Course Descriptions

• 1000 Level
• 2000 Level
• 3000 Level
• 4000 Level
• 5000 Level
• 6000 Level
• 7000 Level
• MAT Courses

The courses described below are offered by the Department of Mathematical Sciences of the College of Arts & Sciences, University of Cincinnati. These descriptions should not be construed as syllabi for the courses. Each description includes the course name, the course number, credit hours, prerequisites* and/or co-requisites, and textbook title(s), when available. See the Course Planning Guide for when courses are offered.

*Prerequisite Policy: A minimum grade of C- is required to satisfy a prerequisite for any MATH or STAT course.  To see a visual display of which courses are prereqs for other courses, see the Math Continuum.

• Each course number is eight characters plus a three-digit section number. The first four characters specify the Discipline. The Math Department offers MATH and STAT courses. The next four characters indicate the course numbers.
• Example: MATH1012 Mathematics in Management Science

• All 1000- and 2000-level courses will partially satisfy the Quantitative Reasoning (QR) Gen Ed requirement of the College of Arts & Sciences.

• Prerequisite: Minimum score of 300 on the Math Placement Test.
• Text: Intermediate Algebra (with MyMathLab), 1e by Messersmith (BOOK NOT REQUIRED)
• A mathematics developmental course that uses technology and individualized instruction to provide a review of basic, introductory, and intermediate algebra. It provides students with the necessary background and skills to be successful in entry-level college mathematics courses. Credit Level:U Credit Hrs:3 Pre-req: See your college advisor for details. Baccalaureate Competency: Critical Thinking.

• Prerequisite: A minimum score of 420 on the Math Placement Test recommended.
• Text: Thinking Mathematically (with MyMathLab), 5e by Blitzer (BOOK NOT REQUIRED)
• The course begins with a study of Polya's four-step problem solving method. We explore sets and use Venn's diagrams to discover properties of set operations. Students use this knowledge to model operations with numbers and analyze properties of different number systems. Students will use mathematical reasoning and the Polya problem solving process to solve various real world problems and interpret their solutions.

• Prerequisite: A minimum score of 420 on the Math Placement Test recommended.
• Text: Using and Understanding Mathematics: A Quantitative Reasoning Approach, 7e by Bennett & Briggs
• Project-based course, emphasizing problem-solving, model-building, and basic data manipulation in real world contexts. Topics include: problem-solving, statistical reasoning, linear and exponential modeling, and modeling with geometry.

• Prerequisite: A minimum score of 420 on the Math Placement Test recommended.
• Text: For All Practical Purposes w/Math Portal (custom), 10e by COMAP
• A quantitative reasoning course for students in the liberal arts. This course examines methods for planning, scheduling, designing routes, and optimizing the use of resources to meet business, government, and individual goals, via linear programming and algorithms that use graphs, networks, and diagrams to model real problems. Also, the course includes a brief introduction to cryptography and investigates mathematical methods to store and transmit information in a way that is accurate, secured, and economical

• Prerequisite: A minimum score of 420 on the Math Placement Test recommended.
• Text: For All Practical Purposes w/Math Portal (custom), 10e by COMAP
• A quantitative reasoning course for students in the liberal arts. Contains the study of voting systems and fair division, apportionment using divisor methods, and game theory.

• Prerequisite: Minimum score of 430 on the Math Placement Test or 25 on ACT-Math.
• Text: 
  • College Algebra with Modeling and Visualization, 6e by Rockswold 
  • College Algebra Workbook, v 2.1 by Bowen-Franz
• Study of linear, polynomial, rational, exponential, and logarithmic functions, systems of linear equations, systems of inequalities and modeling with functions.

• Prerequisite: Minimum score of 550 on the Math Placement Test or 26 on ACT-Math.
• Text: Trigonometry  (w/WebAssign) (not the hybrid), 2e by Stewart, Redlin, and Watson
• Preparation for students who need trigonometry for calculus and/or physics. Right triangle trigonometry, trigonometric functions and graphs, trigonometric identities, vectors, conic sections, polar coordinates.

• Prerequisite:
• Text: Reasoning with Functions I (2016) by The Dana Center

• Prerequisite:
• Text: No Book Needed

• Prerequisite: Minimum score of 550 on the Math Placement Test or 26 on ACT-Math.
• Text: Precalculus  (w/Enhanced WebAssign), 7e by Stewart, Redlin, and Watson
• Study of functions, equations and systems of equations, sequences and series, trigonometry, and vectors, and assumes prior exposure to these topics. This course helps prepare students for the 4 credit hour calculus sequence (MATH1061 and MATH1062).

• Prerequisite: Minimum score of 420 on the Math Placement Test strongly recommended.
• Text: The Basic Practice of Statistics for the Life Sciences, 4e by Baldi & Moore
• A one-semester comprehensive introduction to statistics suitable for students in biology, nursing, allied health, and applied science. Discussion of data, frequency distributions, graphical and numerical summaries, design of statistical studies, and probability as a basis for statistical inference and prediction. The concepts and practice of statistical inference including confidence intervals, one and two sample t-tests, chi-square tests, regression and analysis of variance, with attention to selecting the procedure(s) appropriate for the question and data structure, and interpreting and using the result.

• Prerequisite: At least 420 on the Math Placement Test strongly recommended.
• Text: Introduction to the Practice of Statistics, 9e by Moore, McCabe, and Craig
• An introduction to statistics for students without a calculus background. The course covers data analysis (numerical summaries and graphics for describing and displaying the distributions of numerical and categorical data), the basic principles of data collection from samples and experiments, elementary probability, the application of the normal distribution to the study of random samples, statistical estimation (construction and interpretation of one sample confidence intervals), and an introduction to hypothesis testing (the structure of one sample hypothesis tests and the logic of using them to make decisions).

• Prerequisite: STAT1034
• Text: Introduction to the Practice of Statistics, 9e by Moore, McCabe, and Craig
• An introduction to inferential statistics for students without a calculus background. The course covers one and two-sample hypothesis tests for means and proportions, chi-squared tests, linear regression, analysis of variance, and non-parametric tests based on ranks, with attention to selecting the procedure(s) appropriate for the question and data structure, and interpreting the results.

• Prerequisite: A minimum score of 570 on the Math Placement Test or 26 on ACT-Math.
• Text: Calculus Concepts  (w/WebAssign), 5e by Latorre et al
• The first part of a two semester sequence (MATH1044 and 1045) of courses on calculus appropriate for students in business and life sciences. Topics covered include functions, graphs, limits, continuity, properties of exponential and logarithmic functions, differentiation, curve sketching, optimization and the definite integral.a

• Prerequisite: MATH1044
• Text: Calculus Concepts  (w/WebAssign), 5e by Latorre et al
• The second part of a two semester sequence (MATH1044 and 1045) on calculus appropriate for students in business and life sciences. Topics covered include anti-differentiation, the fundamental theorem of calculus, functions of two variables, partial derivatives, maxima and minima, Lagrange multipliers and applications to probability and other areas.

• Prerequisite: A minimum score of 620 on the Math Placement Test or 27 on ACT-Math and must be in an academic program in the Lindner College of Business.
• Text: Calculus Concepts (w/WebAssign), 5e by Latorre et al
• This is an accelerated calculus course targeted at students in business and is appropriate for students with a strong background in college algebra and wishing to complete calculus in a single semester. Topics covered include functions, graphs, limits, continuity, properties of exponential and logarithmic functions, differentiation, curve sketching, optimization, the definite integral, anti-differentiation, the fundamental theorem of calculus, functions of two variables, partial derivatives, maxima and minima, Lagrange multipliers and applications to probability and other areas.

• Prerequisite: A minimum score of 700 on the Math Placement Test or 28 on ACT-Math.
• Text: Calculus: Early Transcendentals, 9e by Stewart
• The course is an integrated review of functions, equations and systems of equations, sequences and series, trigonometry, and vectors with a comprehensive study of limits and continuity, differentiation, applications of the derivative, optimization, anti-derivatives, fundamental theorem of calculus, definite and indefinite integrals.

• Prerequisite: A minimum score of 750 on the Math Placement Test or 29 on ACT-Math.
• Text: Calculus: Early Transcendentals, 9e by Stewart
• The first part of a three-semester sequence of courses on calculus (MATH1061, MATH1062, MATH2063) for students in engineering and science. Topics covered include functions, limits and continuity, differentiation, applications of the derivative, optimization, anti-derivatives, fundamental theorem of calculus, definite and indefinite integrals.

• Prerequisite: MATH1061
• Text: Calculus: Early Transcendentals, 8e by Stewart
• The second part of a three-semester sequence of courses on calculus (MATH1061, MATH1062, MATH2063) for students in engineering and science. Topics covered include techniques of integration, applications of the integral, sequences and series, and vectors.

• Prerequisite: A minimum of 570 on the Math Placement Test or 26 on ACT-Math.
• Text: Discrete Mathematics with Applications, 4e by Epp
• A course designed for students interested in information technology and programming that includes topics in logic, number systems, set theory, methods of proof, probability, logic networks, and graph theory.

• Prerequisite: See your college advisor for details.
• Text: Applied Statistics and Probability for Engineers, 6e by Montgomery and Runger
• An introduction to probability and statistics for students with a calculus background. The course covers sample spaces and probability laws; discrete and continuous random variables with special emphasis on the binomial, Poisson, hypergeometric, normal and gamma distributions; joint distributions; sampling distributions; one- and two-sample parameter estimation problems; and one- and two-sample tests of hypotheses. This course provides a foundation for the further study of statistics.

• Prerequisite: MATH1062
• Text: Calculus: Early Transcendentals, 9e by Stewart
• Study of lines and planes, vector-valued functions, partial derivatives and their applications, multiple integrals, and calculus of vector fields.

• Prerequisite: See your college advisor for details.
• Text: Elementary Differential Equations  (w/WileyPLUS), 10e by Boyce & DiPrima
• Study of first-order differential equations (linear, separable, exact, homogenous), second-order linear homogeneous differential equations with constant coefficients, Euler equations, higher-order linear differential equations. Covers linear dependence for solutions of a second-order linear homogeneous differential equation, Wronskians, the method of undetermined coefficients, the method of variation of parameters, series solutions of second-order linear differential equations, regular singular points, and the Laplace transform.

• Prerequisite: You must have completed the following course(s) with the minimum grade of C- : MATH1062 or 15 MATH 253 or 15 MATH 253H or 28 MATH 253 or 28 MATH 263 or 34 MATH 263.
• Text: Introduction to Differential Equations with Dynamical Systems, 1e by Campbell & Haberman
• Study of first-order differential equations , second-order linear differential equations with constant coefficients and their applications, higher-order linear differential equations. Covers linear dependence for solutions of a second-order linear homogeneous differential equation. Wronskians, the method of undetermined coefficients, the method of variation of parameters, the Laplace transform, and the qualitative study of two-dimensional dynamical systems through phase-plane analysis.

• Prerequisite: See your college advisor for details.
• Text: Linear Algebrea and its Applications, 6e by Lay, Lay &McDonald
• Study of linear equations, matrices, Euclidean n-space and its subspaces, bases, dimension, coordinates, orthogonality, linear transformations, determinants, eigenvalues and eigenvectors, diagonalization.

• Prerequisite: See your college advisor for details.
• Mathematical Proofs: A Transition to Advanced Mathematics, 3e by Chartrand, Polimeni, and Zhang
• An introduction to writing mathematical proofs with an emphasis on understanding the language of logic and quantifiers. Students will be introduced to the basic concepts of set theory, functions, relations, and cardinality. The students will develop their ability to write correct mathematical proofs by proving elementary results in these areas.

• Prerequisite: See your college advisor for details
• Text: No book needed - using notes by Dr Don Wright
• The course will introduce analysis of functions through a study of the theoretical basis for results used in Calculus. The course will cover properties of the real and rational number systems, properties of real-valued functions, including continuity and differentiability, Riemann integrals and the Fundamental Theorem of Calculus, and properties of sequences and series. The formal definition of a limit will be a unifying theme for many of the concepts studied in the course.

• Prerequisite: See your college advisor for details
• Text: Abstract Algebra: An Introduction, 3e by Hungerford
• The course will focus on an introduction to commutative rings, primarily the integers, the integers modulo n, fields, and polynomials with coefficients in a field. Matrix rings may be presented as an example of a non-commutative ring. Divisibility, factorization, primality and irreducibility in the integers and polynomial rings will be studied. The concepts of homomorphism, isomorphism, congruence classes, ideals and quotient structures will be introduced. Examples of Euclidean domains, principal ideal domains, and unique factorization domains may be studied.

• Prerequisite: See your college advisor for details
• Text: No book needed at this time
• An axiomatic treatment of synthetic geometry is given, beginning with a development of neutral geometry, or geometry without the Parallel Postulate; theorems of neutral geometry are valid in both hyperbolic and Euclidean geometry. The formal development of Euclidean geometry begins with the addition of the Parallel Postulate. The main tools in Euclidean geometry are congruence and similarity of figures; triangles, quadrilaterals, and circles are studied in detail.

• Prerequisite: See your college advisor for details
• Text: No book needed
• Basic ideas of mathematical modeling, using differential equations, numerical methods, and perturbation techniques. Focus will be on learning and applying the techniques of applied mathematics to solve real-world problems.

• Prerequisite: 
• Text: No book needed at this time
• Inquiry-based approach to middle-school content areas of arithmetic (number systems, proportional reasoning, fractions, place value), geometry (shapes, measurement, transformations), algebra (with connections to arithmetic and geometry, as well as real-world problem-solving), functions and graphs, and discrete mathematics. Emphasis on developing mathematical understanding needed to teach these concepts effectively. This first course focuses on the development of number sense, including the representation of numbers, figurate numbers and pattern descriptions, number systems, place value, proportional reasoning, and fractions.

• Prerequisite: MATH3021
• Text: No book needed at this time
• Inquiry-based approach to middle-school content areas of arithmetic (number systems, proportional reasoning, fractions, place value), geometry (shapes, measurement, transformations), algebra (with connections to arithmetic and geometry, as well as real-world problem-solving), functions and graphs, and discrete mathematics. Emphasis on developing mathematical understanding needed to teach these concepts effectively. This second course focuses on the understanding of algebra, including algebraic problem-solving skills, pattern recognition and description, use of variables, using algebra and the coordinate plane to describe geometric objects, and the understanding of algebra as an extension of arithmetic.

• Prerequisite: MATH3022
• Text: No book needed at this time
• Inquiry-based approach to middle-school content areas of arithmetic (number systems, proportional reasoning, fractions, place value), geometry (shapes, measurement, transformations), algebra (with connections to arithmetic and geometry, as well as real-world problem-solving), functions and graphs, and discrete mathematics. Emphasis on developing mathematical understanding needed to teach these concepts effectively. This third course focuses on the understanding of geometry, including geometric problem-solving skills, description of geometric shapes, measurement, transformations of geometric figures, and continued work in using algebra and the coordinate plane to describe geometric objects and to solve geometric problems.

• Prerequisite: STAT2037
• Text: A Second Course in Statistics: Regression Analysis, 7e by Mendenhall & Sincich
• A second course in probability and statistics for students with a calculus background. This course covers chi-square tests used in goodness-of-fit problems as well as contingency tables, model building, simple and multiple linear regression, analysis of variance, experimental design, reliability, and quality control. The SAS software package may be used. This course provides a foundation for the further study of statistics.

• Prerequisite: See your college advisor for details.
• Text: No book needed at this time.
• This occasionally offered course will allow the student to be exposed to topics in mathematics that are not offered as part of our regular sequence of undergraduate mathematics courses. It will allow students to gain appreciation for the breadth of fields that are part of modern mathematics.

• Prerequisite: See your college advisor for details.
• Text: A First Course in Probability, 9e by Ross
• This course is an introduction to mathematical probability suitable as preparation for actuarial science, statistical theory, and mathematical modeling. Topics include: review of general probability rules, conditional probability and Bayes theorem, discrete and continuous random variables, standard discrete and continuous distributions and their properties, with emphasis on moments and moment generating functions, joint, marginal and conditional distributions, transformations of variables, order statistics, and the central limit theorem. Includes practice for the SOA/CAS Actuarial Exam P/1.

• Prerequisite: MATH4008 recommended.
• Text: TBD
• This course is primarily intended for students preparing for the SOA/CAS Actuarial Exam FM/2, although others interested in a general introduction to financial mathematics will find it useful. The course is a mathematical treatment of some fundamental concepts in financial mathematics pertaining to the calculation of present and accumulated values for various streams of cash flows  and includes discussion of interest, annuities, loans, bonds, portfolios, and financial instruments used for risk management. The concept of no-arbitrage pricing will be presented and used. Students will need a strong background in single-variable calculus (MATH1062) and probability theory (STAT2037).
  

• Prerequisite: 
• Text: 

• Prerequisite: See your college advisor for details.
• Topics include number-theoretic functions, congruences, primes and factorization, Diophantine equations, primitive roots and indices, quadratic residues, quadratic reciprocity, quadratic forms, and quadratic fields.

• Prerequisite: See your college advisor for details.
• Text: Differential Geometry of Curves and Surfaces, 1e by Do Carmo
• This is a topics course for advanced undergraduate math majors covering selected ideas from Topology and Differential Geometry. It will serve as an introduction to the ideas, problems, and methods in point set topology and/or differential geometry. Specific topics may include topologies and their bases, construction of topological spaces, metric spaces, open/closed sets, limit points, continuous maps, connectedness, compactness, surfaces in 3-space, tangent planes and the differential of a map, differential forms, orientation, the Gauss map, curvature, vector fields on surfaces, geodesics, the exponential map, the Gauss-Bonnet theorem.

• Prerequisite: See your college advisor for details.
• Text: No book needed at this time
• This occasionally-offered course will allow the student to be exposed to topics in the study of statistics that are not offered as part of our regular sequence of statistics courses. It will allow students to gain appreciation for the breadth of fields that are part of modern statistical science.

• Prerequisite: See your college advisor for details.
• Text: No book needed at this time
• Individual Work in Undergraduate Mathematical Sciences allows students to focus on topics outside in the standard curriculum in Mathematics and Statistics. Students work closely with faculty to develop reading lists and assignments. Permission of the Undergraduate Program Director is required.

• Prerequisite: See your college advisor for details.
• Text: No book needed 
• Capstone Seminar is designed for students in their final year of undergraduate study to explore a specific topic in the mathematical sciences through seminar-style learning. Participants will be responsible for preparing seminar lectures to present to the class, under the direction of the faculty instructor. The topics will be chosen to allow integration of material learned in core curriculum courses applied to mathematical topics not generally taught in other undergraduate courses. Participants will be expected to demonstrate active engagement in the seminar presentations of fellow students through appropriate questions and feedback. Topics chosen will vary each term.

• Prerequisite: See your college advisor for details.
• Text: No book needed 
• Capstone Project is designed to allow students in their final undergraduate year to explore a specific topic in the mathematical sciences through an independent, student-designed project under the mentorship of a faculty instructor. Students will be expected to develop their own project proposal with direction from their faculty mentor. The topic should be chosen to allow integration of material learned in core curriculum courses applied to a mathematical topic not generally taught in other undergraduate courses, or at a depth greater than achieved in such courses. Students will be expected to produce a substantial independent thesis, expository paper, applied mathematics or statistics project, or portfolio of relevant mathematical work. Students will be encouraged to present their project in a public forum.

• Prerequisite: See your college advisor for details.
• Text: The Elements of Real Analysis, 2e by Bartle
• This course studies the analysis of functions on Euclidean space and on metric spaces, starting with basic set theory and axioms of real numbers. Notions of continuity, convergence, differentiation and integration are emphasized. Material covered includes: Axioms of real numbers. Metric spaces. Completeness axiom. Open, closed, and compact sets in Euclidean spaces. Convergent sequences, Cauchy sequences. Upper and lower limits. Bolzano-Weierstrass and Heine-Borel theorems. Series, tests for convergence and absolute convergence. Limits and continuity of functions on metric spaces. Continuity in terms of open sets. Continuity with compactness, connectedness. Derivatives of functions on the real line, product, quotient, chain rules. Mean value, intermediate value, and Taylor theorems. Riemann integration on the real line, integrability of step functions, uniform limits of integrable functions, continuous functions. Change of variable. Students will be expected to have a strong background in single and multivariable calculus (MATH1062 and MATH2063) as well as the prior experience of a proof-based course (MATH3001 or MATH3002 or equivalent).

• Prerequisite: MATH6001 Advanced Calculus I
• Text: The Elements of Real Analysis, 2e by Bartle
• This is a direct continuation of MATH6001 with the emphasis on the calculus of mappings between general Euclidean spaces. Material covered includes: linear maps, differentiability, partial derivatives, differentiability of functions whose partial derivatives are continuous, chain rule, Jacobian, inverse and implicit function theorems. Uniform convergence of sequences of functions, Arzela-Ascoli theorem. Basics of Fourier series. Students will be expected to have completed MATH6001 or the equivalent.

• Prerequisite: See your college advisor for details.
• Text: Linear Algebra Notes (free .pdf) by Leep
• The course will study topics in linear algebra in the abstract setting, including abstract vector spaces, subspaces, isomorphisms, quotient spaces, linear independence, basis, dimension. Additional topics include linear functionals, duals, co-dimension, linear mappings, null space, range, Rank-Nullity theorem, transpositions, similarity, projections, matrices, Gaussian elimination, determinants, eigenvalues, eigenvectors, Spectral Mapping and Cayley-Hamilton theorems, minimal and characteristic polynomials, similarity of matrices, canonical forms.

• Prerequisite: See your college advisor for details.
• Text: Abstract Algebra, 3e by Dummit & Foote
• Definition of groups. Examples: symmetric group, dihedral group, matrixgroup, cyclic and abelian groups. Maps of groups, homomorphisms, epimorphisms, and isomorphisms. Order of a group, finite and infinite groups. Subgroups. Centralizers, normalizers, stabilizers, and kernels. The lattice of subgroups. Co-sets. Normal subgroups and simple groups. The isomoprhisms theorems. Lagrange theorem. Group actions. Permutations representations, Cayley's theorem and action of a group on a set of cosets, order of orbits, index of stabilizer, class equation. Automoprhisms. Sylow theorems. Frobenius' proof, Wieland's proof, simplicity of the alternating group. New groups from old. The isomorphism types of group of order less than 15. The direct product, internal and external. The direct sum, internal and external. The semidirect product. Classes of groups: nilpotent groups, solvable groups, free groups, generators and relations.

• Prerequisite: See your college advisor for details.
• Text: A First Course in Complex Analysis with Applications, 3e by Zill & Shanahan
• Complex numbers considered algebraically and geometrically, polar form, powers and roots, derivative of complex-valued functions, analyticity, Cauchy-Riemann equations, harmonic functions, elementary functions, and their derivatives, visualization of complex-valued functions, conformal mapping, elementary functions as conformal mappings, integration of complex-valued functions, Cauchy's Integral Theorem, Cauchy's Integral Formula, residue theory and applications, basics of Mobius transformations.

• Prerequisite: See your college advisor for details.
• Text: An Introduction to Numerical Analysis, 2e by Atkinson
• Topics will include floating point arithmetic, rootfinding for nonlinear equations, fixed point analysis, stability, interpolation theory, least squares methods for function approximation and numerical methods for integration. A primary focus is on the use of Taylor's theorem to analyze the methods. The analysis will be emphasized here instead of computation. Carefully chosen model or prototype problems will be examined in order to furnish theorems and insight into the behavior of the approximation methods.

• Prerequisite: See your college advisor for details.
• Text: Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, 5e by Haberman
• Heat equation, method of separation of variables, Fourier series. Wave equation: vibrating strings, and membranes. Sturm-Liouville eigenvalue problems. Non-homogenous problems. Green's functions for time-independent problems and/or Infinite domain problems: Fourier transform solutions of partial differential equations.

• Prerequisite: See your college advisor for details.
• Text: Introduction to Probability Models, 11e (free .pdf) by Ross
• A review of random variables and probability theory with an emphasis on conditioning as a technique for computing probabilities and expectations. Detailed study of discrete and continuous time Markov chains and Poisson processes, with introduction to one or more of the following: martingales, Brownian motion, random walks, renewal theory.

• Prerequisite: See your college advisor for details.
• Text: No book needed
• This course begins with models for finite financial markets in discrete time, covering derivatives, arbitrage pricing, market completeness, trading strategies, replicating portfolios, and risk neutral measures in this context, and constructing single and multiple period binomial tree models for modeling stock prices and pricing options. Then the analogous continuous time theory is developed. Concepts and techniques from probability and stochastic processes are introduced, including Brownian motion, martingales and stochastic calculus, in order to derive the martingale (risk-neutral) approach to solving the Black-Scholes p.d.e. and pricing a variety of financial contracts and derivatives. This course will be useful for students preparing for the Financial Economics segment of Actuarial Exam M.

• Prerequisite: See your college advisor for details.
• Text: Computational Financial Mathematics Using Mathematica (2003) by Stojanovic
• The course covers financial mathematics from the basics to advanced techniques and concepts. Financial mathematics and corresponding mathematical concepts are explained and derived mathematically while being implemented through programming in Mathematica at the same time. Knowledge of Mathematica is not required, but will be gained quickly, as it is used extensively. Topics include: Elementary stochastic differential equations (SDE); Monte-Carlo simulations; Ito chain rule; Log-Normal market model; derivation of the Black-Scholes partial differential equation (PDE) - pricing and hedging in complete markets; statistics of SDEs; statistical and implied volatility; local volatility pricing models and numerical PDEs; American options and free boundary problems; optimal portfolio theory; introduction to pricing and hedging in incomplete markets.

• Prerequisite: See your college advisor for details.
• Text: Linear Algebra and Its Applications, 4e by Strang (book might be out of print)
• Gaussian elimination, matrix operations, LDU factorization, inverses. Vector spaces, basis and dimension, the fundamental subspaces of a matrix. Linear transformations, matrix representations, change of bases. Orthogonality, Gram-Schmidt method, QR factorization, projections, least squares. Determinants, properties and applications. Eigenvalues and eigenvectors, diagonalization of a matrix, similarity transformations, symmetric matrices, applications to difference equations and differential equations. The Jordan form.

• Prerequisite: See your college advisor for details.
• Text: Numerical Python (2015) by Johansson
• Applications of mathematical programming using packages such as MATLAB and Mathematica. Projects will encompass calculus, linear algebra, and differential equations.

• Prerequisite: MATH2063 & STAT2037 & MATH2076 Or 15 MATH 264 & 15 STAT 362 & 15 MATH 352Or 15 MATH 254 & 15 STAT 362 & 15 MATH 352
• Text: Introduction to Mathematical Statistics, 7e by Hogg, McKean & Craig
• The purpose of these courses is to understand the theory of statistical inference using techniques, definitions, and concepts that are statistical and that are natural extensions and consequences of the statistical concepts. Specific topics include in Probability and Distributions, Multivariate Distributions, Some Special Statistical Distributions, Unbiasedness, Consistency, and Limiting Distributions and Central Limit Theorem.

• Prerequisite: STAT6021
• Text: Introduction to Mathematical Statistics, 7e by Hogg, McKean & Craig
• The purpose of these courses is to understand the theory of statistical inference using techniques, definitions, and concepts that are statistical and that are natural extensions and consequences of the statistical concepts. Specific topics include in Basics of statistical Inferences including point and interval estimation, Method of Moments and Maximum Likelihood estimation, Hypothesis testing, Sufficiency, Exponential family, Rao-Blackwell Theorem and Rao-Cramer Lower Bounds, Likelihood Ratio Tests, Neymann-Pearson Lemma and its applications.

• Prerequisite: See your college advisor for details.
• Text: Design and Analysis of Experiments, 8e by Montgomery
• The purpose of these courses is to understand statistical inference and data analysis in simple linear regression model and multiple linear regression models including model selections. Specific topics include: correlation coefficient, statistical inference of parameters, checking model assumptions, variable selection, transformations of variables and diagnostics.

• Prerequisite: STAT6031
• Text: Design and Analysis of Experiemnts, 8e by Montgomery
• The course covers the theory and application of analysis of variance with one-, two-, and higher-way layouts, random effects and mixed models. Mathematical and interpretational aspects of the models will be covered along with statistical estimation, confidence intervals and multiple hypothesis testing. SAS statistical software will be used. Specific topics include: ANOVA for some standard experimental designs.

• Prerequisite: See your college advisorfor details
• Text: Introductory Time Series Using R  (2009) by Cowpertwait and Matcalfe
• This course will cover the basics of time series analysis, including autocorrelation, moving averages, autoregressive models, seasonality, forecasting, spectral analysis, Box Jenkins ARIMA models, and transfer function models and multivariate ARIMA models.

• Prerequisite: See your college advisor for details.
• Text:
  • Statistical Methods for Survival Data Analysis, 4e by Lee & Wang 
  • Modeling Survival Data in Medical Research, 3e by Collett (optional)
  • Survival Analysis Using the SAS System, 2e by Allison (optional)
• This course will begin with a detailed description of maximum likelihood. It will then discuss generalized linear models, including logistic and Poisson regression. Finally various topics in survival analysis will be covered: namely Kaplan-Meier curves and log-rank statistics, Weibull regression, and Cox proportional hazard regression. Examples from medicine and engineering will be given. SAS and S-plus statistical software will be used.

• Prerequisite: See your college advisor for details.
• Text: TBD
• Foundation of Bayesian Statistics, basic theory and several applications including Monte Carlo and Markov Chain Monte Carlo Methods for computing Bayesian inference will be covered. Specific topics include: Foundation of Bayesian Approach, Prior and Posterior distributions; Choice of Priors: subjective and non-subjective or default approaches; Inference using posterior distribution for standard models; and Hierarchical models, and their applications. WinBUGS will be introduced.

• Prerequisite: See your college advisor for details.
• Text: Nonparametrics: Statistical Methods Based on Ranks  (2006) by Lehmann
• Rank-based statistical inference will be covered. Topics include, but are not limited to, the one- and two-sample location problems including the Wilcoxon signed-rank and rank-sum test, Spearman correlation coefficient, one- and two-way Analysis-of-Variance tests, and Kolmogorov-Smirnov test for testing different distributions. In addition, the multiple comparisons issue will be discussed, specifically by comparing several treatments with and without a control treatment. Null distributions of test statistics will be discussed in the small sample and asymptotic cases, with and without ties.

• Prerequisite: See your college advisor for details.
• Text: Nonparametrics: Statistical Methods Based on Ranks  (2006) by Lehmann 
• This course will cover the basics of using the SAS and S-Plus statistical software. Topics covered include: importing external files, subsetting and merging data files, performing statistical procedures, graphics, matrix calculations, and macros and functions.

• Prerequisite: See your college adivsor for details.
• Text: TBD
• The course will vary according to the topic.

• Prerequisite: MATH6048
• Text: TBD
• The course will vary according to the topic.

• Prerequisite: See your college advisor for details.
• Text: Ordinary Differential Equations and Applications (1999) by Weiglhofer & Lindsay 
• This course is intended for undergraduates and for graduate students in other departments; it is not intended for graduate students in the mathematical sciences. It covers the theory of ordinary differential equations, with an emphasis on applications. Basic concepts, special types of differential equations of the first order,and problems that lead to them.Linear differential equations of order greater than one and problems that lead to them. Linear vector spaces. Systems of differential equations, linearization of first order systems, problems giving rise to systems. Existence and uniqueness theorem for first order differential equations. Existence and uniqueness theorem for a system of first order differential equations and for linear and nonlinear differential equations of order greater than one. Wronskians. Other supplementary topics: state variable description of systems, fundamental matrix, state transition matrix, matrix exponential, stability of linear systems. Time permitting: Operators and Laplace transforms, series methods.

• Prerequisite: See your college advisor for details.
• Text: Real Analysis, 4e by Royden & Fitzpatrick
• Measure and integration with emphasis on the real line and the plane. Measures and measurable functions, Lusin and Egoroff theorems, Lebesgue integral, Fatou's lemma, monotone and dominated convergence. Convergences: uniform, a.e., in measure, in mean. Product measures, Fubini and Tonelli theorems. Radon-Nikodym theorem. Absolute continuity, bounded variation, and the fundamental theorem of calculus on the real line.

• Prerequisite: See your college advisor for details.
• Text: Topology: A First Course, 2e by Munkres
• Pointset topology (approximately 10 weeks): Topological spaces, closed sets, subspaces, closure, boundary, interior, connectedness, path-connectedness, compactness, normal topology, Hausdorff property, continuity at a point (topological continuity and sequential continuity), continuous maps, Urysohn metrization theorem, Tietze extension theorem, quotient topology, weak topology, Baire category theorem, nets, convergence with respect to nets. Fundamental groups (approximately 4 weeks): Homotopy of paths, homotopy of maps, fundamental groups, fundamental groups of (i) circles, (ii) spheres, (iii) torii, (iv) Möbius strip and (v) Klein bottle, free groups, simply connected spaces, covering spaces, homotopy lifting theorem.

• Prerequisite: See your college advisor for details.
• Text: Differential Equations and Dynamical Systems, 3e by Perko
• Linear systems: linear systems with constant coefficients, phase portraits and dynamical classification, linear systems and exponentials of operators, linear systems and canonical forms of operators. Fundamental theory: existence and uniqueness, continuity and differentiability of solutions in initial conditions, extending solutions, global solutions. Nonlinear systems: nonlinear sinks and sources, hyperbolicity, stability, limit sets, gradient and Hamiltonian systems, other topics at instructor's discretion.

• Prerequisite: See your college advisor for details.
• Text: Partial Differential Equations, 2e by Evans
• Transport equations: smooth and non-smooth solutions.
• Laplace equation: mean-value property, smoothness, maximum principle, uniqueness of solutions, Harnack inequality, Liouville theorem.
• Poisson Equation: Fundamental solution, Greens functions, energy methods.
• Heat Equation: Fundamental solution, maximum principle, uniqueness of solutions on a bounded domain, Duhamel's principle, energy methods.
• Wave equation: Fundamental solutions in 1, 2, and 3 dimensions, energy methods, finite propagation speed.
• Nonlinear first-order equations: Characteristic ODEs, local existence of smooth solutions, conservation law equations, shocks, rarefaction, integral solutions.
• Additional topics (traveling waves, Fourier transform, etc.) at instructor's discretion.

• Prerequisite: STAT6021, STAT6022, STAT6031 or see the professor
• Text: Categorical Data Analysis, 3e by Agresti Regression Analysis of Count Data, 2e by Cameron and Trivedi
• This graduate level course covers methodology and its application of survey sampling: fundamental sampling theories, practical guidance to conduct sample surveys (with using statistical software), and methodological arguments.

• Prerequisite: Minimum Grade of: C in STAT6022 & STAT6032 or 15 STAT 523 & 15 STAT 533.
• Text: TBD
• The course will cover multivariate normal distribution, distributions of quadratic forms, theory of Analysis of variance as applied to linear regression in full-rank models, estimability and testability in non-full-rank models, and generalized inverse and its use in such models, various types of sums of squares in ANOVA of designed models, associated estimable and testable functions in balanced and unbalanced designs with fixed effects, random effects and mixed effects, and nested and crossed factors. Estimation and testing of fixed effects and variance components using ANOVA Sums of Squares will be covered. SAS will be extensively used to apply these concepts with real data.

• Prerequisite: STAT7021
• Text: TBD
• A continuation of STAT7021.

• Prerequisite: STAT6031 & STAT6032
• Text:
  • Design and Analysis of Experiments, 8e by Montgomery
  • Applied Mulitvariate Statistical Analysis (2012) by Johnson & Wichern
• This course will cover the following topics in depth: Random Effect Model; Mixed Model; Repeated Measure Model; Principal Component Analysis; Factor Analysis; Discriminent Analysis.

• Prerequisite: Minimum Grade of: C in STAT6022 or 15 STAT 523
• Text: Theory of Point Estimation  (2003) by Lehmann & Casella
• The course will cover the following topics in depth: Distribution theory, Estimation, Hypotheses testing, Asymptotic behavior of statistics, basics of Bayesian methods, and Decision theory.

• Prerequisite: A good knowledge of multivariable calculus and an introduction to analysis is a must. Advanced Calculus (MATH 6001/6002), Mathematical Statistics (STAT 6021/6022), or equivalent is recommended.
• Text: TBD
• Measure theoretic foundations of probability: random variables, expected value (Lebesgue integral). Laws of large numbers, weak convergence. Characteristic functions, central limit theorem. Conditional probability, conditional expectation. Students will be expected to have a strong background in theoretical mathematics or statistics.

• Prerequisite:
  • MATH6001, MATH6002, MATH6003 required
  • MATH7002 or MATH7004 recommended
• Text:
  • Real Analysis, Modern Techniques and Their Applicaiton, 2e by Folland
  • A Short Course on Spectral Theory (2002) by Arveson
• This course develops some of the theory of infinite dimensional linear algebra. As it turns out, the task requires extensive use of topological concepts like continuity, open/closed sets, and convergence, as well as bits of complex analysis. Topics include: Banach Spaces, examples including Lp spaces, continuous functions, smooth functions, brief introductions to Hilbert spaces. Linear maps between Banach spaces. Duality. Weak, weak*, and operator topologies. Introduction to Banach Algebras. The spectrum and spectral radius of an element. Abelian algebras, Gelfand theory of representations. Time permitting, spectral measures adn functional calculus, or else compact and Fredholm operators.

• Prerequisite: See your college advisor for details.
• Text: No book needed at this time
• Affine varieties. Correspondence between ideals and varieties, Zariski topology, Hilbert's nullstellensatz. Hilbert's basis theorem, Polynomial and rational functions. Projective varieties. Projective space and varieties, maps between projective varieties, adjunction of roots, finite fields. Tangent spaces, smoothness and dimension, localization and the tangent space at a point, smooth and singular points, dimension of a variety. Optional topics: Elliptic Curves. Plane curves. Classification of smooth cubics. Group structure of an elliptic curve. Theory of Curves. Divisors on curves, Bezout's theorem, Linear systems on curves Computational algebraic geometry, Groebner basis algorithm, existence and uniqueness of Groebner bases, implementation of the algorithm.

• Prerequisite: 
• Text: No book needed at this time

• Prerequisite: 
• Text: Partial Differential Equations, 2e by Evans

• Prerequisite: See your college advisor for details.
• Text: No book needed at this time
• Partial differential equations (PDEs) model a wide range of physical phenomena including heat conduction, wave propagation, and fluid flow. Computer approximations to the solutions of the PDE problems that arise in these applications are usually required. This course will focus on the finite element method (FEM) and will use energy (Hilbert space) techniques. The first part of the course will cover error analysis for ordinary differential equations from the Atkinson text (Chapter 6) and also iterative methods for matrices (Sections 8.6-8.8). The second part of this course will discuss the mathematical foundations of the FEM in Sobolev spaces and develop a basic approximation theory. Once this background is established, we will survey error estimates developed in various applications which may include first order hyperbolic equations, nonlinear time-dependent parabolic problems including the Cahn-Hilliard (phase transitions) or the Navier-Stokes (fluid flow) equations. We may also look at discontinuous Galerkin discretizations in time and space. Nonconforming methods are also of interest as well as the development of a posteriori error estimates.

• Prerequisite: 
• Text: 

• Prerequisite: You must have completed the following course(s) with the minimum Grade of: C
  • STAT6043 & STAT7031
  • Or 15 STAT 573 & 15 STAT 632
• Text: The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation, 2e by Christian
• The course will cover, Choice of priors for estimation and testing, Bayes factors and calculation, Model selection and related computational methods, and choice of topics.

• Prerequisite: 
• Text: 

The following courses are offered for the M.A.T. Program and are offered only during the summer term.

• Prerequisite: 
• Text:  
• Congruences, divisibility, primes, number-theoretic functions, number bases and applications.

• Prerequisite: 
• Text:  
• The theory of rings and fields with emphasis on the algebra of polynomials.

• Prerequisite: 
• Text:  
• Probability axioms and finite probability spaces. Combinatorics. Binomial and Normal distributions. Design of statistical studies and methods of statistical inference.

• Prerequisite: 
• Text:  
• Spreadsheets and statistical packages for handling and exploring data, doing simulations, and demonstrating concepts of statistics. Project-oriented with cooperative learning component.

• Prerequisite: 
• Text:  
• Axiomatic geometry, both neutral and Euclidean. Use of Geometer's Sketchpad will be an integral part of the courses.

• Prerequisite: 
• Text:  
• Transformational geometry. Use of Geometer's Sketchpad will be an integral part of the courses.

• Prerequisite: 
• Text:  
• Studies vectors and linear transformations; algebra of matrices. Focus is on dimensions 2 and 3. Isometries and symmetry groups. For students in the MAT program or by permission of the instructor.

• Prerequisite: 
• Text:  
• Technology for teaching geometry, including: dynamic geometry programs; computer graphics; and technical word processing. Design of lessons that use technology. Project-oriented with cooperative learning component. For students in the MAT program or by permission of the instructor.

• Prerequisite: 
• Text:  
• Theory of calculus of one variable. Continuity and differentiability.

• Prerequisite: 
• Text:  
• Theory of calculus of one variable. Riemann integral and infinite series.

• Prerequisite: 
• Text: 
• Development and analysis of mathematical models of discrete and continuous phenomena.

• Prerequisite: 
• Text: Introduction to the use of technology for teaching analysis (pre-calculus and calculus). Graphing calculators, symbolic algebra programs. Design and delivery of lessons that use technology. Project-oriented with cooperative learning component.

• Prerequisite: 
• Text: 
• Preparation and presentation of the Master of Arts in Teaching project.