 or NSCI 3101], instr consent
PSY 5137 - Introduction to Behavioral Genetics
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Genetic methods for studying human/animal behavior. Emphasizes nature/origin of individual differences in behavior. Twin and adoption methods. Cytogenetics, molecular genetics, linkage/association studies. prereq: 3001W or equiv or instr consent
STAT 5101 - Theory of Statistics I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Logical development of probability, basic issues in statistics. Probability spaces. Random variables, their distributions and expected values. Law of large numbers, central limit theorem, generating functions, multivariate normal distribution. prereq: [Math 2263 or Math 2374 or Math 2573H], [CSCI 2033 or Math 2373 or Math 2243]
STAT 8054 - Statistical Methods 4: Advanced Statistical Computing
Credits: 3.0 [max 3.0]
Prerequisites: STAT 8053 or #
Grading Basis: A-F or Aud
Typically offered: Every Spring
Optimization, numerical integration, Markov chain Monte Carlo, related topics. prereq: STAT 8053 or instr consent
STAT 8056 - Statistical Learning and Data Mining
Credits: 3.0 [max 3.0]
Course Equivalencies: 01358 - PubH 7475/PubH 8475/Stat 8056
Grading Basis: OPT No Aud
Typically offered: Periodic Spring
Statistical techniques for extracting useful information from data. Linear discriminant analysis, tree-structured classifiers, feed-forward neural networks, support vector machines, other nonparametric methods, classifier ensembles (such as bagging/boosting), unsupervised learning. prereq: [[[6450, 6451, 6452] or STAT 5303 or equiv], [biostatistics or statistics PhD student]] or instr consent
STAT 8101 - Theory of Statistics 1
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Review of linear algebra. Introduction to probability theory. Random variables, their transformations/expectations. Standard distributions, including multivariate Normal distribution. Probability inequalities. Convergence concepts, including laws of large numbers, Central Limit Theorem. delta method. Sampling distributions. prereq: Statistics grad major or instr consent
STAT 8102 - Theory of Statistics 2
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Statistical inference. Sufficiency. Likelihood-based methods. Point estimation. Confidence intervals. Neyman Pearson hypothesis testing theory. Introduction to theory of linear models. prereq: 8101, Statistics graduate major or instr consent
STAT 8501 - Introduction to Stochastic Processes with Applications
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall
Markov chains in discrete and continuous time, renewal processes, Poisson process, Brownian motion, and other stochastic models encountered in applications. prereq: 5101 or 8101