Mathematics
Both the course offerings and the major in Mathematics reflect the many roles of mathematics itself: the language and tool of the sciences, a cultural phenomenon with a rich historical tradition, and a model of abstract reasoning. The Mathematics program is flexible enough to accommodate a range of interests, and majors have many options after graduation. Some go on to graduate school; others—with or without advanced degrees—teach at high schools and colleges or work in corporate or government laboratories, for large banks or other financial institutions, or for insurance companies as actuaries. The courses discussed below are open to freshmen who are adequately prepared for work in calculus and advanced topics. Other courses, such as MATH 190a, Fractal Geometry, have only high school algebra as a prerequisite. Students taking mathematics often change the level of their course during the first half of the fall term. Students who think they have enrolled in too high or too low a course should not hesitate to consult the DUS or the departmental adviser in their residential college. Placement in Calculus CoursesAll calculus courses require the instructor's permission for enrollment. Incoming students who wish to register for a calculus course must first take an online diagnostic examination, which will be available on the home page of the Department of Mathematics, by the end of August. The results of this examination, together with AP scores, will be used to advise students on an appropriate beginning course. Students should bring the results of the online placement examination to the preregistration session during Freshman Orientation. The time and date of preregistration will be posted on the departmental Web site in August, and details will be published in the YCPS and in the Calendar for the Opening Days. |
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Students who wish to take a higher-level mathematics course are urged to seek placement advice from the DUS or at the preregistration session.
Courses
There is a three-term sequence of calculus courses.
- MATH 112a or b, Calculus of Functions of One Variable I, is the introductory course for well-prepared students. It assumes no prior calculus.
- MATH 115a or b, Calculus of Functions of One Variable II, is a sequel to 112a or b. It is a suitable first course for students with appropriate preparation, most often indicated by a score of 4 or above on the AB Calculus AP test or 3 or above on the BC Calculus AP test.
- MATH 120a or b, Calculus of Functions of Several Variables, is the third term of the basic calculus sequence. It includes vector geometry and algebra as well as the calculus of functions of two and three variables, especially partial derivatives and double integrals. Enrollment in this course normally requires a score of 5 on the AB Calculus AP test, or 4 or 5 on the BC Calculus AP test, or completion of MATH 115a or b.
- MATH 222a or b, Linear Algebra with Applications, and 225a or b, Linear Algebra and Matrix Theory, require a year of calculus and some acquaintance with vector analytic geometry, such as that covered in MATH 120a or b. Freshmen with strong backgrounds (usually indicated by a score of 5 on the BC Calculus AP test) may elect one of them if they take MATH 120a or b concurrently or have previously taken an equivalent course.
- MATH 230, Vector Calculus and Linear Algebra, is a demanding, yearlong course for students with a strong interest in mathematics and a firm command of the techniques and theory of calculus of functions of one variable. It covers in greater depth the material of MATH 120a or b, 225a or b, and 250a, Vector Analysis, emphasizing proofs and more challenging problems. Interested students with a score of 5 on the BC Calculus AP test or equivalent preparation are invited to consult the instructor for permission to enroll. With the instructor's permission, a student may also take this course after MATH 115a or b.
Additional help is available for students in any of these courses. The Mathematics department schedules evening help sessions, which are announced in class, and mathematics and science tutors in the residential colleges are also available to help students. (See under “Academic Resource Centers”.)
Certain courses in other departments, for example, Computer Science, Operations Research, Engineering and Applied Science, and Statistics, may, with permission of the DUS, count toward the major. Qualified students may, with permission, take graduate courses in Mathematics and count them toward the major as well. Mathematics majors who can use computers effectively are at an advantage, as are those who have taken courses in a related area such as physics.
