Professors: John Feroeab, John McCleary
(Chair), Peter C. Pappas, Charles I. Steinhorn; Associate
Professor: Benjamin A. Lotto; Adjunct Instructor:
Doris Haas*
Requirements for Concentration: Mathematics
121/122 (or 125 or permission of the department to enroll in
221), 91/2 units above the 100-level
including 221/222, 301, 321, 361, and two other units at the
300-level. Reading courses are not counted among the
required units. Work used to satisfy major requirements may
not be taken NRO after declaration of the major. At most one
unit at the 300-level taken NRO prior to declaration of the
major may be used to satisfy major requirements.
Senior Year Requirements: Mathematics 301.
Recommendations: Majors are strongly urged to
elect at least 2 units in applications of mathematics to
other fields. A reading knowledge of French, German, or
Russian is advised for those contemplating graduate
study.
Sequence of Courses for Concentration: Students
will normally elect Mathematics 121/122, 221/222, but
freshman eligible for Advanced Placement should confer with
the department. Election of advanced courses should be made
in consultation with a departmental adviser.
Prospective majors in mathematics are strongly advised to
complete Mathematics 121/122 or Mathematics 125 by the end
of the freshman year and Mathematics 221/222 by the end of
the sophomore year. In any case, the first sequence must be
completed by the end of the sophomore year in order to
declare the major and Mathematics 221/222 must be completed
by the end of the junior year.
Advisers: The department.
Correlate Sequence in Mathematics: Students
majoring in other programs may complement their study by
electing a correlate sequence in mathematics. Course
selection should be made in consultation with the department
and the major adviser to ensure exposure to the mathematics
most useful to the field of concentration.
Requirements for the Correlate Sequence:
Mathematics 121/122 (or 125 or permission of the
department to enroll in 221), 4 graded units above the
100level including 221/222 and 1 unit at the 300level.
Advanced Placement: Students receiving 1 unit of
Advanced Placement credit based on either the AB or BC
Mathematics Advanced Placement Examination or the calculus
credit examination administered by the Department of
Mathematics may not be granted credit for Mathematics 101 or
121.
The department recommends that students who have earned a
4 or 5 on the BC examination enroll in Mathematics 221.
Students with a 5 on the AB examination or a 3 on the BC
examination generally are advised to elect Mathematics 221
also, after conferring with the department. Students with a
4 on the AB examination ordinarily are advised to enroll in
Mathematics 125, but should consult with the department.
I. Introductory
100a-101b. PreCalculus and Introduction to Calculus
(1/2, 1)
This sequence is designed for students who wish to take
Mathematics 101, Introduction to Calculus, but whose
mathematical background is deficient. Students with three
years of high school mathematics should begin with
Mathematics 101. Topics of Mathematics 100 include the
algebra of polynomials, operations with fractions, solving
equations and inequalities, exponents and radicals, elements
of coordinate geometry, functions and their graphs,
logarithms and elements of trigonometry. Ms. Haas.
On the satisfactory completion of Mathematics 101, the
student receives 1/2 unit of credit
for Mathematics 100.
Not open to students with AP credit in mathematics or
students who have completed Mathematics 101 or 121.
Prerequisite: high school mathematics. Advice of the
department should be sought before registering for this
course.
101b/102a.
101b. Introduction to Calculus (1)
A course intended for students not majoring in
mathematics or the physical sciences who need a working
knowledge of calculus. The course emphasizes techniques and
applications with relatively little attention to the
rigorous foundations. The department.
Not open to those who have had Mathematics 121 or its
equivalent.
Does not serve as a prerequisite for Mathematics 122,
125, or 200-level mathematics courses.
Prerequisite: at least three years of high school
mathematics.
Three 50-minute periods.
102a. Topics in Calculus (1)
A continuation of Mathematics 101. Topics may include:
matrix methods, use of differentiation and integration,
differential equations, and partial differentiation.
Emphasis is on techniques and applications. The
department.
Not open to those who have had Mathematics 122.
Does not serve as a prerequisite for 200level mathematics
courses.
Prerequisite: Mathematics 101 or equivalent.
121a/122b. Single Variable Calculus (1)
The calculus of one variable and applications are
discussed. Topics include: limits, continuity, derivatives,
applications of derivatives, transcendental functions, the
definite integral, applications of definite integrals,
approximation methods, differential equations, sequences,
and series. The department.
Not open to those who have had Mathematics 101.
Prerequisite: a minimum of three years of high school
mathematics, preferably including trigonometry.
Three 50minute periods; one 50minute problem session.
125a. Topics in Single Variable Calculus (1)
Material from Mathematics 121/122 presented in one
semester for students with previous experience with
calculus. Topics in secondsemester calculus are fully
developed and topics in firstsemester calculus are reviewed.
The department.
Three 50minute periods; one 50minute problem session.
Prerequisite for all intermediate courses: Mathematics
122, 125 or equivalent, unless otherwise indicated.
221a and b. Linear Algebra (1)
The theory of higher dimensional space. Topics include:
geometric properties of n-space, matrices and linear
equations, vector spaces, linear mappings, determinants. The
department.
222a and b. Multivariable Calculus (1)
Continuation of Mathematics 221. Differential calculus of
vector functions, implicit function theorem, extreme values,
multiple integrals, vector field theory. The department.
Prerequisite: Mathematics 221 or the equivalent, or
permission of the instructor.
228b. Methods of Applied Mathematics (1)
Survey of techniques used in the physical sciences.
Topics include: ordinary and partial differential equations,
series representation of functions, integral transforms,
Fourier series and integrals. The department.
231a or b. Topics in Geometry (1)
Topics to be chosen from: conic sections,
transformational geometry, Euclidean geometry, affine
geometry, projective geometry, inversive geometry,
nonEuclidean geometry, spherical geometry, convexity,
fractal geometry, solid geometry, foundations of geometry.
The department.
241a or b. Probability Models (1)
A presentation of commonly applied discrete and
continuous probability distributions, including the use of
expectation, independence, conditional probability, and
related statistical concepts. The department.
261a or b. Introduction to Number Theory (1)
Topics include: divisibility, congruence, modular
arithmetic, diophantine equations, numbertheoretic
functions, distribution of the prime numbers. The
department.
263a or b. Discrete Mathematics (1)
Mathematical induction, elements of set theory and logic,
permutations and combinations, relations, topics in graph
theory, generating functions, recurrence relations, Boolean
algebras. The department.
290. Field Work (1/2 or
1)
Reading Courses
Prerequisite: Mathematics 221 or equivalent, and
permission of instructor.
297.01. Topics in Mathematics
(1/2)
298. Independent Work (1/2 or
1)
Election should be made in consultation with a department
adviser.
Prerequisite for all advanced courses: Mathematics 222,
unless otherwise indicated.
301b. Senior Seminar
(1/2)
Areas of study and units of credit vary from year to
year. The department.
Open only to seniors whose major is mathematics.
A rigorous treatment of topics in the classical theory of
functions of a real variable from the point of view of
metric space topology including limits, continuity,
sequences and series of functions, and the Riemann-Stieltjes
integral. The department.
324a or b. Complex Analysis (1)
Integration and differentiation in the complex plane.
Topics include: holomorphic (differentiable) functions,
power series as holomorphic functions, Taylor and Laurent
series, singularities and residues, complex integration and,
in particular, Cauchy's Theorem and its consequences. The
department.
[327b. Advanced Topics in Real Analysis]
(1)
Continuation of Mathematics 321. Measure theory, the
Lebesgue integral, Banach spaces of measurable functions.
The department.
Prerequisite: Mathematics 321.
Alternate years: not offered in 2000/01.
328b. Theory of Differential Equations (1)
Existence and uniqueness theorems for ordinary
differential equations; general theory and eigenvalue
methods for first order linear systems. The department.
Prerequisite: Mathematics 321 or permission of
instructor.
Alternate years: offered in 2000/01.
335a or b. Topics in Differential Geometry and
Topology (1)
Aspects of the elementary geometry and topology of
differentiable manifolds. Topics vary from year to year. The
department.
Prerequisite: Mathematics 321.
Alternate years: offered in 2000/01.
[336a or b. Algebraic Geometry] (1)
An introduction to the study of algebraic geometry.
Topics may include: projective space, homogeneous
coordinates, plane curves, Bezout's theorem, elliptic
curves, affine and projective varieties, the Zariski
topology, coordinate rings, functions on varieties. The
department.
Prerequisite: Mathematics 361.
Alternate years: not offered in 2000/01.
Introductory pointset and algebraic topology; topological
spaces, metric spaces, continuous mappings, connectedness,
compactness and separation properties; the fundamental
group; simplicial homology. The department.
Prerequisite: Mathematics 321 or 361.
[341b. Mathematical Statistics] (1)
The rigorous development of topics in mathematical
statistics: probability and distributions; multivariate
distributions; special distributions; distributions of
functions of several variables; limiting distributions;
introduction to statistical inference. Additional topics
drawn from sufficient statistics, estimation theory,
statistical testing, and inferences about normal models. The
department
Prerequisite: Mathematics 222 and 241.
Alternate years: not offered in 2000/01.
[351a. Foundations of Mathematics] (1)
An introduction to mathematical logic. Topics are drawn
from computability theory, model theory, and set theory.
Mathematical and philosophical implications also are
discussed. The department.
Prerequisite: Mathematics 321 or 361.
Alternate years: not offered in 2000/01.
361b. Modern Algebra (1)
The theory of groups and an introduction to ring theory.
Topics in group theory include: isomorphism theorems,
generators and relations, group actions, Sylow theorems,
fundamental theorem of finite abelian groups. The
department.
364a or b. Advanced Linear Algebra (1)
Further study in the theory of vector spaces and linear
maps. Topics may include: scalar products and dual space;
symmetric, hermitian and unitary operators; eigenvectors and
eigenvalues; spectral theorems; canonical forms. The
department.
367a. Advanced Topics in Modern Algebra (1)
Continuation of Mathematics 361. Rings and fields, with a
particular emphasis on Galois theory. The department.
Prerequisite: Mathematics 361.
Alternate years: offered in 2000/01.
[380a or b. Topics in Advanced Mathematics]
(1)
Advanced study in an area of mathematics. The
department.
Not offered in 2000/01.
399. Senior Independent Work
(1/2 or 1)
Election requires the approval of a departmental adviser
and of the instructor who supervises the work.
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