Twin Cities campus
 
Twin Cities Campus

Economics Ph.D.

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)
Email: econdgs@umn.edu
Website: https://cla.umn.edu/economics/graduate
  • Program Type: Doctorate
  • Requirements for this program are current for Fall 2023
  • Length of program in credits: 60
  • This program does not require summer semesters for timely completion.
  • Degree: Doctor of Philosophy
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
The preferred undergraduate GPA for admittance to the program is 3.50.
Special Application Requirements:
Coursework in linear algebra and multivariate calculus is required.
Applicants must submit their test score(s) from the following:
  • GRE
    • General Test - Quantitative Reasoning: 162
International applicants must submit score(s) from one of the following tests:
  • TOEFL
    • Internet Based - Total Score: 100
    • Internet Based - Speaking Score: 23
  • IELTS
    • Total Score: 7.5
The preferred English language test is Test of English as Foreign Language.
Key to test abbreviations (GRE, TOEFL, IELTS).
For an online application or for more information about graduate education admissions, see the General Information section of this website.
Program Requirements
24 credits are required in the major.
12 credits are required outside the major.
24 thesis credits are required.
This program may be completed with a minor.
Use of 4xxx courses towards program requirements is not permitted.
A minimum GPA of 3.20 is required for students to remain in good standing.
At least 3 semesters must be completed before filing a Degree Program Form.
Coursework offered on both the A-F and S/N grade basis must be taken A-F, with a minimum grade of C earned. The number of courses taken to prepare for the preliminary examinations is determined through consultation with the advisor. Students may begin doctoral thesis credit registration, with advisor approval starting Year 2 of the program.
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)
Electives (8 credits)
Select 8 credits from the following in consultation with the advisor. ECON 8990 cannot be used to meet degree requirements.
ECON 8xxx
Outside Coursework (12 credits)
Courses are selected in consultation with the director of graduate studies. ECON 8990 cannot be used to meet degree requirements.
CSCI 5302 - Analysis of Numerical Algorithms (3.0 cr)
CSCI 5512 - Artificial Intelligence II (3.0 cr)
CSCI 5521 - Machine Learning Fundamentals (3.0 cr)
CSCI 5523 - Introduction to Data Mining (3.0 cr)
CSCI 5525 - Machine Learning: Analysis and Methods (3.0 cr)
CSCI 5715 - From GPS, Google Maps, and Uber to Spatial Data Science (3.0 cr)
CSCI 5801 - Software Engineering I (3.0 cr)
CSCI 8115 - Human-Computer Interaction and User Interface Technology (3.0 cr)
ECON 8xxx
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 (1.0-4.0 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 5303 - Designing Experiments (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)
Thesis Credits
Take at least 24 doctoral thesis credits.
ECON 8888 - Thesis Credit: Doctoral (1.0-24.0 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
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/CSci 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 - Machine Learning Fundamentals
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, and knowledge of partial derivatives
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: Analysis and Methods
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, Google Maps, and Uber to Spatial Data Science
Credits: 3.0 [max 3.0]
Typically offered: Spring Even Year
Spatial databases and querying, spatial big data mining, spatial data-structures and algorithms, positioning, earth observation, cartography, and geo-visulization. Trends such as spatio-temporal, and geospatial cloud analytics, etc. 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 Fall
Modern asset pricing theory. Static/discrete time frameworks. Fundamental asset pricing equation. Classical finance models: CAPM, consumption-based CAPM, Complete markets, representative agent, Pareto 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: 1.0 -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.
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: 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), (MATH 2142 or CSCI 2033 or MATH 2373 or MATH 2243)
STAT 5303 - Designing Experiments
Credits: 4.0 [max 4.0]
Typically offered: Every Fall, Spring & Summer
Analysis of variance. Multiple comparisons. Variance-stabilizing transformations. Contrasts. Construction/analysis of complete/incomplete block designs. Fractional factorial designs. Confounding split plots. Response surface design. prereq: 3022 or 3032 or 3301 or 4102 or 5021 or 5102 or instr consent
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]
Grading Basis: OPT No Aud
Typically offered: Periodic Spring
STAT8056 covers a range of emerging topics in machine learning and data science, including high-dimensional analysis, recommender systems, undirected and directed graphical models, feed-forward networks, and unstructured data analysis. This course will introduce various statistical and computational techniques for prediction and inference. These techniques are directly applicable to many fields, such as business, engineering, and bioinformatics. This course requires the basic knowledge of machine learning and data mining (e.g., STAT8053).
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
ECON 8888 - Thesis Credit: Doctoral
Credits: 1.0 -24.0 [max 100.0]
Grading Basis: No Grade
Typically offered: Every Fall & Spring
(No description) prereq: Max 18 cr per semester or summer; 24 cr required