Electives and Tracks

List of Elective Courses by Career Tracks

All students completing a Masters of Financial Mathematics must take at least three electives. We developed career concentrations that can guide your selections of elective courses. Tracks are tied to career paths and designed to prepare you for the right job after graduation. More guidance on track’s selection and the selection of courses will be provided on summer orientation, which is part of MFM preparation program.

Track Course Name Course ID
Risk Management
Financial Risk Analysis
    This course focuses on the ways in which risks are quantified and managed by financial institutions by covering the following topics:

  • Introduction to financial institutions, such as banks, insurance companies, mutual funds and hedge funds, and their risk management issues. (The credit crisis of 2007 will be covered in this part as well.)
  • The market risk, including topics on interest risk, Value-at-Risk, volatility, correlations and copulas.
  • Credit risk, including default probability estimation, CVA, DVA and credit value at risk.
  • (If time permits) Other topics, such as operational risk, liquidity risk, model risk, etc.
FIM/MA 549
Database Applications in Industrial Engineering
    Rapid application development (RAD) tools to design and implement database-based applications including:

  • SQL query language
  • VBA in database application construction
  • a standard RAD environment and how to access information in a database
  • entity/attribute modeling of the database structure
  • anomalies of database structures that create problems for applications
  • modeling of application system’s functionality
  • and integrating these tools together to design and implement engineering applications
  • examples from manufacturing and production systems.
ISE 519
Enterprise Risk Management
  • Expose students to techniques all types of organizations are implementing to manage
    the ever-increasing portfolio of risks threatening the organization’s business model and strategic plan
  • Begin with obtaining an understanding of the growing expectations being placed on boards of directors and senior executives for more effective oversight of risks
  • Walk through the core elements of an ERM process entities use to identify, assess, manage, and monitor its most important risks to their business model
MBA 518
Corporate Risk Management
  • Fundamentals of corporate risk management from a strategic decision-making perspective
  • Emphasis on how exposures to financial risks (foreign currency, credit, interest rate, etc.) affect the firm, and how risk exposures can be re-engineered to enhance shareholder value
  • Topics include the major sources of risk, the measurement of risk exposures, methods, and strategies for managing and controlling risk
  • Introduce tools of the financial engineer–futures, options, swaps, and other derivatives
MBA 527
Advanced Corporate Finance
  • Introduction, TVM, Bond and Stock valuation
  • Capital budgeting, Estimating incremental FCF, NPV
  • Estimating cost of debt, beta, cost of equity
  • Bond and Stock valuation (DDM)
  • Introduction to WRDS. Capital Structure ‐ Ideal mode
  • Capital Structure ‐ Taxes, bankruptcy costs
  • Capital Structure – In Practice
  • How Firms Raise External Capital
  • FCF valuation in practice
  • Leasing
  • Mergers and Acquisitions
  • Options ‐ Valuation, Real Options
  • Derivatives valuation and risk management
MBA 521
Data Science for Finance
Database Applications in Industrial Engineering
    Rapid application development (RAD) tools to design and implement database-based applications, including different method and programming language:

  • SQL query language
  • Visual Basic for Applications in database application
  • Standard RAD environment and how to access information in a database construction
  • Entity/attribute modeling of the database structure
  • Anomalies of database structures that create problems for applications
  • Modeling of application system’s functionality
  • Integrating these tools together to design and implement engineering applications
ISE 519
Fundamentals of Linear Models and Regression
  • Estimation and testing in full and non-full rank linear models
  • Normal theory distributional properties
  • Least squares principle and the Gauss-Markov theorem
  • Estimability, analysis of variance and co variance in a unified manner
  • Practical model-building in linear regression including residual analysis, regression diagnostics, and variable selection
  • Emphasis on use of the computer to apply methods with data sets
ST 503
Experimental Statistics for Engineers II
  • General statistical concepts and techniques useful to research workers in engineering, textiles, wood technology, etc
  • Probability distributions, measurement of precision, simple and multiple regression
  • Tests of significance, analysis of variance, enumeration data and experimental designs
ST 516
Applied Bayesian Analysis
  • Introduction to Bayesian concepts of statistical inference
  • Bayesian learning; Markov chain Monte Carlo methods using existing software (SAS and OpenBUGS)
  • Linear and hierarchical models
  • model selection and diagnostics
ST 540
Applied Time Series
  • Exploratory analysis of time series
  • Time domain methods, such as ARIMA models
  • Frequency domain methods (periodogram, spectrum,…) analysis, filtering, and transfer functions
  • Transfer function modeling in the time domain
  • Further topics, such as long memory and conditional heteroscedasticity models, and nonparametric time series methods, as time permits
ST 590
Data Mining with SAS Enterprise Miner
  • This is a hands-on course using modeling techniques designed mostly for large observational studies
  • Estimation topics include recursive splitting, ordinary and logistic regression, neural networks, and discriminant analysis
  • Clustering and association analysis are covered under the topic “unsupervised learning,” and the use of training and validation data sets are emphasized
  • Model evaluation alternatives to statistical significance include lift charts and receiver operating characteristic curves
  • SAS Enterprise Miner is used in the demonstrations, and some knowledge of basic SAS programming is helpful
ST 562
Statistical Programming I
    To be added…
ST 555
Portfolio Management
Introduction to Mathematical Programming
  • A survey course in the theory and methods of mathematical programming to meet the needs of students from a variety of backgrounds
  • A wide array of topics and applications in linear and nonlinear programming comprise the course
  • The major prerequisite is familiarity with vector and matrix manipulations
  • Some differential calculus is required for the discussion of nonlinear programming
OR(ISE) 504
Linear Programming
    Provide the fundamental understanding to the theory and algorithms of linear optimization. It involves mathematical analysis, theorem proving, algorithm design and numerical methods:

  • Introduction to LP
  • Geometric Interpretation of LP
  • Simplex Method
  • Duality and Sensitivity Analysis
  • Interior Point Method
  • Robust Optimization
OR(ISE) 505
Algorithmic Methods in Nonlinear Programming
  • Introduction to methods for obtaining approximate solutions to unconstrained and constrained minimization problems of moderate size
  • Emphasis on geometrical interpretation and actual coordinate descent, steepest descent, Newton and quasi-Newton methods
  • Conjugate gradient search, gradient projection and penalty function methods for constrained problems
  • Specialized problems and algorithms treated as time permits
OR 506
Investment Theory and Practice
  • Advanced topics in investments with a focus on underlying theory and practical application using real world data
  • Stock valuation models
  • Bond valuation
  • Derivatives, portfolio performance evaluation
  • Investment strategies, efficient market theory
  • Other current issues in investment finance
MBA 523
Equity Valuation
    Advanced quantitative course on applied equity valuation.Students conduct stock valuation analysis which is then used to select stocks for the student-managed SunTrust MBA fund. Topics include:

  • The investment decision making process
  • Empirical evidence on securities returns
  • Forecasting financial statements
  • Industry and macro-economic analysis
  • Valuation models
  • Portfolio performance evaluation and performance attribution
MBA 524
Dynamic Systems and Multivariable Control I
  • Introduction to modeling, analysis and control of linear discrete-time and continuous-time dynamical systems
  • State space representations and transfer methods
  • Applications to biological, chemical, economic, electrical, mechanical and sociological systems
MA(OR,E) 531
Database Applications in Industrial Engineering
    Rapid application development (RAD) tools to design and implement database-based applications, including different method and programming language:

  • SQL query language
  • Visual Basic for Applications in database application
  • Standard RAD environment and how to access information in a database construction
  • Entity/attribute modeling of the database structure
  • Anomalies of database structures that create problems for applications
  • Modeling of application system’s functionality
  • Integrating these tools together to design and implement engineering applications
ISE 519
Actuarial Science
Microeconomics I & II
  • Theory of consumer behavior
  • Primal-dual relationships in consumer theory including indirect utility functions and consumer expenditure functions
  • Properties of consumer demand functions
  • Consumer welfare measurement
  • Long-run market equilibrium in a competitive market environment
  • Market equilibrium with upward sloping input supply equations. The theory of monopoly
  • General equilibrium
  • Economics of information and uncertainty
  • Game theory
  • Mechanism design and social choice
ECG 701 & 702
Introduction to Econometric Methods
  • Introduction to principles of estimation of linear regression models, such as ordinary least squares and generalized least squares
  • Extensions to time series and panel data
  • Consideration of endogeneity and instrumental variables estimation
  • Limited dependent variable and sample selection models
  • Attention to implementation of econometric methods using a statistical package and microeconomic and macroeconomic data sets
ECG(ST) 750
Econometric Methods
    Discussion of important concepts in the asymptotic statistical analysis of vector process with application to the inference procedures based on the aforementioned estimation methods. Introduction to important econometric methods of estimation such as:

  • Least Squares, instrumentatl Variables
  • Maximum Likelihood, and Generalized Method of Moments
  • Their application to the estimation of linear models for cross-sectional ecomomic data
ECG(ST) 751
Time Series Econometrics
  • The characteristics of macroeconomic and financial time series data
  • Discussion of stationarity and non-stationarity as they relate to economic time series
  • Linear models for stationary economic time series: autoregressive moving average (ARMA) models; vector autoregressive (VAR) models
  • Linear models for nonstationary data: deterministic and stochastic trends
  • Methods for capturing volatility of financial time series such as autoregressive conditional heteroscedasticity (ARCH) models
  • Generalized Method of Moments estimation of nonlinear dynamic models
ECG(ST) 752
Microeconometrics
    The characteristics of microeconomic data. Limited dependent variable models for cross-sectional microeconomic data:

  • Logit/probit models
  • Tobit models
  • Methods for accounting for sample selection
  • Count data models
  • Duration analysis
  • Non-parametricmethods
  • Panel data models
  • Limited dependent variables and panel data analysis
ECG(ST) 753
Probability and Stochastic Processes II
  • Conditional expectation, Martingales, submartingales, supermartingales
  • Doob’s decomposition, Doob’s inequality, Uniform integrability
  • Convergence theorems, Optional stopping theorems
  • Markov chains: Discrete-time, examples of Markov chains (queueing, birth-death, etc.) properties of Markov chains (recurrence, transient, etc.) and stationary measures
  • Brownian motion: Probability spaces for continuous-time processes (E.g. “path space”), definition and some properties of Brownian motion and applications with Brownian motion models
MA(ST) 747
Enterprise Risk Management
  • Expose students to techniques all types of organizations are implementing to manage the ever-increasing portfolio of risks threatening the organization’s business model and strategic plan
  • Begin with obtaining an understanding of the growing expectations being placed on boards of directors and senior executives for more effective oversight of risks
  • Walk through the core elements of an ERM process entities use to identify, assess, manage, and monitor its most important risks to their business model
MBA 518
PhD Preparation
Linear Programming
    Provide the fundamental understanding to the theory and algorithms of linear optimization. It involves mathematical analysis, theorem proving, algorithm design and numerical methods:

  • Introduction to LP
  • Geometric Interpretation of LP
  • Simplex Method
  • Duality and Sensitivity Analysis
  • Interior Point Method
  • Robust Optimization
OR(ISE) 505
Econometric Methods
    Discussion of important concepts in the asymptotic statistical analysis of vector process with application to the inference procedures based on the aforementioned estimation methods. Introduction to important econometric methods of estimation such as:

  • Least Squares, instrumentatl Variables
  • Maximum Likelihood, and Generalized Method of Moments
  • Their application to the estimation of linear models for cross-sectional ecomomic data
ECG(ST) 751
Time Series Econometrics
  • The characteristics of macroeconomic and financial time series data
  • Discussion of stationarity and non-stationarity as they relate to economic time series
  • Linear models for stationary economic time series: autoregressive moving average (ARMA) models; vector autoregressive (VAR) models
  • Linear models for nonstationary data: deterministic and stochastic trends
  • Methods for capturing volatility of financial time series such as autoregressive conditional heteroscedasticity (ARCH) models
  • Generalized Method of Moments estimation of nonlinear dynamic models
ECG(ST) 752
Linear Transformations and Matrix Theory
  • Vector spaces, linear transformations and matrices
  • Orthogonality, orthogonal transformations with emphasis on rotations and reflections
  • Matrix norms, projectors
  • Least squares
  • Generalized inverses
  • Definite matrices and ingular values
MA 523
Uncertainty Quantification for Physical Models
  • Motivating applications and prototypical models
  • Fundamental aspects of probability, random processes and statistics
  • Representation of random inputs
  • Parameter selection techniques
  • Frequentist and Bayesian model calibration
  • Uncertainty propagation in models
  • Stochastic spectral methods and sparse grid techniques
  • Prediction in the presence of model discrepancy
  • Surrogate models
  • Global sensitivity analysis
MA 540
Probability and Stochastic Processes I
  • Foundation of probability theory including random variables, conditioning, independence
  • Limit theorems in the context of independent random variables/vectors
  • Probability distributions and conditional expectations
  • Characteristic functions, Gaussian processes, sums of independent random variables
  • Laws of large numbers and central limit theorem
MA(ST) 546
Applied Time Series Analysis

To be updated…

ST 730
Bayesian Inference and Analysis
  • Introduction to Bayesian inference
  • Specifying prior distributions
  • Conjugate priors, summarizing posterior information, predictive distributions, hierachical models, asymptotic consistency and asymptotic normality
  • Markov Chain Monte Carlo (MCMC) methods and the use of exising software(e.g., WinBUGS)
ST 740
Functional Analysis
    Spectral Theory of Linear Operators in Normed Spaces:

  • Spectral theory in finite dimensional normed spaces
  • Resolvent and spectrum
  • Spectral properties of bounded linear operators
  • Compact linear operators and their spectral analysis
  • Spectral properties of bounded self-adjoint linear operators
    Semigroups of Bounded Linear Operators:

  • Uniformly continuous semigroups of bounded linear operators
  • Strongly continuous semigroups of bounded linear operators
  • The Hille-Yosida Theorem, The Lumer Phillips Theorem, Infinitesimal generators of C0 semigroups
    Unbounded Linear Operators in Hilbert Spaces:

  • Hilbertadjoint operators
  • Symmetric and self-adjoint linear operators
  • Spectral properties of self-adjoint linear operators
  • Closed linear operators
MA 791

 
 
 

List of Elective Courses by Departments

 
The following list is the most updated list of electives for FM students as of Spring 2018.

Computer Science Department (CSC)

Economics Department (ECG)

Industrial Engineering Department (ISE)

Business Administration Department (MBA)

Mathematics Department (MA)

Operational Research Department (OR)
  • OR/ISE 501 Introduction to Operations Research
  • OR/MA 504 Introduction to Mathematical Programming
  • OR/ISE/MA 505 Linear Programming
  • OR 506 Algorithmic Methods in Nonlinear Programming
  • OR/E/MA 531 Dynamic Systems and Multivariable Control I
  • OR/MA 719 Vector Space Methods in System Optimization
  • OR/ISE 772 Stochastic Simulation Design and Analysis
  • OR/BMA/MA/ST 773 Stochastic Modeling

Statistics Department (ST)
  • ST 503 Fundamentals of Linear Models and Regression
  • ST 505 Applied Nonparametric Statistics
  • ST 512 Experimental Statistics For Biological Sciences II
  • ST 552 Linear Models and Variance Components
  • ST 555 Statistical Programming I
  • ST 556 Statistical Programming II
  • ST 563 Introduction to Statistical Learning (available soon)
  • ST 564 Statistical Thinking and Big Data (available soon)

 
 
Notes:
1. To complete a track, complete 3 or more electives in a particular list. Participating in a track
will have no impact on your official transcript and is not a requirement of the program, but adding
a track to your resume can help with your career search.
2. Courses in the Data Science Foundations Graduate Certificate Program also count towards
the Data Science for Finance Track.
3. Only 2 MBA classes can be used as electives.
4. Students following the actuarial track are encouraged to take MA(ST) 412 and MA(ST) 413;
however, these courses will not count towards the MFM degree.
5. If a course does not appear on this list, seek approval from your academic adviser.
6. You can also take classes at UNC or Duke through NCSU Exchange Program.
7. For the most updated list of available NCSU courses for each semester please search here.
 
 
Availability of courses: Seeing a course listed as an elective is not a promise to offer the class.
Similarly, courses in these Tracks are necessarily offered on a regular basis. When courses are
offered, they are not necessarily available to MFM students.