Undergraduate Course Descriptions

MAUY.0914 Precalculus for Engineers
4 points. Offered every term.
Prerequisites:
Diagnostic exam.
Corequisites:
EXUY 1
Notes:
Credit for this course may not be used to satisfy the minimum credit requirement for graduation.
Description:
This course covers: foundations of algebra, exponents, multiplication of algebraic expressions, factoring algebraic expressions, working with algebraic fractions, proportionality, rates of change, equations of lines, completing squares, the quadratic formula, solving equations, systems of linear equations, inequalities, domain and range of functions, exponential and logarithmic functions, compositions of functions, transformations of functions, right triangles, trigonometry of triangles.

MAUY.1024 Calculus I for Engineers
4 points. Offered every term.
Prerequisites:
Diagnostic Exam or a grade of B or better in MAUY 914.
Corequisites:
EXUY 1
Description:
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 rules, the chain rule, applications of the chain rule, maxima and minima, optimization. The definite integral, the Fundamental Theorem of Calculus and interpretations, theorems about definite integrals, antiderivatives. MAUY 1324 is for students who wish to take MAUY 1024 but need more review of precalculus. MAUY 1324 covers the same material as MAUY 1024 but with more contact hours per week, incorporating a full discussion of the required precalculus topics.

MAUY.1124 Calculus II for Engineers
4 points. Offered every term.
Prerequisites:
MAUY 1024 or a grade of B or better in MAUY 1324.
Corequisites:
EXUY 1
Description:
This course covers 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, functions of two variables, graphs of functions of two variables, contour diagrams, linear functions, functions of three variables. MAUY 1424 is for students who wish to take MAUY 1124 but need more review of precalculus. MAUY 1424 covers the same material as MAUY 1124 but with more contact hours per week, incorporating a full discussion of the required precalculus topics.

MAUY.1324 Integrated Calculus I for Engineers
4 points. Offered every term.
Prerequisites:
Diagnostic Exam or MAUY 914.
Corequisites:
EXUY 1
Description:
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 rules, the chain rule, applications of the chain rule, maxima and minima, optimization. The definite integral, the Fundamental Theorem of Calculus and interpretations, theorems about definite integrals, antiderivatives. MAUY 1324 is for students who wish to take MAUY 1024 but need more review of precalculus. MAUY 1324 covers the same material as MAUY 1024 but with more contact hours per week, incorporating a full discussion of the required precalculus topics.

MAUY.1424 Integrated Calculus II for Engineers
4 points. Offered every term.
Prerequisites:
MAUY 1324.
Corequisites:
EXUY 1
Description:
This course covers 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, functions of two variables, graphs of functions of two variables, contour diagrams, linear functions, functions of three variables. MAUY 1424 is for students who wish to take MAUY 1124 but need more review of precalculus. MAUY 1424 covers the same material as MAUY 1124 but with more contact hours per week, incorporating a full discussion of the required precalculus topics.

MAUY.2034 Linear Algebra and Differential Equations
4 points. Offered every term.
Prerequisites:
MAUY 1124 or MAUY 1424.
Notes:
Not open to students who have taken MAUY 3044 or MAUY 3054 or MAUY 4204 or MAUY 4254.
Description:
MAUY 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.

MAUY.2114 Calculus III: MultiDimensional Calculus
4 points. Offered every term.
Prerequisites:
MAUY 1124 or MAUY 1424.
Description:
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.

MAUY.2224 Data Analysis
4 points. Offered every term.
Prerequisites:
MAUY 1124 or MAUY 1424.
Notes:
Not open to math majors or students who have taken or will take MAUY 2054 or MAUY 2414 or MAUY 3014 or MAUY 3514.
Description:
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 distributions of sample mean and sample variance; normal, t, and Chisquare distributions; confidence intervals; testing of hypotheses; least squares regression model. Applications to scientific, industrial, and financial data are integrated into the course.

MAUY.2314 Discrete Mathematics
4 points. Offered in the fall and the spring.
Prerequisites:
Math Diagnostic Exam or MAUY 914 (minimum calculus level required). Prerequisite for Shanghai students: MATHSHU 110.
Notes:
This course and CSGY 6003 cannot both be taken for credit.
Description:
Logic, proofs, set theory, functions, relations, asymptotic notation, recurrences, modeling computation, graph theory.

MAUY.2414 Basic Practice of Statistics
4 points. Offered in the fall and the spring.
Prerequisites:
None.
Notes:
Not open to math majors or students who have taken or will take MAUY 2054 or MAUY 2224 or MAUY 3014 or MAUY 3514.
Description:
We are inundated by data, but data alone do 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 Sustainable Urban Environments (SUE) students, please see your advisor.

MAUY.2514 Honors Calculus III
Identical to MATHUA 129.
4 points. Offered in the fall and the spring.
Prerequisites:
(MAUY 1124 or MAUY 1424) with a grade of A or better OR a 5 on the AP Calculus BC Exam and Department Permission.
Description:
Similar to MAUY 2114 Calculus III, but at a faster pace and deeper level. 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. Theorem of Gauss and Stokes. Students pursuing an honors mathematics degree are especially encouraged to consider this course.

MAUY.3014 Applied Probability
Identical to MATHUA 233.
4 points. Offered in the fall and the spring.
Prerequisites:
A grade of C or better in (MAUY 2114 or MAUY 2514) and (MAUY 2034 or MAUY 3044 or MAUY 3054).
Notes:
Not open to students who have taken or will take MAUY 2224, ECEUY 2233, or MAUY 3514.
Description:
An introduction to the mathematical treatment of random phenomena occurring in the natural, physical, and social sciences. Axioms of mathematical probability, combinatorial analysis, binomial distribution, Poisson and normal approximation, random variables and probability distributions, generating functions, the Central Limit Theorem and Laws of Large Numbers, Markov Chains, and basic stochastic processes.

MAUY.3044 Linear Algebra
Identical to MATHUA 140.
4 points. Offered every term.
Prerequisites:
A grade of C or better in MAUY 1024 or MAUY 1324.
Notes:
Not open to students who have taken or will take MAUY 2034, MAUY 3054, or MAUY 3113.
Description:
Systems of linear equations, Gaussian elimination, matrices, determinants, Cramer's rule. Vectors, vector spaces, basis and dimension, linear transformations. Eigenvalues, eigenvectors, and quadratic forms. Restricted to Tandon math and CS majors and students with a permission code from the math department. Fulfills linear algebra requirement for the BS Math and BS CS degrees.

MAUY.3054 Honors Linear Algebra
Identical to MATHUA 148.
4 points. Offered in the fall and the spring.
Prerequisites:
A grade of A or better in MAUY 1024 or MAUY 1324.
Notes:
Not open to students who have taken or will take MAUY 2034, MAUY 3044, or MAUY 3113.
Description:
This honors section of Linear Algebra is intended for wellprepared students who have already developed some mathematical maturity. Its scope will include the usual Linear Algebra (MAUY 3044) syllabus; however, this class will move faster, covering additional topics and going deeper. Vector spaces, linear dependence, basis and dimension, matrices, determinants, solving linear equations, eigenvalues and eigenvectors, quadratic forms, applications such as optimization or linear regression.

MAUY.3113 Advanced Linear Algebra and Complex Variables
3 points. Offered in the fall and the spring.
Prerequisites:
(MAUY 2114 or MAUY 2514) and (MAUY 2034 or MAUY 3044 or MAUY 3054).
Notes:
Not open to math majors or students who have taken or will take MAUY 4434.
Description:
This course provides a deeper understanding of topics introduced in MAUY 2012 and MAUY 2034 and continues the development of those topics, while also covering functions of a Complex Variable. Topics covered include: The GramSchmidt process, inner product spaces and applications, singular value decomposition, LU decomposition. Derivatives and CauchyRiemann equations, integrals and Cauchy integral theorem. Power and Laurent Series, residue theory.

MAUY.3204 Linear and Nonlinear Optimization
Identical to MATHUA 253.
4 points. Offered in the fall and the spring.
Prerequisites:
A grade of C or better in (MAUY 2114 or MAUY 2514) and (MAUY 2034 or MAUY 3044 or MAUY 3054).
Description:
This course provides an applicationoriented introduction to linear programming and convex optimization, with a balanced combination of theory, algorithms, and numerical implementation. Theoretical topics will include linear programming, convexity, duality, and dynamic programming. Algorithmic topics will include the simplex method for linear programming, selected techniques for smooth multidimensional optimization, and stochastic gradient descent. Applications will be drawn from many areas, but will emphasize economics (eg twoperson zerosum games, matching and assignment problems, optimal resource allocation), data science (eg regression, sparse inverse problems, tuning of neural networks) and operations research (eg shortest paths in networks and optimization of network flows). While no prior experience in programming is expected, the required coursework will include numerical implementations, including some programming; students will be introduced to appropriate computational tools, with which they will gain experience as they do the assignments. 
MAUY.3514 Honors Probability
Identical to MATHUA 238.
4 Points. Offered in the spring.
Prerequisites:
A grade of B+ or better in (MAUY 2114 or MAUY 2514) and (MAUY 2034 or MAUY 3044 or MAUY 3054) and MAUY 2314
Notes:
Not open to students who have taken or will take MAUY 2224, ECEUY 2233, or MAUY 3014.
Description:
The aim of this class is to introduce students to probability theory, with a greater emphasis on rigor, more material, and a faster pace than the Theory of Probability/Applied Probability class. The material will include discrete and continuous probability, and the most fundamental limit theorems (law of large numbers and Central Limit Theorem). Students will be made familiar with the classical models, computations on densities, and convergence to universal distributions. They will also be expected to understand the proofs of all the results seen in class, and be able to argue with mathematical rigor.

MAUY.4014 Theory of Numbers
Identical to MATHUA 248.
4 points. Offered in the fall and spring.
Prerequisites:
A grade of C or better in MAUY 1124 or MAUY 1424.
Description:
Divisibility and prime numbers. Linear and quadratic congruences. The classical numbertheoretic functions. Continued fractions. Diophantine equations.

MAUY.4044 Algebra
Identical to MATHUA 343.
4 points. Offered in the fall and the spring.
Prerequisites:
A grade of C or better in (MAUY 4614 or MAUY 4644) and (MAUY 3044 or MAUY 3054 or MAUY 3113), or permission of instructor.
Notes:
Cannot receive credit for both MAUY 4044 and MAUY 4054.
Description:
Introduction to abstract algebraic structures, including groups, rings, and fields. Sets and relations. Congruences and unique factorization of integers. Groups, permutation groups, homomorphisms and quotient groups. Rings and quotient rings, Euclidean rings, polynomial rings. Fields, finite extensions.

MAUY.4054 Honors Algebra I
Identical to MATHUA 348.
4 points. Offered in the fall.
Prerequisites:
A grade of B or better in (MAUY 4614 or MAUY 4644) and (MAUY 3044 or MAUY 3054 or MAUY 3113) or instructor permission.
Notes:
Cannot receive credit for both MAUY 4044 and MAUY 4054.
Description:
Introduction to abstract algebraic structures, including groups, rings, and fields. Sets and relations. Congruences and unique factorization of integers. Groups, permutation groups, group actions, homomorphisms and quotient groups, direct products, classification of finitely generated abelian groups, Sylow theorems. Rings, ideals and quotient rings, Euclidean rings, polynomial rings, unique factorization.

MAUY.4064 Honors Algebra II
Identical to MATHUA 349.
4 points. Offered in the spring.
Prerequisites:
A grade of C or better in MAUY 4054 or (a grade of A in MAUY 4044 and instructor permission).
Description:
Fields, finite extensions, constructions with ruler and compass, Galois theory, solvability by radicals.

MAUY.4114 Applied Statistics
4 points. Offered in the fall and spring
Prerequisites:
MAUY 3014 or MAUY 3514.
Notes:
Not open to students who have taken or will take MAUY 2224.
Description:
An introduction to the mathematical foundations and techniques of modern statistical analysis for the interpretation of data in the quantitative sciences. Mathematical theory of sampling; normal populations and distributions; chisquare, t, and F distributions; hypothesis testing; estimation; confidence intervals; sequential analysis; correlation, regression; analysis of variance. Applications to the sciences. Use of Matlab for doing computations of the statistical measures listed above.

MAUY.4204 Ordinary Differential Equations
Identical to MATHUA 262.
4 points. Offered in the fall and the spring.
Prerequisites:
A grade of C or better in (MAUY 2114 or MAUY 2514) and (MAUY 3044 or MAUY 3054 or MAUY 3113).
Notes:
Not open to students who have taken or will take MAUY 2034 or MAUY 4254.
Description:
A first course in ordinary differential equations, including analytical solution methods, elementary numerical methods, and modeling. Topics to be covered include: firstorder equations including integrating factors; secondorder equations including variation of parameters; series solutions; elementary numerical methods including Euler's methods, RungeKutta methods, and error analysis; Laplace transforms; systems of linear equations; boundaryvalue problems. Restricted to Tandon math majors and students with a permission code from the math department. Fulfills ordinary differential equations requirement for the BS Math degree.

MAUY 4254 Honors Ordinary Differential Equations
Identical to MATHUA 268.
4 points. Offered in the fall.
Prerequisites:
A grade of A or better in MAUY 4614 Applied Analysis OR a grade of B+ or better in MAUY 4644 Honors Analysis I.
Notes: Not open to students who have taken or will take MAUY 2034 or MAUY 4204.
Description:
This class will develop rigorously the basic theory of Ordinary Differential Equations (ODEs).
Existence and uniqueness of solutions to ODEs are first investigated, for linear and nonlinear problems, set on the real line or the complex plane. More qualitative questions are then considered, about the behavior of the solutions, with possible prolongations to various topics in Dynamical Systems theory. Applications to Physics and Biology will appear naturally when discussing examples. 
MAUY.4314 Combinatorics
Identical to MATHUA 240.
4 points. Offered in the fall and spring.
Prerequisites:
A grade of C or better in MAUY 1124 or MAUY 1424.
Description:
Techniques for counting and enumeration including generating functions, the principle of inclusion and exclusion, and Polya counting. Graph theory. Modern algorithms and data structures for graphtheoretic problems.

MAUY.4324 Mathematics of Finance
Identical to MATHUA 250.
4 points. Offered in the fall and the spring.
Prerequisites:
A grade of C+ or better in (MAUY 2114 or MAUY 2514) and (MAUY 2054 or MAUY 2224 or MAUY 2414 or MAUY 3014 or MAUY 3514 or MAUY 4114).
Description:
Introduction to the mathematics of finance. Topics include: Linear programming with application pricing and quadratic. Interest rates and present value. Basic probability: random walks, central limit theorem, Brownian motion, lognormal model of stock prices. BlackScholes theory of options. Dynamic programming with application to portfolio optimization.

MAUY.4414 Applied Partial Differential Equations
Identical to MATHUA 263.
4 points. Offered in the fall and spring.
Prerequisites:
MAUY 2034 or MAUY 4204 or MAUY 4254
Description:
Modeling of physical processes. Classification of equations. Formulation and treatment of boundary and initialvalue problems. Green’s functions. Maximum principle. Separation of variables. Fourier series and integrals. Quasilinear firstorder equations and characteristics. D’Alembert solution of wave equation. Conservation laws and shock waves.

MAUY.4424 Numerical Analysis
Identical to MATHUA 252.
4 points. Offered in the fall and the spring.
Prerequisites:
A grade of C or better in (MAUY 2114 or MAUY 2514) and (MAUY 3044 or MAUY 3054 or MAUY 3113).
Description:
In numerical analysis one explores how mathematical problems can be analyzed and solved with a computer. As such, numerical analysis has very broad applications in mathematics, physics, engineering, finance, and the life sciences. This course gives an introduction to this subject for mathematics majors. Theory and practical examples using Matlab will be combined to study a range of topics ranging from simple rootfinding procedures to differential equations and the finite element method.

MAUY.4434 Applied Complex Variables
4 points. Offered in the spring
Prerequisites:
A grade of C or better in (MAUY 2114 or MAUY 2514) and (MAUY 2034 or MAUY 3044 or MAUY 3054).
Notes:
Not open to students who have taken MAUY 3113.
Description:
A first course in complex analysis, with a focus on applications. Topics to be covered include the complex plane, analytic functions, complex differentiation, the CauchyRiemann equations, branch cuts, contour integration, the residue theorem, conformal mapping, applications to potential theory and fluid flow.

MAUY.4444 Intro to Math Modeling
Identical to MATHUA 251.
4 points. Offered in the fall and the spring.
Prerequisites:
A grade of C or better in (MAUY 2114 or MAUY 2514) and (MAUY 2034 or MAUY 3044 or MAUY 3054).
Description:
Formulation and analysis of mathematical models. Mathematical tools include dimensional analysis, optimization, simulation, probability, and elementary differential equations. Applications to biology, sports, economics, and other areas of science. The necessary mathematical and scientific background will be developed as needed. Students participate in formulating models as well as in analyzing them.

MAUY.4474 Chaos and Dynamical Systems
Identical to MATHUA 264.
4 points. Offered in the spring.
Prerequisites:
A grade of C or better in (MAUY 1124 or MAUY 1424) and (MAUY 3044 or MAUY 3054 or MAUY 3113).
Description:
Topics will include dynamics of maps and of first order and secondorder differential equations, stability, bifurcations, limit cycles, dissection of systems with fast and slow time scales. Geometric viewpoint, including phase planes, will be stressed. Chaotic behavior will be introduced in the context of onevariable maps (the logistic), fractal sets, etc. Applications will be drawn from physics and biology. There will be homework and projects, and a few computer lab sessions (programming experience is not a prerequisite).

MAUY.4614 Applied Analysis
4 points. Offered in the fall
Prerequisites:
A grade of C or better in (MAUY 2114 or MAUY 2514) and (MAUY 2034 or MAUY 3044 or MAUY 3054).
Notes:
Cannot receive credit for both MAUY 4614 and MAUY 4644.
Description:
Limits of real and complex sequences and series; topology of metric spaces; continuity and differentiability of functions; definition, properties, and approximations of Riemann integrals; convergence of sequences and series of functions; Fourier series and other orthogonal systems of functions, approximations theorems.

MAUY.4644 Honors Analysis I
Identical to MATHUA 328.
4 points. Offered in the fall and spring.
Prerequisites:
A grade of C or better in (MAUY 2114 or MAUY 2514) and (MAUY 2034 or MAUY 3044 or MAUY 3054).
Notes:
Cannot receive credit for both MAUY 4614 and MAUY 4644.
Description:
This is an introduction to the rigorous treatment of the foundations of real analysis in one variable. It is based entirely on proofs. Students are expected to know what a mathematical proof is and are also expected to be able to read a proof before taking this class. Topics include: properties of the real number system, sequences, continuous functions, topology of the real line, compactness, derivatives, the Riemann integral, sequences of functions, uniform convergence, infinite series and Fourier series. Additional topics may include: Lebesgue measure and integral on the real line, metric spaces, and analysis on metric spaces.

MAUY.4654 Honors Analysis II
Identical to MATHUA 329.
4 points. Offered in the spring.
Prerequisites:
A grade of C or better in MAUY 4644 or a grade of A in MAUY 4614 in conjunction with permission by instructor.
Description:
This is a continuation of MAUY 4644 Honors Analysis I. Topics include: metric spaces, differentiation of functions of several real variables, the implicit and inverse function theorems, Riemann integral on Rn, Lebesgue measure on Rn, the Lebesgue integral.

MAUY.4674 Differential Geometry
Identical to MATHUA 377.
4 points. Offered in the spring.
Prerequisites:
A grade of C or better in (MAUY 2114 or MAUY 2514) and (MAUY 2034 or MAUY 3044 or MAUY 3054).
Description:
The geometry of curves and surfaces in Euclidean space. Frenet formulas, the isoperimetric inequality, local theory of surfaces in Euclidean space, first and second fundamental forms. Gaussian and mean curvature, isometries, geodesics, parallelism, the GaussBonnet Theorem.

MAUY.4684 Topology
Identical to MATHUA 375.
4 points. Offered in the spring.
Prerequisites:
A grade of C or better in (MAUY 4614 or MAUY 4644)
Description:
Settheoretic preliminaries. Metric spaces, topological spaces, compactness, connectedness, covering spaces, and homotopy groups.

MAUY 4814 Honors I
Identical to MATHUA 393.
4 points. Offered in the fall of even years.
Prerequisites:
Prerequisite varies according to topic. Department Consent Required for Enrollment.
Description:
A lecture/seminar course on advanced topics. Topics vary yearly and are updated from time to time. Detailed course descriptions are available during preregistration.

MAUY 4824 Honors II
Identical to MATHUA 394.
4 points. Offered in the spring of odd years.
Prerequisites:
Prerequisite varies according to topic. Department Consent Required for Enrollment.
Description:
A lecture/seminar course on advanced topics. Topics vary yearly and are updated from time to time. Detailed course descriptions are available during preregistration.

MAUY 4834 Honors III
Identical to MATHUA 397.
4 points. Offered in the fall of odd years.
Prerequisites:
Prerequisite varies according to topic. Department Consent Required for Enrollment.
Description:
A lecture/seminar course on advanced topics. Topics vary yearly and are updated from time to time. Detailed course descriptions are available during preregistration.

MAUY 4844 Honors IV
Identical to MATHUA 398.
4 points. Offered in the spring of even years
Prerequisites:
Prerequisite varies according to topic. Department Consent Required for Enrollment.
Description:
A lecture/seminar course on advanced topics. Topics vary yearly and are updated from time to time. Detailed course descriptions are available during preregistration.

MAUY.492X Independent Study
14 points. Offered in fall and spring.
Prerequisites:
Departmental adviser’s approval.
Notes:
This course is repeatable for credit.
Description:
In this course, students read, study and investigate selected topics in mathematics. Students discuss and present problems.