|
Chair: Thomas R. Shemanske
Vice Chair: Marcia J. Groszek
Professors M. Arkowitz, P. Doyle, C. S. Gordon, M. J. Groszek, C. D.
Lahr, C. B. Pomerance, D. Rockmore, T. R. Shemanske, D. I. Wallace, D. L. Webb,
D. P. Williams, P. Winkler; Associate Professors R. C. Orellana, J. D. Trout;
Assistant Professors A. Barnett, V. V. Chernov, S. D. Pauls, C. J. Sutton, R.
A. Weber; Research Instructors O. Dearricott, S. Elizalde, M. Ionescu, S. A.
Treneer; Visiting Assistant Professor S. McGuinness; Adjunct Professor E.
Demidenko; Adjunct Associate Professor B. F. Cole.
INTRODUCTORY COURSES
The three courses Mathematics 3, 8, and 13 provide a coherent three-term
sequence in calculus. Mathematics 3 and 8 cover the basic calculus of functions
of a single variable, as well as vector geometry and calculus of scalar-valued
functions of several variables. In addition, these two courses are prerequisite
for many advanced courses in Mathematics and Computer Science. Mathematics 13
covers the basic calculus of vector-valued functions of several variables.
Mathematics 11 is a special version of Mathematics 13 for first-year students
with two terms of advanced placement. Most students planning advanced work in
mathematics or the physical sciences will need a fourth course in calculus,
Mathematics 23. Students interested in physical and engineering sciences are
encouraged to consider Mathematics 33. Students with two terms of advanced
placement credit who possibly are interested in a mathematics major or minor
should consider Mathematics 17 as an option in their first term. Mathematics
17, "An Introduction to Mathematics Beyond Calculus", is a course
designed for students interested in learning about some of the aspects of
mathematics not usually encountered in the first years of mathematical studies.
Topics change from year to year but may include aspects of combinatorics,
algebra, analysis, number theory, geometry, and/or topology. Students planning
to take upper-level mathematics courses are strongly encouraged to take
Mathematics 22 or 24 (linear algebra) early in their curriculum.
A student wishing to devote only two to three terms to the study of
mathematics is encouraged to choose among courses 3, 5, 6, and 10 (as well as 1
and 2 if his or her background indicates this is desirable). The combination of
Mathematics 3 and 6 will introduce the student to the ideas and applications of
the differential and integral calculus as well as to several branches of modern
mathematics. Mathematics 5 is a topics and sometimes interdisciplinary course.
Recent topics include "Chance," "The World According to
Mathematics," "Pattern," "Geometry in Art and
Architecture," "A Matter of Time," "Applications of
Calculus to Medicine and Biology," "Music and Computers," and
"Geometry and the Imagination." Mathematics 10 covers the fundamental
concepts of statistics.
THE MAJOR IN MATHEMATICS
The major in mathematics is intended both for students who plan careers in
mathematics and related fields, and for those who simply find mathematics
interesting and wish to continue its study. The content of the major is quite
flexible, and courses may be selected largely to reflect student interests.
Students who major in mathematics have an opportunity to participate in
activities that bring them in close contact with a faculty member-for example,
through a small seminar or through an independent research project under the
direction of a faculty member. In addition to regular course offerings, a
student with specialized interests, not reflected in our current course
offerings, often arranges for an independent reading course. Proposals for
independent activities should be directed to the Departmental Advisor to
Mathematics Majors.
In general, the mathematics major requires the student to pass eight
mathematics or computer science courses beyond prerequisites. At least six of
the required eight courses must be mathematics, and at least four of these
courses must be taken at Dartmouth. In addition, a student must fulfill the
College's requirement for a culminating experience in the major (see below).
Additional requirements for honors are described below in a separate
section.
Students are encouraged to take Mathematics 22/24 as soon as feasible, since
not only is it an explicit prerequisite to many upper-division courses, but
also the level of mathematical sophistication developed in Mathematics 22/24
will be presumed in many upper-division courses for which Mathematics 22/24 is
not an explicit prerequisite.
MATHEMATICS MAJOR REQUIREMENTS
Prerequisite Courses: Mathematics 3; 8; 13; 22 or 24
Requirements: To complete the major, it is necessary to complete
successfully at least eight courses in addition to the prerequisites, as well
as a culminating experience (which may or may not be part of the eight major
courses). These eight courses must include:
1. (Algebra) Mathematics 31 or 71;
2. (Analysis) At least one of Mathematics 35, 43, or 63;
3. Six additional Mathematics/Computer Science courses numbered 20 or
above.
Caveats:
Also acceptable: Mathematics 16, 17
Computer Science 5, 16, 18
Not acceptable: Mathematics 97
Computer Science 97
At most two Computer Science courses may be used. The culminating experience
requirements are described in a separate section below.
COURSES FOR THE MAJOR
While the student interested only in a general exposure to mathematics may
choose their major courses subject only to the constraints above, those with
more focused interests (pure mathematics, applied mathematics, and mathematics
education), will want to consider the course recommendations below.
A.) (Pure Mathematics) For students interested in pure mathematics,
Mathematics 24 is preferable to Mathematics 22 as prerequisite.
We recommend that the following courses be included among the eight courses
needed for the major:
(Algebra) Mathematics 71 and 81;
(Analysis) Mathematics 63, and 43 or 73;
(Topology/Geometry) Mathematics 54, and at least one of 74, 32, 42 or
72.
Students planning to attend graduate school should take substantially more
than the minimum requirements for the major. In particular, such students are
strongly urged to take both Mathematics 43 and 73; moreover, undergraduates
with adequate preparation are encouraged to enroll in graduate courses.
B.) (Applied Mathematics) Applied mathematics now encompasses a wide expanse
of mathematical activity in the sciences, ranging across finance, sociology,
psychology, biology, physics, computer science, and engineering. Students
interested in applied mathematics, especially those considering graduate school
in applied mathematics or any of the sciences, are advised to take Mathematics
23, 20 or 60, 46, and 50.
We recommend choosing additional courses from among the following:
Mathematics 26, 28, 36, 38, 42, 43, 46, 53, 56, 75, 76, 83, 88.
We do not make any specific recommendations concerning the choice of
Mathematics 22 versus 24 as prerequisite and the choices for requirements (1)
Algebra and (2) Analysis; these choices depend on the interest of the
student.
All students planning to attend graduate school should take substantially
more than the minimum requirements for the major. In particular, undergraduates
with adequate preparation are encouraged to enroll in graduate courses.
C.) (Mathematics Education) Certification as a public school Mathematics
teacher is available through partnership with the Education Department. Contact
the Education Department for details about course requirements.
Students who are considering a career in teaching should pay close attention
to the recommendations of the National Council of Teachers of Mathematics
(NCTM). The NCTM has endorsed a series of recommendations for a suggested
course of study for those people interested in teaching mathematics at the
secondary level. In general, their recommendations (www.nctm.org) are for a
vigorous course of study. At the moment, these recommendations far exceed the
requirements for obtaining a teaching certificate, but indicate the direction
in which the NCTM hopes that educators will proceed. Highly qualified teachers
in the elementary and secondary schools are of vital national importance, and
these guidelines should be carefully considered. Dartmouth courses that closely
fit the recommendations of the NCTM are (in addition to the prerequisites):
Mathematics 20 or 60; 23 or 36; 25 or 75; 28, 38 or 68; 31 or 71; 32 or 42 or
72; 35 or 43 or 63; 50
CULMINATING EXPERIENCE
The Department will accept any of the following in satisfaction of the
requirement of a culminating experience:
1. Submission of an Honors thesis acceptable for honors or high honors.
2. Satisfactory completion of any graduate course in mathematics.
3. Satisfactory completion of a one-term independent research project
(subject to approval by the advisor to majors).
4. Satisfactory completion of an advanced undergraduate course from among:
Mathematics 56, 68, 69, 70, 72, 73, 74, 75, 76, 81, 83, 89, 98.
MINORS IN MATHEMATICS
The following minors are available to all students who are not majoring in
mathematics and who do not have a modified major with the Mathematics
Department. For each minor, the prerequisites and required courses are listed
below. Approval of a minor can be obtained through the Department's Advisor to
Mathematics Majors.
I. Mathematics
Prerequisites: Mathematics 3, 8, 13, 22
Courses: Mathematics 31 or 71; Mathematics 33 or 35 or 43 or 63;
plus two other Mathematics courses numbered 20 or above. Computer Science 5 and
Mathematics 5 or 10 or 15.3 or 16 are also acceptable.
II. Applied Mathematics for Physical and Engineering Sciences
Prerequisites: Mathematics 3, 8, 13 or 22, Computer Science 5
Courses: Mathematics 23; 46; 50 or 60; 43 or 53 or 76
III. Applied Mathematics for Biological and Social Sciences
Prerequisites: Mathematics 3, 8, 13, 22
Courses: Mathematics 20; 23; 27, 28 or 36; 50 or 53 or 76
THE HONORS PROGRAM IN MATHEMATICS
A student who satisfies the requirements of the College for admission to the
Honors Program and is interested in doing independent work is strongly
encouraged to participate in the departmental Honors Program. Students who
successfully complete the Honors Program will have their degrees conferred with
'Honors' or 'High Honors' in mathematics; high honors is awarded only if the
student submits a written thesis. Interested students should read this section
of the ORC carefully and consult the Department Advisor to Mathematics
Majors. This program can be especially important to those who contemplate
graduate work in mathematics or a related field.
Admission: Admission to the Honors Program requires a general College
average of B, and a B average in the Mathematics Department at the time of
admission and at the time of graduation. Moreover, a B+ average is
required in the work of the Honors Program. The B average in the Department is
computed as follows: Courses prerequisite to the major and undergraduate
research courses (Mathematics 97) are not counted, but all other
courses titled (or cross-listed with) mathematics which the student has
taken are counted, whether or not these courses form part of the student's
formal major. In the case of a modified major, this average may include courses
outside the Mathematics Department. The B+ average required in the work of the
Honors Program is defined to be a grade of B+ given by the faculty advisor on
the research project. Questions about this requirement should be directed to
the Departmental Advisor to Mathematics Majors.
Requirements: Under the supervision of a faculty member, the
student must complete an independent research project or thesis beyond what is
required as part of a course. Often the subject of the project or thesis will
be motivated by concepts or the content of an advanced seminar or course in
which the student has participated, and, typically, the project or thesis will
be completed over a period of three terms. The student should consult with
his/her prospective faculty advisor and submit to the Advisor to Mathematics
Majors a brief written proposal of the project that has the written approval of
the faculty advisor. The Advisor to Majors will then review the student's
proposal and the courses that have been selected for the Honors major. Approval
of the proposal and course selection constitutes formal admission into the
Honors Program. This procedure should be completed by the beginning of fall
term of the student's senior year. The student may then register for (at most
two terms of) Mathematics 97, Undergraduate Research.
In the first week of the student's final term in residence, the student must
register with his/her faculty advisor for 'Honors Thesis/Project Supervision.'
This is not an official College course; rather, it represents a declaration of
intent to the Department that the student wishes to be considered for honors at
the time of graduation. Forms for this purpose are available from the Advisor
to Majors. No student who has failed to file this intent form with the
Advisor to Majors will be considered for honors in the major.
After the thesis is completed and submitted to the faculty advisor, the
student will give a short presentation of their results. The advisor can then
offer a recommendation for honors or high honors on behalf of the student; this
recommendation must be ratified by a vote of the Department faculty.
MODIFIED MAJORS
Modified Major with Mathematics as the primary Department
Prerequisite: Same as mathematics major plus some additional
prerequisites from modifying major (subject to approval of Advisor to
Majors).
Requirements: An algebra and an analysis course that satisfy the
requirements of the mathematics major, together with four additional courses
that normally count towards the major in mathematics, including one course that
satisfies the culminating experience requirement (choice subject to approval of
Advisor to Majors). Subject to the approval of the Advisor to Majors, the
algebra course can be replaced by one of the following courses: Mathematics 28,
38, 39, 54, 69, 89.
Four additional courses from the secondary department selected with the
approval of the Advisor to Majors and the secondary department. In particular,
these ten non-prerequisite courses must form a coherent unit that renders the
modified major academically more valuable than an abbreviated major together
with a minor in the secondary department.
THE GRADUATE PROGRAM IN MATHEMATICS
Dartmouth College offers a program of graduate study leading to the Ph.D.
degree in mathematics. This program is designed to meet the need for
mathematicians who are highly qualified in both teaching and scholarship. The
College provides an environment in which a doctoral candidate can pursue
professional study in mathematics and prepare to be an effective teacher.
REQUIREMENTS FOR THE MASTER'S DEGREE (A.M.)
With rare exceptions, the A.M. in mathematics is offered only to those
enrolled in the Ph.D. program. Normally the requirements for the A.M. must be
fulfilled within two years after entering and enrolling as a graduate student
in the Mathematics Department at Dartmouth. In addition to the general College
requirements for the master's degree, given on page XXX, the requirement is
departmental certification in algebra, analysis, topology, and one other
area.
Note (1): Continuation in the program for a second year is contingent on a
review of a student's work by the Mathematics Graduate Program Committee, the
review to take place early in the spring term of the first year.
Note (2): The general College requirements referred to above are three terms
in residence at Dartmouth and credit in eight courses of graduate quality;
these courses may sometimes, up to a limit of four, be replaced by approved
research or special study.
REQUIREMENTS FOR THE DOCTOR'S DEGREE (PH.D.)
The requirements for the Ph.D. degree in mathematics are as follows:
1. Departmental certification in algebra, analysis, topology, and one other
area.*
2. Admission to Ph.D. candidacy by the departmental Graduate Program
Committee as a result of its second review, which takes place at the end of the
spring term of the second year of graduate study. This review will take account
of all the relevant information that the Graduate Program Committee can gather,
such as the student's record in courses and seminars, the student's performance
during the certification process, and an estimate of the student's ability to
write an acceptable thesis.
3. Demonstration of a reading knowledge of a foreign language normally
chosen from French, German, and Russian. The Graduate Program Committee will
monitor students' progress in its annual review.
4. Completion of a doctoral thesis of acceptable quality, and its defense in
an oral examination.
5. Preparation for the teaching seminar through such activities as tutoring
in the years before admission to candidacy, completion of the teaching seminar,
and teaching at least one course (or the equivalent) for each year following
admission to candidacy. This requirement is met by receiving credit for
Mathematics 107 once during each year preceding admission to candidacy, credit
for Mathematics 147, and credit for Mathematics 149 once during each year
following admission to candidacy. The Graduate Program Committee may approve
substitutions subject to the minimum requirements: each student must earn
credit for Mathematics 107 at least once, credit for Mathematics 147, and
credit for Mathematics 149 at least twice.
COURSES
Course Numbering System: For most courses numbered 20 or above, the
last digit in the course number indicates the field of mathematics as follows:
probability and statistics, 0; algebra, 1; geometry, 2; analysis, 3; topology,
4; number theory, 5; applications, 6; combinatorics, 8; logic and foundations,
9.
Course Prerequisites: In all cases in which a prerequisite to a course is
listed, the honors or advanced placement equivalent of that course may be
substituted. For example, wherever Mathematics 13 appears as a prerequisite,
Mathematics 14 will serve.
UNDERGRADUATE COURSES
1. Calculus with Algebra
06F: 10, 12 07F: Arrange
The course description is given under Mathematics 2. This course is open
only to students having the permission of the Department. Dist: QDS. The
staff.
2. Calculus with Algebra and Trigonometry
07W: 9L, 11 08W: Arrange
Mathematics 1-2 is a two-term sequence. Its purpose is to cover the calculus
of Mathematics 3, the standard introduction to calculus, and, at the same time,
to develop proficiency in algebra. The sequence is specifically designed for
first-year students whose manipulative skill with the techniques of
secondary-school algebra is inadequate for Mathematics 3. The objective is to
introduce and develop algebraic techniques as they are needed to study the
ideas of calculus. The techniques will be taught in class, and the students
will be required to practice by solving many drill problems for homework. There
will be tutorial-help sessions.
Mathematics 1 will include the concepts of function and graph and the basic
ideas and applications of differential and integral calculus, at least as they
pertain to polynomial functions. In the second course, Mathematics 2, the study
of calculus will be continued so that by the end of the sequence the students
will have been introduced to the algebra and calculus of the exponential and
logarithm functions and the trigonometric functions and to differential
equations.
Prerequisite: Mathematics 1, or permission of the Department. Dist:
QDS. The staff.
3. Introduction to Calculus
06F: 9L, 10, 11, 12, 2 07W: 10 07F, 08W: Arrange
This course is the basic introduction to calculus. Students planning to
specialize in mathematics, computer science, chemistry, physics, or engineering
should elect this course in the fall term. Others may elect it in the
winter.
A study of polynomials and rational functions leads to the introduction of
the basic ideas of differential and integral calculus. The course also
introduces exponential, logarithmic, and trigonometric functions. The emphasis
throughout is on fundamental ideas and problem solving.
Mathematics 3 is open to all students who have had intermediate algebra and
plane geometry. No knowledge of trigonometry is required. The lectures are
supplemented by problem sessions. Dist: QDS. The staff.
4. Applications of Calculus to Medicine and Biology
07W: 10A 08W: Arrange
This course will establish the relevance of calculus to medicine. It will
develop mathematical tools extending the techniques of introductory calculus,
including some matrix algebra and solution techniques for first order
differential equations. These methods will be used to construct simple and
elegant models of phenomena such as the mutation of HIV, spread of infectious
disease, and biological disposition of drugs and inorganic toxins, enzyme
kinetics and population growth.
Prerequisite: Mathematics 3. Note: This is a second-term calculus course,
but it does not cover the same material as Mathematics 8, and does not serve as
a prerequisite for Mathematics 13. There is a version of this course suitable
for major credit: see Mathematics 27. Dist: QDS. Wallace.
5. Exploring Mathematics
07W: 10 07S: 12 07F, 08W: Arrange
In 07W, A Matter of Time (Identical to Comparative Literature 65 in
07W). Everybody knows about time. Our everyday language bears witness
to the centrality of time with scores of words and expressions that refer to it
as a measure, a frame of reference, or an ordering factor for our lives,
feelings, dreams, and histories. Playing with time has been a favorite game in
works of high culture-from the Greek sophists to cubism-and in popular
culture-from H.G. Wells to Monty Python. And time is at the center of one of
the most revolutionary scientific theories of all time: Einstein's Theory of
Relativity. In this course we will use mathematics, literature, and the arts to
travel through history, to explore and understand Time as a key concept and
reality in the development of Western culture and in our own twentieth century
view of ourselves and the world.
Dist: QDS. Lahr, Pastor.
In 07S, The Mathematics of Music and Sound. Sound and music are
integral parts of all cultures and are critical to human and animal
communications. The production, transmission, and perception of sound is woven
through with mathematics. With the goal of expanding both scientific and
artistic horizons, we explore vibration, resonance, waves, musical instruments,
the human ear, speech, architectural acoustics, harmony and dissonance, tuning
systems, and musical composition. Hands-on project work may include
time-frequency analysis, sound synthesis, inventing and building a new
instrument.
Prerequisite: high-school physics. Familiarity with musical notation or an
instrument will help. Dist: QDS. Barnett.
6. Introduction to Finite Mathematics
07S: 11 07X, 08S: Arrange
This course is designed for students whose interests lie outside the
physical sciences. The course includes an introduction to sets and logic,
elementary counting techniques, an introduction to probability, and topics in
matrix algebra including the solution of systems of equations and matrix
inverses. Illustrative examples and problems will be chosen from the social,
managerial, and biological sciences. Computing may be used to illustrate
concepts and solve problems. No background in computer programming is assumed.
The course is appropriate for the student who plans to take no advanced courses
in mathematics. Dist: QDS. The staff.
7. First-Year Seminar in Mathematics
Consult special listing
8. Calculus of Functions of One and Several Variables
06F: 9L, 11, 12 07W: 11, 12 07S: 11 07F, 08W, 08S: Arrange
This course is a sequel to Mathematics 3 and is appropriate for students who
have successfully completed an AB calculus curriculum in secondary school.
Roughly half of the course is devoted to topics in one-variable calculus:
techniques of integrations, areas, volumes, trigonometric integrals and
substitutions, numerical integration, sequences and series including Taylor
series.
The second half of the course generally studies scalar valued functions of
several variables. It begins with the study of vector geometry, equations of
lines and planes, and space curves (velocity, acceleration, arclength). The
rest of the course is devoted to studying differential calculus of functions of
several variables. Topics include limits and continuity, partial derivatives,
tangent planes and differentials, the Chain Rule, directional derivatives and
applications, and optimization problems including the use of Lagrange
multipliers.
Prerequisite: Mathematics 3 or equivalent. Dist: QDS. Williams,
Ionescu, Treneer (fall), Arkowitz, Ionescu (winter), Treneer (spring).
9. Calculus of Functions of One and Several Variables, Honors Section
Not offered in the period from 06F through 07S
Sections of Mathematics 8 for students who have been invited by the
Department Chair based on their record in high school or exceptional work in
Mathematics 3. Dist: QDS.
10. Introductory Statistics
07S: 2 08S: Arrange
An introduction to the basic concepts of statistics. Topics include
elementary probability theory, descriptive statistics, the binomial and normal
distributions, confidence intervals, basic concepts of tests of hypotheses,
chi-square tests, nonparametric tests, normal theory t-tests, correlation, and
simple regression. Packaged statistical programs will be used. Because of the
large overlap in material covered, no student may receive credit for more than
one of the courses Economics 10, Government 10, Mathematics 10, Psychology 10,
Social Sciences 10, or Sociology 10 except by special petition. Dist:
QDS. McGuinness.
11. Multivariable Calculus for Two-Term Advanced Placement First-Year
Students.
06F: 9L, 11, 12 07F: Arrange
This course can be viewed as equivalent to Mathematics 13, but is designed
especially for first-year students who have successfully completed a BC
calculus curriculum in secondary school. In particular, as part of its syllabus
it includes most of the multivariable calculus material present in Mathematics
8.
Topics include vector geometry, equations of lines and planes, and space
curves (velocity, acceleration, arclength), limits and continuity, partial
derivatives, tangent planes and differentials, the Chain Rule, directional
derivatives and applications, and optimization problems. It continues with
multiple integration, vector fields, line integrals, and finishes with a study
of Green's and Stokes' theorem. Dist: QDS. Lahr, Sutton, Elizalde.
12. Calculus Plus
06F: 12 07F: Arrange
This version of Mathematics 11 is designed for students who are curious
about the broader role of calculus within mathematics and the sciences.
Non-routine problems and examples will be discussed, and side topics explored.
Some of the more routine calculus skills will be left to students to learn on
their own or in groups. Open to students who have placed into Mathematics 11.
Dist: QDS. Pauls.
13. Calculus of Vector-Valued Functions
06F: 12 07W: 10, 2 07S: 12 07F, 08W, 08S: Arrange
This course is a sequel to Mathematics 8 and provides an introduction to
calculus of vector-valued functions. Topics include differentiation and
integration of parametrically defined functions with interpretations of
velocity, acceleration, arclength and curvature. Other topics include iterated,
double, triple and surface integrals including change of coordinates. The
remainder of the course is devoted to vector fields, line integrals, Green's
theorem, curl and divergence, and Stokes' theorem.
Prerequisite: Mathematics 8 or equivalent. Note: First-year students who
have received two terms on the BC exam generally should take Mathematics 11
instead. On the other hand, if the student has had substantial exposure to
multivariable techniques, they are encouraged to take a placement exam during
orientation week to determine if placement into Mathematics 13 is more
appropriate. Dist: QDS. McGuinness (fall), Treneer, Dearricott
(winter), Dearricott (spring).
14. Calculus of Vector-Valued Functions, Honors Section
07W: 2 08W: Arrange
Sections of Mathematics 13 for students who have done satisfactory work in
Mathematics 9 or by invitation or approval of Department Chair based on
exceptional work in Mathematics 8. Dist: QDS. Gordon.
15.1 Mathematics for the Physical Sciences
Not offered in the period from 06F through 07S
The two parts of Mathematics 15, referred to as 15.1 and 15.2, are a
two-term introduction to the mathematics related to physics for students
intending advanced work in physical science, engineering or applied
mathematics. We advise students to take Physics 13 concurrently with
Mathematics 15.1 if possible.
First-order differential equations and integration techniques, second-order
constant-coefficient differential equations, vectors, lines and planes, dot
product and Euclidean geometry, vector functions of one variable, line
integrals, matrix algebra and linear equations.
Prerequisite: Credit for Mathematics 3, Physics 13 concurrently, or the
equivalent, or permission of the instructor. Mathematics 15.1 can be
substituted for Mathematics 8 as a prerequisite for any course or program.
Dist: QDS.
15.2 Mathematics for the Physical Sciences
Not offered in the period from 06F through 07S
The two parts of Mathematics 15, referred to as 15.1 and 15.2, are a
two-term introduction to the mathematics related to physics for students
intending advanced work in physical science, engineering, or applied
mathematics.
Differentiable functions of several variables, gradient fields, general
chain rule for differentiable functions, max-min techniques, iterated and
multiple integrals, centroids and moments, improper integrals, curvilinear
coordinates, divergence and curl of a vector field, Green's theorem,
conservative fields, Gauss's theorem, Stokes' theorem, Taylor and Fourier
series.
Prerequisite: Mathematics 15.1, Physics 14 concurrently, or permission of
the instructor. Mathematics 15.2 can be substituted for Mathematics 13 as a
prerequisite for any course or program. Dist: QDS.
16. Linear Programming (Identical to Computer Science 16)
07S: 11 Offered only as Computer Science 16 effective 07F
This course introduces one of the fundamental tools of modern business
planning and an exciting area of current mathematical and computer science
research. The course begins with a discussion of the kinds of problems to which
linear programming applies, followed by an introduction to the simplex
algorithm and duality and shadow prices. After a discussion of some pitfalls of
the simplex algorithm, the course turns to the revised simplex method, the
solution of general linear programming problems, the general theory of duality
and feasibility, a discussion of the applications of linear programming to the
efficient allocation of scarce resources, and such problems as production
scheduling and inventory. The course will close with topics selected from
applications to matrix games, connections with geometry, connections to optimal
matchings, network flows and transportation problems or the nature and
implications of interior point methods in linear programming.
Prerequisite: Mathematics 6 or 8 or equivalent knowledge of matrix algebra
and permission of instructor. Dist: TAS. The staff.
17. An Introduction to Mathematics Beyond Calculus
07W: 11 08W: Arrange
Gives prospective Mathematics majors an early opportunity to delve into
topics outside the standard calculus sequence. Specific topics will vary from
term to term, according to the interests and expertise of the instructor.
Designed to be accessible to bright and curious students who have mastered BC
Calculus, or its equivalent. This course counts toward the Mathematics major,
and is open to all students, but enrollment may be limited, with preference
given to first-year students.
Prerequisite: Mathematics 8, or placement into Mathematics 11. Dist:
QDS. Trout.
19. Discrete Mathematics in Computer Science
06F: 12 07F: Arrange
This course integrates discrete mathematics with algorithms and data
structures, using computer science applications to motivate the mathematics. It
is designed to be taken simultaneously with Computer Science 15 or 18. However,
students who are unable to complete it in this way may take it after Computer
Science 15 or 18 but before Computer Science 25.
The course introduces counting techniques and number theory, with an
emphasis on the application to RSA public key cryptography. It covers logic and
proofs, including mathematical induction. Relationships among recursive
algorithms, recurrence relations, and mathematical induction are discussed with
particular attention to trees as a recursive data structure. Issues of expected
running time for algorithms and the technique of "hashing" data files
for quick recovery of information guides the discussion of probability through
independent trials, experiments, and expected values.
Prerequisite: Concurrent enrollment in Computer Science 15 or 18 or
completion of Computer Science 15 or 18. Dist: QDS. Pomerance
(fall).
20. Discrete Probability
06F: 2 07S: 10 07X, 07F: Arrange
Basic concepts of probability are introduced in terms of finite probability
spaces and stochastic processes having a finite number of outcomes on each
experiment. The basic theory is first illustrated in terms of simple models
such as coin tossing, random walks, and casino games. Also included are Markov
chain models and their applications in the social and physical sciences. The
computer will be used to suggest and motivate theoretical results and to study
applications in some depth. There is an honors version of this course: see
Mathematics 60.
Prerequisite: Mathematics 8. Dist: QDS. Williams (fall), Dearricott
(spring).
22. Linear Algebra with Applications
06F: 2 07S: 10 07X, 07F, 08S: Arrange
This course presents the fundamental concepts and applications of linear
algebra with emphasis on Euclidean space. Significant goals of the course are
that the student develop the ability to perform meaningful computations and to
write accurate proofs. Topics include bases, subspaces, dimension,
determinants, characteristic polynomials, eigenvalues, eigenvectors, and
especially matrix representations of linear transformations and change of
basis. Applications may be drawn from areas such as optimization, statistics,
biology, physics, and signal processing.
Students who plan to take either Mathematics 63 or Mathematics 71 are
strongly encouraged to take Mathematics 24.
Prerequisite: Mathematics 8. Dist: QDS. Gordon (fall), Weber
(spring).
23. Differential Equations
06F: 10 07W: 2 07S: 12 07F, 08W, 08S: Arrange
This course is a survey of important types of differential equations, both
linear and nonlinear. Topics include the study of systems of ordinary
differential equations using eigenvectors and eigenvalues, numerical solutions
of first and second order equations and of systems, and the solution of
elementary partial differential equations using Fourier series.
Prerequisite: Mathematics 13. Dist: QDS. Sutton (fall), Dearricott
(winter), Pauls (spring).
24. Linear Algebra
06F: 2 07W, 07S: 10 08W, 08S: Arrange
This course is an introduction to the fundamental concepts of linear algebra
in abstract vector spaces. The topics and goals of this course are similar to
those of Mathematics 22, but with an additional emphasis on mathematical
abstraction and theory.
(Mathematics 24 can be substituted for Mathematics 22 as a prerequisite for
any course or program.)
Dist: QDS. Treneer (fall), Ionescu (winter), Sutton (spring).
25. Number Theory
06F: 11 07F: Arrange
This course is a survey of the elementary arithmetic of the integers (prime
numbers, factorization, congruences, diophantine equations) with some
historical study of important problems. There is an honors section of this
course: see Mathematics 75. Offered in alternate years.
Prerequisite: Mathematics 13. Dist: QDS. The staff.
26. Numerical Methods in Computation (Identical to Computer Science 26
and Engineering Sciences 91)
06F, 07F: 12
A study and analysis of important numerical and computational methods for
solving engineering and scientific problems. The course will include methods
for solving linear and nonlinear equations, doing polynomial interpolation,
evaluating integrals, solving ordinary differential equations, and determining
eigenvalues and eigenvectors of matrices. The student will be required to write
programs and run them on the computer.
Prerequisite: Mathematics 23, and Computer Science 5 or 14. Dist:
QDS.
27. Advanced Calculus and Dynamics in Biology and Medicine
07W: 10A 08W: Arrange
This course will prepare students to read the technical literature in
mathematical biology, epidemiology, pharmacokinetics, ecological modeling and
related areas. Topics include systems of nonlinear ordinary differential
equations, equilibria and steady state solutions, phase portraits, bifurcation
diagrams, and some aspects of stability analysis. Emphasis is placed on the
student's ability to analyze phenomena and create mathematical models. This
interdisciplinary course is open to mathematics majors, biology majors, and
students preparing for a career in medicine.
Prerequisite: Mathematics 22. Note: Students without the mathematical
prerequisites can take this course as Mathematics 4: no student may take both
Mathematics 4 and 27 for credit, and only Mathematics 27 is eligible to count
towards the major in mathematics. Dist: QDS. Wallace.
28. Introduction to Combinatorics
07W: 12 08W: Arrange
Beginning with techniques for counting - permutations and combinations,
inclusion-exclusion, recursions, and generating functions - the course then
takes up graphs and directed graphs and ordered sets, and concludes with some
examples of maximum-minimum problems of finite sets. Topics in the course have
application in the areas of probability, statistics, and computing.
Prerequisite: Mathematics 8, or Mathematics 3 and 6. Dist: QDS.
McGuinness.
29. Introduction to Computability
07S: 12
Several approaches that formalize the notion of computability are presented.
The equivalence of these formalizations is discussed, as well as Church's
Thesis, which claims that these formalizations capture the intuitive notion of
computability. Universal machines and undecidable problems are discussed. The
course concludes with a study of recursive and recursively enumerable sets, and
an introduction to relative computability and degrees of unsolvability. Offered
in alternate years.
Prerequisite: Mathematics 22, or Computer Science 49, or permission of the
instructor. Dist: QDS. Weber.
30. Introduction to Linear Models
Not offered in the period from 06F through 08S
This course provides an introduction to the most common model used in
statistical data analysis. Simple linear regression, multiple regression, and
analysis of variance are covered, as well as statistical model-building
strategies. Regression diagnostics, analysis of complex data sets and
scientific writing skills are emphasized. Methods are illustrated with data
sets drawn from the health, biological, and social sciences. Computations
require the use of a statistical software package such as STATA. Offered in
alternate years.
Prerequisite: Mathematics 10, another elementary statistics course, or
permission of the instructor. Dist: TAS.
31. Topics in Algebra
06F: 10 07X, 07F: Arrange
This course will provide an introduction to fundamental algebraic
structures, and may include significant applications. The majority of the
course will consist of an introduction to the basic algebraic structures of
groups and rings. Additional work will consist either of the development of
further algebraic structures or applications of the previously developed theory
to areas such as coding theory or crystallography. As a result of the
variable syllabus, this course may not serve as an adequate prerequisite for
Mathematics 81. Students who contemplate taking Mathematics 81 should consider
taking Mathematics 71 instead of this course.
Prerequisite: Mathematics 22. Dist: QDS. Orellana.
32. The Shape of Space
08W: Arrange
Topics in intuitive geometry and topology, for example: how to turn a sphere
inside out; knots, links, and their invariants; polyhedra in 2, 3, and 4
dimensions; the classification of surfaces; curvature and the Gauss-Bonnet
theorem; spherical and hyperbolic geometry; Escher patterns and their
quotients; the shape of the universe. Offered in alternate years.
Prerequisite: Mathematics 22 or 24. Dist: QDS.
33. Mathematics in the Sciences and Engineering
Not offered in the period from 06F through 08S
This course provides an overview of the mathematical tools used for
analyzing common problems in science and engineering. Particular attention will
be given to problems involving linear operators. Topics include partial
differential equations, Fourier analysis, linear spaces and operators (in
particular, matrix operators), and the calculus of variations. Both analytical
and numerical methods will be covered.
Prerequisite: Mathematics 23. Dist: TAS.
35. Real Analysis
07W: 12 08W: Arrange
This course introduces the basic concepts of real-variable theory. Topics
include real numbers and cardinality of sets, sequences and series of real
numbers, metric spaces, continuous functions, integration theory, sequences and
series of functions, and polynomial approximation. Some applications of the
theory may be presented. Mathematics 63 presents similar material, but from a
more sophisticated point of view. This course may not serve as an adequate
prerequisite for either Mathematics 73 or 83. Students who contemplate taking
one of these two advanced courses should consider taking Mathematics 63 instead
of this course.
Prerequisite: Mathematics 13 and permission of the instructor, or
Mathematics 22. Dist: QDS. Chernov.
36. Mathematical Models in the Social Sciences (Identical to
Mathematics and Social Science 36)
07W: 10A 07F: Arrange
Disciplines such as anthropology, economics, sociology, psychology, and
linguistics all now make extensive use of mathematical models, using the tools
of calculus, probability, game theory, network theory, often mixed with a
healthy dose of computing. This course introduces students to a range of
techniques using current and relevant examples. Students interested in further
study of these and related topics are referred to the courses listed in the
Mathematics and Social Sciences program.
Prerequisite: Mathematics 13, 20. Dist: TAS. Rockmore.
38. Graph Theory
07S: 12 08S: Arrange
The theory of graphs has roots in both practical and recreational
mathematics. Today there are major applications of graph theory in management
science (operations research) and computer science. This course is a survey of
the theory and applications of graphs. Topics will be chosen from among
connectivity, trees, and Hamiltonian and Eulerian paths and cycles; isomorphism
and reconstructability; planarity, duality, and genus; independence and
coloring problems, including interval graphs, interval orderings and perfect
graphs, color-critical graphs and the four-color theorem; matchings; network
flows, including applications to matchings, higher connectivity, and
transportation problems; matroids and their relationship with optimization.
Prerequisite: Mathematics 22 (or Computer Science 25 and permission of the
instructor). Dist: QDS. Elizalde.
39. Logic
07F: Arrange
This course begins with a brief treatment of sentential logic and then
concentrates on first-order logic. Both proof theory and model theory are taken
up. The course ends with a proof of the G√δdel incompleteness theorem.
Connections with the philosophy of mathematics are discussed. There is an
honors version of this course: see Mathematics 69. Offered in alternate
years.
Prerequisite: one of Mathematics 22, 28, and 29, or Philosophy 10 by
permission of the instructor. Dist: QDS.
40. Topics in Applied Probability
Not offered in the period from 06F through 08S
This is a continuation of Mathematics 20 (60). The course studies
probability models chosen from queueing theory, genetics, statistical physics,
and gambling. Additional probability concepts such as continuous probability
and stochastic processes will be discussed in the context of these models.
Offered in alternate years.
Prerequisite: Mathematics 13 and 20, or permission of the instructor.
Dist: QDS.
42. Differential Geometry I
Not offered in the period from 06F through 08S
This course will cover curves and surfaces in Euclidean 3-dimensional space.
Topics include curvature and torsion of curves, the Frenet-Serret equations,
Gaussian and mean curvature of surfaces, geodesics and parallel transport,
isometries and Gauss's Theorem Egregium, the Riemann Curvature tensor. One or
more of the following topics will be studied if time permits: vector fields,
tangent bundles, hypersurfaces, connections, and curvature. Offered in
alternate years.
Prerequisite: Mathematics 22 or permission of the instructor, and
Mathematics 23. Dist: QDS.
43. Functions of a Complex Variable
07S: 11 08S: Arrange
This course covers the differential and integral calculus of complex
variables including such topics as Cauchy's theorem, Cauchy's integral formula
and their consequences; singularities, Laurent's theorem, and the residue
calculus; harmonic functions and conformal mapping. Applications will include
two-dimensional potential theory, fluid flow, and aspects of Fourier
analysis.
Prerequisite: Mathematics 13. Dist: QDS. Chernov.
46. Introduction to Applied Mathematics
07S: 10 08S: Arrange
Develops tools to analyze phenomena in the physical and life sciences, from
cell aggregation to vibrating drums to traffic jams. Focus is on applied linear
and nonlinear partial differential equations: methods for Laplace, heat and
wave equations (Fourier transform, Green's functions, eigenfunction
expansions), Burger's and reaction-diffusion equation. Further topics may
include linear and integral operators, nonlinear optimization, linear
programming, asymptotics, boundary layers, or inverse problems. Students will
develop numerical skills with a package like MATLAB/Octave.
Prerequisite: Mathematics 22 and 23, or permission of the instructor.
Dist: TAS. Barnett.
50. Probability and Statistical Inference
07W: 2A 08W: Arrange
Introduction to continuous probability and statistical inference for data
analysis. Includes the theory of estimation and the theory of hypothesis
testing using normal theory t-tests and nonparametric tests for means and
medians, tests for variances, chi-square tests, and an introduction to the
theory of the analysis of variance and regression analysis. Analysis of
explicit data sets and computation are an important part of this hands-on
statistics course.
Prerequisite: Mathematics 13 and 20, or permission of the instructor.
Dist: QDS. Demidenko.
53. Chaos!
07F: Arrange
Chaotic dynamical systems are everywhere: weather patterns, swinging
pendula, population dynamics, even human heart rhythms. With a balance of
theory and applications, this course will introduce: flows, fixed points,
bifurcations, Lorenz equations, Lyapunov exponent, one-dimensional maps,
period-doubling, Julia sets, fractal dimension. Optional topics may include:
Hamiltonian systems, symbolic dynamics. Numerical explorations will involve a
package like MATLAB/Octave, and students will present a final project
investigating a related topic. Offered in alternate years.
Prerequisite: Mathematics 22 and 23, or permission of the instructor.
Dist: QDS.
54. Topology I
07X: Arrange
This course begins with the definitions of topological space, open sets,
closed sets, neighborhoods, bases and subbases, closure operator, continuous
functions, and homeomorphisms. The course will study constructions of spaces
including subspaces, product spaces, and quotient spaces. Special categories of
spaces and their interrelations will be covered, including the categories
defined by the various separation axioms, first and second countable spaces,
compact spaces, and connected spaces. Subspaces of Euclidean and general metric
spaces will be among the examples studied in some detail.
Prerequisite: Mathematics 13 and 22. Dist: QDS.
56. Numerical Analysis (Identical to Computer Science 56)
Not offered in the period from 06F through 08S
This course introduces the student to the concepts of modern numerical
analysis. The main emphasis will be on developing effective numerical methods
to solve problems in ordinary and partial differential equations. Other topics
will be chosen from optimization, approximation, Fourier Transform, and Monte
Carlo methods. The specific content will depend in part on the instructor.
Offered in alternate years.
Prerequisite: Mathematics 33 and Computer Science 5 or 14, or permission of
the instructor. Dist: QDS.
60. Probability (Honors Section of Mathematics 20)
08S: Arrange
This course is a more theoretical introduction to probability theory than
Mathematics 20. In addition to the basic content of Mathematics 20, the course
will include other topics such as continuous probability distributions and
their applications. Offered in alternate years.
Prerequisite: Mathematics 13, or permission of the instructor. Dist:
QDS.
63. Real Analysis
07W: 12 08W: Arrange
This course introduces the basic concepts of real-variable theory. Topics
include real numbers and cardinality of sets, sequences and series of real
numbers, metric spaces, continuous functions, integration theory, sequences and
series of functions, and polynomial approximation. Students may not take both
Mathematics 35 and 63 for credit.
Prerequisite: Mathematics 22 or 24, or Mathematics 13 and permission of the
instructor. Dist: QDS. Lahr.
66. Mathematical Topics in Modern Physics
07S: 2
This introductory course presents mathematical topics that are relevant to
issues in modern physics. It is mainly designed for two audiences: mathematics
majors who would like to see modern physics and the historical motivations for
theory in their coursework, and physics majors who want to learn mathematics
beyond linear algebra and calculus. Possible topics include (but are not
limited to) introductory Hilbert space theory, quantum logics, quantum
computing, symplectic geometry, Einstein's theory of special relativity, Lie
groups in quantum field theory, etc. No background in physics is assumed.
Offered in alternate years.
Prerequisites: Mathematics 24, or Mathematics 22 and permission of the
instructor. Dist: QDS. Trout.
68. Algebraic Combinatorics
07F: Arrange
This course covers the use of abstract algebra in studying the existence,
construction, enumeration, and classification of combinatorial structures. The
theory of enumeration, including both Polya Theory and the Incidence Algebra,
and culminating in a study of algebras of generating functions, will be a
central theme in the course. Other topics that may be included if time permits
are the construction of block designs, error-correcting codes, lattice theory,
the combinatorial theory of the symmetric group, and incidence matrices of
combinatorial structures. Offered in alternate years.
Prerequisite: Mathematics 28 and 31, or Mathematics 71, or permission of the
instructor. Dist: QDS.
69. Logic (Honors Section of Mathematics 39)
07W: 11
This course begins with a study of relational systems as they occur in
mathematics. First-order languages suitable for formalizing such systems are
treated in detail, and several important theorems about such languages,
including the compactness and Lowenheim-Skolem theorems, are studied. The
implications of these theorems for the mathematical theories being formulated
are assessed. Emphasis is placed on those problems relating to first-order
languages that are of fundamental interest in logic. Offered in alternate
years.
Prerequisite: experience with mathematical structures and proofs, as offered
by such courses as Mathematics 71, 54, or 24; or permission of the instructor.
Dist: QDS. Winkler.
70. Mathematical Statistics
07S: 11
This course will be a continuation of the study of the theory of statistical
inference that was begun in Mathematics 50. Topics will include the
mathematical development of normal theory t-tests and nonparametric tests for
means and medians, tests for variances, chi-square tests, and an introduction
to the theory of the analysis of variance and regression analysis. Offered in
alternate years.
Prerequisite: Mathematics 50. Dist: QDS. Demidenko.
71. Algebra
06F: 10 07F: Arrange
The sequence Mathematics 71 and 81 is intended as an introduction to
abstract algebra. Mathematics 71 develops basic theorems on groups, rings,
fields, and vector spaces.
Prerequisite: Mathematics 22 or 24. Dist: QDS. Pomerance.
72. Topics in Geometry
07S: 2
This course develops one or more topics in geometry. Possible topics include
hyperbolic geometry; Riemannian geometry; the geometry of special and general
relativity; Lie groups and algebras; algebraic geometry; projective geometry.
Offered in alternate years.
Prerequisite: Mathematics 71, or permission of the instructor. Depending on
the specific topics covered, Mathematics 31 may not be an acceptable
prerequisite; however, in consultation with the instructor, Mathematics 31
together with some outside reading should be adequate preparation for the
course.. Dist: QDS. Doyle.
73. Multi-Variable Analysis
07S: 12 08S: Arrange
This course develops aspects of the general theory of differentiation and
integration in Euclidean space. Primary topics include the Implicit and Inverse
Function Theorems, differential forms, and Stokes' Theorem.
Prerequisite: Mathematics 63. In general, Mathematics 35 is not an
acceptable prerequisite; however in consultation with the instructor,
Mathematics 35 together with some outside reading should be adequate
preparation for the course. Dist: QDS. Webb.
74. Topics in Topology
08S: Arrange
This course develops one or more topics in topology. Possible topics include
classification of surfaces, fundamental group and covering spaces, knot theory,
combinatorial topology, and fixed point theory. Offered in alternate years.
Prerequisite: Mathematics 31/71 and 54, or permission of the instructor.
Dist: QDS.
75. Applied Topics in Number Theory and Algebra
08S: Arrange
Provides some applications of number theory and algebra. Specific topics
will vary; two possibilities are cryptology and coding theory. The former
allows for secure communication and authentication on the Internet, while the
latter allows for efficient and error-free electronic communication over noisy
channels. Offered in alternate years.
Prerequisite: Mathematics 25 or 31, or permission of the instructor.
Dist: QDS.
76. Topics in Applied Mathematics
08W: Arrange
The numerical nature of twenty-first century society means that applied
mathematics is everywhere: animation studios, search engines, hedge funds and
derivatives markets, and drug design. Students will gain an in-depth
introduction to an advanced topic in applied mathematics. Possible subjects
include digital signal and image processing, quantum chaos, computational
biology, cryptography, coding theory, waves in nature, inverse problems,
information theory, stochastic processes, machine learning, and mathematical
finance.
Prerequisite: Mathematics 22, 23, or permission of the instructor. Dist:
QDS.
81. Abstract Algebra
07W: 10 08W: Arrange
This course is the second term of the basic algebra sequence begun in
Mathematics 71. While the content of this course varies somewhat from year to
year, the topics treated will usually be chosen from among permutation groups,
Sylow theory, factorization theory in commutative rings, Galois theory,
modules, Wedderburn-Artin theory of semi-simple rings, Noetherian rings,
integral extensions, and Dedekind domains.
Prerequisite: Mathematics 71. In general, Mathematics 31 is not an
acceptable prerequisite; however, in consultation with the instructor,
Mathematics 31 together with some outside reading should be adequate
preparation for the course. Dist: QDS. Arkowitz.
83. Fourier Analysis and Integration
Not offered in the period from 06F through 08S
From its beginnings in the eighteenth century, Fourier analysis has branched
in many directions that are central to applied mathematics. The core of the
course consists of the main ideas of one-dimensional Fourier analysis of both
periodic and non-periodic phenomena, coupled with an introduction to Lebesgue
integration sufficient for understanding the contemporary foundations of the
subject. Additional topics are drawn from such areas as signal processing,
probability limit laws, and number theory. Offered in alternate years.
Prerequisite: Mathematics 63. In general, Mathematics 35 is not an
acceptable prerequisite, however, in consultation with the instructor,
Mathematics 35 together with some out side reading should be adequate
preparation for the course. Dist: QDS.
87. Reading Course
All terms: Arrange
Advanced undergraduates occasionally arrange with a faculty member a reading
course in a subject not occurring in the regularly scheduled curriculum.
88. Special Topics
Not offered in the period from 06F through 08S
From time to time a section of Mathematics 88 may be offered in order to
provide an advanced course in a topic which would not otherwise appear in the
curriculum. Consult the advisor to majors for details about topics to be
covered. Dist: QDS.
89. Seminar in Logic
08W: Arrange
A study of selected topics in logic, such as model theory, set theory,
recursive function theory, or undecidability and incompleteness. Offered in
alternate years.
Prerequisite: Mathematics 39 or 69. Dist: QDS.
97. Undergraduate Research
All terms: Arrange
Open only to students who are officially registered in the Honors Program.
Permission of the adviser to majors and thesis adviser required. This course
does not serve for major credit nor for distributive credit, and may be taken
at most twice.
98. Senior Seminar
Not offered in the period from 06F through 08S
This course satisfies the college's requirement for a culminating
experience. The topic of the seminar will be chosen by the instructor. After an
introduction by the instructor, students will prepare and present short talks
on various aspects of the topic in order to develop and refine their ability to
present mathematics orally. Each student will then make a formal oral
presentation and prepare a written report on a topic chosen by the student and
instructor. Students will prepare drafts of their report for feedback from the
seminar participants and revise their work in light of this feedback. Students
also doing an Honors Project may submit their project in lieu of the final
written report.
GRADUATE COURSES
A qualified honors major may apply to the course instructor for permission
to elect a graduate course. This listing covers 100-level offerings for 2006
fall through 2007 spring only. Courses marked with an asterisk (*) are not
offered in this period.
100. Topics in probability theory.
07S: Arrange.
Doyle.
101. Topics in algebra.
06F: Arrange. Shemanske.
*102. Topics in geometry
103. Topics in analysis
06F: Arrange. Ionescu.
*104. Topics in topology
105. Topics in number theory
07S: Arrange. Wallace.
*106. Topics in applied mathematics
107. Supervised Tutoring
Tutoring or assisting with teaching under the supervision of a faculty
member.
108. Topics in combinatorics
06F: Arrange. Elizalde.
*109. Topics in mathematical logic
*110. Probability theory
111. Algebra
07S: Arrange. Shemanske.
112. Geometry
07S: Arrange. Pauls.
113. Analysis
07W: Arrange. Williams.
114. Algebraic topology
06X: Arrange. Webb.
*115. Number Theory
*116. Applied mathematics
*118. Combinatorics
*119. Mathematical Logic
*120. Current problems in probability theory
*121. Current problems in algebra
*122. Topics in analysis
*123. Current problems in analysis
124. Current problems in topology
06F: Arrange. Gordon.
*125. Current problems in number theory
126. Current problems in applied mathematics
07W: Arrange. Rockmore.
127. Reading Course
Advanced graduate students may elect a program of supervised reading
continuing the topics of their course work.
*128. Current problems in combinatorics
*129. Current problems in mathematical logic
137. Independent Reading
Advanced graduate students may, with the approval of the advisor to graduate
students, engage in an independent reading program.
*147. Teaching Seminar
A seminar to help prepare graduate students for teaching. (This course does
not count toward the general College requirements for the master's degree.)
148. Independent Project
A graduate student may, with the approval of the advisor to graduate
students, engage in an independent study project. Groups of graduate students
may, for example, prepare joint work including reading and informal seminars
aimed at mastering a certain topic.
149. Supervised Teaching
Teaching under the supervision of a faculty member.
156. Graduate Research
Research under the guidance of a staff member.
157. Thesis Research
Research under the guidance of the student's thesis advisor. Open to
candidates for the Ph.D. degree.
158. Independent Research
Advanced graduate students may, with the approval of the advisor to graduate
students, engage in an independent research project.
|
