# Courses

## ACMS 10140. Elements of Statistics

(3 credits)

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 10145. Statistics for Business I

(3 credits)

A conceptual introduction to the science of data for students of business. 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

(3 credits)

**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 20010. Applied Mathematical Financial Economics I

(3 credits)

**Prerequisite**: MATH 10560 or MATH 10092 or MATH 10860. This course will prepare students to understand call and put options, other financial derivatives and financial strategies such as bull spread, bear spread and others. Financial models such as the binomial model and Black Scholes will also be utilized and students will prepare their own models. Calculus will not be widely used, but an understanding is necessary. This course prepares students for the IFM actuarial exam and also uses present value concepts.

## ACMS 20210. Scientific Computing

(3 credits Prior to Fall 2013) (3.5 credits beginning Fall 2013)

**Prerequisite**: MATH 10560 or MATH 10092 or MATH 10860 or MATH 10360 or MATH 14360. 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

(3 credits)

**Prerequisite**: MATH 10360 or MATH 10460 or MATH 10560 or MATH 10092 or MATH 14360. 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, MATH 20340 and ACMS 20340. Not open to students who have taken MATH/ACMS 30540.

## ACMS 20550. Introduction to Applied Mathematics Methods I

(3.5 credits)

**Prerequisite**: MATH 10560 or MATH 10092 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

(3 credits)

**Prerequisite**: MATH 10550 or MATH 10091. 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

(3.5 credits)

**Prerequisite**: ACMS 20550 or PHYS 20451 or MATH 20550 or MATH 10093. 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, and 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 30010. Applied Mathematical Financial Economics II

(3 credits)

**Prerequisite**: MATH 20550 or MATH 10093 or ACMS 20550 and ACMS 20010. This course is a continuation of the Financial Economics I material and is the second of a 2-course sequence that prepares students for the Society of Actuaries' Exam MFE (Models for Financial Economics). It is a core exam course for preparing students to become future actuaries. This course prepares students to apply mathematical models to financial assets and manage risk in an insurance setting. The second semester moves to corporate finance issues.

## ACMS 30440. Probability and Statistics

(3 credits)

**Prerequisite**: MATH 20550 or MATH 10093 or ACMS 20550 or MATH 20850. 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

(3 credits)

**Prerequisite**: MATH 20550 or MATH 10093 or ACMS 20550 or MATH 20850. 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. Statistics A

(3 credits)

**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 30550. Mathematical Statistics

(3 credits)

**Prerequisite**: ACMS 30600. An introduction to mathematical statistics. Topics include distributions involved in convergence concepts, estimators and their properties, confidence intervals, hypothesis testing, and linear models and estimation by least squares.

## ACMS 30600. Statistical Methods & Data Analysis I

(3 credits Prior to Fall 2013) (3.5 credits 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

(3 credits)

**Prerequisite**: ACMS 20550 or ACMS 20620 or ACMS 20750 or ACMS 30530. The course serves as a preparation for first actuarial exam in financial mathematics, 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 derivative 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 37020. Projects in Actuarial Science

(1 credit)

**Prerequisite**: ACMS 30600. This course provides students with exposure to real world actuarial science projects, which involve substantial use of probability concepts and financial mathematics throughout. This course will be created in conjunction with an industry partner. Case studies and projects will vary by semester.

## ACMS 40212. Advanced Scientific Computing

(3 credits)

**Prerequisite**: ACMS 40390. 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

(3 credits)

**Prerequisite**: (MATH 20750 or MATH 20860 or MATH 30650 or ACMS 20750 or PHYS 20452) and (ACMS 20620 or MATH 20610) and ACMS 20210. 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

(3 credits)

**Prerequisite**: (MATH 20610 or ACMS 20620) and (ACMS 40390 or MATH 40390). 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

(3 credits)

**Prerequisite**: (ACMS 20750 or PHYS 20452 or MATH 40480) and (ACMS 20620 or MATH 20610) and (ACMS 40390 or PHYS 50051 or MATH 40390). 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

(3 credits)

**Prerequisite**: (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

(3 credits)

**Prerequisite**: (ACMS 20750 or MATH 20750 or MATH 30650) and ACMS 20210. 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 phase 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 solutions. This course will be self-contained.

## ACMS 40730. Mathematical and Computational Modeling

(3 credits)

**Prerequisite**: (ACMS 20750 or MATH 20750 or MATH 30650) and ACMS 20210. Introductory course on applied mathematics and computational modeling with emphasis on modeling of 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 40740. Mathematical and Computational Modeling in Neuroscience

(3 credits)

**Prerequisite**: (MATH 20480 or MATH 20580 or MATH 10094 or MATH 20750 or ACMS 20620 or MATH 20670 or AME 30314 or PHYS 20452) and (PSY 30100 or ACMS 20340 or ACMS 30440 or ACMS 30530 or MATH 30530 or BIOS 40411). This course will introduce students to some of the most common computational and mathematical models used in neuroscience. The models will progress gradually from the scale of ion channels to the systems scale. In addition to developing a deeper understanding of the biological processes modeled in the course, the students will learn numerical and analytical approaches to studying dynamical systems and random processes. The course is appropriate as an elective for Neuroscience or ACMS majors. After completing the course, students will be able to create models of neural systems, simulate these models in MATLAB and use basic techniques from dynamical systems theory and probability theory to analyze these models. Students are expected to have some exposure to ordinary differential equations and probability before taking the course.

## ACMS 40750. Partial Differential Equations

(3 credits)

**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 40760. Introduction to Stochastic Modeling

(3 credits)

**Prerequisite**: ACMS 30440 or ACMS 30530 or MATH 30530. Stochastic modeling is a technique of presenting data or predicting outcomes that takes into account a certain degree of randomness, or unpredictability. Topics include (i) Short Review of Probability - Major discrete and continuous distributions, properties of random variables. (ii) Conditional probability and conditional expectation, sums of random variables, martingales. (iii) Introduction to Discrete Markov Chains - Transition probability matrix of a Markov chain, some Markov chain models, first step analysis, the absorbing Markov chains, various types and classification of Markov chains. (iv) Long Run (asymptotic) Behavior of Markov Chains: Limiting distribution, the classification of states, irreducible Markov chains, periodicity of Markov chains, recurrent and transient states, the basic limit theorem of Markov chains. (v) Poisson Processes - The Poisson distribution and the Poisson process, the law of rare events, distributions associated with the Poisson process, the Uniform distribution and Poisson processes. (vi) Continuous Time Markov Chains - Pure birth and death processes and it's limiting behavior. (vii) Introduction to Brownian Motion, Drift and Diffusion, Geometric Brownian motion, Ornstein-Uhlenbeck process and it's long run behavior. (viii) Monte Carlo Simulations for Diffusion.

## ACMS 40790. Topics in Applied Mathematics

(3 credits)

**Prerequisite**: ACMS 30600 or ACMS 30540 or ACMS 30550. Selected Topics in Applied and Computational Mathematics

## ACMS 40842. Time Series Analysis

(3 credits)

**Prerequisite**: ACMS 30540 or ACMS 30600. 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. Advanced Biostatistical Methods

(3 credits)

**Prerequisite**: ACMS 30600. This course introduces advanced 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 data types arising from biological and health research including Gaussian data, categorical data, count data, survival data, correlated/clustered data models, and diagnostic tests. All statistical methods are illustrated with examples from the biology and health sciences. Students are expected to have basic knowledge in R programming, probabilities and distribution theory, descriptive statistics, statistical inferences including hypothesis testing and estimation, and working knowledge of linear regression, before they can register for the course. Upon completion of the course, students are able to recognize and give examples of different types of data arising in biological and health studies, and apply appropriate methods to analyze such data.

## ACMS 40855. Spatio-Temporal Statistics for Environmental Applications

(3 credits)

**Prerequisite**: ACMS 30600 and (ACMS 30540 or MATH 30540 or ACMS 30550). This course aims at providing the foundations of methods for spatio-temporal models for environmental Statistics. The main topic covered will be Gaussian processes in space and time and related notions of stationarity, co-variance functions and optimal interpolation (kriging). Exploratory analysis and inference, with particular emphasis on approximation methods for very large data sets, will be covered in the second part of the course. The last part of the course will be either dedicated to more methodological (e.g. asymptotics for spatial processes) or applied problems (e.g. climate model emulation, air pollution, visualization in Virtual Reality), depending on the class interests.

## ACMS 40860. Statistical Methods in Molecular Biology

(3 credits)

**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 analysis and network models, will also be introduced. Moreover, guest lectures may be given by visiting speakers.

## ACMS 40875. Statistical Methods in Data Mining and Prediction

(3 credits)

**Prerequisite**: ACMS 30600. 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 40878. Statistical Computing with R

(3 credits)

**Prerequisite**: ACMS 20210 and ACMS 30600. This course introduces basic computing methods for statistics. Topics are organized into two major parts: optimization and integral approximation. Optimization techniques are commonly used in statistics for finding maximum likelihood estimators, minimizing risks in a Bayesian decision problem, solving nonlinear least square problems, and a wide variety of other tasks all involving optimizations. Approximation of integrals is frequently required for Bayesian inference, since a posterior distribution may not belong to a familiar distributional family. Integral approximation is also useful in some maximum likelihood inference problems when the likelihood itself is a function of one or more integrals.

## ACMS 40880. Statistical Methods in Pattern Recognition and Prediction

(3 credits)

**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

(3 credits)

**Prerequisite**: ACMS 30600 or ACMS 30540 or MATH 30540. 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 40950. Topics in Statistics: Computational Statistics

(3 credits)

**Prerequisite**: ACMS 30600. Selected advanced topics in Statistics. Possible topics include, but are not limited to, applied logistic and ordinal regression modeling including fitting, building, and interpreting regression models for binary and ordinal response variables, various modeling strategies addressing different sampling and experimental designs such as case-control studies and longitudinal data, advanced experimental designs, survey research, big data analysis, Bayesian analysis, survival analysis, spatial and longitudinal analysis, commonly-used nonparametric statistics, basics of robust statistics, tests of association in contingency tables, permutation tests, the bootstrap, introduction to data mining techniques, etc. Applications in a variety of fields such as medical biology, psychology, global health, psychiatry, etc will be introduced. The topic of the course could vary from one semester to another depending on the interests of the faculty member and the students. The course could potentially involve a student project in the area of the interests of the faculty member and could change from one semester to another. The course will count for science credit, ACMS elective credit as well as STAT major elective credit.

## ACMS 50550. Functional Analysis

(3 credits)

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.