The Department of Mathematics offers a variety of undergraduate and graduate mathematics courses throughout the academic year. Some courses have pre-requisites which will be checked for each student at the begin of each semester.

#### Courses on this page:

## Undergraduate

- 2 Credits The Art of Mathematics MA-UY 1002
- This is an introductory course about Mathematics. Areas of Mathematics. History of Mathematics. Mathematical Methods. Great Mathematicians. Famous open and solved mathematical problems. The study of Mathematics. Mathematical Software.

Prerequisite: Only first-year students are permitted to enroll in this introductory level course. - 4 Credits Basic Practice of Statistics for Social Science MA-UY 2414
- We are inundated by data, but data alone does not translate into useful information. Statistics provides the means for organizing, summarizing, and therefore better analyzing data so that we can understand what the data tell us about critical questions. If one collects data then understanding how to use statistical methods is critical, but it is also necessary to understand and interpret all the information we consume on a daily basis. This course provides these basic statistical approaches and techniques. This course may not be acceptable as a substitute for any other Probability and Statistics course. For SUE students. See your advisor.

### Precalculus

- 4 Credits Precalculus for Engineers MA-UY 914
- This course covers foundations of algebra: exponents, multiplication of algebraic expressions, factoring algebraic expressions, working with algebraic fractions, proportionality, rates of change, equation of a line, completing squares, the quadratic formula, solving equations, systems of linear equations, inequalities, domain and range of functions, exponential and logarithmic functions, compositions, transformations of functions, right triangles, trigonometry of triangles.

Prerequisite: placement exam. Note: credit for this course may not be used to satisfy the minimum credit requirement for graduation. Corequisite: EX-UY 1 - 4 Credits Precalculus MA-UY 954
- This course covers the fundamentals of algebra with a focus on Management and the Life Sciences. The topics include: foundations of algebra, solving equations, exponents, working with algebraic expressions, working with algebraic fractions, proportionality, rates of change, lines in the plane, completing squares, the quadratic formula, systems of linear equations, inequalities, graphs, exponentials, logarithms, inverses, compositions, transformations of functions and right angle trigonometry.

Prerequisite: placement exam. Note: Course required only for specific Majors in place of MA 914. Credit for this course may not be used to satisfy the minimum credit requirement for graduation. Corequisite: EX-UY 1

### Freshman

- 4 Credits Calculus I With Pre-Calculus MA-UY 1054
- This course covers limits, definition of the derivative, differentiation rules for polynomial and trigonometric functions, applications of the chain rule and introduction to optimization. This Calculus I course provides an in-depth review of precalculus.

Prerequisite: Placement exam or MA-UY 912 or equivalent. Note: Course required only for specific Majors in place of MA-UY 1024/1324. Corequisite: EX-UY 1. - 4 Credits Calculus II With Pre-Calculus MA-UY 1154
- This course uses the first and second derivative, optimization problems, antiderivatives, fundamental theorem of calculus, techniques of integration, logarithmic and exponential functions, numerical methods of integration, applications of integration, introduction to differential equations, introduction to series. This Calculus II course provides an in-depth review of precalculus.

Prerequisite: MA-UY 1054. Note: Course required only for specific Majors in place of MA-UY 1124/1424. Corequisite: EX-UY 1 - 2 Credits Calculus for Business and Life Sciences IIa MA-UY 1252
- This course covers antidifferentiation, the definite integral, integration by substitution, The Fundamental Theorem of Calculus, Area between curves, average value, integration by parts, introduction to differential equations, improper integrals, numerical integration.

Prerequisite: MA-UY 1054. Note: Course required only for specific Majors. Corequisite: EX-UY 1 - 4 Credits Calculus I for Engineers MA-UY 1024
- This course covers library of Functions: functions of one variable. Limits, derivatives of functions defined by graphs, tables and formulas, differentiation rules for power, polynomial, exponential and logarithmic functions, derivatives of trigonometric functions, the product and quotient rule, the chain rule, applications of the chain rule, maxima and minima, optimization. MA 1324 is for students who wish to take MA 1024 but need more review of precalculus. MA1324 covers the same material as MA1024 but with more contact hours a week, incorporating a full discussion of the required precalculus topics.

Prerequisite: Placement Exam or MA-UY 912 or MA-UY 914. Corequisite: EX-UY 1 - 4 Credits Calculus II for Engineers MA-UY 1124
- This course covers definite integrals, theorems about integrals, anti-derivatives, second fundamental theorem of calculus, techniques of integration, introduction to ordinary differential equations, improper integrals, numerical methods of integration, applications of integration, sequences, series, power series, approximations of functions via Taylor polynomials, Taylor series.

Prerequisites: MA-UY 1024 or MA-UY 1324 (B or better) or MA-UY 1022 or MA-UY 1322 (B or better).

Corequisite: EX-UY 1. - 4 Credits Integrated Calculus I for Engineers MA-UY 1324
- MA-UY 1324 is for students who wish to take MA-UY 1024 but need more review of precalculus. MA-UY 1324 covers the same material as MA-UY 1024 but with more contact hours a week, incorporating a full discussion of the required precalculus topics.

Prerequisite: Placement Exam or MA-UY 912 or MA-UY 914. Corequisite: EX-UY 1. - 4 Credits Integrated Calculus II for Engineers MA-UY 1424
- This course MA-UY 1424 is for students who wish to take MA-UY 1124 but need more review of precalculus. MA-UY 1424 covers the same material as MA-UY 1124 but with more contact hours a week, incorporating a full discussion of the required precalculus topics.

Prerequisites: For MA-UY 1124: MA-UY 1024 or MA-UY 1324; for MA-UY 1424: MA-UY 1324 or MA-UY 1024 or MA-UY 1022 or MA-UY 1322. Note: credit for this course may be used to satisfy the minimum credit requirement for graduation. Corequisite: EX-UY 1 - 2 Credits Numerical Methods for Calculus MA-UY 1132
- Parametrized family of curves. Elementary Numerical Analysis. Introduction to differential equations. Solution of first and second order linear differential equations with constant coefficients. Use of mathematical software to solve differential equations. Fourier series.

Prerequisite: AP credit or transfer credit for Calculus I and II or MA-UY 1112 or (MA-UY 1054 and MA-UY 1154)

Corequisite: EX-UY 1.

### Sophomore

- 4 Credits Applied Business Data Analysis I MA-UY 2054
- This course covers applications of theories of random phenomena to problems in business management. Topics include probability theory, discrete and continuous probability distributions, sampling, measures of central value and dispersion, sampling distributions, statistical estimation and introduction to hypothesis testing. Use of statistical software is integrated with the previous topics; examples are drawn from problems in business decision-making. Applications to advanced statistical applications in business management. Emphasis is on application of concepts. Use of statistical software integrated with the previous topics.

Prerequisite: MA-UY 1054 or equivalent. Note: Course required only for Management Majors. Credit for this course may not be used to satisfy the requirements for other majors. - 2 Credits Elements of Linear Algebra I MA-UY 2012
- This course introduces vector concepts. Linear transformations.Matrices and Determinants. Characteristic roots and eigenfunctions.

Prerequisite: MA-UY 1124 or equivalent. - 2 Credits Ordinary Differential Equations MA-UY 2132
- This course covers first order differential equations: modeling and solving. Stability of autonomous equations. Higher order linear ordinary differential equations: Solution bases, Wronskian and initial value problems. Linear system of first-order differential equations with constant coefficients: Elimination and eigenvalue method of solution. Elementary concepts of numerical analysis. Numerical solution of initial value problems for ordinary differential equations.

Prerequisite or Corequisite: MA-UY 2012. - 2 Credits Multivariable Calculus A MA-UY 2112
- This course introduces Multivariable Calculus. Analysis of functions of several variables, vector valued functions, partial derivatives and multiple integrals.

Prerequisite: MA-UY 2012. - 2 Credits Multivariable Calculus B MA-UY 2122
- This course continues Multivariable Calculus. Optimization techniques, parametric equations, line integrals, surface integrals and major theorems concerning their applications.

Prerequisite: MA-UY 2112. - 2 Credits Data Analysis I MA-UY 2212
- This course covers basic theory of probability. Random variables. Distributions. Expectation. Functions of a random variable. Descriptive statistics. Data description. Sampling distributions. Use of statistical software is integrated with previous topics.

Prerequisite: MA-UY 1124 or equivalent. - 2 Credits Data Analysis II MA-UY 2222
- This course covers point and interval estimation. Hypothesis testing. Linear regression. One-way analysis of variance. Use of statistical software is integrated with the previous topics.

Prerequisite: MA-UY 2212. - 2 Credits Discrete Math 1 MA-UY 2312
- This course covers logic and induction. Sets and functions. Recursive definitions. Counting techniques. Inclusion-exclusion principle.

Prerequisite: MA-UY 1124 or equivalent. - 2 Credits Discrete Math 2 MA-UY 2322
- This course covers recurrence relations and generating functions. Equivalence relations and partial orderings. Graphs and connectivity of graphs. Trees and sorting. Boolean algebra, languages and finite state machines.

Prerequisite: MA-UY 2312. - 4 Credits Linear Algebra and Differential Equations MA-UY 2034
- MA-UY 2034 is an introduction to ordinary differential equations and linear algebra. The course develops the techniques for the analytic and numeric solutions of ordinary differential equations (and systems) that are widely used in modern engineering and science. Linear algebra is used as a tool for solving systems of linear equations as well as for understanding the structure of solutions to linear (systems) of differential equations. Topics covered include the fundamental concepts of linear algebra such as Gaussian elimination, matrix theory, linear transformations, vector spaces, subspaces, basis, eigenvectors, eigenvalues and the diagonalization of matrices, as well as the techniques for the analytic and numeric solutions of ordinary differential equations (and systems) that commonly appear in modern engineering and science.

Prerequisite: MA-UY 1124, MA-UY 1424 or MA-UY 1132. - 4 Credits Calculus III: Multi-Dimensional Calculus MA-UY 2114
- Functions of several variables. Vectors in the plane and space. Partial derivatives with applications, especially Lagrange multipliers. Double and triple integrals. Spherical and cylindrical coordinates. Surface and line integrals. Divergence, gradient, and curl. Theorems of Gauss and Stokes.

Prerequisite: MA-UY 1124, MA-UY 1424, or MA-UY 1132. - 4 Credits Data Analysis MA-UY 2224
- An introductory course to probability and statistics. It affords the student some acquaintance with both probability and statistics in a single term. Topics in Probability include mathematical treatment of chance; combinatorics; binomial, Poisson, and Gaussian distributions; the Central Limit Theorem and the normal approximation. Topics in Statistics include sampling distribution of sample mean and sample variance; normal, t-, and Chi-square distributions; confidence intervals; testing of hypotheses; least square regression model. Applications to scientific, industrial, and financial data are integrated into the course. NOTE: Cannot be taken if student is also taking or has already taken MA-UY 3012 or MA-UY 3022.

Prerequisite: MA-UY 1124, MA-UY1424, or MA-UY 1132

### Junior

- 2 Credits Introduction to Probability I MA-UY 3012
- This course covers probability of events. Random variables. Discrete and continuous distributions. Joint distributions. Expectation. Functions of a random variable. Central limit theorem.

Prerequisite: MA-UY 2112 or MA-UY 2114. - 2 Credits Complex Variables I MA-UY 3112
- This course covers functions of a complex variable. Derivatives and Cauchy-Riemann equations. Integrals and Cauchy integral theorem. Power and Laurent Series. Residue theory.

Prerequisite: MA-UY 2122 or equivalent. - 3 Credits Problem Solving and Proofs MA-UY 3103
- This course covers mathematical problem-solving, proofs and innovative reasoning. Discussion of independent challenging problems from Analysis, Complex Analysis, Probability, Combinatorics, Linear Algebra, Number Theory and Graph Theory.

Prerequisites: MA-UY 2312, MA-UY 2012. - 3 Credits Linear Optimization MA-UY 3203
- This course examines linear optimization problems with constraints; optimality conditions and duality theory, the simplex method, complexity of the simplex method, interior point methods, selected applications, network flow problems and the network simplex method.

Prerequisites: MA-UY 2312, MA-UY 2112. - 3 Credits Differential Geometry MA-UY 3303
- This course covers curves and Surfaces. Curvature. First and second fundamental form. Gaussian curvature. Geodesics, Minimal Surfaces. Gauss-Bonnet Theorem.

Prerequisite: MA-UY 2122 or MA-UY 2114. - 4 Credits Project in Mathematics I MA-UY 3914
- In this course, students reading, study and investigation of selected topics in mathematics. Problems are discussed and presented by participating students.

Prerequisite: approval of departmental adviser.

### Senior

- 3 Credits Introduction to Number Theory MA-UY 4013
- This course covers properties of integers and prime numbers. Congruences. Theorems of Fermat, Euler and Wilson. Quadratic residues. Diophantine equations.

Prerequisite: MA-UY 1124 or equivalent. - 3 Credits Elements of Abstract Algebra MA-UY 4023
- This course covers basic properties of groups, rings, fields, Euclidean rings and modules. Field extensions and Galois theory. Finite fields.

Prerequisite: MA-UY 2012. - 3 Credits Introduction to Mathematical Statistics MA-UY 4113
- Standard first course in mathematical statistics, recommended for those planning to take advanced courses in statistics. Sampling distributions, tests of hypotheses, significance tests, point and interval estimation, regression and analysis of variance.

Prerequisites: MA-UY 2233. - 3 Credits Statistical Methods MA-UY 4123
- This course covers analysis of variance with simple experimental designs. Topics covered: Sampling procedures, including sequential analysis. Nonparametric statistical methods. Statistical decisions.

Prerequisite: MA-UY 4113. - 3 Credits Time Series MA-UY 4133
- This course examines properties of time series, regression methods, linear processes, moving average processes, autoregressive processes, ARIMA models, autocorrelation, nonstationarity, parameter estimation, forecasting,
regression models, ARCH, GARCH models, applications.

Prerequisite: MA-UY 2222. - 3 Credits Applied Partial Differential Equations MA-UY 4413
- Modeling of physical processes. Classification of equations. Formulation and treatment of boundary- and initial-value problems. Greens functions. Maximum principle. Separation of variables. Fourier series and integrals. Quasilinear first-order equations and characteristics. DAlembert solution of wave equation. Conservation laws and shock waves.

Prerequisites: MA-UY 108 or Departmental adviser’s approval. - 3 Credits Introductory Numerical Analysis MA-UY 4423
- This course covers: Polynomial interpolation and approximation of functions. Divided differences. Least-squares data fitting, orthogonal polynomials. Numerical differentiation and integration. Solution of nonlinear equations. Gaussian elimination, pivoting, iterative refinement, conditioning of matrices. Numerical solution of ordinary differential equations.

Prerequisites: MA-UY 2132, MA-UY 2034 or MA-UY 108. - 3 Credits Complex Variables MA-UY 4433
- This course covers: Functions of a complex variable. Derivatives and Cauchy-Riemann equations. Integrals and Cauchy integral theory. Power and Laurent series. Residue theory. Conformal mappings. Schwarz-Christoffel transformations.

Prerequisites: MA-UY 2132 and MA-UY 3112. - 3 Credits Analysis I MA-UY 4613
- This course covers the study of basic topics in analysis with emphasis on methods. Sequences, series, functions, uniform convergence, continuity, partial differentiation, extreme value problems with constraints, Riemann integrals, line integrals, improper integrals, integrals with parameters, transformations, Riemann-Stieltjes integral, uniform and absolute convergence of integrals. Beta and Gamma functions.

Prerequisites: MA-UY 2122 or MA-UY 2114 and MA-UY 2132 or MA-UY 2034. - 3 Credits Analysis II MA-UY 4623
- This course covers the study of basic topics in analysis with emphasis on methods. Sequences, series, functions, uniform convergence, continuity, partial differentiation, extreme value problems with constraints, Riemann integrals, line integrals, improper integrals, integrals with parameters, transformations, Riemann-Stieltjes integral, uniform and absolute convergence of integrals. Beta and Gamma functions.

Prerequisites: MA-UY 4613 - MA-UY 4924 (Please refer to the bulletin)
- 3 Credits Thesis for Bachelor of Science Degree MA-UY 4993
- The course provides the framework for a bachelor’s thesis. In the bachelor’s thesis, a student reports on an independent investigation of a topic in Mathematics that demonstrates an in-depth knowledge of that area of Mathematics and proficiency in using its specific methods.

Prerequisite: Departmental adviser’s approval.

## Graduate

- 3 Credits Elements of Real Analysis II MA-GY 6223
- This course continues MA-GY 6213. The topics are integration, series of real numbers, sequences and series of functions and Fourier series. Important concepts and theorems include Riemann and Riemann-Stieltjes integral, fundamental theorem of calculus, the mean value theorem of integrals, Dirichlet test, absolute and conditional convergence, uniform convergence, Weierstrass test, power series, orthogonal functions and Fourier series.

Prerequisite: MA-GY 6213. - 3 Credits Theory of Partial Differential Equations I MA-GY 6253
- This course covers: Partial differential equations. Cauchy-Kowalewski theorem. First-order differential equations, systems of differential equations in two variables, characteristics and classification, hyperbolic, parabolic and elliptic systems. Well-posedness.

Prerequisites: MA-GY 6213 and MA-GY 6223 - 3 Credits Elements of Geometry and Topology MA-GY 6403
- This course covers: Differential geometry in the plane. Introduction to transformation groups. Space curves and ruled surfaces. Tensors and exterior forms. Manifolds and tensor fields. Theory of surfaces. Introduction to Riemannian geometry.

Prerequisite: MA-GY 2122 and MA-GY 2132 or equivalent. - 3 Credits Applied Statistics I (Data Analysis) MA-GY 6513
- This course covers: Treatment of statistical methods and application to analysis of data, fitting of functions to data. Estimation of population parameters, t-tests, chi square tests, rank tests.

Prerequisite: MA-UY 1124 or equivalent. - 3 Credits Stochastic Processes MA-GY 6823
- This course covers: Normal and stationary processes, Wiener processes, Poisson and renewal processes, Markov processes.

Prerequisite: MA-GY 6813 or equivalent. - 3 Credits Linear Algebra I MA-GY 7033
- This course covers: Basic ideas of linear algebra: Groups, Rings, Fields, vector spaces, basis, dependence, independence, dimension. Relation to solving systems of linear equations and matrices. Homomorphisms, duality, inner products, adjoints and similarity.

Prerequisites: MA-UY 2034 and MA-UY 2114 or Graduate Standing - 3 Credits Linear Algebra II MA-GY 7043
- This course continues MA-GY 7033. Topics covered: Basic concepts of linear algebra continuing with: Range, nullity, determinants and eigenvalues of matrices and linear homomorphisms, the polar decomposition and spectral properties of linear maps, orthogonality, adjointness and its applications.

Prerequisite: MA-GY 7033. - 3 Credits Measure Theory I MA-GY 7333
- This course presents a unified treatment of that part of measure theory that is most useful for its application in modern analysis. Topics covered: Sets and classes, measures and outer measures, measurable functions, integration, general set functions, product spaces, transformations, probability. The dominated convergence theorem, Riesz Representation Theorem, Vitali-Caratheodory theorem, etc. are covered in conjunction with many examples.

Prerequisite: Graduate status. - 3 Credits Measure Theory II MA-GY 7343
- This course continues MA-GY 7333 and presents a unified treatment of that part of measure theory that is most useful for applications in modern analysis. Topics covered: Fubini’s theorem, convolutions and distributions are applied to explicit examples. In this part, Baire’s theorem,the Banach-Steinhaus theorem, the Open Mapping theorem, the Hahn-Banach Theorem are derived with the properties of the Radon-Nikodym derivatives to naturally generalize calculus both differential and integral.

Prerequisite: MA-GY 7333. - 3 Credits Topics in Geometry I MA-GY 7683
- Course content varies.

Prerequisites: MA-GY 6403 and MA-GY 7693 - 3 Credits Topics in Geometry II MA-GY 7693
- Course content varies.

Prerequisites: MA-GY 7683 - 3 Credits Advanced Topics in Applied Mathematics I MA-GY 8163
- Course content varies.

Prerequisite: MA-GY 6003

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