Course Catalog 2011-2012 [ARCHIVED CATALOG]
Mathematics
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Susan Jane Colley, Andrew and Pauline Delaney Professor; Department Chair
Robert A. Bosch, Robert and Eleanor Biggs Professor of Natural Science
Jack Calcut, Assistant Professor
Michael Gilman Henle, Professor
Joshua Lesperance, Visiting Assistant Professor
Kay M. Knight, Lecturer
Matthew Gardner Spencer, Visiting Assistant Professor
James A. Walsh, Professor
Elizabeth Wilmer, Associate Professor
Jeffrey Alvin Witmer, Professor
Kevin Woods, Assistant Professor
Robert M. Young, James F. Clark Professor
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.
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 precalculus 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 below (see Initial Placement and Course Sequence Suggestions) in consultation with a member of the Mathematics Department.
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 with numbers less than 100.
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 085–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 in Mathematics 220 before taking Mathematics 232.
First-year students should not register for a 300-level mathematics course without consulting a member of the Mathematics Department.
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Major
A major in mathematics consists of 11courses, which must include: A. Mathematics 133, 134, 220, 231 and 232.
B. Four 300-level mathematics courses, which must include 1. Mathematics 301 and 327.
2. One modeling course from among Mathematics 331, 335, 336, 337, 338, 342, 343, 345 or 348. C. Two additional mathematics courses numbered 200 or above. Note: One or both of the courses in item C above can be replaced by a course or courses from the following list: i. (a) Computer Science 150 or 151. Only one of the two may count towards the mathematics major. (b) Any computer science course numbered 200 or above which counts towards the computer science major. ii. Physics and Astronomy 290, 301, 302, 310, 311, 312, 316, 340, 410, 411 - 12 (the module courses PHYS 411 and PHYS 412 together count as one course). iii. Chemistry 339, 349. iv. Economics 342, 351, 353, 355. 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 requirement B.2 above. Important Notes
Courses in which a student has earned a letter grade lower than a C-/CR/P cannot be used to fulfill the requirements of the major. 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. All students interested in graduate work in mathematics should plan their major carefully with the advice of a member of the Mathematics Department. Students interested in graduate work in pure mathematics should complete at least a second algebra course (Mathematics 317, 328, 329) and a second analysis course (Mathematics 302, 356, 358). Moreover, Mathematics 350 and Mathematics 353 provide introductions to fundamental areas of pure mathematics. Students interested in graduate studies in applied mathematics have several options. In the area of Operations Research, students should complete Mathematics 331, 335 and 338. Students with interests in probability and statistics should take Mathematics 335, 336 and 337. The courses Mathematics 342, 343, 345 and 348 serve as introductions to fundamental areas of discrete applied mathematics. The minimum requirement of 11 courses is appropriate for students using mathematics as preparation for careers in fields such as secondary-school teaching, medicine, law, or business. Students having related interests in chemistry, computer science, economics or physics should note that up to two courses from those listed after item C above can count towards the mathematics major. This option supports our belief that mathematics majors should obtain substantial background in some field that uses mathematics. 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 2010 and are available to sponsor projects. Normally, Winter Term projects do not entail the learning of material taught in any of our regularly offered courses. 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 $200 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 $3000 prize is awarded annually by the Mathematics Department on the basis of scholastic achievement and promise for future professional accomplishment. Introductory Courses
- MATH 050 - Dots, Lines and Coin Flips Semester Offered: Second Semester
- MATH 113 - Stat Methods for the Social and Behavioral Sciences Semester Offered: First Semester, Second Semester
- MATH 114 - Statistical Methods for the Biological Sciences Semester Offered: First Semester, Second Semester
- MATH 131 - Calculus Ia: Limits, Continuity and Differentiation Semester Offered: First Semester
- MATH 132 - Calculus Ib: Integration and Applications Semester Offered: Second Semester
- MATH 133 - Calculus I: Limits, Continuity, Differentiation, Integration and Applications Semester Offered: First Semester, Second Semester
- MATH 134 - Calculus II: Special Functions, Integration Techniques and Power Series Semester Offered: First Semester, Second Semester
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