Undergraduate Course Descriptions
Course Schedule
MATHUA 009 Algebra
and Calculus
4 points. Fall and spring terms.
Prerequisite: High school math or permission of the
department.
Intensive course in intermediate algebra and trigonometry.
Topics
include algebraic, exponential, logarithmic, trigonometric
functions
and their graphs.
MATHUA 120
Discrete
Mathematics
4 points. Fall and spring term.
Prerequisite: Calculus I (MATHUA 121) Refer to Calculus
website:http://math.nyu.edu/degree/undergrad/calculus.html
A first course in discrete mathematics. Sets, algorithms,
induction. Combinatorics. Graphs and trees. Combinatorial
circuits. Logic and Boolean algebra.
MATHUA
121 Calculus I
4 points. Fall and spring terms.
PREREQUISITES FOR STUDENTS WHO MATRICULATE TO NYU FALL 2012
OR LATER

a. SAT score of 650 or higher
b. ACT/ACTE Math score of 30 or higher
c. AB score of 3 or higher.
d. BC score of 3 or higher.
e. 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)
f. AS level Maths score of B or higher
g. IB HL score of 5 or higher
h. IB SL score of 6 or higher
i. Completion of Algebra and Calculus (MATHUA 009) with a grade of C or higher
j. Passing placement exam

a. SAT score of 750 or higher
b. ACT/ACTE Math score of 34 or higher
c. AB 4 or higher
d. BC 3 or higher
e. Completion of Algebra and Calculus (MATHUA 009) with a grade of C or higher.
f. passing placement exam.
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
122 Calculus II 4 points. Fall and spring terms.
PREREQUISITES FOR STUDENTS WHO MATRICULATED TO NYU FALL
2012 OR LATER
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.
PREREQUISITES FOR STUDENTS WHO MATRICULATED TO NYU BEFORE
FALL 2012
Passing MATHUA
121 Calculus I with a grade of C or better, a BC of 4 or
higher, or passsing a placement test.
Techniques of integration. Further applications. Plane
analytic geometry. Polar coordinates and parametric
equations. Infinite series, including power series.
MATHUA
123 Calculus III
4 points. Fall and spring terms.
PREREQUISITES FOR STUDENTS WHO MATRICULATED TO NYU FALL
2012 OR LATER
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)
PREREQUISITES FOR STUDENTS WHO MATRICULATED TO NYU BEFORE
FALL 2012
Passing MATHUA
122 Calculus II with a grade of C or higher or passing
placement test.
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 130 Set Theory  identical to PHILUA 73
4 points.
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 140 Linear Algebra
4 points. Fall and spring term.
Prerequisite: A grade of C or better in MATHUA 121 Calculus I or MATHUA 211 Math for Economics I (for Economics majors) or the equivalent.
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 141 Honors Linear Algebra I  identical to G63.2110
4 points. Fall term.
Prerequisite: A grade of B or better in MATHUA 325 Analysis or MATHUA 343 Algebra or the permission of the instructor.
Linear spaces, subspaces, and quotient spaces; linear dependence and independence; basis and dimensions. Linear transformation and matrices; dual spaces and transposition. Solving linear equations. Determinants. Quadratic forms and their relation to local extrema of multivariable functions.
MATHUA 142 Honors Linear Algebra II  identical to G63.2120
4 points. Spring term.
Prerequisite: MATHUA 141 Intensive Linear Algebra I.
Special theory, eigenvalues and eigenvectors; Jordan canonical forms. Inner product and orthogonality. Selfadjoint mappings, matrix inequalities. Normal linear spaces and linear transformation between them positive matrices. Applications.
MATHUA 144 Introduction to Computer Simulation  Identical to CSCIUA 330
4 points. Spring term.
Prerequisite: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.
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 211,212 Mathematics for Economics I and II.
4 points. Fall and spring terms,respectively. Includes a recitation section.
Prerequisites: The same as for Calculus I.
Cannot apply both Calculus courses and Math for Economics courses towards your major.
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, along with Math for Economics III.
To be offered in fall 2011 and spring 2012 and every fall and spring thereafter. 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; series, including geometric and Taylor series; ordinary differential equations; matrix algebra; eigenvalues; and (possibly) dynamic optimization and multivariable integration.
MATHUA 213 Mathematics for Economics III
4 points. Fall and spring terms, respectively. Includes a recitation section.
Prerequisites: MATHUA 212 Mathematics for Economics II.
Cannot apply both Calculus courses and Math for Economics courses towards your major.
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 221 Honors Calculus I: Accelerated Calculus with Linear Algebra I
5 points. Fall term.
PREREQUISITES FOR STUDENTS WHO MATRICULATED TO NYU FALL 2012 OR LATER One of the following: (a) a score of 4 or higher on the Advanced Placement Calculus BC exam, 4 or higher on the AB exam, A level Maths of B or higher, or IB HL of 6 or higher; or (b) MATHUA 121 Calculus I and permission of the instructor.
PREREQUISITES FOR STUDENTS WHO MATRICULATED TO NYU BEFORE FALL 2012 One of the following: (a) a score of 4 or higher on the Advanced Placement Calculus BC exam or 5 on the AB exam; or (b) MATHUA 121 Calculus I and permission of the instructor.
This is the first semester of a yearlong course that covers the essential content of Calculus II, Calculus III and Linear Algebra. The first 1/3 semester discusses sequences and series, Taylor's theorem, and power series. The next 1/3 semester introduces concepts from linear algebra including: linear systems of equations; matrices and LU decomposition; determinants; vector spaces; eigenvalues and eigenvectors. The last 1/3 semester introduces topics from vector calculus including: functions of several variables; vectorvalued functions; partial derivatives; various applications including maxima and minima.
MATHUA 222 Honors Calculus II : Accelerated Calculus with Linear Algebra II5 points. Spring term
Prerequisite: MATHUA 221 Honors Calculus I with a B or better.
This is the second semester of a yearlong course that covers the essential content of Calculus II, Calculus III and Linear Algebra. Topics covered in the spring are multidimensional differentiation (e.g. differentials, gradients, Taylor expansions, applications), multidimensional integration (e.g. double and triple integrals, Green's theorem, divergence theorem, applications), differential equations (e.g. firstorder linear equations, secondorder linear equations, applications), and additional topics in linear algebra (e.g. inner products, orthogonality, applications).
MATHUA 224 Vector Analysis
4 points. Spring term.
Prerequisite: Prerequisite: Passing MATHUA 325 Analysis with a grade of C or better.
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 228 Earth's Atmosphere and Ocean: Fluid Dynamics & Climate
4 points.
Prerequisites:
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).
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 230 Introduction to Fluid Dynamics  Identical to PHYSUA 180
4 Points. Spring Term
Prerequisite: 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
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 233 Theory of Probability
4 points. Fall and Spring Terms.
Prerequisite: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.
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.
Not open to students who have taken MATHUA 235 Probability and Statistics.
MATHUA 234 Mathematical Statistics
4 points. Spring term.
Prerequisite: 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.
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 235 Probability and Statistics
4 points. Spring term.
Prerequisite: 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.
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 240 Combinatorics
4 points. Spring term
Prerequisite: 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.
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 246 Abstract Algebra
4 points. Spring term 2010
Prerequisite: 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. Course not open to math majors and/or students who have taken Algebra MATHUA 343.
An introduction to the main concepts, constructs, and applications of modern algebra. Groups, transformation groups, Sylow theorems and structure theory; rings, polynomial rings and unique factorization; introduction to fields and Galois theory.
NOTES:
This course does not
count toward the math major because of its considerable
overlap with
the more
intensive Algebra, MATHUA 343, required as part of the
majors
program
in
Mathematics. It is, however, accepted toward the math minor,
and is a
strongly
recommended course in the Steinhardt Math Ed major.
MATHUA 248
Theory of
Numbers
4 points. Fall term.
Prerequisite: 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.
Divisibility theory and prime numbers. Linear and quadratic
congruences. The classical numbertheoretic functions.
Continued fractions. Diophantine equations.
MATHUA 250
Mathematics
of Finance
4 points. Fall term.
Prerequisite: 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 103
Statistics for Business Control and Regression/Forecasting
Models or equivalent) with a grade of C+ or better.
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 251
Introduction
to
Mathematical Modeling
4 points. Spring term.
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.
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 252
Numerical
Analysis
4 points. Spring term.
Prerequisite: 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.
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 255
Mathematics
in
Medicine and Biology  identical to G23.1501
4 points. Fall term.
Prerequisite: MATHUA
121
Calculus
I or MATHUA 212 Math for Economics II (for Economics
majors) and V23.0011
Principles
of
Biology
I or permission of the instructor.
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 256
Computers in
Medicine
and Biology  identical to G23.1502
4 points. Spring term.
Prerequisite: 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.
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 262
Ordinary
Differential
Equations
4 points. Fall and spring terms.
Prerequisite: 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.
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 263
Partial
Differential
Equations
4 points. Spring term.
Prerequisite: MATHUA 262 Ordinary
Differential Equations with a grade of C or better or
the equivalent.
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 264
Chaos and
Dynamical
Systems
4 points. Spring term.
Prerequisite: 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.
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 270
Transformations and
Geometries
4 points. Fall term of odd years.
Prerequisite: MATHUA 122 Calculus II
or MATHUA 212 Math for Economics II (for Economics
majors) with
a grade of C or better or the equivalent. Also, MATHUA 140
Linear Algebra with the grade of C or better is strongly
suggested.
This is a thorough course in planar Euclidean geometry. Emphasis is placed on development of students' proofwriting and problemsolving skills. It begins with a study of the basic structures (e.g., angles, lines, arcs) and concepts (e.g.,construction, congruence, similarity) known to Euclid and builds toward modern results. The second half of the course will focus on isometries of the plane, their classification, and applications of complex numbers and conformal maps to geometry. Time permitting, contrasts will be made with some nonEuclidean geometries.
MATHUA 282
Functions of
a Complex
Variable
4 points. Spring term.
Prerequisite: 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.
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 325
Analysis
4 points. Fall and spring term.
Prerequisite: 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.
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 326
Analysis II
4 points. Fall and Spring term.
Prerequisite: MATHUA 325 Analysis
or
permission of the department.
Functions of several variables. Limits and continuity. Partial
derivatives. The implicit function theorem. Transformation of
multiple integrals. The Riemann integral and
its extensions.
MATHUA 328 Honors Analysis I
4 points. Fall term.
Prerequisite: 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.
Recommended: Intensive calculus versions MATHUA 221 Honors Calculus I and MATHUA 222 Honors Calculus II.
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 329 Honors Analysis II
4 points. Spring term.
Prerequisite: 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.
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 343 Algebra
4 points. Fall term and Spring terms
Prerequisite: 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.
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 344
Algebra II
4 points. Fall and Spring terms.
Prerequisite: MATHUA 343 Algebra
with a grade of C or better
Extension fields, roots of polynomials. Construction with
straightedge and compass. Elements of Galois theory.
MATHUA 348 Honors Algebra I
4 points. Fall term.
Prerequisite: MATHUA 123 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.
Recommended: Intensive calculus versions MATHUA 221 Honors Calculus I and MATHUA 222 Honors Calculus II.
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 349 Honors Algebra II
4 points. Spring term.
Prerequisite: 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.
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 375 Topology
4 points. Spring Term.
Prerequisite: MATHUA 325 Analysis with a grade of C or higher
or permission of the department.
Settheoretic preliminaries. Metric spaces, topological
spaces,
compactness, connectedness, covering spaces, and homotopy
groups.
MATHUA 377
Differential
Geometry
4 points. Spring term.
Prerequisite: MATHUA 329 Honors Analysis II with a grade of C or higher
or permission of the department.
The differential properties of curves and surfaces.
Introduction
to differential manifolds and Riemannian geometry.
MATHUA 393 Honors I
4 points. Fall term of even years.
Prerequisite: Honors standing or approval of the director of the honors program.
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 394 Honors II
4 points. Spring term of odd years.
Prerequisite: Honors standing or approval of the director of the honors program.
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 395396 Special Topics I, II
4 points each term. Offered on request.
Prerequisite: Permission of the department.
Covers topics not offered regularly; experimental courses and
courses
offered on student demand. Detailed course descriptions are
available during preregistration.
MATHUA 397 Honors III
4 points. Fall term of odd years.
Prerequisite: Honors standing or approval of the director of the honors program.
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 398 Honors IV
4 points. Spring term of even years.
Prerequisite: Honors standing or approval of the director of the honors program.
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 997998 Independent Study
2 or 4 points each term. Fall and spring terms.
Prerequisite: Permission of the department.
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.