Spring 2005
Undergraduate MATH Course Descriptions
MATH 103:
Mathematical Explorations
3 credits.
This course is for students who wish to experience how mathematical ideas
naturally evolve. The homework consists of the students actively investigating
mathematical ideas. The course emphasizes ideas and imagination as opposed
to techniques and calculations. Topics vary depending on the instructor
and are announced (www.math.cornell.edu) several weeks before the semester
begins. Some assessment is done through writing assignments.
MATH 106:
Calculus for the Life and Social Sciences
3 credits. Prerequisite: Readiness for calculus, such
as can be obtained from 3 years of high school mathematics (including
trigonometry and logarithms) or from MATH 100, MATH 109 or EDUC 115.
MATH 111, rather than 106, is recommended for those planning to take
112.
Course serves as an introduction to differential and integral calculus,
partial derivatives, elementary differential equations. Examples from
biology and the social sciences are used.
MATH 111:
Calculus I
4 credits. Prerequisite: MATH 109 or 3 years of high
school mathematics, including trigonometry and logarithms.
Course topics include: functions and graphs, limits and continuity, differentiation
and integration of algebraic, trigonometric, inverse trig, logarithmic,
and exponential functions; applications of differentiation, including
graphing, max-min problems, tangent line approximation, implicit differentiation,
and applications to the sciences; the mean value theorem; and antiderivatives,
definite and indefinite integrals, the fundamental theorem of calculus,
substitution in integration, the area under a curve. Graphing calculators
are used, and their pitfalls are discussed, as applicable to the above
topics. MATH 111 can serve as a one-semester introduction to calculus
or as part of a two-semester sequence in which it is followed by MATH
112 or 122.
MATH 112:
Calculus II
4 credits. Prerequisite: MATH 111 with a grade of C or
better or excellent performance in MATH 106. Those who do well in MATH
111 and expect to major in mathematics or a strongly mathematics-related
field should take 122 instead of 112.
Course focus is on integration: applications, including volumes and arc
length; techniques of integration, approximate integration with error
estimates, improper integrals, differential equations (separation of variables,
initial conditions, systems, some applications). Also covered are infinite
sequences and series: definition and tests for convergence, power series,
Taylor series with remainder, and parametric equations.
MATH 122:
Honors Calculus II
4 credits. Prerequisite: 1 semester of alculus with a
high performance or permission of the department. Students planning
to continue with MATH 213 are advised to take 112 instead of this course.
The approach of this course to calculus is more theoretical than that
in MATH 112. Topics covered include: differentiation and integration of
elementary transcendental functions, techniques of integration, applications,
polar coordinates, infinite series, and complex numbers, as well as an
introduction to proving theorems.
MATH 135:
The Art of Secret Writing
3 credits. Prerequisite: 3 years of high school mathematics.
The course examines classical and modern methods of message encryption,
decryption, and cryptoanalysis. We develop mathematical tools to describe
these methods (modular arithmetic, probability, matrix arithmetic, number
theory) and become acquainted with some of the fascinating history of
the methods and people involved.
MATH 171:
Statistical Theory and Application In The Real World
4 credits. Prerequisite: High school mathematics. No
credit if taken after ECON 319, 320 or 321.
This introductory statistics course discusses techniques for analyzing
data occurring in the real world and the mathematical and philosophical
justification for these techniques. Topics include: population and sample
distributions, central limit theorem, statistical theories of point estimation,
confidence intervals, testing hypotheses, the linear model, and the least
squares estimator. The course concludes with a discussion of tests and
estimates for regression and analysis of variance (if time permits). The
computer is used to demonstrate some aspects of the theory, such as sampling
distributions and the Central Limit Theorem. In the lab portion of the
course, students learn and use computer-based methods for implementing
the statistical methodology presented in the lectures. (No previous familiarity
with computers is presumed.)
MATH 191:
Calculus For Engineers
4 credits. Prerequisite: 3 years of high school mathematics,
including trigonometry and logarithms, and at least one course in differential
and integral calculus.
This course has changed significantly from last year, and is essentially
a second course in calculus. Course topics include: techniques of integration,
finding areas and volumes by integration, exponential growth, partial
fractions, infinite sequences and series, and power series.
MATH 192:
Calculus For Engineers
4 credits. Prerequisite: MATH 190 or 191.
This course is an introduction to multivariable calculus. Topics include:
calculus of functions of several variables, double and triple integrals,
line integrals, vector fields, Green’s theorem, Stokes’ theorem, and the
divergence theorem.
MATH 213:
Calculus III
4 credits. Prerequisite: MATH 112, 122, 190 or 191.
This course is designed for students who wish to master the basic techniques
of multivariable calculus, but whose major will not require a substantial
amount of mathematics. Course topics include: vectors and vector-valued
functions; multivariable and vector calculus including multiple and line
integrals; first- and second-order differential equations with applications;
systems of differential equations; and elementary partial differential
equations. The course may emphasize different topics in the syllabus in
different semesters.
MATH 221:
Linear Algebra and Differential Equations
4 credits. Prerequisite: 2 semesters of calculus with
high performance or permission of the department.
This course is recommended for students who plan to major in mathematics
or in a related field. Course covers linear algebra and differential equations.
Topics include: vector algebra, linear transformations, matrices, and
linear differential equations, as well as an introduction to proving theorems.
MATH 222:
Multivariable Calculus
4 credits. Prerequisite: MATH 221.
This course is recommended for students who plan to major in mathematics
or in a related field. It covers differential and integral calculus of
functions in several variables, line and surface integrals as well as
the theorems of Green, Stokes and Gauss.
MATH 224:
Theoretical Linear Algebra and Calculus
4 credits. Prerequisite: MATH 223.
Course topics include: vector fields; line integrals; differential forms
and exterior derivative; work, flux, and density forms; integration of
forms over parametrized domains; and Green's, Stoke's, and divergence
theorems.
MATH 231:
Linear Algebra with Applications
3 credits. Prerequisite: MATH 111 or equivalent. Students
interested in the mathematics major should take MATH 221 or 294.
This course is an introduction to linear algebra. A wide range of applications
are discussed and computer software may be used. The main topics are systems
of linear equations, matrices, determinants, vector spaces, orthogonality,
and eigenvalues. Typical applications are population models, input/output
models, least squares, and difference equations.
MATH 275:
Living in a Random World
3 credits. Prerequisite: 1 semester of calculus
This course concentrates on applications of probability in the physical,
biological, and social sciences, and to understanding the world around
us: games, lotteries, option pricing, opinion polls, etc. Some familiarity
with integration and differentiation is useful but the equivalent of a
one-semester course in calculus is more than enough.
MATH 293:
Engineering Mathematics
4 credits. Prerequisite: MATH 192.
In fall: The conclusion of vector calculus, including line integrals,
vector fields, Green's theorem, Stokes' theorem, and the divergence theorem;
followed by an introduction to ordinary and partial differential equations,
including Fourier series and boundary value problems. May include computer
use in solving problems. In spring and summer: Introduction to ordinary
and partial differential equations. Topics include: first order equations
(separable, linear, homogeneous, exact); mathematical modeling (e.g.,
population growth, terminal velocity); qualitative methods (slope fields,
phase plots, equilibria and stability); numerical methods; second order
equations (method of undetermined coefficients, application to oscillations
and resonance, boundary value problems and eigenvalues); Fourier series;
linear partial differential equations (heat flow, waves, Laplace equation);
linear systems of ordinary differential equations.
MATH 294:
Engineering Mathematics
4 credits. Prerequisite: MATH 192.
Linear algebra and its applications. Topics include matrices, determinants,
vector spaces, eigenvalues and eigenvectors, orthogonality and inner product
spaces; applications include brief introductions to difference equations,
Markov chains, and systems of linear ordinary differential equations.
May include computer use in solving problems.
MATH 304:
Prove It!
4 credits. Prerequisite: MATH 221, 223, 293, or permission
of instructor.
In mathematics the methodology of proof provides a central tool for confirming
the validity of mathematical assertions, functioning much as the experimental
method does in the physical sciences. In this course, students will learn
various methods of mathematical proof, starting with basic techniques
in propositional and predicate calculus and in set theory and combinatorics,
and then moving to applications and illustrations of these via topics
in the three main pillars of mathematics: algebra, analysis, and geometry.
Since cogent communication of mathematical ideas is important in the presentation
of proofs, the course will emphasize clear, concise exposition. This course
will be useful for all students who wish to improve their skills in mathematical
proof and exposition, or who intend to study more advanced topics in mathematics.
MATH 311:
Introduction to Analysis
4 credits. Prerequisite: MATH 221-222, 223-224 or 293-294.
Provides a transition from calculus to real analysis. Topics include:
rigorous treatment of fundamental concepts in calculus: including limits
and convergence of sequences and series, compact sets; continuity, uniform
continuity and differentiability of functions. Emphasis will be placed
upon understanding and constructing mathematical proofs.
MATH 335:
Introduction to Cryptology (also COM S 480)
3 credits. Prerequisite: MATH 222 or 294, and COM S 100
or equivalent.
This course is an introduction to the algorithmic and mathematical concepts
of cryptanalysis. Topics will include security vs. feasibility and different
types of cryptographic attack, elementary probability, number theory,
cryptographic hash functions, secret and public key cryptography.
MATH 336:
Applicable Algebra
4 credits. Prerequisite: MATH 221, 223, 231 or 294.
An introduction to the concepts and methods of abstract algebra and number
theory that are of interest in applications. Course covers the basic theory
of groups, rings and fields and their applications to such areas as public-key
cryptography, error-correcting codes, parallel computing, and experimental
designs. Applications include the RSA cryptosystem and use of finite fields
to construct error-correcting codes and Latin squares. Topics include
elementary number theory, Euclidean algorithm, prime factorization, congruences,
theorems of Fermat and Euler, elementary group theory, Chinese remainder
theorem, factorization in the ring of polynomials, and classification
of finite fields.
MATH 356:
Groups and Geometry
4 credits. Prerequisite: MATH 221, 223, 231 or 294.
Groups were introduced in the nineteenth century as the sets of symmetries
of algebraic or geometric objects. This viewpoint has become central in
modern mathematics. This course studies the geometry of the plane and
of patterns in the plane in terms of the group of symmetries ("isometries")
of the plane. Prior knowledge of group theory is not a prerequisite. The
purpose of the course is to prepare students for the 400-level courses
in several ways. On one hand, the course offers experience in modern algebra
and geometry (including the geometry of complex numbers). It presents
some very beautiful and important topics and a sense of the unity of mathematics.
On the other hand, special care is taken to initiate the student into
the writing of proofs and the language of mathematics. Topics include:
Symmetries, groups of transformations, subgroups and cosets. Homomorphisms
and isomorphisms. Orbits and fixed points. Frieze groups, wallpaper groups
("2-dimensional crystallographic groups") and the associated tesselations
of the Euclidean plane.
MATH 401:
Honors Seminar: Topics In Modern Mathematics
4 credits. Prerequisite: 2 courses in mathematics numbered
300 or higher or permission of instructor.
This course is a participatory seminar primarily aimed at introducing
senior and junior mathematics majors to some of the challenging problems
and areas of modern mathematics. The seminar helps students develop research
and expository skills in mathematics, which is important for careers in
any field that makes significant use of the mathematical sciences (i.e.,
pure or applied mathematics, physical or biological sciences, business
and industry, medicine). The content varies from year to year.
MATH 403:
History of Mathematics
4 credits. Prerequisite: 2 courses in mathematics above
300, or permission of instructor.
Survey of the development of mathematics from antiquity to the present,
with an emphasis on the achievements, problems, and mathematical viewpoints
of each historical period and the evolution of such basic concepts as
number, geometry, construction, and proof. Readings from original sources
in translation. Students are required to give oral and written reports.
MATH 408:
Mathematics In Perspective
4 credits. Prerequisite: Consent of instructor.
This course examines several basic topics in mathematics, topics that
are usually introduced in high school, from the perspective gained through
a completed or nearly completed Cornell math major. The course will emphasize
the connections between branches of mathematics and the role of careful
definitions and proofs in both deepening our understanding of mathematics
and generating new mathematical ideas. In addition the course will relate
these basic subjects to topics of current mathematical interest. Specific
topics may include induction and recursion, synthetic and analytic geometry,
number systems, the geometry of complex numbers, angle measurement and
trigonometry, and the so-called elementary functions.
MATH 413:
Honors Introduction to Analysis I
4 credits. Prerequisite: a high level of performance
in MATH 221-222, 223-224, or 293-294 and a familiarity with proofs.
Students who do not intend to take MATH 414 are encouraged to take MATH
413 in the spring.
This course provides an introduction to the rigorous theory underlying
calculus, covering the real number system and functions of one variable.
The course is entirely based on proofs, and the student is expected to
know how to read and, to some extent, construct proofs before taking this
course. Topics typically include: Construction of the real number system,
properties of the real number system, continuous functions, differential
and integral calculus of functions of one variable, sequences and series
of functions.
MATH 414:
Honors Introduction to Analysis II
4 credits. Prerequisite: MATH 413.
This is a proof-based introduction to further topics in analysis. Topics
may include: the Lebesgue measure and integration, functions of several
variables, differential Calculus, implicit function theorem, infinite
dimensional normed and metric spaces, Fourier series, ordinary differential
equations.
MATH 418:
Introduction To The Theory of Functions of One Complex Variable
4 credits. Prerequisite: MATH 223-224, 311, 411 or 413,
or permission of instructor.
A theoretical and rigorous introduction to complex variable theory. Topics
include: complex numbers, differential and integral calculus for functions
of a complex variable including Cauchy's theorem and the calculus of residues,
elements of conformal mapping. Students interested in the applications
of complex analysis should consider MATH 422.
MATH 420:
Differential Equations and Dynamical Systems
4 credits. Prerequisite: High level of performance in
MATH 293-294, 221-222, 223-224, or permission of instructor.
Course covers ordinary differential equations in one and higher dimensions:
qualitative, analytic, and numerical methods. Emphasis is on differential
equations as models and the implications of the theory for the behavior
of the system being modeled and includes an introduction to bifurcations.
MATH 422:
Applied Complex Analysis
4 credits. Prerequisite: MATH 221-222, 223-224, 293-294,
or 213 and 231.
Course covers complex variables, Fourier transforms, Laplace transforms
and applications to partial differential equations. Additional topics
may include an introduction to generalized functions. Undergraduates who
plan to attend graduate school should take MATH 418.
MATH 424:
Wavelets and Fourier Series
4 credits. Prerequisite: MATH 221-222, 223-224, 293-294,
or permission of instructor.
Both Fourier series and wavelets provide methods to represent or approximate
general functions in terms of simple building blocks. Such representations
have important consequences, both for pure mathematics and for applications.
Fourier series use natural sinusoidal building blocks and may be used
to help solve differential equations. Wavelets use artificial building
blocks that have the advantage of localization in space. A full understanding
of both topics requires a background involving Lebesgue integration theory
and functional analysis. This course presents as much as possible on both
topics without such formidable prerequisites. The emphasis is on clear
statements of results and key ideas of proofs, working out examples, and
applications. Related topics that may be included in the course: Fourier
transforms, Heisenberg uncertainty principle, Shannon sampling theorem,
and Poisson summation formula.
MATH 428:
Introduction To Partial Differential Equations
4 credits. Prerequisite: MATH 221-222, 223-224, or 293-294
or permission of instructor.
Topics will be selected from first-order quasilinear equations, classification
of second-order equations, with emphasis on maximum principles, existence,
uniqueness, stability, Fourier series methods, approximation methods.
MATH 432:
Introduction to Algebra
4 credits. Prerequisite: MATH 332, 336, 431 or 433, or
permission of instructor. Undergraduates who plan to attend graduate
school in mathematics should take MATH 433-434.
An introduction to various topics in abstract algebra, including groups,
rings, fields, factorization of polynomials and integers, congruences,
and the structure of finitely generated abelian groups. Optional topics
are modules over Euclidean domains and Sylow theorems.
MATH 434:
Honors Introduction to Algebra
4 credits. Prerequisite: MATH 332, 336, 431, or 433,
or permission of instructor.
This is the honors version of a course in abstract algebra, which treats
the subject from an abstract and axiomatic viewpoint, including universal
mapping properties. Topics include groups, groups acting on sets, Sylow
theorems; rings, factorization: Euclidean rings, principal ideal domains,
the structure of finitely generated modules over a principal ideal domain,
fields, and Galois theory. The course emphasizes understanding the theory
with proofs in both homework and exams. An optional computational component
using the computer language GAP is available. A less theoretical course
that covers similar subject matter is MATH 432.
MATH 452:
Classical Geometries
4 credits. Prerequisite: MATH 221, 223, 231, or 294,
or permission of instructor.
This is an introduction to hyperbolic and projective geometry — the classical
geometries that developed as Euclidean geometry was better understood.
For example, the historical problem of the independence of Euclid's fifth
postulate is understood when the existence of the hyperbolic plane is
realized. Straightedge (and compass) constructions and stereographic projection
in Euclidean geometry can be understood within the structure of projective
geometry. Topics in hyperbolic geometry include: models of the hyperbolic
plane and relations to spherical geometry. Topics in projective geometry
include: homogeneous coordinates and the classical theorems about conics
and configurations of points and lines. Optional topics include: principles
of perspective drawing, finite projective planes, orthogonal Latin squares,
and the cross ratio.
MATH 454:
Introduction to Differential Geometry
4 credits. Prerequisite: MATH 221-222, 223-224, or 293-294,
plus at least one mathematics course numbered 300 or above. MATH 453
is not a prerequisite.
Course covers differential geometry of curves and surfaces. Also covers
curvature, geodesics, and differential forms. Serves as an introduction
to n-dimensional Riemannian manifolds. This material provides some background
for the study of general relativity; connections with the latter are indicated.
MATH 472:
Statistics
4 credits. Prerequisite: MATH 471 and knowledge of linear
algebra such as taught in MATH 221. Some knowledge of multivariable
calculus helpful but not necessary.
Statistics have proved to be an important research tool in nearly all
of the physical, biological, and social sciences. This course will serve
as an introduction to statistics for students who already have some background
in calculus, linear algebra, and probability theory. Topics covered in
the course will include parameter estimation, hypothesis testing, and
linear regression. The course will emphasize both the mathematical theory
of statistics as well as techniques for data analysis that are useful
in solving scientific problems.
MATH 481:
Mathematical Logic (also PHIL 431)
4 credits. Prerequisite: MATH 222 or 223 and preferably
some additional course involving proofs in mathematics, computer science
or philosophy.
A first course in mathematical logic providing precise definitions of
the language of mathematics and the notion of proof (propositional and
predicate logic). The completeness theorem says that we have all the rules
of proof we could ever have. The Gödel incompleteness theorem says that
they are not enough to decide all statements even about arithmetic. The
compactness theorem exploits the finiteness of proofs to show that theories
have unintended (nonstandard) models. Possible additional topics: the
mathematical definition of an algorithm and the existence of noncomputable
functions; the basics of set theory to cardinality and the uncountability
of the real numbers.
MATH 482:
Topics In Logic (also PHIL 432)
4 credits. Prerequisite: 1 logic course from the Mathematics
Department at the 200 level or higher, 1 logic course from the Philosophy
Department at the 300 level or higher, or permission of the instructor.
For description, see PHIL 432.
MATH 486:
Applied Logic (also COM S 486)
4 credits. Prerequisite: MATH 221-222, 223-224, or 293-294;
COM S 280 or equivalent (such as MATH 332, 336, 432, 434, or 481); and
some additional course in mathematics or theoretical computer science.
Course covers: propositional and predicate logic; compactness and completeness
by tableaux, natural deduction, and resolution. Other possible topics
include: equational logic; Herbrand Universes and unification; rewrite
rules and equational logic, Knuth-Bendix method and the congruence-closure
algorithm and lambda-calculus reduction strategies; topics in Prolog,
LISP, ML, or Nuprl; and applications to expert systems and program verification.
MATH 490:
Supervised Reading and Research
1-6 credits.
Supervised reading and research by arrangement with individual professors.
Not for material currently available in regularly scheduled courses.
MATH 507:
Teaching Secondary Mathematics: Theory and Practices
4 credits.
This course provides direct experience of new approaches, curricula and
standards in mathematics education. Discussion of articles, activities
for the secondary classroom and videotape of classroom teaching is tied
to in-class exploration of math problems. Experience in the computer lab,
examining software environments and their use in the mathematics classroom
is included. Participants are expected to write short papers, share ideas
in class and present their opinions on issues.
MATH 508:
Mathematics For Secondary School Teachers
1-6 credits. Prerequisite: Secondary school mathematics
teacher or permission of instructor.
An examination of the principles underlying the content of the secondary
school mathematics curriculum, including connections with the history
of mathematics and current mathematics research.
MATH 612:
Complex Analysis
4 credits.
MATH 611-612 are the core analysis courses in the mathematics graduate
program. MATH 612 covers complex analysis, Fourier analysis, and distribution
theory.
MATH 614:
Topics In Analysis
4 credits.
MATH 618:
Smooth Ergodic Theory
4 credits.
Topics include: invariant measures; entropy; Hausdorff dimension and
related concepts; hyperbolic invariant sets: stable manifolds, Markov
partitions and symbolic dynamics; equilibrium measures of hyperbolic attractors;
ergodic theorems; Pesin theory: stable manifolds of nonhyperbolic systems;
Liapunov exponents; and relations between entropy, exponents, and dimensions.
MATH 622:
Applied Functional Analysis
4 credits.
Course covers basic theory of Hilbert and Banach spaces and operations
on them. Applications.
MATH 632:
Algebra
4 credits.
MATH 631-632 are the core algebra courses in the mathematics graduate
program. MATH 632 covers Galois theory, representation theory of finite
groups, introduction to homological algebra. Familiarity with the material
of a standard undergraduate course in abstract algebra will be assumed.
MATH 633:
Noncommutative Algebra
4 credits.
Course covers Wedderburn structure theorem, Brauer group, and group cohomology.
MATH 651:
Introductory Algebraic Topology
4 credits.
This is on of the core topology courses in the mathematics graduate program.
An introductory study of certain geometric processes for associating algebraic
objects such as groups to topological spaces. The most important of these
are homology groups and homotopy groups, especially the first homotopy
group or fundamental group, with the related notions of covering spaces
and group actions. The development of homology theory focuses on verification
of the Eilenberg-Steenrod axioms and on effective methods of calculation
such as simplicial and cellular homology and Mayer-Vietoris sequences.
If time permits, the cohomology ring of a space may be introduced.
MATH 653:
Differentiable Manifolds II
4 credits. Prerequisite: MATH 652 or equivalent.
Advanced topics from differential geometry and differential topology
selected by instructor. Examples of eligible topics include: transversality,
cobordism, Morse theory, classification of vector bundles and principal
bundles, characteristic classes, microlocal analysis, conformal geometry,
geometric analysis and partial differential equations, and Atiyah-Singer
index theorem.
MATH 662:
Riemannian Geometry
4 credits.
Course topics include: linear connections, Riemannian metrics and parallel
translation; covariant differentiation and curvature tensors; the exponential
map, the Gauss Lemma and completeness of the metric; isometries and space
forms, Jacobi fields and the theorem of Cartan-Hadamard; the first and
second variation formulas; the index form of Morse and the theorem of
Bonnet-Myers; the Rauch, Hessian, and Laplacian comparison theorems; the
Morse index theorem; the conjugate and cut loci; and submanifolds and
the Second Fundamental form.
MATH 672:
Probability Theory II
4 credits. Prerequisite: MATH 671.
Topics for MATH 671-672 include: properties and examples of probability
spaces; sample space, random variables, and distribution functions; expectation
and moments; independence, Borel-Cantelli lemma, zero-one law; convergence
of random variables, probability measures, and characteristic functions;
law of large numbers; selected limit theorems for sums of independent
random variables; Markov chains, recurrent events; ergodic and renewal
theorems; Martingale theory; and Brownian motion and processes with independent
increments.
MATH 674:
Introduction To Mathematical Statistics
4 credits. Prerequisite: MATH 671 and OR&IE 670 or permission
of instructor.
Topics include an introduction to the theory of point estimation, hypothesis
testing and confidence intervals, consistency, efficiency, and the method
of maximum likelihood. Basic concepts of decision theory are discussed;
the key role of the sufficiency principle is highlighted and applications
are given for finding Bayesian, minimax and unbiased optimal decisions.
Some statistical distances for probability measures are introduced, like
Hellinger and total variation distance and also the Kullback-Leibler relative
entropy. The latter will be motivated by a discussion of source coding
for information transmission. Asymptotic methods are introduced and developed
in detail, with an emphasis on the concept of contiguity and its application
to nonparametric hypothesis testing.
MATH 681:
Logic
4 credits.
Course covers basic topics in mathematical logic, including propositional
and predicate calculus; formal number theory and recursive functions;
completeness and incompleteness theorems, compactness and Skolem-Loewenheim
theorems. Other topics as time permits.
MATH 703:
Topics in the History of Mathematics
4 credits. Prerequisite: Undergraduate algebra and analysis.
Topics in the history of modern mathematics at the level of F. Klein's
Evolution of Mathematics in the 19th Century, J. Dieudonne's Abrege D'Histoire
Des Mathematiques 1700-1900, and G. Birkhoff's Source Book of Classical
Analysis.
MATH 712:
Seminar In Analysis
4 credits.
MATH 713:
Functional Analysis
4 credits.
Course covers: topological vector spaces, Banach and Hilbert spaces,
and Banach algebras. Additional topics selected by instructor.
MATH 715:
Fourier Analysis
4 credits.
MATH 732:
Seminar In Algebra
4 credits.
MATH 739:
Topics In Algebra
4 credits.
Selection of advanced topics from algebra, algebraic number theory, and
algebraic geometry. Course content varies.
MATH 752:
Seminar In Topology
4 credits.
MATH 756:
Topology and Geometric Group Theory Seminar
4 credits.
MATH 758:
Topics In Topology
4 credits.
Selection of advanced topics from modern algebraic, differential, and
geometric topology. Course content varies.
MATH 762:
Seminar In Geometry
4 credits.
MATH 772:
Seminar In Probability and Statistics
4 credits.
MATH 778:
Stochastic Processes
4 credits.
MATH 782:
Seminar In Logic
4 credits.
MATH 787:
Set Theory
4 credits.
A first course in axiomatic set theory at the level of the book by Kunen.
MATH 790:
Supervised Reading and Research
1-6 credits.
Last modified:
August 25, 2004
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