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Mathematics

As mathematics is both a cultural and a technical field of study, the curriculum is planned with the following objectives: (1) to offer students an introduction to mathematics as an important area of human thought; (2) to prepare students for graduate study in pure or applied mathematics, and in such related fields as statistics and operations research; (3) to serve the needs of students in fields that rely substantially on mathematics, such as the physical, biological, social and information sciences, engineering, and business administration; and (4) to provide liberal arts students with an introduction to the kinds of mathematical and quantitative thinking important in the contemporary world.

Individual guidance in the selection of courses and the design of course sequences to serve particular needs and interests is offered by all members of the Department to all students, but the following information will provide a preliminary basis for making plans and choices.

Advanced Placement. Students who have taken one of the two College Board Advanced Placement Program examinations in calculus, or the examination in statistics, will receive credit as follows. Students scoring 4 or 5 on the BC examination in calculus receive eight hours credit, equivalent to Mathematics 133 and 134. Students scoring 3 on the BC examination in calculus with an AB sub-score of 4 or 5 receive four hours credit, equivalent to Mathematics 133. Students scoring 4 or 5 on the AB examination in calculus receive four hours credit, equivalent to Mathematics 133. Students scoring 4 or 5 on the examination in statistics receive four hours credit, equivalent to Mathematics 113.

Students given credit for one or more courses in this way do not need to take a Mathematics Placement Exam. They are encouraged to place themselves at the appropriate level in the mathematics curriculum according to the guidelines given below (see Initial Placement and Course Sequence Suggestions) in consultation with a member of the Mathematics Department.

Mathematics Placement Exams. Students wishing to enroll in an entry-level calculus course (Mathematics 131, 132, or 133) must take the Calculus Readiness Exam. Likewise, students wishing to enroll in an entry-level statistics course (Mathematics 113 or 114) must take the Statistics Readiness Exam. The placement exams are given twice during orientation. At other times they may be taken by arrangement with the Mathematics Department secretary. Please note that all students, regardless of their examination scores, are encouraged to consult with a member of the Mathematics Department concerning their placement in the mathematics curriculum.

Initial Placement and Course Sequence Suggestions. Students who wish to continue their study of mathematics can choose among the following courses:

Courses Without Prerequisites. Students who wish to satisfy the quantitative proficiency requirement, or who, simply out of curiosity, want to take a course in mathematics are encouraged to consider the courses numbered 100 and below.

Entry-level Statistics Courses. Students whose primary interest is in the social or behavioral sciences and who have no need for calculus are encouraged to consider enrolling in Mathematics 113 - Statistical Methods for the Social and Behavioral Sciences or Mathematics 114 - Statistical Methods for the Biological Sciences. These courses presuppose good algebra skills and require an appropriate score on the Statistics Readiness Exam. Students with less background are encouraged to consider enrolling in Mathematics 100 - Elementary Statistics.

Entry-level Calculus Courses. Students whose interests are in mathematics, or in a field requiring calculus, will normally enroll in Mathematics 131 - Calculus Ia: Limits, Continuity, and Differentiation, or in Mathematics 133 - Calculus I: Limits, Continuity, Differentiation, Integration, and Applications. The particular course, Mathematics 131 or Mathematics 133, depends on the student's score on the Calculus Readiness Exam. Note that students who wish to continue with calculus after completing Mathematics 131 should take its sequel, Mathematics 132 - Calculus Ib: Integration and Applications. The two-semester sequence Mathematics 131, 132 is equivalent to the more intensive single semester course, Mathematics 133.

Courses Following Entry-level Calculus. Students whose secondary-school preparation includes satisfactory work in calculus obtained in the College Board Advanced Placement Program or in another comparable course of study, as well as students who have completed either Mathematics 132 or 133, can continue their study of calculus with Mathematics 134 - Calculus II: Special Functions, Integration Techniques, and Power Series. This course completes the standard introduction to the calculus of functions of one variable.

Courses Following Calculus. Students who have completed Mathematics 134 or have been granted credit for this course through the College Board Advanced Placement Program or another comparable course of study can register for Mathematics 220 - Discrete Mathematics, or Mathematics 231 - Multivariable Calculus, or Mathematics 232 - Linear Algebra. Students planning to major in mathematics are strongly encouraged to enroll first in Mathematics 220, and thereafter in Mathematics 231 and Mathematics 232. Students planning a concentration in Applied Mathematics will also need to take Mathematics 113 - Statistical Methods for the Social and Behavioral Sciences or Mathematics 114 - Statistical Methods for the Biological Sciences. First-year students should not register for a 300-level mathematics course without consulting with a member of the Mathematics Department.

Major. A major in mathematics consists of thirty-four hours, including Mathematics 220, 231 and 232. In addition, students select one of the following two concentrations:

Concentration in applied mathematics. Students selecting this concentration must take either Mathematics 113 or Mathematics 114, and at least 12 hours of advanced mathematics courses numbered 300 and above, including either Mathematics 301 or 327, and three courses from among 331, 335, 336, 337, 338, and 340.

Concentration in pure mathematics. Students selecting this concentration must take at least 12 hours of advanced mathematics courses numbered 300 and above, including both Mathematics 301 and 327, and at least one of the following two-course sequences: Mathematics 301/302, 301/356, 301/358, 327/328 or 327/329.

Important note: Students planning to pursue graduate work in mathematics, or a closely related field, need to complete more than the minimum requirements for the mathematics major. Such students should plan their major carefully with the advice of a member of the Mathematics Department.

It is strongly urged that students specializing in mathematics also obtain substantial background in some field that uses mathematics. In particular, students majoring in mathematics are encouraged to gain some experience with computing. To that end, credit for one computer science course (that would also count toward a Computer Science major) may also be counted toward the thirty-four hour requirement for the major in mathematics. Private readings are also available, with the consent of an instructor, in any area of mathematics appropriate for a student's major. Finally, interdisciplinary majors involving a coherent program of work in mathematics and a related field can be arranged through the College Individual Majors Committee to suit special student interests and needs.

Minor. A minor in mathematics consists of at least fifteen hours of course work, including any three of Mathematics 220, 231, 232, 234, and at least six hours of courses numbered 300 and above.

Honors. At the end of their junior year, students with outstanding records are invited to participate in the Mathematics honors program. Seniors in the program normally elect three hours of independent study each semester. This special study is supervised by a faculty advisor who works closely with the student. Honors students take a comprehensive examination, written and oral, at the end of the senior year. This honors examination is conducted by an outside examiner and is designed to test both the candidate's knowledge of undergraduate mathematics and mastery of the subjects emphasized in his or her independent honors study.

Winter Term. Most members of the Mathematics Department will be participating in Winter Term 2002, and will be available to sponsor projects.

Mathematical interests in the department include abstract algebra, algebraic geometry, combinatorics, dynamical systems, mathematics and computation, differential equations, differential geometry, history of mathematics, mathematics education, non-Euclidean geometry, number theory, operations research, probability, real and complex analysis, topology, and statistics.

Avocational interests of Department members which could form the basis for a sponsored Winter Term project include electronic composition and synthesis of music, games of strategy, and juggling. For further information regarding these possibilities, inquire in the Mathematics Department office.

Distinguished Visiting Scholar. Thanks to the generosity of alumni, the Mathematics Department is able to sponsor an annual visit by an eminent mathematical scientist who will conduct classes and deliver a public lecture.

John D. Baum Memorial Prize in Mathematics. Established by the Mathematics Department, this $100 prize is awarded annually to the Oberlin College student who has achieved the highest score on the William Lowell Putnam Mathematical Competition.

Rebecca Cary Orr Memorial Prize in Mathematics. Established by the family and friends of Rebecca Cary Orr, this $2000 prize is awarded annually by the Mathematics Department on the basis of scholastic achievement and promise for future professional accomplishment.

 

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Introductory Courses

030. Topics in Contemporary Mathematics 3 hours
3NS, QPf

The interaction of mathematics with the social sciences is the central theme. Topics are drawn from: graph theory, game theory, linear programming, coding theory, exploratory data analysis, and combinatorics. Applications are given to social choice, decision-making, management and ecological modeling. Prerequisites: A working knowledge of elementary algebra and geometry. Notes: This course does not count toward a major in Mathematics. It is intended for students who have not satisfied the quantitative proficiency requirement. Enrollment Limit: 30.

Sem 1 MATH-030-01 MWF 3:30-4:20 Mr. Henle

Sem 2 MATH-030-01 MWF 9:00-9:50 Mr. Balasuriya

050. Dots, Lines, and Coin Flips 3 hours
3NS, QPf

Next offered 2002-2003.

080. Lies, Damned Lies, and Decisions 3 hours
3NS, QPf

An introduction to the use of data in everyday life, particularly decision-making. Topics include descriptive statistics and graphics, data collection methods, probability trees, utility theory, and decision trees. Notes: This course is not equivalent to elementary statistics (MATH 100, MATH 113, or MATH 114) and does not count toward a major in mathematics. It is intended for students who have not satisfied the quantitative proficiency requirement. Students may not receive credit for both MATH 080 and any of MATH 100, MATH 113, or MATH 114. Enrollment Limit: 30.
Sem 1 MATH-080-01 MWF 1:30-2:20 Mr. Witmer

090. Environmental Mathematics 3 hours
3NS, QPh

This course focuses on the application of mathematics to problems concerning the environment. Topics include simulation (models of population growth, predator-prey relationships, and epidemics); optimization (applications to groundwater hydrology, herbivore foraging, and transportation of hazardous wastes); and decision analysis (applications to management of endangered species and resolution of environmental disputes). Notes: This course does not count toward a major in mathematics. It is intended for students who have not satisfied the quantitative proficiency requirement. Not open to any student who has received credit for a course in mathematics numbered 133 or higher. Enrollment Limit: 20.

Sem 2 MATH 090-01 MWF 2:30-3:20 Mr. Bosch

100. Elementary Statistics 4 hours
4NS, QPf

An introduction to the statistical analysis of data. Topics include exploratory data analysis, probability, sampling, estimation, and hypothesis testing. Statistical software is introduced, but no prior computer experience is assumed. This course focuses on statistical ideas and downplays mathematical formulas. It is intended for students in the social sciences and humanities with minimal mathematical experience who have not satisfied the quantitative proficiency requirement. Notes: MATH 100 does not count toward a mathematics major and is not open to students who have completed a semester of calculus. Students may not receive credit for more than one of MATH 100, MATH 113, and MATH 114. Enrollment Limit: 36.

Sem 1 MATH-100-01 MTuThF 1:30-2:20 Mr. Bosch

Sem 2 MATH-100-01 MTuThF 1:30-2:20 Mr. Andrews, Mr. Bosch

113. Statistical Methods for the Social and Behavioral Sciences 4 hours
4NS, QPf

A standard introduction to statistics for students with a good background in mathematics. Topics covered include exploratory data analysis, descriptive statistics, probability, sampling, estimation, and statistical inference. A broad spectrum of examples is employed. Statistical software is introduced, but no prior computer experience is assumed. Prerequisite: An appropriate score on the Statistics Readiness Exam. Notes: The statistical content of this course is largely the same as MATH 114; the applications are different. Students may not receive credit for more than one of MATH 100, MATH 113, and MATH 114. Consent of instructor required.

Sem 1 MATH-113-01 MWF 10:00-10:50 Mr. Andrews Limit: 36

Laboratories
MATH-113-02 Tu 9:00-9:50 Mr. Andrews Limit: 18
MATH-113-03 Th 10:00-10:50 Mr. Andrews Limit: 18
Sem 2 MATH-113-01 MWF 10:00-10:50 Mr. Witmer Limit: 36

Laboratories
MATH-113-02 Tu 9:00-9:50 Mr. Witmer Limit: 18

MATH-113-03 Th 10:00-10:50 Mr. Witmer Limit: 18

114. Statistical Methods for the Biological Sciences 4 hours
4NS, QPf

A standard introduction to statistics for students with a good background in mathematics. Topics covered include exploratory data analysis, descriptive statistics, probability, sampling, estimation, and statistical inference. Biological and medical examples are emphasized. Statistical software is introduced, but no prior computer experience is assumed. Prerequisites: An appropriate score on the Statistics Readiness Exam. Notes: The statistical content of this course is largely the same as MATH 113; the applications are different. Students may not receive credit for more than one of MATH 100, MATH 113, and MATH 114. Consent of instructor required.

Sem 1 MATH-114-01 MWF 9:00-9:50 Mr. Andrews Limit: 36

Laboratories
MATH-114-02 Tu 10:00-10:50 Mr. Andrews Limit: 18
MATH-114-03 Th 9:00-9:50 Mr. Andrews Limit: 18
Sem 2 MATH-114-01 MWF 9:00-9:50 Mr. Andrews Limit: 36

Laboratories
MATH-114-02 Tu 10:00-10:50 Mr. Andrews Limit: 18

MATH-114-03 Th 9:00-9:50 Mr. Andrews Limit: 18

131. Calculus Ia: Limits, Continuity and Differentiation 4 hours
4NS, QPh

A first course in the calculus of functions of one variable including supporting material from algebra and trigonometry. Topics include limits, continuous functions, solution of equations and inequalities, differentiation of real-valued functions of one variable, and the graphical analysis of functions. The two-course sequence MATH 131, MATH 132 is equivalent to the more intensive MATH 133. Prerequisite: An appropriate score on the Calculus Readiness Exam. Consent of instructor required. Enrollment Limit: 32

Sem 1 MATH-131-01 MTuThF 10:00-10:50 Ms. Knight

MATH-131-02 MTuThF 1:30-2:20 Mr. Henle


132. Calculus Ib: Integration and Applications 4 hours

4NS, QPf

Continuation of MATH 131. Topics include integration of real-valued functions of one variable, basic properties of the trigonometric and exponential functions, the fundamental theorems of the calculus, and applications. Prerequisite: MATH 131 or an appropriate score on the Calculus Readiness Exam. Consent of instructor required. Enrollment Limit: 32.

Sem 2 MATH-132-01 MTuThF 9:00-9:50 Ms. Knight

MATH-132-02 MF 10:00-10:50,

W 9:00-10:50 Mr. Schirokauer


133. Calculus I: Limits, Continuity, Differentiation, 4 hours
Integration, and Applications

4NS, QPf

A standard first course in the calculus of functions of one variable. Topics include limits, continuous functions, differentiation and integration of real-valued functions of one variable, the fundamental theorems of calculus, and applications. This course is equivalent to the two-course sequence MATH 131, MATH 132. Prerequisite: An appropriate score on the Calculus Readiness Exam. Consent of instructor required. Enrollment Limit: 32.
Sem 1 MATH-133-01 MTuThF 8:00-8:50 Ms. Colley
MATH-133-02 MTuThF 9:00-9:50 Ms. Colley
MATH-133-03 MTuThF 1:30-2:20 Mr. Balasuriya
Sem 2 MATH-133-01 MTuThF 10:00-10:50 Mr. Balasuriya
 

134. Calculus II: Special Functions, Integration Techniques, and Power Series 4 hours
4NS, QPf

Continuation of the study of the calculus of functions of one variable. Topics include logarithmic, exponential and the inverse trigonometric functions, techniques of integration, polar coordinates, parametric equations, infinite series, and applications. The course sequences MATH 133, 134 and MATH 131, 132, 134 both provide a standard introduction to single-variable calculus. Prerequisites: MATH 132 or MATH 133. Enrollment Limit: 32.
Sem 1 MATH-134-01 MTuThF 10:00-10:50 Mr. Balasuriya
MATH-134-02 MTuThF 1:30-2:20 Ms. Colley
Sem 2 MATH-134-01 MTuThF 9:00-9:50 Mr. Walsh
MATH-134-02 MTuThF 1:30-2:20 Mr. Young

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Intermediate Courses

210. Chaos and Fractals: An Introduction 3 hours
3NS, QPf

Next offered 2002-2003.

220. Discrete Mathematics 3 hours
3NS, QPf

An introduction to a wide variety of mathematical ideas and techniques that do not involve calculus. Topics such as graph theory, combinatorics, difference equations, elementary number theory, recursion, mathematical induction, and logic. Prerequisite: MATH 133. Enrollment Limit: 32.
Sem 1 MATH-220-01 TuTh 11:00-12:20 Mr. Schirokauer
MATH-220-02 TuTh 1:30-2:50 Mr. Schirokauer
Sem 2 MATH-220-01 MWF 11:00-11:50 Mr. Henle
MATH-220-02 MWF 1:30-2:20 Mr. Henle

231. Multivariable Calculus 3 hours
3NS, QPf

An introduction to the calculus of several variables. Topics considered include vectors and solid analytic geometry, multidimensional differentiation and integration, and a selection of applications. Prerequisite: MATH 134. Enrollment Limit: 32.
Sem 1 MATH-231-01 MWF 11:00-11:50 Mr. Young
Sem 2 MATH-231-01 MWF 11:00-11:50 Mr. Young
MATH-231-02 MWF 3:30-4:20 Mr. Young

232. Linear Algebra 3 hours
3NS, QPf

An introduction to linear algebra. Topics considered include the algebra and geometry of Euclidean n-space, matrices, determinants, abstract vector spaces, linear transformations, and diagonalization. Prerequisites: MATH 134 or MATH 220. Enrollment Limit: 32.
Sem 1 MATH-232-01 TuTh 8:35-9:55 Mr. Walsh
Sem 2 MATH-232-01 MWF 9:00-9:50 Ms. Colley
MATH-232-02 MWF 2:30-3:20 Mr. Walsh

234. Differential Equations 3 hours
3NS, QPf

An introduction to analytic, qualitative and numerical methods for solving ordinary differential equations. Topics include general first order equations, linear first and second order equations, numerical methods (Euler, Runge-Kutta), systems of first order equations, phase plane analysis, and Laplace Transforms. There is emphasis throughout the course on geometric and qualitative interpretations of differential equations, as well as applications to the natural sciences. Prerequisite: MATH 231. Enrollment Limit: 32.

Sem 1 MATH-234-01 TuTh 11:00-12:20 Mr. Walsh

240. Applied Mathematics 3 hours
3NS, QPf

This course will cover several areas of applied mathematical modeling including linear programming and optimization, multiple regression, and dynamical systems. Knowledge of these topics will permit students to construct models that accurately represent data in a wide range of fields from image compression to economic theory to population dynamics. Students will use a variety of software packages to analyze real world data. Prerequisites: MATH 133 and either MATH 113 or MATH 114. Enrollment Limit: 20.

Sem 2 MATH-240-01 MWF 11:00-11:50 Mr. Andrews, Mr. Bosch

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Advanced Courses

301. Advanced Calculus 3 hours
3NS, QPf

A rigorous examination of the basic elements of analysis. The structure of the real number system, continuity, differentiability, uniform continuity, integrability of functions of a single variable, sequences, series, and uniform convergence are typical topics to be explored. Prerequisite: MATH 231. MATH 220 is also highly recommended.

Sem 1 MATH-301-01 MWF 1:30-2:20 Mr. Young

302. Topics in Advanced Calculus: Chaos, Fractals and Dynamics 3 hours
3NS, QPf

This course applies the techniques of Advanced Calculus to the study of chaotic dynamical systems. One and two dimensional dynamics, attractors, iterated function systems, and fractal dimension are typical topics to be explored. Application to the physical sciences, computer graphics and other branches of mathematics will be given. Prerequisite: MATH 301 or consent of instructor. Note: Given in alternate years only.

Sem 2 MATH-302-01 MWF 11:00-11:50 Mr. Walsh

305. Partial Differential Equations 3 hours
3NS, QPf

A course on analytical solution techniques for partial differential equations (PDEs) and boundary value problems. Topics include separation of variables, Fourier series, solutions to classical PDEs in standard geometries, Sturm-Liouville theory, and Fourier transforms. Based on student interest, additional topics may be chosen from among: numerical solutions techniques to PDEs, Green's functions, method of characteristics, discrete Fourier transforms, and specific applications. Note: Given in alternate years only. Prerequisite: MATH 234.

Sem 1 MATH-305-01 MWF 3:30-4:20 Mr. Balasuriya

317. Number Theory 3 hours
3NS, QPf

This course is an introduction to number theory. Topics include primality, divisibility, modular arithmetic, finite fields, cryptography, and elliptic curves. Emphasis will be placed both on theoretical questions and on algorithms for computation. Prerequisite: MATH 301 or consent of the instructor. Note: Given in alternate years only.

Sem 2 MATH-317-01 MWF 2:30-3:20 Mr. Schirokauer

327. Group Theory 3 hours
3NS, QPf

A first course in the modern algebraic structures and techniques fundamental to mathematics and useful in many areas of science and engineering. Topics include: groups, subgroups, quotient groups, isomorphism theorems, permutation groups, finite groups, and applications to combinatorics, geometry, symmetry, and crystallography. Prerequisite: MATH 232. MATH 220 is also highly recommended.

Sem 2 MATH-327-01 MWF 1:30-2:20 Ms. Colley

328. Computational Algebra and Algebraic Geometry 3 hours
3NS, QPf

Next offered 2002-2003.

329. Abstract Algebra: Rings and Fields 3 hours
3NS, QPf

This is one of two courses introducing algebraic structures and techniques fundamental to mathematics and useful in many areas of science and engineering. Topics include: rings, subrings, ideals, fields, integral domains, polynomial rings, extension fields, finite fields, famous impossible constructions. Galois theory, and algebraic coding theory. Prerequisite: MATH 232. In addition, MATH 220 is highly recommended. Note: Given in alternate years only.

Sem 1 MATH-329-01 MWF 9:00-9:50 Mr. Schirokauer

331. Optimization 3 hours
3NS, QPf

An introduction to linear, integer, and nonlinear programming. Emphasis is placed on the theory of mathematical programming and the analysis of optimization algorithms. These are applied to significant problems in the fields of medicine, finance, public policy, transportation, and telecommunications. Prerequisites: MATH 231 and MATH 232.

Sem 1 MATH-331-01 MWF 3:30-4:20 Mr. Bosch

335. Probability 3 hours
3NS, QPf

An introduction to the mathematical theory of probability and its applications. Topics include discrete and continuous sample spaces, combinatorial problems, random variables, probability densities, probability distributions, limit theorems, and stochastic processes. Prerequisite: MATH 231. MATH 220 is also strongly recommended.

Sem 1 MATH-335-01 MWF 2:30-3:20 Mr. Andrews

336. Mathematical Statistics 3 hours
3NS, QPf

Next offered 2002-2003.

337. Data Analysis 3 hours
3NS, QPf
In this course students will be given an introduction to the theory and use of regression graphics. Special regression and graphics software will be used to study relationships among several variables. Topics will include regression smoothing, residual plots, scatterplot matrices, three-dimensional plots, transformations of predictors and of response variables, and added-variable plots. Note: Given in alternate years only. Prerequisites: MATH 113 or 114 and MATH 232 or consent of the instructor.

Sem 2 MATH-337-01 MWF 3:30-4:20 Mr. Witmer

338. Probability Models and Random Processes 3 hours
3NS, QPf

An introduction to operations research models which incorporate methods of probability theory. Topics will be chosen from inventory theory, queueing theory, decision analysis, game theory, simulation, Markov chains, and project management. Computer software for selected topics will also be discussed and utilized. Note: Given in alternate years only. Prerequisite: MATH 335.

Sem 2 MATH-338-01 TuTh 3:00-4:20 Mr. Bosch

340. Practicum in Applied Mathematics 3 hours
3NS, QPf

Next offered 2002-2003.

343. Combinatorics 3 hours
3NS, QPf

Next offered 2002-2003.

350. Geometry 3 hours
3NS, QPf

This course explores some of the mathematics used to describe space and distance. Topics will include some or all of the following: comparison of Euclidean and non-Euclidean geometries, models of hyperbolic spaces, constructibility problems, and the differential geometry of curves and surfaces in three-space. Notes: Given in alternate years only. Prerequisite: MATH 220.
MATH 231 and MATH 232 are also strongly recommended.

Sem 1 MATH-350-01 MWF 10:00-10:50 Mr. Henle

353. Topology 3 hours
3NS, QPf

Next offered 2002-2003.

356. Complex Analysis 3 hours
3NS, QPf

Next offered 2002-2003.

401. Honors 2-4 hours
2-4NS

Consent of instructor required.

995. Private Reading 1-3 hours
1-3NS

Consent of instructor required.

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