For well over two thousand years, mathematics has been a part of the human search for understanding. Mathematical discoveries have come both from the attempt to describe the natural world and from the desire to arrive at a form of inescapable truth through careful reasoning that begins with a small set of self-evident assumptions. These remain fruitful and important motivations for mathematical thinking, but in the last century mathematics has been successfully applied to many other aspects of the human world: voting trends in politics, the dating of ancient artifacts, the analysis of automobile traffic patterns, and long-term strategies for the sustainable harvest of deciduous forests, to mention a few. Today, mathematics as a mode of thought and expression is more valuable than ever before. Learning to think in mathematical terms is an essential part of becoming a liberally educated person.

Mathematics is an engaging field, rich in beauty, with powerful applications to other subjects. Thus we strive to ensure that Kenyon students encounter and learn to solve problems using a number of contrasting but complementary mathematical perspectives: continuous and discrete, algebraic and geometric, deterministic and stochastic, theoretical and applied. In our courses we stress mathematical thinking and communication skills. And in courses where it makes sense to incorporate technological tools, our students learn to solve mathematical problems using computer algebra systems, statistical packages, and computer programming languages.

New Students

For those students who want only an introduction to mathematics, or perhaps a course to satisfy a distribution requirement, selection from MATH 105, 106, 111, 116, 128 and SCMP 118 is appropriate. Students who think they might want to continue the study of mathematics beyond one year, either by pursuing a major or minor in mathematics or as a foundation for courses in other disciplines, usually begin with the calculus sequence (MATH 111, 112, and 213). Students who have already had calculus or who want to take more than one math course may choose to begin with the Elements of Statistics (MATH 106) and Data Analysis (MATH 206) or Introduction to Programming (SCMP 118). A few especially well-prepared students take Linear Algebra (MATH 224) or Foundations (MATH 222) in their first year. (Please see the department chair for further information.)

MATH 111 is an introductory course in calculus. Students who have completed a substantial course in calculus might qualify for one of the successor courses, MATH 112 or 213. MATH 106 is an introduction to statistics, which focuses on quantitative reasoning skills and the analysis of data. SCMP 118 introduces students to computer programming.

To facilitate proper placement of students in calculus courses, the department offers placement tests that help students decide which level of calculus course is appropriate for them. This and other entrance information is used during the orientation period to give students advice about course selection in mathematics. We encourage all students who do not have Advanced Placement credit to take the placement exam that is appropriate for them.

The ready availability of powerful computers has made the computer one of the primary tools of the mathematician. Students will be expected to use appropriate computer software in many of the mathematics courses. However, no prior experience with the software packages or programming is expected, except in advanced courses that presuppose earlier courses in which use of the software or programming was taught.

Course Requirements for the Major

There are two concentrations within the mathematics major: classical mathematics and statistics. The coursework required for completion of the major in each concentration is given below.

Classical Mathematics
A student must have credit for the following core courses:

• Three semesters of calculus (MATH 111, 112, 213, or the equivalent)
• One semester of statistics (MATH 106 or 436, or the equivalent)
• SCMP 118 Introduction to Programming
• MATH 222 Foundations
• MATH 224 Linear Algebra I
• MATH 335 Abstract Algebra I or MATH 341 Real Analysis I

In addition, majors must have credit for at least three other elective courses selected with the consent of the department. MATH 110 may not be used to satisfy the requirements for the major.

Statistics
A student must have credit for the following core courses:

• Three semesters of calculus (MATH 111, 112, 213 or the equivalent)
• SCMP 118 Introduction to Programming
• MATH 222 Foundations
• MATH 224 Linear Algebra I
• MATH 336 Probability
• MATH 341 Real Analysis I
• MATH 416 Linear Regression Models or MATH 436 Mathematical Statistics

In addition to the core courses, majors must also have credit for two elective courses from the following list:

• MATH 106 Elements of Statistics
• MATH 206 Data Analysis
• MATH 216 Nonparametric Statistics
• MATH 236 Random Structures
• MATH 416 Linear Regression Models
• MATH 436 Mathematical Statistics

Applications of Math Requirement

Mathematics is a vital component in the methods used by other disciplines, and the applied math requirement is designed to expose majors to this vitality. There are two ways to satisfy the requirement:

a) Earn credit for two courses (at least 1 unit) from a single department or program that use mathematics in significant ways. Typically, majors will choose a two-course sequence from the following list; other two-course sequences require departmental approval:

• PHYS 140/145
• ECON 101/102
• PSYC 200 together with a 400-level Research Methods in Psychology course

b) Earn credit for a single math course that focuses on the development and analysis of mathematical models used to answer questions arising in other fields. The following courses satisfy the requirement, but other courses may satisfy the requirement with approval of the department:

• MATH 258 Mathematical Biology
• MATH 347 Mathematical Models

Classical mathematics majors may also use MATH 206, MATH 216, MATH 226, or MATH 416 to satisfy the requirement. Additionally, students choosing this option may not use the applied math course as one of the elective courses required for the major.

Depth Requirement

 Majors are expected to attain a depth of study within mathematics, as well as breadth. Therefore majors should earn credit in one of four two-course upper-level sequences:

• MATH 335/435 Abstract Algebra I & II
• MATH 341/441 Real Analysis I & II
• MATH 336/436 Probability and Mathematical Statistics
• MATH 336/416 Probability and Linear Regression Models

Other two-course sequences may satisfy the requirement with approval from the department.

Senior Exercise

The Senior Exercise begins promptly in the fall of the senior year with independent study on a topic of interest to the student and approved by the department. The independent study culminates in the writing of a paper, which is due in November. (Juniors are encouraged to begin thinking about possible topics before they leave for the summer.) Students are also required to take the Major Field Test in Mathematics produced by the Educational Testing Service. Evaluation of the Senior Exercise is based on the student's performance on the paper and the standardized exam. A detailed guide on the Senior Exercise is available on the math department Web site under the link "mathematics academic program."

Suggestions for Majoring in Mathematics

Students wishing to keep open the option of a major in mathematics typically begin with the study of calculus and normally complete the calculus sequence, MATH 222 (Foundations), and either SCMP 118 or MATH 106 by the end of the sophomore year. A major is usually declared no later than the second semester of the sophomore year. Those considering a mathematics major should consult with a member of the mathematics department to plan their course of study.

The requirements for the major are minimal. Anyone who is planning a career in the mathematical sciences, or who intends to read for honors, is encouraged to consult with one or more members of the department concerning further studies that would be appropriate. Similarly, any student who wishes to propose a variation of the major program is encouraged to discuss the plan with a member of the department prior to submitting a written proposal for a decision by the department.

Students who are interested in teaching mathematics at the high-school level should take MATH 230 (Geometry) and MATH 335 (Abstract Algebra I), since these courses are required for certification in most states, including Ohio.

Honors in Mathematics

Eligibility

To be eligible to enroll in the Mathematics Honors Seminar, by the end of junior year students must have completed one depth sequence (MATH 335-435, MATH 336-416, MATH 336-436, MATH 341-441) and have earned a GPA of at least 3.33, with a GPA in Kenyon mathematics courses of at least 3.6. The student must also have, in the estimation of the mathematics faculty, a reasonable expectation of fulfilling the requirements for Honors, listed below.

To earn Honors in mathematics, a student must: (1) Complete two depth sequences (see list above); (2) Complete at least six 0.5-unit courses in mathematics numbered 300 or above; (3) Pass the Senior Exercise in the fall semester; (4) Pass the Mathematics Honors Seminar MATH 498; (5) Present the results of independent work in MATH 498 to a committee consisting of an outside examiner and members of the Kenyon Mathematics Department; (6) successfully complete an examination written by an outside examiner covering material from MATH 498 and previous mathematics courses; (7) Maintain an overall Kenyon GPA of at least 3.33; (8) Maintain a Mathematics Department GPA of at least 3.6.

Awarding Honors

Based on performance in all of the above-mentioned areas, the department (in consultation with the outside examiner) can elect to award Honors, High Honors, or Highest Honors; or not to award honors at all.

Requirements for the Minors

There are two minors in mathematics. Each minor deals with core material of a part of the discipline, and each reflects the logically structured nature of mathematics through a pattern of prerequisites. A minor consists of satisfactory completion of the courses indicated.

Mathematics
The calculus sequence MATH 111, 112, 213, and four courses from the following: MATH 105, 106, 108, 116, 128, 222, 224, 227, 230, 232, 236, 258, 324, 327, 328, 333, 335, 336, 341, 347, 352, 416, 435, 441, 460, SCMP 118. (Students may count at most one of the following: MATH 105, 106, 108, 116, 128, SCMP 118.) Other courses numbered 200 or above (e.g., special-topics courses) may be counted with the consent of the department.

Statistics
Five courses in statistics from the following: MATH 106 or 116, 206, 216, 236, 336, 416, 436. (Students may count at most one statistics course from another department. For example, ECON 375 or PSYC 200 may be substituted for one of the courses listed above.)

Our goal is to provide a solid introduction to basic statistical methods, including data analysis, design and analysis of experiments, statistical inference, and statistical models, using professional software such as Minitab, SAS, Maple, and R.

Deviations from the list of approved minor courses must be ratified by the Mathematics Department. Students considering a minor in mathematics or statistics are urged to speak with a member of the department about the selection of courses.

Cross-listed course
The following course is cross-listed in biology and will satisfy the natural science requirement:
MATH 258 Mathematical Biology