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Modified 7/12/2000 aileen

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