103. Patterns and Order
Mathematics can be viewed
as a search for patterns and order. This course gives an overview of the
approaches used in various branches of mathematics to recognize and understand
patterns. Through reading, writing, discussion, and problem solving, students
explore such topics as number, shape, change, and position, each of which has
been central in the development of modern mathematics. Not open to students who have credit for any mathematics course numbered above 120, except by permission of instructor.
110. Statistical Concepts.
An introduction to the
concepts and reasoning underlying the interpretation of data and chance.
Emphasis is on understanding how statistical analysis is used to gain insight
into a wide variety of areas of human interest. Topics include elements of
descriptive statistics, design of experiments, laws of probability, and
inference from a sample to a population (including confidence intervals and
hypothesis testing). Not open to students who have credit for Mathematics 125 or
161.
125. Modeling and Differential Calculus
An introduction to mathematical modeling and the use of differential calculus. Topics include: analysis and manipulation of elementary functions, including trigonometric, exponential, and logarithmic functions; the differential calculus of such functions; and optimization. An ongoing emphasis will be the use of elementary functions as well as the differential calculus to model phenomena in the natural, social and life sciences. Not open to students
who have credit for Mathematics 161. Prerequisite: Two years of high school
algebra.
161. Calculus I
The sequence Mathematics 161, 162, 263 provides and introduction to calculus for students of mathematics, engineering, and the sciences. Iopics include limits, derivatives, techniques of differentiation, definite integrals, the Fundamental Theorem of Calculus, and applications of derivatives and integrals. Prerequisite: High school trigonometry.
162. Calculus II
A continuation of Mathematics 161. Topics include techniques and applications of integration, introduction to differential equations, parametric curves and polar coordinates, infinite
series and Taylor approximation. Prerequisite: A grade of C- or better in Mathematics 161 or 165.
165. Calculus I+
A course which covers the
same topics as Mathematics 161 while using a workshop experience and
collaborative learning to give special emphasis to the development of
problem-solving skills. Enrollment is by
invitation of the Department of Mathematics. Prerequisite: High school trigonometry.
166. Calculus II+
A course which covers the same topics as Mathematics 162
while using a workshop experience and collaborative learning to give special
emphasis to the development of problem-solving skills. Enrollment is by invitation of the Department of Mathematics. Prerequisite: A grade of C- or better in Mathematics 161 or 165.
182. Discrete Structures
An introduction
to discrete structures and algorithms and some mathematical tools and methods of
reasoning that aid in their development and analysis. Topics include: sets,
counting, algorithms, mathematical induction, relations, graphs, and trees.
Prerequisite: Computer Science 102, Mathematics 161. Offered in spring semester.
186. Applied Statistics
An introductory course
emphasizing standard methods and reasoning used in analyzing data. Topics
include exploratory data analysis, design of experiments, least squares
analysis, probability, sampling distributions and methods of inferential
statistics. Includes an introduction to a statistical computing package.
Not open to students who have credit for Psychology 120. Prerequisite: Mathematics 125 or 161, or permission of instructor.
263. Calculus III
A continuation of Mathematics 162.
Topics include vector algebra, vector calculus, partial derivatives, gradients and directional derivatives, tangent planes, the chain rule, multiple integrals and line integrals.
Prerequisite: A grade of C- or better in Mathematics 162 or 166.
264. Differential Equations with Linear Algebra
A introductory course in ordinary
differential equations including techniques of elementary linear algebra. Emphasis is on first-order equations, and higher-order linear
equations and systems of equations. Topics include qualitative analysis of differential equations, analytical and numerical solutions, Laplace
transforms, existence and uniqueness of solutions, and elemental models in science and engineering. Prerequisite: Mathematics 263.
272. Linear Algebra with Applications
An introductory
course in linear algebra emphasizing applications to fields such as economics,
natural sciences, computer science, statistics, and engineering. The course
covers solutions of systems of equations, matrix algebra, vector spaces, linear
transformations, determinants, eigenvalues and eigenvectors. Not open to students who have credit for Mathematics 300. Corequisite:
Mathematics 263 or permission of instructor.
282. Techniques of Mathematical Modeling
A course
that introduces students to the fundamentals of mathematical modeling through
the formulation, analysis, and testing of mathematical models in a variety of
areas. Modeling techniques covered include proportionality, curve fitting,
elementary linear programming, and simulation. Prerequisite: Mathematics 162 or
166. Offered in spring semester.
290. Transition to Theoretical Mathematics
An introduction to the concepts and techniques that permeate advanced mathematics. Topics include set theory, propositional logic, proof techniques, relations, and functions. Special emphasis on developing students' facility for reading and writing mathematical proofs. Examples and additional topics are included from various branches of mathematics, at the discretion of the instructor. Corequisite: Math 263 or permission of instructor.
300. Vector Spaces
A first course in theoretical linear algebra, emphasizing the reading and writing of proofs. Topics include systems of linear equations, matrix algebra, vector spaces and linear transformations, eigenvectors and diagonalization, inner product spaces, and the Spectral Theorem. Not open to students who have credit for Math 272. Prerequisite: Math 290 or permission of instructor.
301. Case Studies in Mathematical Modeling [W]
A course which engages students in the creation of
mathematical models to answer questions about a variety of phenomena. Students
work in small teams on a sequence of projects which require the formulation,
analysis, and critical evaluation of a mathematical model and conclude with the
submission of a written report by each student. Prerequisite: Mathematics 272 or
300. Offered in fall semester.
306. Operations Research
A study of some mathematical methods of decision making. Topics
include: linear programming (maximizing linear functions subject to linear
constraints), the simplex algorithm for solving linear programming problems,
networks, probability, queueing and inventory problems, and applications.
Prerequisite: Mathematics 272 or 300, or permission of instructor. Offered in
spring semester.
310. Ordinary Differential Equations
A course in the theory and applications of ordinary
differential equations which emphasizes qualitative aspects of the subject.
Topics include analytic and numerical solution techniques for systems of
equations, graphical analysis, stability, existence-uniqueness theorems, and
applications. Prerequisites: Mathematics 263, and 272 or 300. Offered in spring
semester of even-numbered years.
312. Partial Differential Equations
An introduction to partial differential equations
and their applications. Formulation of initial and boundary value problems for
these equations and methods for their solution are emphasized. Separation of
variables and Fourier analysis are developed. The course includes interpretation
of classical equations and their solutions in terms of applications.
Prerequisite: Mathematics 263. Offered in spring semester of odd-numbered years.
323. Geometry
Various geometries are considered including absolute, Euclidean, and the classical
non-Euclidean geometries. General properties of axiomatic systems, models, and
the role of Euclidean geometry in the development of other branches of
mathematics are discussed. Prerequisite: Mathematics 162 or permission of
instructor. Offered in fall semester of even-numbered years.
325. Combinatorics
An introduction to the techniques and
theory of enumeration of finite sets. Topics include combinations, permutations,
generating functions, recurrence relations, the inclusion-exclusion principle,
block designs, and graph theory. Prerequisite: Mathematics 263, or permission of
instructor. Offered in fall semester of odd-numbered years.
328. Number Theory
An introduction to the theory of the
integers and techniques for their study and application. Topics include
primality, modular arithmetic, arithmetic functions, quadratic residues, and
diophantine equations. Prerequisite: Mathematics 263 or permission of
instructor. Offered in spring semester of odd-numbered years.
335. Probability
A development of basic probability
theory including the axioms, random variables, expected value, the law of large
numbers and the central limit theorem. Additional topics include distribution
functions and generating functions. Prerequisite: Mathematics 263. Offered in
fall semester.
336. Mathematical Statistics
A
mathematical development of fundamental results and techniques in statistics.
Topics include estimation, sampling distributions, hypothesis testing,
correlation and regression. Prerequisite: Mathematics 335. Offered in spring
semester.
343. Advanced Multivariable Calculus
A
continuation of the study of some of the topics of Mathematics 263 including a
treatment of series of functions and an emphasis on the concepts and techniques
of the calculus of vector functions and functions of several variables and its
applications. Prerequisites: Mathematics 263, and 272 or 300. Offered in fall
semester of odd-numbered years.
345. Complex Analysis
An introductory course in the calculus of complex functions including
the algebra and geometry of complex numbers, elementary mappings, complex
derivatives and integrals, Cauchy-Riemann equations, harmonic functions, Cauchy's Integral Theory, Taylor and Laurent series, residues. Prerequisite: Mathematics
263. Offered in fall semester of even-numbered years.
351.
Abstract Algebra I
An introduction to some of the fundamental ideas
and structures of abstract algebra. Homomorphisms and isomorphisms,
substructures and quotient structures are discussed for algebraic objects such
as fields, vector spaces, rings, and groups. Other topics may include
factorization in rings, and finite group theory. Prerequisite: Mathematics 290. Offered in fall semester.
352.
Abstract Algebra II
Topics may include extension fields, geometric
constructions, algebraic coding theory, and algebraic number theory.
Prerequisite: Mathematics 351. Corequisite: Mathematics 300. Offered in spring semester of even-numbered
years.
356. Introduction to Real Analysis
A
rigorous development of the calculus of functions of one real variable including
the topology of the real line, limits, continuity, differentiation and
integration. Prerequisite: Mathematics 290. Offered in spring semester.
358. Topology
The main topics
are set theory, the separation axioms, connectedness, compactness, and the
continuity of functions. Classical general topological spaces are studied
including regular spaces, normal spaces, first or second countable spaces, and
metrizable spaces. Prerequisite: Mathematics 356 or permission of instructor.
Offered in fall semester of even-numbered years.
360. History of Mathematics [W]
Mathematics is a living, changing subject whose truths, once identified, have remarkable staying power. In this course students analyze various episodes in the history of mathematics that illustrate how mathematical knowledge has developed over the years. Topics include: Egyptian and Babylonian mathematics, indigenous mathematics from outside the Western tradition, the contributions of Euclid and Ancient Greek mathematics, the birth of calculus, and selected topics from the 19th and 20th centuries. Prerequisite: Math 162. Offered in fall semester of odd-numbered years.
372.
Mathematics Seminar
This course offers a major branch of mathematics not
covered by the regular offerings of the department. Course descriptions are sent
to potential students and are available in the department office. Prerequisite:
Depend on subject matter. Usually, completion of the calculus sequence
constitutes a minimal prerequisite. Offered as needed.
375-386. Advanced Special Topics
Chosen from among a wide
range of mathematical topics accessible to junior and senior mathematics majors.
When offered, the special topic to be studied will be listed in the Semester
Course and Hour Schedule and course descriptions will be available in the
department office. Course descriptions for upcoming Special Topics courses can be found here.
391-394. Independent
Study
Study by an individual student, under the supervision of a
mathematics faculty member, of a mathematical subject not covered by courses
offered by the department. The program of study must be drawn up by the student
and the faculty supervisor and approved by an ad hoc committee of the
department. A sampling of recent independent study courses, and honors theses can be found here.
400. Senior Seminar [W]
A course in which
each student undertakes a thorough and independent study of one or more topics
in mathematics. Students are required to make oral presentations on their work
and to prepare written reports on their topics. Prerequisite: Senior standing
and satisfactory completion of at least two 300-level courses in mathematics.
Offered in spring semester.
495, 496.
Thesis [496:W]
Students desiring to take Honors in Mathematics should inform
their department advisers early in the second semester of the junior year.
Honors work involves a guided program of independent study culminating in a
thesis on a topic to be selected by the student in consultation with his or her
adviser and approved by the department. A sampling of recent honors theses and independent study courses can be found here.
