ACMS 10140. Elements of Statistics
This course is intended for those students who may or may not plan to use statistics in their chosen careers, but wish nevertheless to become informed and astute consumers. Topics include statistical decision making, sampling, data representation, random variables, elementary probability, conditional probabilities, independence, and Bayes’ rule. The methodology will focus on a hands-on approach. Concepts and terminology will be introduced only after thorough exposure to situations that necessitate the concepts and terms. Care will be exercised to select a variety of situations from the many fields where statistics are used in modern society. Examples will be taken from biology and medicine (e.g. drug testing, wild animal counts), the social sciences, psychology, and economics. This course counts only as general elective credit for students in the College of Science.
ACMS 10141. Statistical Reasoning in Politics
Essential concepts of statistical reasoning are explored through the analysis of politics, elections, and media. Topics covered include data exploration, measures of variability, inference, correlation, and linear regression. Real datasets are used to illustrate many concepts, and concepts are introduced by references to actual events. Calculations will be conducted in Microsoft Excel and/or with a graphing calculator. This course will be submitted to satisfy the university mathematics requirement.
ACMS 10145. Statistics for Business and Economics I
A conceptual introduction to the science of data for students of business and economics. Descriptive statistics: graphical methods, measures of central tendency, spread, and association. Basic probability theory and probability models for random variables. Introduction to statistical inference: confidence intervals and hypothesis tests. Many examples will be based on real, current business and economics datasets. Calculations will be illustrated in Microsoft Excel. Not eligible for science credit for students in the College of Science. Credit is not given if a student takes both ACMS 10145 and ACMS 10140 or ACMS 10145 and ACMS 10141. This course is proposed to satisfy one university mathematics requirement.
ACMS 10150. Elements of Statistics II
Prerequisite: MATH 10140. The goal of this course is to give students an introduction to a variety of the most commonly used statistical tools. A hands-on approach with real data gathered from many disciplines will be followed. Topics include inferences based on two samples, analysis of variance, simple linear regression, categorical data analysis, and non-parametric statistics. This course counts only as general elective credit for students in the College of Science.
ACMS 20210. Scientific Computing
(3-0-3 Prior to Fall 2013) (3.5-0-3.5 beginning Fall 2013)
Prerequisite: MATH 10560. An introduction to solving mathematical problems using computer programming in high-level languages such as C. Matlab and other software for solving computational problems will be used.
ACMS 20340. Statistics for the Life Sciences
Prerequisite: MATH 10360 OR MATH 10560. An introduction to the principles of statistical inference following a brief introduction to probability theory. This course does not count as a science or mathematics elective for mathematics majors or ACMS majors. NOTE: Students may not take both BIOS 40411 (411), MATH 20340 and ACMS 20340. Not open to students who have taken MATH/ACMS 30540.
ACMS 20550. Introduction to Applied Mathematics Methods I
Prerequisite: MATH 10560 or MATH 10860. An introduction to the methods of applied mathematics. Topics include: basic linear algebra, partial derivatives, Taylor and power series in multiple variables, Lagrange multipliers, multiple integrals, gradient and line integrals, Green's theorem, Stokes theorem and divergence, Fourier series and transforms, introduction to ordinary differential equations. Applications to real-world problems in science, engineering, the social sciences and business will be emphasized in this course and ACMS 20750. Computational methods will be taught. Credit is not given for both ACMS 20550 and PHYS 20451.
ACMS 20620. Applied Linear Algebra
The objective of this class is to impart the fundamental knowledge in linear algebra and computational linear algebra that are needed to solve matrix algebra problems in application areas. Appropriate software packages will be used.
ACMS 20750. Introduction to Applied Mathematics Methods II
Prerequisite: ACMS 20550 or PHYS 20451. The fundamental methods of applied mathematics are continued in this course. Topics include: variational calculus, special functions, series solutions of ordinary differential equations, (ODE) orthogonal functions in the solution of ODE, basic partial differential equations and modeling heat flow, vibrating string and steady-state temperature. Topics in complex function theory include contour integrals, Laurent series and residue calculus, conformal mapping. The course concludes with a basic introduction to probability and statistics. Credit is not given for both ACMS 20750 and PHYS 20452.
ACMS 30440. Probability and Statistics
An introduction to the theory of probability and statistics, with applications to the computer sciences and engineering. Topics include discrete and continuous random variables, joint probability distributions, the central limit theorem, point and interval estimation and hypothesis testing.
ACMS 30530. Introduction to Probability
Prerequisite: MATH 20850 OR MATH 20550 OR ACMS 20550. An introduction to the theory of probability, with applications to the physical sciences and engineering. Topics include discrete and continuous random variables, conditional probability and independent events, generating functions, special discrete and continuous random variables, laws of large numbers, and the central limit theorem. The course emphasizes computations with the standard distributions of probability theory and classical applications of them.
ACMS 30540. Mathematical Statistics
Prerequisite: ACMS/MATH 30530. An introduction to mathematical statistics. Topics include distributions involved in random sampling, estimators and their properties, confidence intervals, hypothesis testing including the goodness-of-fit test and contingency tables, the general linear model, and analysis of variance.
ACMS 30600. Statistical Methods & Data Analysis I
(3-0-3 Prior to Fall 2013) (3.5-0-3.5 beginning Fall 2013)
Prerequisite: ACMS 30440 OR ACMS 30530 OR MATH 30530. Introduction to statistical methods with an emphasis on analysis of data. Estimation of central values. Parametric and nonparametric hypothesis tests. Categorical data analysis. Simple and multiple regression. Introduction to time series. The SOA has approved this course for VEE credit in Applied Statistics.
ACMS 30610. Introduction to Financial Mathematics
Prerequisite: ACMS 20550 OR ACMS 20620 OR ACMS 20750 OR ACMS 30530. The course serves as a preparation for first actuarial exam in financial math- ematics, known as Exam FM or Exam 2. The first part of the course deals with pricing of fixed income securities, such as bonds and annuities. The second part of the course can serve as an introduction to deriva- tive securities such as options and futures. Although the amount of material for both parts is almost the same, Exam FM devotes usually about 2/3 of its questions to Part 1. Therefore, about 2/3 of the course is devoted to Part 1.Topics covered: interest rates, annuities, loans and bonds, forwards, options, hedging, and swaps.
ACMS 40212. Advanced Scientific Computing
This course covers fundamental material necessary for using high performance computing in science and engineering. There is a special emphasis on algorithm development, computer implementation, and the application of these methods to specific problems in science and engineering.
ACMS 40390. Numerical Analysis
Prerequisite: ACMS 20750 OR MATH 20750 OR MATH 20860 OR MATH 30650. An introduction to the numerical solution of ordinary and partial differential equations. Topics include the finite difference method, projection methods, cubic splines, interpolation, numerical integration methods, analysis of numerical errors, numerical linear algebra and eigenvalue problems, and continuation methods.
ACMS 40395. Numerical Linear Algebra
The course will cover numerical linear algebra algorithms which are useful for solving problems in science and engineering. Algorithm design, analysis and computer implementation will be discussed.
ACMS 40485. Applied Complex Analysis
Complex analysis is a core part of applied and computational mathematics. Asymptotic methods for evaluation of functions and integrals, special functions (Gamma, elliptic, Bessel, ...), and conformal mappings arise naturally in applications, e.g., in the solution of physical models from electromagnetism, optics, tumor growth, fluid flow... In this course, an introduction to complex analysis will be given with special regard to those topics occurring in modeling and computation.
ACMS 40570. Mathematical Methods in Financial Economics
Prerequisites: (ACMS/MATH 30530) AND (MATH 20750 OR MATH 30650 OR ACMS 20750) AND (MATH 30750 OR MATH 30850) OR (FIN 30600) OR (FIN 70670). Cross-listed with MATH 40570. An introduction to financial economic problems using mathematical methods, including the portfolio decision of an investor and the determination of the equilibrium price of stocks in both discrete and continuous time, will be discussed. The pricing of derivative securities in continuous time including various stock and interest rate options will also be included. Projects reflecting students’ interests and background are an integral part of this course.
ACMS 40630. Nonlinear Dynamical Systems
Theory of nonlinear dynamical systems has applications to a wide variety of fields, from physics, biology, and chemistry, to engineering, economics, and medicine. This is one of its most exciting aspects -- that it brings researchers from many disciplines together with a common language. A dynamical system consists of an abstract plase space or state space, whose coordinates describe the dynamical state at any instant; and a dynamical rule which specifies the immediate future trend of all state variables, given only the present values of those same state variables. Dynamical systems are "deterministic" if there is a unique consequent to every state, and "stochastic" or "random" if there is more than one consequent chosen from some probability distribution. A dynamical system can have discrete or continuous time. The discrete case is defined by a map and the continuous case is defined by a "flow." Nonlinear dynamical systems have been shown to exhibit surprising and complex effects that would never be anticipated by a scientist trained only in linear techniques. Prominent examples of these include bifurcation, chaos, and solitons. This course will be self-contained.
ACMS 40730. Mathematical and Computational Modeling in Biology and Physics
Prerequisites: (ACMS 20750 OR MATH 20750 OR MATH 30650). Introductory course on applied mathematics methods with emphasis on modeling of physical, mechanical and biological problems in terms of differential equations, and stochastic dynamical systems. Students will be working in groups on several projects and will present them in class at the end of the course.
ACMS 40750. Partial Differential Equations
Prerequisite: (MATH 20750 OR MATH 30650 OR MATH 30850). An introduction to partial differential equations. Topics include Fourier series, solutions of boundary value problems for the heat equation, wave equation and Laplace’s equation, Fourier transforms, and applications to solving heat, wave, and Laplace’s equations in unbounded domains.
ACMS 40790. Topics in Applied Mathematics
Selected Topics in Applied and Computational Mathematics
ACMS 40842. Time Series Analysis
This is an introductory and applied course in time series analysis. Popular time series models and computational techniques for model estimation, diagnostic and forecasting will be discussed. Although the book focuses on financial data sets, other data sets, such as climate data, earthquake data and biological data, will also be included and discussed within the same theoretical framework.
ACMS 40852. Statistical Methods in the Biological and Health Sciences
This course surveys the statistical methods used in biological and biomedical research. Topics include study designs commonly used in health research including case-control, cross-sectional, prospective and retrospective studies; statistical analysis of different types of data arising from biological and health research including categorial data analysis, count data analysis, survival analysis, linear mixed models, lab data, and diagnostic tests. Design and analysis of clinical trials, relative risk assessment, statistical power and sample size calculations will also be covered by the class. Additional topics of introduction to statistical genetics and bioinformatics might also be covered. Students are expected to have basic knowledge in statistics, such as random variables, distributions, estimation, and hypothesis testing.
ACMS 40860. Statistical Methods in Molecular Biology
Prerequisite: ACMS 30600. This is an introductory and applied course in statistical genetics and bioinformatics. Problems and statistical techniques in various fields of genetics, genomics and bioinformatics will be discussed. Since knowledge in these areas is evolving rapidly, novel and prevailing methods, such as next generation sequencing data analyis and network models, will also be introduced. Moreover, guest lectures may be given by visiting speakers.
ACMS 40870. Statistical Methods in Social Sciences
Prerequisite: ACMS 30600. This course introduces statistical methods that are critical for the social, behavioral, and educational sciences. Examples will be drawn from the social sciences throughout the course to illustrate correct applications of the statistical methods and practical interpretation of the results. In addition to advanced statistical techniques, such as hierarchal and latent variables modeling, for analyzing common data types in the social sciences, survey sampling that is used for data collection will also be covered.
ACMS 40875. Statistical Methods in Data Mining
Data mining is widely used to discover useful patterns and relationships in data. We will emphasize on large complex datasets such as those in very large databases or web-based mining. The topics will include data visualization, decision trees, association rules, clustering, case based methods, etc.
ACMS 40880. Statistical Methods in Pattern Recognition and Prediction
Prerequisite: ACMS 30600. Statistical theories and computational techniques for extracting information from large data sets. Building and testing predictive models.
ACMS 40890. Statistical Methods for Financial Risk Management
This course is an introduction to some of the models and statistical methodology used in the practice of managing market risk for portfolios of financial assets. Throughout the course, the emphasis will be on the so-called loss distribution approach, a mapping from the individual asset returns to portfolio losses. Methodology presented will include both univariate and multivariate statistical modeling, Monte Carlo simulation, and statistical inference. This course will make heavy use of the R statistical computing environment.
ACMS 50550. Functional Analysis
This one semester course will cover selected topics in Functional Analysis. The theory will be built on Banach and Hilbert spaces and will be applied to selected examples from application including Laplace equations, heat equations, and wave equations. Tools and methods such as fixed point theorems, Dirichlet principle, Semi-group, etc. will be covered in the course.