As mathematics is both a technical and cultural field of study, the curriculum is planned with the following varied 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.

Students seeking guidance in the selection of courses are strongly urged to confer with a member of the department, all of whom are happy to be consulted. The following information will provide a preliminary basis for making plans and choices.

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 want to take a course in mathematics (simply out of curiosity) are encouraged to consider the courses numbered 100 and below.

Entry-Level Statistics Courses. Students whose primary interest is in the social, behavioral, or biological 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, and who have not yet taken 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 equivalent to Mathematics 133, obtained in the College Board Advanced Placement Program or a 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 a standard year-long 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 a comparable course of study can register for any of several intermediate level courses, Mathematics 220 Discrete Mathematics or Mathematics 231 Multivariable Calculus or Mathematics 232 Linear Algebra or Mathematics 234 Differential Equations. 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 a member of the Mathematics Department.

Placement Exams. Students wishing to enroll in an entry-level calculus course (Mathematics 131, 132, or 133) must take the Calculus Readiness Exam (which covers pre-calculus only). Likewise, students wishing to enroll in an entry-level statistics course (Mathematics 113 or 114) must take the Statistics Readiness Exam. Placement exams are given twice during orientation. At other times they may be taken by arrangement with the Mathematics Department Administrative Assistant. 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.

Important Note: Only students interested in Mathematics 113, 114, 131, 132 or 133 need to take a placement exam. Students who need work in algebra or other basic quantitative skills should consult the "Learning
Assistance Program" section of this catalog.

Advanced Placement. Students who have taken one of the 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 above (see Initial Placement and Course Sequence Suggestions) in consultation with a member of the Mathematics Department.

Major. A major in mathematics consists of 34 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. This must include either Mathematics 301 or 327 and three courses from among 331, 335, 336, 337, 338, 360, and 362.

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, 327/328 or 327/329.

The department frequently offers a 300-level seminar in addition to its regular offerings. Students should check with the instructor to find out whether the seminar can be used to fulfill the requirements for one of the above concentrations.

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 (one would also count toward a Computer Science major) may be counted toward the 34 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 15 hours of coursework, including any three of Mathematics 220, 231, 232, and 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. For their senior year, honors students normally elect three hours of independent study each semester. This special study, which is supervised by a faculty advisor who works closely with the student, results in an Honors paper. Honors students also take a comprehensive written examination at the end of Winter Term and, at the end of the academic year, an oral examination on the material in their Honors paper. These examinations are conducted by an outside examiner. More detailed information on the Honors Program is available from the department secretary.

Winter Term. Most members of the Mathematics Department will be participating in Winter Term 2006 and are available to sponsor projects.

Mathematical interests in the department include abstract algebra, algebraic geometry, combinatorics, cryptography, 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 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.

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.

030. Topics in Contemporary Mathematics
3 hours, 3NS, QPf
Second Semester.
The interaction of mathematics with the social sciences is the central theme of this course. Topics are drawn from: graph theory, voting systems, discrete models, coding theory, exploratory data analysis, and combinatorics. Applications are given to social choice, decision-making, management and ecological modeling. Prerequisite: A working knowledge of elementary algebra and geometry. Notes: This course does not count toward a major in Mathematics and is not open to any student who has received credit for a math course numbered 131 or higher. It is intended for students who have not satisfied the quantitative proficiency requirement. Enrollment Limit: 30.
Mr. Henle

050. Dots, Lines, and Coin Flips
3 hours, 3NS, QPf
Next offered 2006-2007.

090. Environmental Mathematics
3 hours, 3NS, QPf
First Semester.
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 and is not open to any student who has received credit for a math course numbered 131 or higher. Enrollment Limit: 20.
Mr. Bosch

100. Elementary Statistics
3 hours, 3NS, QPf
First and Second Semester.
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. Note: MATH 100 does not count toward a mathematics or economics 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: 30.
Mr. Bosch, Mr. Lenstra

113. Statistical Methods for the Social and Behavioral Sciences
4 hours, 4NS, QPf
First and Second Semester.
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. Note: 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. Enrollment Limit: 36.
Mr. Bosch, Mr. Lenstra

114. Statistical Methods for the Biological Sciences
4 hours, 4NS, QPf
Next offered 2006-2007.

131. Calculus Ia: Limits, Continuity and Differentiation
3 hours, 3NS, QPh
First Semester.
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.
Mr. Henle, Ms. Knight

132. Calculus Ib: Integration and Applications
3 hours, 3NS, QPf
Second Semester.
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.
Ms. Knight

133. Calculus I: Limits, Continuity, Differentiation, Integration,
and Applications
4 hours, 4NS, QPf
First and Second Semester.
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.
Mr. Thomas, Mr. Walsh

134. Calculus II: Special Functions, Integration Techniques,
and Power Series
4 hours, 4NS, QPf
First and Second Semester.
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. Prerequisite: MATH 132 or MATH 133. Enrollment Limit: 32.
Mr. Schirokauer, Mr. Young

220. Discrete Mathematics
3 hours, 3NS, QPf
First and Second Semester.
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.
Mr. Schirokauer, Ms. Wilmer

231. Multivariable Calculus
3 hours, 3NS, QPf
First and Second Semester.
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.
Mr. Henle, Ms. Wilmer, Mr. Young

232. Linear Algebra
3 hours, 3NS, QPf
First and Second Semester.
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. Prerequisite: MATH 134 or MATH 220. Enrollment Limit: 32.
Mr. Henle, Mr. Thomas

234. Differential Equations
3 hours, 3NS, QPf
First Semester.
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.
Mr. Walsh

236. Partial Differential Equations and Applied Complex Analysis
3 hours, 3NS, QPf
Second Semester.
An introduction to complex analysis in the context of applications to partial differential equations. Topics to include: analytic functions, complex integration and residue calculus techniques; Fourier series; partial differential equations in rectangular, cylindrical and spherical coordinates, and associated special functions; Fourier and Laplace transforms. Depending on student interest, numerical methods including finite difference and finite element techniques may be covered. Prerequisite: MATH 231. Enrollment Limit: 32.
Mr. Thomas

301. Advanced Calculus
3 hours, 3NS, QPf
First Semester.
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. Note: MATH 220 is also highly recommended.
Mr. Young

302. Dynamical Systems
3 hours, 3NS, QPf
Second Semester.
A first course in continuous and discrete dynamical systems in dimensions one and higher. Topics include phase portraits, periodic orbits, hyperbolicity, bifurcations, symbolic dynamics, chaos and fractals. Prerequisite: MATH 231 and 232. Notes: MATH 234 is also highly recommended. Taught in alternate years only.
Mr. Walsh

317. Number Theory
3 hours, 3NS, QPf
Next offered 2006-2007.

327. Group Theory
3 hours, 3NS, QPf
Second Semester.
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. Note: MATH 220 is also highly recommended.
Ms. Wilmer

328. Computational Algebra and Algebraic Geometry
3 hours, 3NS, QPf
Next offered 2006-2007.

329. Rings and Fields
3 hours, 3NS, QPf
First Semester.
This is one of two courses introducing algebraic structures and techniques fundamental to modern mathematics. Topics include: rings, subrings, ideals, fields, integral domains, polynomial rings, extension fields, finite fields, famous impossible constructions, and Galois theory. Prerequisite: MATH 327. Note: Taught in alternate years only.
Mr. Schirokauer

331. Optimization
3 hours, 3NS, QPf
First Semester.
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.
Mr. Bosch

335. Probability
3 hours, 3NS, QPf
First Semester.
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.
Mr. Lenstra

336. Mathematical Statistics
3 hours, 3NS, QPf
Next offered 2006-2007.

337. Data Analysis
3 hours, 3NS, QPf
Next offered 2006-2007.

338. Probability Models and Random Processes
3 hours, 3NS, QPf
Second Semester.
An introduction to operations research models which incorporate methods of probability theory. Topics will be chosen from inventory theory, queuing theory, decision analysis, game theory, simulation, Markov chains, and project management. Computer software for selected topics will also be discussed and utilized. Prerequisite: MATH 335. Note: Taught in alternate years only.
Mr. Bosch

343. Combinatorics
3 hours, 3NS, QPf
First Semester.
An advanced course in discrete mathematics. Topics covered include enumeration, combinatorial identities, generating functions, partitions, and set systems. Prerequisite: Any one of MATH 317, 327, 328, 329, or 335. Ms. Wilmer

350. Geometry
3 hours, 3NS, QPf
First Semester.
This course takes a modern approach to geometry based on group theory and the Erlangen Programm making possible the survey of a wide spectrum of geometries, Euclidean and non-Euclidean. Geometries treated include Moebius geometry, hyperbolic geometry, elliptic geometry, and absolute geometry. The discovery of these geometries in the 19th century caused a scientific and philosophical revolution second only to the Copernican revolution. Prerequisite: MATH 220 or consent of instructor.
Mr. Henle

353. Topology
3 hours, 3NS, QPf
Next offered 2006-2007.

356. Complex Analysis
3 hours, 3NS, QPf
Next offered 2006-2007.

360. Mathematical Methods for Computational Neuroscience
3 hours, 3NS, QPf
Next offered 2006-2007.

362. Mathematical Biology
3 hours, 3NS, QPf
Second Semester.
A research-oriented seminar course on the mathematical modeling of biological systems. Topics include: applications of ODEs and PDEs, Monte Carlo methods, stochastic differential equations and bifurcation theory. Biological topics include: synchronization, population dynamics, patterning in growth and development, reaction-diffusion systems, coordination of movement and chemotaxis. Student research projects will comprise a significant part of the course. Prerequisite: MATH 231 and consent of the instructor.
Mr. Thomas

401. Honors
2-4 hours,
2-4NS
Consent of instructor required.

550, 551. Research
1-2 hours, 1-2NS
First and Second Semester.
Projects for original investigation. Interested students are encouraged to talk to individual faculty members about possible projects. Consent of the department chair required.

995. Private Reading
1-3 hours, 1-3NS
Consent of instructor required.