# Catalog

## Mathematics

Professors Haines, Wong (chair), and Rhodes; Associate Professors Ross and Shulman; Assistant Professors Greer and Jayawant; Visiting Assistant Professor Shor; Visiting Instructor Dzhelepov; Lecturers Harder and Coulombe

A dynamic subject, with connections to many disciplines, mathematics is an integral part of a liberal arts education, and is increasingly vital in understanding science, technology, and society. Entry-level courses introduce students to basic concepts and hint at some of the power and beauty behind these fundamental results. Upper-level courses and the capstone experience provide majors with the opportunity to explore mathematical topics in greater depth and sophistication, and to delight in the fascination of this important discipline.

During new-student orientation the department assists students planning to study mathematics in choosing an appropriate starting course. Based on a student's academic background and skills, the department recommends Mathematics 101, 105, 106, 110, 205, 206, or a more advanced course.

The mathematics department offers a major and a secondary concentration in mathematics. More information on the mathematics department is available on the Web site (www.bates.edu/MATH.xml).

#### Cross-listed Courses

Note that unless otherwise specified, when a department/program references a course or unit in the department/program, it includes courses and units cross-listed with the department/program.#### Major Requirements

The mathematics major requirements accommodate a wide variety of interests and career goals. The courses provide broad training in undergraduate mathematics, preparing majors for graduate study, and for positions in government, industry, and the teaching profession.The major in mathematics consists of:

1) Mathematics 205 and 206;

2) Mathematics s21, which should be taken during Short Term of the first year;

3) Mathematics 301 and 309, which should be taken before beginning a senior thesis or the senior seminar;

4) four elective mathematics courses numbered 200 or higher, not including 360, 395, 457, 458, or s50;

5) completion of either a one-semester thesis (Mathematics 457 or 458), a two-semester thesis (Mathematics 457-458), or the senior seminar (Mathematics 395). The thesis option requires departmental approval.

Any mathematics Short Term unit numbered 30 or above may be used as one of the electives in 4). One elective may also be replaced by a departmentally approved course from another department.

While students must consult with their major advisors in designing appropriate courses of study, the following suggestions may be helpful: For majors considering a career in secondary education the department suggests Mathematics 312, 314, 315, and 341. Students interested in operations research, business, or actuarial science should consider Mathematics 218, 314, 315, and 341. Students interested in applied mathematics in the physical and engineering sciences should consider Mathematics 218, 219, 308, 314, 315, and 341. Majors planning on graduate study in pure mathematics should particularly consider Mathematics 308, 313, and 457-458. Mathematics majors may pursue individual research either through Independent Study (360 or s50), or Senior Thesis (457 and/or 458).

#### Pass/Fail Grading Option

Pass/fail grading may not be elected for courses applied toward the major.#### Secondary Concentration in Mathematics

Designed either to complement another major, or to be pursued for its own sake, the secondary concentration in mathematics provides a structure for obtaining a significant depth in mathematical study. It consists of seven mathematics courses, four of which must be Mathematics 105, 106, 205, and 206. (Successful completion of Mathematics 206 is sufficient to fulfill the requirements for Mathematics 105 and 106, even if no course credit for these has been granted by Bates.)The other three courses must be mathematics courses at the 150-level or above (or units at the s20 level or above). At least one of these three must be taken at Bates.

Elective courses should relate to each other with a common theme. Possible combinations include:

1) Analysis:

MATH 218. Numerical Analysis.

MATH 301. Real Analysis.

MATH 308. Complex Analysis.

2) Geometry:

MATH 312. Geometry.

MATH 313. Topology.

3) Mathematical Biology:

BI/MA 155. Mathematical Models in Biology.

MATH 219. Differential Equations.

MATH 341. Mathematical Modeling.

4) Actuarial Science:

MATH 218. Numerical Analysis.

MATH 314. Probability.

MATH 315. Statistics.

5) Statistics:

MATH 301. Real Analysis.

MATH 314. Probability.

MATH 315. Statistics.

6) Applied/Engineering Mathematics:

MATH 218. Numerical Analysis.

MATH 219. Differential Equations.

MATH 308. Complex Analysis.

MATH 341. Mathematical Modeling.

The following do not count toward the mathematics secondary concentration: Mathematics 360, 457, 458, and s50.

#### Pass/Fail Grading Option

Pass/fail grading may not be elected for courses applied toward the secondary concentration in mathematics.#### General Education

The quantitative requirement is satisfied by any of the mathematics courses or units and FYS 317. Advanced Placement, International Baccalaureate, or A-Level credit awarded by the department for mathematics, computer science, or statistics may also satisfy the quantitative requirement. Courses##### MATH 101. Working with Data.

Techniques for analyzing data are described in ordinary English without emphasis on mathematical formulas. The course focuses on graphical and descriptive techniques for summarizing data, design of experiments, sampling, analyzing relationships, statistical models, and statistical inference. Applications are drawn from everyday life: drug testing, legal discrimination cases, and public opinion polling. Not open to students who have received credit for Biology 244, Economics 250 or 255, Environmental Studies 181, Mathematics 315, Psychology 218, or Sociology 305. Enrollment limited to 30 per section. Normally offered every year. G. Coulombe, B. Shulman.##### MATH 105. Calculus I.

While the word*calculus*originally meant any method of calculating, it has come to refer more specifically to the fundamental ideas of differentiation and integration that were first developed in the seventeenth century. The subject's early development was intimately connected with understanding rates of change within the context of the physical sciences. Nonetheless, it has proven to be widely applicable throughout the natural sciences and some social sciences, as well as crucial to the development of most modern technology. This course develops the key notions of derivatives and integrals and their interrelationship, as well as applications. An emphasis is placed on conceptual understanding and interpretation, as well as on calculational skills. Graphing calculators are used in the course. Students are required to attend approximately six additional 50-minute laboratory sessions at times to be arranged. Students must read the mathematics department calculus FAQs before registering (http://abacus.bates.edu/acad/depts/math/faq.html). Enrollment limited to 25 per section. Normally offered every semester. P. Jayawant, C. Shor.