Undergraduate Course Descriptions

MATHUA.0009 Algebra And Calculus
4 points. Offered every term. Course homepage.
Prerequisites:
High school mathematics or permission of the department.
Description:
Intensive course in intermediate algebra and trigonometry. Topics include algebraic, exponential, logarithmic, trigonometric functions and their graphs.

MATHUA.0120 Discrete Mathematics
4 points. Offered every term. Course homepage.
Prerequisites:
One of the following:
 SAT score of 670 or higher on mathematics portion March 2016 and later
 SAT score of 650 or higher on mathematics portion before March 2016
 ACT/ACTE Math score of 30 or higher
 AB score of 3 or higher
 BC score of 3 or higher
 A level Maths score of C or higher (anyone who took Further Maths should contact the math department as it varies depending on the exam board)
 AS level Maths score of B or higher
 IB HL score of 5 or higher
 IB SL score of 6 or higher
 Completion of Algebra and Calculus (MATHUA 009) with a grade of C or higher
 Passing placement exam
Description:
A first course in discrete mathematics. Sets, algorithms, induction. Combinatorics. Graphs and trees. Combinatorial circuits. Logic and Boolean algebra.

MATHUA.0121 Calculus I
4 points. Offered every term. Course homepage.
Prerequisites:
One of the following:
 SAT score of 670 or higher on mathematics portion March 2016 and later
 SAT score of 650 or higher on mathematics portion before March 2016
 ACT/ACTE Math score of 30 or higher
 AB score of 3 or higher
 BC score of 3 or higher
 A level Maths score of C or higher (anyone who took Further Maths should contact the math department as it varies depending on the exam board)
 AS level Maths score of B or higher
 IB HL score of 5 or higher
 IB SL score of 6 or higher
 Completion of Algebra and Calculus (MATHUA 009) with a grade of C or higher
 Passing placement exam
Refer to the Calculus information page for more information.
Description:
Derivatives, antiderivatives, and integrals of functions of one real variable. Trigonometric, inverse trigonometric, logarithmic and exponential functions. Applications, including graphing, maximizing and minimizing functions. Areas and volumes.

MATHUA.0122 Calculus II
4 points. Offered every term. Course homepage.
Prerequisites:
Passing MATHUA 121 Calculus I with a grade of C or better, an AB or a BC of 4 or higher, A level Maths of B or higher, IB HL of 6 or higher, or passing a placement test.
Refer the the Calculus information page for more information.
Description:
Techniques of integration. Further applications. Plane analytic geometry. Polar coordinates and parametric equations. Infinite series, including power series.

MATHUA.0123 Calculus III
4 points. Offered every term. Course homepage.
Prerequisites:
Passing MATHUA 122 Calculus II with a grade of C or higher, BC of 5, or passing placement test. (anyone who took Further Maths should contact the math department as it varies depending on the exam board)
Refer to the Calculus information page for more information.
Description:
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.

MATHUA.0129 Honors Calculus III
4 points. Offered in the fall and the spring. Course homepage.
Prerequisites:
A in MATHUA 122 or equivalent or a 5 on the AP Calculus BC and permission from instructor using enrollment request form.
Description:
Similar to MATHUA 123 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 interested in an honors mathematics degree are especially encouraged to consider this course.

MATHUA.0140 Linear Algebra
4 points. Offered every term. Course homepage.
Prerequisites:
One of the following:
 SAT score of 670 or higher on mathematics portion March 2016 and later
 SAT score of 650 or higher on mathematics portion before March 2016
 ACT/ACTE Math score of 30 or higher
 AB score of 3 or higher
 BC score of 3 or higher
 A level Maths score of C or higher (anyone who took Further Maths should contact the math department as it varies depending on the exam board)
 AS level Maths score of B or higher
 IB HL score of 5 or higher
 IB SL score of 6 or higher
 Completion of Algebra and Calculus (MATHUA 009) with a grade of C or higher
 Passing placement exam
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.

MATHUA.0144 Introduction To Computer Simulation
Identical to CSCIUA 330.
4 points. Offered in the spring. Course homepage.
Prerequisites:
A grade of C or higher in MATHUA 121 Calculus I or MATHUA 212 Math for Economics II (for Economics majors) and PHYSUA 11 General Physics.
Description:
In this course, students will learn how to do computer simulations of such phenomena as orbits (Kepler problem and Nbody problem), epidemic and endemic disease (including evolution in response to the selective pressure of a malaria), musical stringed instruments (piano, guitar, and violin), and traffic flow in a city (with lights, breakdowns, and gridlock at corners). The simulations are based on mathematical models, numerical methods, and Matlab programming techniques that will be taught in class. The use of animations (and sound where appropriate) to present the results of simulations will be emphasized.

MATHUA.0148 Honors Linear Algebra
4 points. Offered in the fall and the spring. Course homepage.
Prerequisites:
Please reference the section "Are you ready for this class?" in the course syllabus. If you feel you are ready you also need one of the following:
 SAT score of 670 or higher on mathematics portion March 2016 and later
 SAT score of 650 or higher on mathematics portion before March 2016
 ACT/ACTE Math score of 30 or higher
 AB score of 3 or higher
 BC score of 3 or higher
 A level Maths score of C or higher (anyone who took Further Maths should contact the math department as it varies depending on the exam board)
 AS level Maths score of B or higher
 IB HL score of 5 or higher
 IB SL score of 6 or higher
 Completion of Algebra and Calculus (MATHUA 009) with a grade of A or higher
 Passing placement exam into Calculus I or Math for Economics I (MATHUA 121 or 211)
Description:
This honors section of Linear Algebra is a proofbased course intended for wellprepared students who have already developed some mathematical maturity and ease with abstraction. Its scope will include the usual Linear Algebra (MATHUA 140) syllabus; however this class will be faster, more abstract and proofbased, covering additional topics.Topics covered are: Vector spaces, linear dependence, basis and dimension, matrices, determinants, solving linear equations, linear transformations, eigenvalues and eigenvectors, diagonalization, inner products, applications. 
MATHUA.0211 Math For Economics
4 points. Offered every term. Course homepage.
Prerequisites:
The same as for Calculus I. Cannot apply both Calculus courses and Math for Economics courses towards your major.
Description:
This course is only open to Economics Majors and prospective majors. If an Economics Major decides to double or joint major in Math these courses will replace Calculus I  III.
Elements of calculus and linear algebra are important to the study of economics. This class is designed to provide the appropriate tools for study in the policy concentration. Examples and motivation are drawn from important topics in economics. Topics covered include derivatives of functions of one and several variables; interpretations of the derivatives; convexity; constrained and unconstrained optimization.

MATHUA.0212 Math For Economics II
4 points. Offered every term. Course homepage.
Prerequisites:
Completion of MATHUA 211 Math for Economics I with a grade of C or higher, or passing departmental placement exam.
Description:
A continuation of Mathematics for Economics I. Matrix algebra; eigenvalues; Ordinary differential equations and stability analysis, multivariable integration and (possibly) dynamic optimization.

MATHUA.0213 Math For Economics III
4 points. Offered in the fall and the spring. Course homepage.
Prerequisites:
MATHUA 212 Mathematics for Economics II. Cannot apply both Calculus courses and Math for Economics courses towards your major.
Description:
This course is only open to Economics Majors and prospective majors. If an Economics Major decides to double major in Math these courses will replace Calculus I  III.
Further topics in vector calculus. Vector spaces, matrix analysis. Linear and nonlinear programming with applications to game theory. This course will provide economics students who have taken MATHUA 211 Mathematics for Economics I and MATHUA 212 Mathematics for Economics II with the tools to take higherlevel mathematics courses.

MATHUA.0224 Vector Analysis
4 points. Offered in the spring. Course homepage.
Prerequisites:
Passing MATHUA 325 Analysis with a grade of C or better.
Description:
Brief review of multivariate calculus: partial derivatives, chain rule, Riemann integral, change of variables, line integrals. Lagrange multipliers. Inverse and implicit function theorems and their applications. Introduction to calculus on manifolds: definition and examples of manifolds, tangent vectors and vector fields, differential forms, exterior derivative, line integrals and integration of forms. Gauss' and Stokes' theorems on manifolds.

MATHUA.0228 Earthâ€™s Atmosphere and Ocean: Fluid Dynamics and Climate
Identical to ENVSTUA 360.
4 points. Offered in the spring. Course homepage.
Prerequisites:
MATHUA 121 Calculus I (or equivalent) or MATHUA 212 Math for Economics II (for Economics majors), with a grade of B or better, though completion of MATHUA 123 Calculus III (multivariate calculus) or MATHUA 213 Math for Economics III (for Economics majors) is preferred and recommended. Students should also have some familiarity with introductory physics (even at the advanced high school level).
Description:
An introduction to the dynamical processes that drive the circulation of the atmosphere and ocean, and their interaction. This is the core of climate science. Lectures will be guided by consideration of observations and experiments, but the goal is to develop an understanding of the unifying principles of planetary fluid dynamics. Topics include the global energy balance, convection and radiation (the greenhouse effect), effects of planetary rotation (the Coriolis force), structure of the atmospheric circulation (the Hadley cell and wind patterns), structure of the oceanic circulation (winddriven currents and the thermohaline circulation), climate and climate variability (including El Nino and anthropogenic warming).

MATHUA.0230 Introduction To Fluid Dynamics
Identical to PHYSUA 180.
4 points. Offered in the spring. Course homepage.
Prerequisites:
A grade of C or higher in MATHUA 123 Calculus III or MATHUA 213 Math for Economics III (for Economics majors) Suggested: PHYSUA 106 Mathematical Physics
Description:
Fluid dynamics is the branch of physics that describes motions of fluids as varied as the flow of blood in the human body, the flight of an insect or the motions of weather systems on Earth. The course introduces the key concepts of fluid dynamics: the formalism of continuum mechanics, the conservation of mass, energy and momentum in a fluid, the Euler and NavierStokes equations, viscosity and vorticity. These concepts are applied to study classic problems in fluid dynamics, such as potential flow around a cylinder, the Stokes flow, the propagation of sound and gravity waves and the onset of instability in shear flow.

MATHUA.0232 Set Theory
Identical to PHILUA 73.
4 points. Offered at the discretion of the Department of Philosophy.
Prerequisites:
None
Description:
Among the topics to be covered are: the axioms of set theory; Boolean operations on sets; settheoretic representation of relations, functions and orderings; the natural numbers; theory of transfinite cardinal and ordinal numbers; the axiom of choice and its equivalents; and the foundations of analysis. If time permits we may also consider some more advanced topics, such as large cardinals or the independence results.

MATHUA.0233 Theory Of Probability
4 points. Offered every term. Course homepage.
Prerequisites:
MATHUA 123 Calculus III or MATHUA 213 Math for Economics III (for Economics majors) with a grade of C or better and/or the equivalent, and MATHUA 140 Linear Algebra or MATHUA 148 Honors Linear Algebra with a grade of C or better and/or the equivalent. Not open to students who have taken MATHUA 235 Probability and Statistics.
Note: This course is intended for math majors and other students with a strong interest in mathematics. It requires fluency in topics such as multivariable integration and therefore a grade of B or better in MATHUA 123 or MATHUA 213 (or the equivalent) is strongly recommended.
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, Markov chains applications.

MATHUA.0234 Mathematical Statistics
4 points. Offered in the fall and the spring. Course homepage.
Prerequisites:
MATHUA 233 Theory of Probability with a grade of C or better and/or the equivalent. Not open to students who have taken MATHUA 235 Probability and Statistics.
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.

MATHUA.0235 Probability And Statistics
4 points. Offered in the spring. Course homepage.
Prerequisites:
MATHUA 122 Calculus II or MATHUA 212 Math for Economics II (for Economics majors) with a grade of C or better and/or the equivalent. Not open to students who have taken MATHUA 233 Theory of Probability and/or MATHUA 234 Mathematical Statistics.
Description:
A combination of MATHUA 233 Theory of Probability and MATHUA 234 Mathematical Statistics at a more elementary level, so as to afford the student some acquaintance with both probability and statistics in a single term. In probability: mathematical treatment of chance; combinatorics; binomial, Poisson, and Gaussian distributions; law of large numbers and the normal approximation; application to cointossing, radioactive decay, etc. In statistics: sampling; normal and other useful distributions; testing of hypotheses; confidence intervals; correlation and regression; applications to scientific, industrial, and financial data.

MATHUA.0238 Honors Theory Of Probability
4 points. Offered in the spring.
Prerequisites:
MATHUA 123 Calculus III or MATHUA 129 Honors Calculus III or MATHUA 213 Math for Economics III (for Economics majors) with a grade of B+ or better and/or the equivalent, and MATHUA 140 Linear Algebra or MATHUA 148 Honors Linear Algebra with a grade of B+ or better and/or the equivalent, and MATHUA 120 Discrete Math with a grade of B+ or better and/or the equivalent.. Not open to students who have taken MATHUA 235 Probability and Statistics. While B+ or higher is the standard requirement for this course, the department will consider petitions if you are on the borderline of that requirement.
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 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.

MATHUA.0240 Combinatorics
4 points. Offered in the spring. Course homepage.
Prerequisites:
MATHUA 122 Calculus II or MATHUA 212 Math for Economics II (for Economics majors) or MATHUA 221 Honors Calculus I with a grade of C or better and/or the equivalent.
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.

MATHUA.0248 Theory Of Numbers
4 points. Offered in the fall. Course homepage.
Prerequisites:
MATHUA 122 Calculus II or MATHUA 212 Math for Economics II (for Economics majors) with a grade of C or better and/or the equivalent.
Description:
Divisibility theory and prime numbers. Linear and quadratic congruences. The classical numbertheoretic functions. Continued fractions. Diophantine equations.

MATHUA.0250 Mathematics Of Finance
4 points. Offered in the fall and the spring. Course homepage.
Prerequisites:
MATHUA 123 Calculus III or MATHUA 213 Math for Economics III (for Economics majors), and an introductory course in probability or statistics, MATHUA 233 Theory of Probability, MATHUA 235 Probability and Statistics, ECONUA 18 Statistics, ECONUA 20 Analytical Statistics, STATUB 14 Intro Theory of Probability, STATUB 103 Statistics for Business Control and Regression/Forecasting Models or equivalent) with a grade of C+ or better.
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.

MATHUA.0251 Introduction To Mathematical Modeling
4 points. Offered in the fall and the spring. Course homepage.
Prerequisites:
MATHUA 123 Calculus III or MATHUA 213 Math for Economics III (for Economics majors) with a grade of C or better or permission of the instructor.
Description:
Formulation and analysis of mathematical models. Mathematical tool 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 will participate in formulating models as well as in analyzing them.

MATHUA.0252 Numerical Analysis
4 points. Offered in the fall and the spring. Course homepage.
Prerequisites:
MATHUA 123 Calculus III or MATHUA 213 Math for Economics III (for Economics majors), MATHUA 140 Linear Algebra with a grade of C or better.
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.

MATHUA.0255 Mathematics In Medicine And Biology
Identical to BIOLUA 255.
4 points. Offered in the fall. Course homepage.
Prerequisites:
MATHUA 121 Calculus I or MATHUA 212 Math for Economics II (for Economics majors) and BIOLUA 11 Principles of Biology I or permission of the instructor.
Description:
Intended primarily for premedical students with interest and ability in mathematics. Topics of medical importance using mathematics as a tool: control of the heart, optimal principles in the lung, cell membranes, electrophysiology, countercurrent exchange in the kidney, acidbase balance, muscle, cardiac catheterization, computer diagnosis. Material from the physical sciences and mathematics is introduced as needed and developed within the course.

MATHUA.0256 Computers In Medicine And Biology
Identical to BIOLUA 256.
4 points. Offered in the spring. Course homepage.
Prerequisites:
MATHUA 255 Mathematics in Medicine and Biology, or permission of the instructor. Familiarity with a programming language is recommended. The language used in the course will be MATLAB, but prior experience with MATLAB is not required.
Description:
Introduces students to the use of computer simulation as a tool for investigating biological phenomena. The course requirement is to construct three computer models during the semester, to report on results to the class, and to hand in a writeup describing each project. These projects can be done individually, or as part of a team. Topics discussed in class are the circulation of the blood, gas exchange in the lung, electrophysiology of neurons and neural networks, the renal countercurrent mechanism, crossbridge dynamics in muscle, and the dynamics of epidemic and endemic diseases. Projects are normally chosen from this list, but may be chosen otherwise by students with other interests.

MATHUA.0262 Ordinary Differential Equations
4 points. Offered in the fall and the spring. Course homepage.
Prerequisites:
MATHUA 123 Calculus III or MATHUA 213 Math for Economics III (for Economics majors) and MATHUA 140 Linear Algebra with a grade of C or better or the equivalent.
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. Some optional topics to be chosen at the instructor's discretion include: nonlinear dynamics including phaseplane description; elementary partial differential equations and Fourier series.

MATHUA.0263 Partial Differential Equations
4 points. Offered in the fall and the spring. Course homepage.
Prerequisites:
MATHUA 262 Ordinary Differential Equations with a grade of C or better or the equivalent.
Description:
Many laws of physics are formulated as partial differential equations. This course discusses the simplest examples, such as waves, diffusion, gravity, and static electricity. Nonlinear conservation laws and the theory of shock waves are discussed. Further applications to physics, chemistry, biology, and population dynamics.

MATHUA.0264 Chaos And Dynamical Systems
4 points. Offered in the spring. Course homepage.
Prerequisites:
MATHUA 122 Calculus II or MATHUA 212 Math for Economics II (for Economics majors) and MATHUA 140 Linear Algebra with a grade of C or better or the equivalent.
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).

MATHUA.0282 Functions Of A Complex Variable
4 points. Offered in the spring. Course homepage.
Prerequisites:
MATHUA 123 Calculus III or MATHUA 213 Math for Economics III (for Economics majors) plus one higher level course such as MATHUA 140 Linear Algebra with the grade of C or better.
Description:
Complex numbers and complex functions. Differentiation and the CauchyRiemann equations. Cauchy's theorem and the Cauchy integral formula. Singularities, residues, and Laurent series. Fractional Linear transformations and conformal mapping. Analytic continuation. Applications to fluid flow etc.

MATHUA.0325 Analysis
4 points. Offered in the fall and the spring. Course homepage.
Prerequisites:
MATHUA 123 Calculus III or MATHUA 213 Math for Economics III (for Economics majors) and MATHUA 140 Linear Algebra with a grade of C or better or the equivalent.
Description:
This course is an introduction to rigorous analysis on the real line. Topics include: the real number system, sequences and series of numbers, functions of a real variable (continuity and differentiability), the Riemann integral, basic topological notions in a metric space, sequences and series of functions including Taylor and Fourier series.

MATHUA.0328 Honors Analysis I
4 points. Offered in the fall and spring. Course homepage.
Prerequisites:
MATHUA 123 Calculus III or MATHUA 213 Math for Economics III (for Economics majors) and MATHUA 140 Linear Algebra with a grade of A or better or the equivalent. Recommended: MATHUA 129 Honors Calculus III and MATHUA 148 Honors Linear Algebra with a grade of B+ or better or the equivalent.
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.

MATHUA.0329 Honors Analysis II
4 points. Offered in the spring. Course homepage.
Prerequisites:
A grade of C or better in MATHUA 328 Honors Analysis I or grade of A in MATHUA 325 Analysis in conjunction with permission by instructor, and MATHUA 140 Linear Algebra with a grade of C or better or the equivalent.
Description:
This is a continuation of MATHUA 328 Honors Analysis I. Topics include: metric spaces, differentiation of functions of several real variables, the implicit and inverse function theorems, Riemann integral on R^{n}, Lebesgue measure on R^{n}, the Lebesgue integral.

MATHUA.0343 Algebra
4 points. Offered in the fall and the spring. Course homepage.
Prerequisites:
MATHUA 123 Calculus III or MATHUA 213 Math for Economics III (for Economics majors), and MATHUA 140 Linear Algebra with a grade of C or better and/or the equivalent. Additionally, it is suggested for students to have taken MATHUA 325 Analysis as a prerequisite.
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.

MATHUA.0348 Honors Algebra I
4 points. Offered in the fall. Course homepage.
Prerequisites:
MATHUA 123 Calculus III or MATHUA 213 Math for Economics III (for Economics majors) and MATHUA 140 Linear Algebra with a grade of A or better or the equivalent. Recommended: MATHUA 129 Honors Calculus III and MATHUA 148 Honors Linear Algebra with a grade of B+ or better or the equivalent.
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.

MATHUA.0349 Honors Algebra II
4 points. Offered in the spring. Course homepage.
Prerequisites:
A grade of C or better in MATHUA 348 Honors Algebra I, or grade of A in MATHUA 343 Algebra in conjunction with permission by instructor.
Description:
Principle ideal domains, polynomial rings in several variables, unique factorization domains. Fields, finite extensions, constructions with ruler and compass, Galois theory, solvability by radicals.

MATHUA.0375 Topology
4 points. Offered in the spring. Course homepage.
Prerequisites:
MATHUA 325 Analysis with a grade of C or higher or permission of the department.
Description:
Settheoretic preliminaries. Metric spaces, topological spaces, compactness, connectedness, covering spaces, and homotopy groups.

MATHUA.0377 Differential Geometry
4 points. Offered in the spring. Course homepage.
Prerequisites:
MATHUA 123 Calculus III and MATHUA 140 Linear algebra or MATHUA 148 Honors Linear Algebra. Recommended: MATHUA 325 Analysis or MATHUA 328 Honors Analysis I.
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.

MATHUA.0393 Honors I
4 points. Offered in the fall of even years.
Prerequisites:
Honors standing or approval of the director of the honors program.
Prerequisite varies according to topic.
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.

MATHUA.0394 Honors II
4 points. Offered in the spring of odd years.
Prerequisites:
Honors standing or approval of the director of the honors program.
Prerequisite varies according to topic.
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.

MATHUA.0395 Special Topics I
4 points. Offered on request in the Fall.
Prerequisites:
Prerequisite varies according to topic.
Description:
Please see Albert for course topic and description.

MATHUA.0396 Special Topics II
4 points. Offered on request in the Fall.
Prerequisites:
Prerequisite varies according to topic.
Description:
Please see Albert for course topic and description.

MATHUA.0397 Honors III
4 points. Offered in the fall of odd years.
Prerequisites:
Honors standing or approval of the director of the honors program.
Prerequisite varies according to topic.
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.

MATHUA.0398 Honors IV
4 points. Offered in the spring of even years.
Prerequisites:
Honors standing or approval of the director of the honors program.
Prerequisite varies according to topic.
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.

MATHUA.0897 Internship
2 or 4 points. Offered in the Fall and first Summer Session.
Prerequisites:
Permission of the department. Student must be a declared Math major, have a math GPA of 3.5 and an overall GPA of 3.0, and have at least 50% of the Math major courses completed.
Description:
To register for this course a student must complete the Enrollment Request Form and have the approval of the Director of Undergraduate Studies.

MATHUA.0898 Internship
2 or 4 points. Offered in the Spring and second Summer Session.
Prerequisites:
Permission of the department. Student must be a declared Math major, have a math GPA of 3.5 and an overall GPA of 3.0, and have at least 50% of the Math major courses completed.
Description:
To register for this course a student must complete the Enrollment Request Form and have the approval of the Director of Undergraduate Studies.

MATHUA.0997 Independent Study
2 or 4 points. Offered in the Fall.
Prerequisites:
Permission of the department.
Description:
To register for this course a student must complete an application form for Independent Study and have the approval of a faculty sponsor and the Director of Undergraduate Studies.

MATHUA.0998 Independent Study
2 or 4 points. Offered in the Spring.
Prerequisites:
Permission of the department.
Description:
To register for this course a student must complete an application form for Independent Study and have the approval of a faculty sponsor and the Director of Undergraduate Studies.

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 MAUY 912 or MAUY 914 (with a grade of B or better).
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:
Prerequisites: MAUY 1022 or MAUY 1024 or MAUY 1322 (with a grade of B or better) or MAUY 1324 (with a grade of B or better).
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:
Prerequisites: Diagnostic Exam or MAUY 912 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 1022 or MAUY 1024 or 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 1132 or MAUY 1424.
Notes:
Not open to students who have taken MAUY 3044 or MAUY 3054.
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.2054 Applied Business Data Analysis I
4 points. Offered in the spring.
Prerequisites:
MAUY 1054 or equivalent.
Notes:
Course required only for Management Majors. Credit for this course may not be used to satisfy the requirements for other majors.
Description:
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 decisionmaking. Applications to advanced statistical applications in business management. Emphasis is on application of concepts. Use of statistical software integrated with the previous topics.

MAUY.2114 Calculus III: MultiDimensional Calculus
4 points. Offered every term.
Prerequisites:
MAUY 1124 or MAUY 1132 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 1132 or MAUY 1424.
Notes:
Not open to students who have taken MAUY 2054 or MAUY 2233 or MAUY 3012 or MAUY 3022.
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.2233 Introduction to Probability
Identical to EEUY 2233.
3 points. Offered every term.
Prerequisites:
MAUY 2114 or MAUY 2514
Notes:
Not open to students who have taken MAUY 2224 or MAUY 3012 or MAUY 3022.
Description:
Standard first course in probability, recommended for those planning further work in probability or statistics. Probability of events, random variables and expectations, discrete and continuous distributions, joint and conditional distributions, moment generating functions, the central limit theorem.

MAUY.2314 Discrete Mathematics
4 points. Offered in the fall and the spring.
Prerequisites:
Math Diagnostic Exam or MAUY 912 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:
This course does not count towards degree if student has already taken MAUY 2224 or MAUY 2054.
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
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 permission from instructor using enrollment request form.
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 Theory of Probability.
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 3034 or MAUY 3044 or MAUY 3054).
Notes:
Not open to students who have taken MAUY 2224, MAUY 2233/EEUY 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.3034 Applied Linear Algebra
4 points.
Prerequisites:
MAUY 1024 or MAUY 1324
Description:
Systems of linear equations, matrices, determinants, vector spaces, eigenvalues and eigenvectors, orthogonality and least squares fit, singular value decompositions, computational techniques, conditioning, pseudoinverses.

MAUY.3044 Linear Algebra
Identical to MATHUA 140.
4 points. Offered every term.
Prerequisites:
A grade of C or better in MAUY 1022 or MAUY 1024 or MAUY 1324.
Notes:
Not open to students who have taken MAUY 1533, 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 1022 or MAUY 1024 or MAUY 1324.
Notes:
Not open to students who have taken MAUY 1533, 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:
A grade of C or better in (MAUY 2114 or MAUY 2514) and (MAUY 2034 or 3034 or MAUY 3044 or MAUY 3054).
Notes:
Not open to students who have taken MAUY 1533, MAUY 3112, or MAUY 4433.
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.3514 Honors Probability
4 Points. Offered in the spring.
Prerequisites:
A grade of C or better in (MAUY 2114 or MAUY 2514) and (MAUY 2034 or 3034 or MAUY 3044 or MAUY 3054).
Notes:
Not open to students who have taken MAUY 2224, MAUY 2233/EEUY 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.
Prerequisites:
A grade of C or better in MAUY 1124 or MAUY 1132 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 4613 or MAUY 4614) 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 4613 or MAUY 4614) 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.
Prerequisites:
MAUY 2233 or MAUY 3014 or MAUY 3514
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.
Notes:
Not open to students who have taken MAUY 2224

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 2034 or 3034 or MAUY 3044 or MAUY 3054).
Notes:
Not open to students who have taken MAUY 2034 or MAUY 3083.
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.4214 Applied Ordinary Differential Equations
4 points.
Prerequisites:
A grade of C or better in (MAUY 2114 or MAUY 2514) and (MAUY 2034 or 3034 or MAUY 3044 or MAUY 3054).
Notes:
Not open to students who have taken MAUY 2034 or MAUY 4204.
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.4314 Combinatorics
Identical to MATHUA 240.
4 points. Offered in the spring.
Prerequisites:
A grade of C or better in MAUY 1124 or MAUY 1132 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 2034 or 3034 or MAUY 3044 or MAUY 3054).
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
4 points. Offered in the fall.
Prerequisites:
MAUY 2034 or MAUY 4204 or MAUY 4214
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 Numerical Analysis.
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 3034 or MAUY 3044 or MAUY 3054).
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.
Prerequisites:
A grade of C or better in (MAUY 2114 or MAUY 2514) and (MAUY 2034 or 3034 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 3034 or MAUY 3044 or MAUY 3054).
Notes:
Not open to students who have taken MAUY 2393.
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 1132 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.
Prerequisites:
A grade of C or better in (MAUY 2114 or MAUY 2514) and (MAUY 2034 or 3034 or MAUY 3044 or MAUY 3054).
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.4634 Vector Analysis
Identical to MATHUA 224.
4 points. Offered in the spring.
Prerequisites:
A grade of C or better in MAUY 4613.
Description:
Brief review of multivariate calculus: partial derivatives, chain rule, Riemann integral, change of variables, line integrals. Lagrange multipliers. Inverse and implicit function theorems and their applications. Introduction to calculus on manifolds: definition and examples of manifolds, tangent vectors and vector fields, differential forms, exterior derivative, line integrals and integration of forms. Gauss' and Stokes' theorems on manifolds.

MAUY.4644 Honors Analysis I
4 points. Offered in the fall.
Prerequisites:
A grade of C or better in (MAUY 2114 or MAUY 2514) and (MAUY 2034 or 3034 or MAUY 3044 or MAUY 3054).
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 3034 or MAUY 3044 or MAUY 3054).
Notes:
Not open to students who have taken MAUY 3303.
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.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.

MAUY.4993 B.S. Thesis in Mathematics
3 points. Offered periodically.
Prerequisites:
Departmental adviser’s approval.
Description:
This 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 indepth knowledge of that area of Mathematics and proficiency in using its specific methods.