Mathematics
Professors: Baird, McKeon; Associate Professors: Balasuriya, Hammond; Assistant Professor: Chandler; Senior Lecturer: Robertson; Professor Susskind, chair
The Major in Mathematics
The mathematics major consists of five core courses (210, 212, 226, 301, and 303), as well as the mathematics seminar (495) and additional mathematics courses based on the track or concentration.
Students selecting the general track must take four additional courses: one course from 309, 317, 402, or 404; one elective at the 200 level or higher; and two further electives at the 300 level or higher.
Students selecting the statistics concentration must take five additional courses: 207, 208, 316, 317, and one elective at the 300 level or higher.
All mathematics majors are strongly encouraged to take at least one course in computer science. Students planning to attend graduate school in mathematics or statistics should consult with their adviser to develop an appropriate course of study.
Advisers: B. Baird, S. Balasuriya, G. Chandler, C. Hammond, K. McKeon, P. Susskind
The Minor in Mathematics
The minor in mathematics consists of a minimum of five courses: 113 (or 114), 212, 226, and two additional mathematics courses at the 200 level or higher. Students may, in consultation with their adviser, substitute appropriate courses at the same level or higher. Advanced Placement credit may only be counted toward the minor under exceptional circumstances, with permission of the department.
The Minor in Applied Statistics
The interdisciplinary minor in applied statistics is designed to help students develop a broad understanding of methods for collecting, analyzing, and interpreting data. Students learn the fundamental principles of statistics, experiment with techniques for examining and drawing conclusions from data, and study concrete applications of statistics to a variety of fields.
The minor consists of five courses chosen from the following: Mathematics 107, 111, 112, 113, 114, 206, 207, 208, 212, 316, 317; Economics 230, 354; Psychology 201, 202, 407; Biology 208, 307; Botany 315. An individual study involving a substantial statistical component may also serve as one of the five courses. Students must take at least one two-course sequence in mathematics (either 207, 208 or 316, 317) and at least one course from a department other than Mathematics. No more than one calculus course (Mathematics 111, 112, 113, 114, or 212) and one introductory statistics course (Mathematics 107, 206, or Psychology 201) may be counted toward the minor; students may not use Advanced Placement credit as a substitute for more than one course. Mathematics majors may not minor in applied statistics, but are encouraged instead to select the statistics concentration within the major.
Students considering graduate study in statistics or in quantitative areas of other fields are strongly advised to take Mathematics 212, 226, and 301.
Advisers: P. Barnes (Biology), G. Chandler (Mathematics), J. Nier (Psychology), Y. Park (Economics)
Courses
MATHEMATICS 105 INTRODUCTION TO MATHEMATICAL THOUGHT Mathematics as a creative and evolving discipline. Traditional and modern mathematical concepts presented by surveying different areas in mathematics or focusing on a particular theme such as number theory or mathematics and politics. Focus on mathematical concepts rather than on drill.
Not
open to students who have received credit for a college-level mathematics
course. Enrollment limited to 30
students. This course satisfies General
Education Area 2. Staff
MATHEMATICS 107
INTRODUCTION TO STATISTICS An introduction to basic statistical methods and concepts. Topics include exploratory data analysis,
experimental design, sampling, inference for means and proportions, regression,
and categorical data. Statistical
software used to analyze real data.
Students may not receive credit for both Courses 107 and 206.
Students with previous credit for a
200- or 300-level course in mathematics must receive permission of the
instructor. Enrollment limited to 30
students. This course satisfies General
Education Area 2. Staff
MATHEMATICS 108 MATHEMATICS OF MONEY An introduction to elementary mathematical concepts relating to finance, including simple and compound interest, annuities, mortgages, and bonds. Emphasis on the use of mathematics both to understand financial topics and to draw conclusions about them.
Not open to students who have
received credit for a college-level mathematics course. Enrollment limited to 30 students. This course satisfies General Education Area
2. Staff
MATHEMATICS 110 GRAPH THEORY AND ITS
APPLICATIONS An introduction to the use of discrete
graphs as modeling tools in a wide variety of applications. Examples include representing chemical
compounds, routing snowplows, scheduling courses, sequencing traffic lights,
representing data in a computer, describing interpersonal relationships, and
solving puzzles and games.
Enrollment
limited to 25 students. This course
satisfies General Education Area 2. K. McKeon
MATHEMATICS 111 CONCEPTS OF CALCULUS An introduction to differential and integral calculus. The list of topics is similar to that of Course 112, but not as comprehensive; emphasis is placed instead on understanding key concepts. Students may not receive credit for both Courses 111 and 112.
Students
with a strong background in mathematics or who intend to take additional
courses in the calculus sequence should take Course 112 rather than Course
111. Course 111 is not a prerequisite
for Course 113. Enrollment limited to
30 students. This course satisfies
General Education Area 2. Staff
MATHEMATICS 112 CALCULUS
I
An introduction to
differential and integral calculus.
Topics include functions (both algebraic and transcendental), limits,
continuity, derivatives, and antiderivatives; techniques of differentiation and
integration; velocity and acceleration, related rates, extremal problems, area,
and other applications. Students may
not receive credit for both Courses 111 and 112.
Students are encouraged to have a
departmental interview to determine the appropriate level at which to enter the
calculus sequence. Enrollment limited
to 30 students. Offered both semesters. This course satisfies General Education Area
2. Staff
MATHEMATICS 113
CALCULUS IIA A continuation of the material
introduced in Course 112. Topics
include definite and indefinite integrals; further techniques of integration;
applications of the definite integral, including area, volume, arc length, and
surface area; improper integrals; infinite sequences and series. Students may not receive credit for both
Courses 113 and 114.
Prerequisite: Course 112 or permission of the instructor. Students are encouraged to have a
departmental interview to determine the appropriate level at which to enter the
calculus sequence. Enrollment limited
to 30 students. Offered both semesters. This course satisfies General Education Area
2. Staff
MATHEMATICS 114 CALCULUS IIB An alternative to Course 113, intended for incoming students with a strong background in calculus. Topics include improper integrals, infinite sequences and series, parametric equations, and polar coordinates. Additional topics may include arc length, surface area, probability, elementary differential equations, and combinatorics. This course is particularly appropriate for students who have received Advanced Placement credit for the Calculus AB examination. Students may not receive credit for both Courses 113 and 114.
Open to freshmen only. Students are encouraged to have a departmental interview to determine the appropriate level at which to enter the calculus sequence. Enrollment limited to 30 students. Offered first semester. This course satisfies General Education Area 2. Staff
MATHEMATICS 115 MATHEMATICS FROM A CULTURAL PERSPECTIVE Seminar focusing on the practice of mathematics within different cultural groups and societies, in either historical or contemporary settings. Groups are defined according to ethnic, geographic, or social criteria. Specific themes chosen from concepts such as infinity, number, symbols, and the geometric.
Enrollment limited to 16 students. This course satisfies General Education Area
2. Staff
MATHEMATICS 120, 220, 320 SERVICE-LEARNING PRACTICUM IN MATHEMATICS Service in an area school to enhance understanding of a concurrent mathematics course by working with students at an area school for a minimum of two hours per week. Specific projects to teach the students about the subject of the related mathematics course are developed in consultation with the professor and schoolteacher. Students electing Course 120, 220, 320 must concurrently enroll in a four credit mathematics course. Two credit hours. This course may be taken for credit two times.
Permission
of the instructor. Staff
MATHEMATICS 205 ENVIRONMENTAL MODELING An introduction to the use of mathematics to understand and describe issues relating to the environment. Applications to geophysics (atmospheric carbon content, surface water runoff, pollutant dispersion, resource depletion) and biology (population growth, harvesting, extinction) will be considered. Students will both develop and implement mathematical models. This is the same course as Environmental Studies 205.
Prerequisite: Any calculus course (111, 112, 113, 114, or 212) or permission of
the instructor. Enrollment limited to
16 students. S. Balasuriya
MATHEMATICS 206
INTRODUCTION TO STATISTICS WITH CALCULUS An introduction to statistics, covering similar topics to
Course 107, but for students who have taken a semester or more of
calculus. Topics include exploratory
data analysis, probability, inference for means and proportions, regression,
and categorical data. Weekly computer
labs using the statistical software R to analyze real data. Students may not receive credit for both
Courses 107 and 206.
Prerequisite: Any calculus course (111, 112, 113, 114,
or 212) or permission of the instructor.
Enrollment limited to 30 students.
This course satisfies General Education Area 2. G. Chandler
MATHEMATICS 207
ADVANCED REGRESSION TECHNIQUES An introduction to two-sample comparisons, simple linear
regression, multiple regression, model diagnostics, logistic regression for
binary response variables and binomial counts, and nonparametric methods. The course employs a case-study approach,
with extensive use of the statistical software R to examine real data. Emphasis on problem-solving, as well as the
use and interpretation of mathematical models.
No knowledge of calculus is required.
Prerequisite: Any
introductory statistics course (Course 107, 206, or Psychology 201); or Course
113, 114, or 212; or permission of the instructor. Enrollment limited to 30 students. Offered alternating years.
This course satisfies General Education Area 2. G.
Chandler
MATHEMATICS 208
DESIGN AND ANALYSIS OF EXPERIMENTS
An introduction to simple comparative designs, factorial
designs, block designs, and post-hoc comparisons. Additional topics chosen from nested designs, repeated measures,
and random effects models. The course
employs a case-study approach, with extensive use of the statistical software R
to examine real data. Emphasis on
problem-solving, as well as the use and interpretation of mathematical
models. No knowledge of calculus is
required.
Prerequisite: Any statistics course (Course 107, 206, 207,
317, or Psychology 201) or permission of the instructor. Enrollment limited to 30 students. Offered alternating years. This course satisfies General Education Area
2. G.
Chandler
MATHEMATICS 210 DISCRETE MATHEMATICS An introduction to topics in discrete mathematics, including set theory, logic, equivalence relations, mathematical induction, combinatorics, graphs, trees, algorithm analysis, and elementary number theory. Applications to computer science will be considered.
Prerequisite: Any calculus course (111, 112, 113, 114, or
212) or Computer Science 110.
Enrollment limited to 30 students.
Offered first semester. This
course satisfies General Education Area 2.
Staff
MATHEMATICS 212 MULTIVARIABLE CALCULUS An introduction to vectors in Euclidean spaces, functions of several variables, partial derivatives, multiple integrals, vector fields, and line integrals, culminating with a treatment of Green's theorem. Applications include curvature, tangent planes, volumes, and extremal problems with and without constraints.
Prerequisite: Course 113 or 114, or permission of the
instructor. Students are encouraged to have a departmental interview to determine the appropriate level at which to enter the calculus
sequence. Enrollment limited to 30 students.
Offered both semesters. This
course satisfies General Education Area 2. Staff
MATHEMATICS 225
ORDINARY DIFFERENTIAL EQUATIONS Techniques for solving first
order differential equations and higher order linear equations, including
methods involving power series and Laplace transforms. Applications may include exponential growth
and decay, physical vibrations, electrical circuits, planetary motion, falling
bodies, and population growth.
Prerequisite: Course 113, 114, or 212; or permission of
the instructor. Enrollment limited to
30 students. Offered second semester. This course satisfies General Education Area
2. Staff
MATHEMATICS 226 LINEAR ALGEBRA An introduction to standard topics in linear algebra, including systems of linear equations, matrices, determinants, vectors, vector spaces, linear transformations, eigenvalues, and eigenvectors. Applications to calculus, geometry, economics, and the physical sciences may be considered.
Prerequisite: Course 113, 114, or 212; or permission of
the instructor. Enrollment limited to
30 students. Offered both semesters. This course satisfies General Education Area
2. Staff
MATHEMATICS 232 MATHEMATICS OF FINANCE An introduction to mathematical techniques used to define and analyze securities and investments, including concepts such as cash flow, investments, markets, arbitrage, dynamics, risk aversion, pricing, and hedging.
Prerequisite: Course 113, 114, or 212; or permission
of the instructor. Enrollment limited
to 30 students. This course satisfies
General Education Area 2. P. Susskind
MATHEMATICS 301
REAL ANALYSIS I An introduction to the rigorous study of real analysis. Topics include elementary set theory,
the real number system, sequences, series, basic topological properties,
continuous functions, and derivatives.
Additional topics may include metric spaces, uniform convergence,
special functions, Riemann integrals, and Stieltjes integrals. Emphasis on understanding and writing
mathematical proofs.
Prerequisite: Course 212 and either 225 or 226, or
permission of the instructor.
Enrollment limited to 30 students.
Offered first semester. Staff
MATHEMATICS 303 ABSTRACT ALGEBRA I An introduction to abstract algebraic structures. Topics include groups, subgroups, permutation groups, cosets, homomorphisms, factor groups, rings, rings of polynomials, and fields. Emphasis on understanding and writing mathematical proofs.
Prerequisite: Courses 210 and 226, or permission of the
instructor. Enrollment limited to 30
students. Offered second semester. Staff
MATHEMATICS 305, 306 SELECTED TOPICS A study of topics selected from any area of pure mathematics, applied mathematics, or statistics. Topics vary from year to year and may include number theory, chaos and dynamical systems, numerical analysis, or statistical computing. Computer software may be used for research and experimentation. May be repeated for credit.
Prerequisites vary depending on the choice of topics, and will be communicated to students by the department. Enrollment limited to 30 students. Staff
MATHEMATICS 309
COMPLEX ANALYSIS An
introduction to functions of a complex variable, with particular emphasis on
the theory of analytic functions.
Topics include the algebraic and geometric structure of the complex
number system; the extension of exponential, trigonometric, and logarithmic
functions to complex arguments; differentiation and integration in the complex
plane; series representations for analytic and meromorphic functions; and the
calculus of residues.
Prerequisite: Course 301; or 212 and either 225 or 226; or permission of the instructor. Enrollment limited to 30 students. Staff
MATHEMATICS 310 GRAPH THEORY Structure and properties of graphs and their applications. Topics include traversability, trees, connectivity, network flow, graph coloring, chromatic number, and planarity. Discussion of the application of graph theory to computer science, transportation, scheduling, communication, chemistry, and a variety of other fields.
Prerequisite: Course 210. Enrollment limited to 30 students. K. McKeon
MATHEMATICS 311 ADVANCED LINEAR
ALGEBRA A continuation of the material introduced
in Course 226, with emphasis on the underlying mathematical theory. Topics include invariant subspaces, inner
product spaces, orthonormal bases, orthogonal projections, linear functionals,
adjoints, self-adjoint and normal operators, and the spectral theorem.
Prerequisite:
Course 226. Enrollment limited
to 30 students. C. Hammond
MATHEMATICS 312 MATHEMATICAL METHODS FOR THE PHYSICAL SCIENCES Topics important in both advanced mathematics and the sciences, principally physics. These may include complex functions and power series; multiple integration; change of variables; the Jacobian; elementary Fourier analysis; series solutions of differential equations; orthogonal bases, e.g., Legendre polynomials, and special functions; partial differential equations, e.g. Laplace's, Poisson's, diffusion or heat flow equations; integral transforms; and physical examples.
Prerequisite: Course 225 and one of Course 226 or Course
212, or permission of the instructor. Enrollment limited to 30 students. S.
Balasuriya, P. Susskind
MATHEMATICS 313 THEORY OF COMPUTATION An introduction to the classical and contemporary theory of computation, including abstract automata theory, formal languages, computability by Turing machines and recursive functions, computability and decidability, and computational complexity.
Prerequisite: Course 210. Enrollment limited to 30 students. P. Susskind
MATHEMATICS 314 EUCLIDEAN AND NONEUCLIDEAN GEOMETRY A study of Euclidean and one or more non-Euclidean geometries. The geometric theory, its historical setting, its physical and philosophical implications will all be treated. The purpose of the course will be to clarify the role of Euclidean geometry in mathematics, to introduce the ideas of axiom systems and their central role in mathematics, and to shed further light on the nature of mathematics.
Prerequisite: Course 113 or Course 226, and permission of
the instructor. Enrollment limited to
30 students. P. Susskind
MATHEMATICS 315 TOPOLOGY An introduction to point-set topology, with emphasis on connections to analysis and geometry. Topics include topological spaces, product spaces, continuous functions, metric spaces, connectedness, compactness, countability conditions, and separation axioms.
Prerequisite: Courses 210 and 301, or permission of the instructor. Enrollment limited to 30 students. C. Hammond
MATHEMATICS 316 PROBABILITY A study of the theory relating to problems of randomness and uncertainty. Topics include conditional probabilities, random variables, discrete and continuous distributions, expected value and variance, joint distributions, and the law of large numbers. Applications to a variety of disciplines will be considered. Emphasis on preparation for Course 317.
Prerequisite: Courses 113 (or 114) and 210; or Course 212;
or permission of the instructor.
Enrollment limited to 30 students.
Offered every third semester. G. Chandler, K. McKeon
MATHEMATICS 317
MATHEMATICAL STATISTICS An introduction to methods of statistical inference, with emphasis
on the underlying mathematical theory.
Topics include estimation, hypothesis testing, and modes of convergence.
Prerequisite: Course 316.
Enrollment limited to 30 students.
G. Chandler
MATHEMATICS 402
REAL ANALYSIS II A continuation of topics from
Course 301.
Prerequisite: Course 301.
Enrollment limited to 16 students.
Staff
MATHEMATICS 404
ABSTRACT ALGEBRA II A
continuation of topics from Course 303.
Prerequisite: Course 303.
Enrollment limited to 16 students.
Staff
MATHEMATICS 495 SEMINAR IN MATHEMATICS Lectures and discussions on topics of current interest to the mathematical community. These discussions will be led by Connecticut College faculty, advanced students, and visiting mathematicians.
Prerequisite: Course 301 or 303, and permission of the instructor. One meeting per week throughout the semester. Two credit hours. This course may be taken for credit two times. Enrollment limited to 16 students.
MATHEMATICS 291, 292 INDIVIDUAL STUDY
MATHEMATICS 391, 392
INDIVIDUAL STUDY
MATHEMATICS 491, 492
INDIVIDUAL STUDY
MATHEMATICS 497-498
HONORS STUDY
Last Modified: Monday, November 16, 2009 9:39 AM