Credit hour requirements
The PACM program consists of 27 credits of academic training in data analysis, mathematical modeling, business communication, and management, as well as 3 credits of research internship. The core courses are broken up into 1-credit modules that will be updated as needed to keep the program current. Also, this format allows for more flexible scheduling, including night or weekend classes, and summer or J-Term sessions.
- Required credit hours in analytical mathematical modeling (9 cr.)
- Required credit hours in statistical data analysis (9 cr.)
- Required credit hours in PLUS courses (9 cr.)
- Required credit hours in Project (3 cr.)
TOTAL REQUIREMENTS...30 credit hours
To see full content for a specific course, please click on each name below.
Analytical Mathematical Modeling (9 cr.)
ACM 600 Mathematical Modeling and Applications I (1 cr.)
Processes of mathematical modeling, use of dimensional analysis, scaling, and elementary perturbation methods, constrained and unconstrained optimization, sensitivity analysis, derivation and analysis of system of discrete dynamical models.
ACM 601 Mathematical Modeling and Applications II (1 cr.)
Mathematical modeling and applications of differential equations, simulation of dynamical systems, and partial differential equations.
ACM 602 Mathematical Modeling and Applications III (1 cr.)
Applications of series and integral transforms, and the study and simulations of probability models.
ACM 610 Continuous Foundations of Applied Math From a Problem Solving Perspective (1 cr.)
Problem solving and applications of Continuous Mathematics, including Real Analysis, single and multivariable Calculus, Differential Equations, Optimization and Fourier Analysis. Emphasis on team building and group management through problem solving activities.
ACM 611 Discrete Foundations of Applied Math From a Problem Solving Perspective (1 cr.)
Problem solving and applications of Discrete Mathematics, including Combinatorics, Graph Theory, Logic, Linear Algebra, Number Theory and Set Theory. Emphasis on team building and group management through problem solving activities.
ACM 612 Computational Foundations of Applied Mathematics From a Problem Solving Perspective (1 cr.)
Introduction to algorithm design to implement mathematical models, procedural and functional programming, programming paradigms, higher-level languages, typesetting software for science and mathematics, computer networking basic.
ACM 613 Spreadsheets and Databases for Math and Science Professionals (1 cr.)
Applications of spreadsheet and database software programming to solve real life problems in computational mathematics. Analysis of data to produce reports and presentations for diverse audiences.
ACM 614 Statistical and Data Analysis Software for Math and Science Professionals (1 cr.)
Survey of statistical and data programming software and their applications to real life problems in computational mathematics. Analysis of data to produce reports and presentations for diverse audiences with a focus on understanding the syntax and use of statistical programming languages.
ACM 620 Optimization of Discrete Models (1 cr.)
Realworld problems which optimize linear objective functions subject to systems of linear inequalities are formulated mathematically and solved by the twophase revised simplex method. Applications are given in diverse areas such as business management, industry, economics, finance, and game theory.
ACM 621 Empirical Model Building (1 cr.)
Exploratory data analysis; polynomial interpolation; curve fitting; least squares; cubic splines; minimax polynomial; Taylor and Chebyshev series; applications to fitting experimental data.
ACM 622 Modeling Change with Dynamical Systems (1 cr.)
Difference equations; systems of differential equations; Euler and RungeKutta methods; error analyses; logistic models; applications to ecology, finance, conflicts, natural and social sciences.
ACM 630 Numerical Linear Algebra (1 cr.)
Numerical algorithms for linear algebra problems, matrix operations, matrix decompositions, solving systems of linear equations.
ACM 631 Eigenvalue Problems (1 cr.)
Numerical algorithms for eigenvalue problems, matrix factorization, matrices, vectors, eigenvalues, eigenvectors, eigenspaces, eigenvalue algorithms.
ACM 632 Numerical Calculus (1 cr.)
Numerical methods and algorithms for finding roots of nonlinear equations, numerical integrals, Fourier series and Laplace transform.
Statistical Data Analysis (9-10 cr.)
ACM 640 Regression and Correlation (1 cr.)
Simple linear regression and correlation, multiple linear regression, multicollinearity, multiple and partial correlations, confounding and interaction, sequential methods of model selection.
ACM 641 Design and Analysis of Experiments (1 cr.)
Design of experiments (one, two and three factors), multiple comparisons, randomized complete block designs, Latin square design.
ACM 642 Nonparametric Tests (1 cr.)
Introduction to nonparametric tests such as signtest, signed rank test, rank sum test, two way analysis of variance by ranks, tests of randomness, rank correlation coefficient, and other topics as time permits.
ACM 650 Random Walks and Brownian Motion (1 cr.)
Symmetric random walks, ballot theorem, returns to origin and arcsine laws; gambler’s ruin; Brownian motion, conditional distributions, hitting times and maxima.
ACM 651 Markov Chains (1 cr.)
Transition matrices, classification of states, limiting probabilities, applications.
ACM 652 Continuous-time Stochastic Processes (1 cr.)
Exponential distribution; Poisson, Yule, pure birth, and birth and death processes; applications.
ACM 653 Markov Chain Models in Credit Risk Management (1 cr.)
Covered topics will include Markov chain applications to risk reporting and segmenting, probability of default, loss given default, house price dynamics, and loss forecasting with consideration of micro and macro-factors. Students will read financial industry reports and make extensive use of the statistical software package SAS to analyze loan-level datasets. Assessment will include problem sets, in-class quizzes on reading, and a course project involving mortgage loss forecasting that will include both written and oral components.
ACM 654 Mathematics of Finance I: Modeling, Analysis and Numerical Methods (1 cr.)
Put-call parity equation, risk-neutral probability, binomial tree analysis.
ACM 655 Mathematics of Finance II: Modeling, Analysis and Numerical Methods (1 cr.)
Black-Scholes equation, partial differential equations, risk-neutral probability, Brownian motion, hedging, continuous and discrete stochastic models.
ACM 660 Logistic Regression (1 cr.)
Comparison of linear and logistic regression, multiple logistic regression, regression diagnostics, indicator variables, multicollinearity, confounding and interaction, model selection, maximum likelihood techniques, polychotomous logistic regression.
ACM 661 Survival Analysis (1 cr.)
Survival and Hazard functions, life tables, KaplanMeier survival analysis, Cox regression proportional hazards model and Cox regression with timedependent variables, comparison with logistic regression approaches.
ACM 662 Time Series Analysis (1 cr.)
Time and frequency domain techniques including topics such as autocorrelation, spectral analysis, autoregressive moving average and integrated moving average models, Box Jenkins methodology, fitting, forecasting and seasonal adjustments.
Business fundamentals for PSM (9-cr)
PSM 601 Project Management for Math and Science Professionals (3 cr.)
Practices in project management as applied to math and science projects: Hands-on experiences with the skills, tools, and techniques required in different phases of a project's life cycle; Techniques for communicating and motivating teams throughout the project life cycle; Emphasis on team building and practicing project management techniques through the use of science-based cases.
PSM 602 Business and Technical Communication for Math and Science Professionals (3 cr.)
Communications in business settings intended to develop strategic thinking about communication and aid in improving writing, presentation, and interpersonal communication skills within a managerial setting. Team and meeting management. Written communication, technical and non-technical. Oral/verbal communication - technical and non-technical. Inter and cross cultural communication. Communication in the job search
Project (3 cr.)
ACM 690 Master’s Project (2-3 cr.)
Study undertaken by one or more individuals under the supervision of a member of the graduate mathematics faculty, on a problem of special interest submitted in acceptable form according to directions given by the Mathematics Department. The PACM program requires the project to be part of an internship.