Requirements: Mathematics and Statistics
Natural Sciences Division
For more than 2,000 years, mathematics has been a part of the human search for understanding. Mathematical discoveries have come from both the attempt to describe the natural world and 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 and statistics have been successfully applied to many other aspects of the human world: voting trends in politics, dating of ancient artifacts, analysis of automobile traffic patterns and long-term strategies for the sustainable harvest of deciduous forests, to mention a few. Today, statistics 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 and statistics are engaging fields, 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 and statistical thinking and communication skills. In courses where it makes sense to incorporate technological tools, our students learn to solve problems using computer algebra systems, statistical packages and computer programming languages.
- New Students
- Requirements for the Majors
- Senior Capstone
- Suggestions for Majoring
- Requirements for the Minors
- Transfer Credit
- Cross-listed Courses
Those students interested only in an introduction to mathematics or statistics or a course to satisfy a distribution requirement may select from MATH 105, 111, 128, STAT 106, 116 and COMP 118.
First-year students who are interested in majoring in mathematics or statistics are encouraged to enroll in MATH 100.
Students wanting to continue the study of mathematics or statistics beyond one year, by pursuing a major or minor or 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 want to take more than one math course may choose to begin with STAT 106 and 206 or COMP 118. A few well-prepared students may take MATH 222 or 224 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. STAT 106 is an introduction to statistics, which focuses on quantitative reasoning skills and the analysis of data. COMP 118 introduces students to computer programming.
To facilitate proper placement in calculus courses, the department offers tests that help students decide which level of calculus is appropriate for them. This and other entrance information is used during Orientation to give students advice about course selection in mathematics and statistics. We encourage all students who do not have Advanced Placement credit to take the placement exam that is appropriate for them. Students who have Advanced Placement credit for STAT 106 should consider enrolling in STAT 206 or 216.
The ready availability of powerful computers has made the computer one of the primary tools of the mathematician and absolutely indispensable for the statistician. Students are expected to use appropriate computer software in many of the mathematics and statistics courses. However, no 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.
There are three different areas of emphasis within the major: classical mathematics, applied mathematics and statistics. Regardless of one's concentration, all math majors are required to complete the same eight core courses.
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 (STAT 106, 116 or the equivalent)
- One semester of computer programming (COMP 118 or PHYS 270)
- MATH 222: Foundations
- MATH 224: Linear Algebra
Beyond the core are three other types of requirements: the "area of focus" requirement, the "depth" requirement and the "breadth" requirement. It is the "area of focus" requirement that determines a student's emphasis within the math major.
Area of Focus Requirement
Every math major is required to take at least three courses from a single column in the table given below. Additionally, at least one of those courses must be a MATH or STAT course at or above the 300 level. (Note: special topics courses may also count toward a major's area of focus, even though they are not listed in the table; the department chair signs off on such courses when appropriate.)
|Category I||Category II|
|A. Algebraic||B. Continuous/ Analytic||C. Discrete/ Combinatorial||D. Computational/ Modeling/ Applied||E. Statistical/ Data Science|
|MATH 335 Abstract Algebra I||MATH 341
Real Analysis I
|MATH 435 Abstract Algebra II||MATH 441
Real Analysis II
|STAT 436 Mathematical Stats|
|MATH 327 Number Theory||MATH 360 Topology||MATH 327
|MATH 328 Coding Theory||MATH 230 Geometry||MATH 227
Applied Differential Equations
|STAT 216 Nonparametrics Statistics|
|MATH 322 Mathematical Logic||MATH 352
Principles of Applied Math
Statistical Computing in R
|MATH 336 Probability||STAT 306
Topics in Statistics
The major's choice of column determines both the area of emphasis and the area of focus within the major.
1. Classical Mathematics
To earn a math major with an emphasis in classical mathematics, the student must choose an area of focus within Category 1. For example, a math major taking three courses from the first column would have an emphasis in classical mathematics and a focus on algebra.
2. Applied Mathematics
To earn a math major with an emphasis in applied mathematics, the student must take three courses in column D. Applied mathematics is also the area of focus for this student.
To earn a math major with an emphasis in statistics, the student must take three courses from column E. Statistics is also the area of focus for this student.
Majors are expected to attain a depth of study within mathematics or statistics. To this end, every major must take at least two MATH or STAT courses at or above the 300 level. At least one of these 300- or 400-level courses must be within the major's area of focus.
Majors are also expected to attain a breadth of knowledge spanning pure and applied mathematics and statistics. Hence, every major must take courses in at least two different columns that are not the area of focus. (These courses must not also be listed within the area of focus.) A course listed in two columns may be counted only once. Additionally, every major must take at least one course from Category I and one course from Category II.
For instance, a student pursuing a major with an emphasis in classical mathematics and a continuous/analytic focus must choose a course from each of two columns besides column B, and at least one of these columns must be in Category II. Neither of these additional courses can be MATH 336 (Probability) because it is in the student's area of focus.
To summarize, a student earning a major in mathematics will take (or have credit for) at least 13 courses: eight core courses, three courses in an area of focus and two additional courses outside the area of focus and spanning Categories I and II. Students with AP credit can place out of some of the introductory core coursework, decreasing the number of required courses to fewer than 13.
The Senior Capstone 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 should begin thinking about possible topics before they leave for the summer. Evaluation of the Senior Capstone is based on the student's performance on the paper. Detailed information on the Senior Capstone is available on the department website.
Students wishing to keep open the option of a major in mathematics and statistics typically begin with the study of calculus and normally complete the calculus sequence, MATH 222 and either COMP 118 or STAT 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 and statistics major should consult with a member of the mathematics and statistics 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 intends to read for honors is encouraged to consult with one or more members of the department concerning further appropriate studies. 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.
Students who are interested in teaching mathematics at the high-school level should take MATH 230 and 335, since these courses are required for certification in most states, including Ohio.
To be eligible to enroll in the "Mathematics Honors Seminar" by the end of junior year, students must have:
- Completed one of the following yearlong sequences: MATH 335/435, MATH 336/STAT 416, MATH 336/STAT 436 or MATH 341/441
- Earned an overall Kenyon GPA of at least 3.33
- A GPA in Kenyon mathematics and statistics courses of at least 3.6
- In the estimation of the mathematics and statistics faculty, a reasonable expectation of fulfilling the requirements to earn honors (listed below)
To earn honors students must:
- Indicate interest in pursuing honors in their capstone proposal
- Complete two of the yearlong sequences: MATH 335/435, MATH 336/STAT 416, MATH 336/STAT 436 or MATH 341/441
- Complete at least six courses in mathematics and statistics numbered 300 or above
- Pass the Senior Capstone in the fall semester
- Pass MATH 498 (Mathematics Honors Seminar) or STAT 498 (Statistics Honors Seminar)
- Present the results of independent work in MATH 498 or STAT 498 to a committee consisting of an outside examiner and members of the mathematics and statistics department
- Successfully complete an examination written by an outside examiner covering material from MATH 498 and previous mathematics or statistics courses
- Maintain an overall Kenyon GPA of at least 3.33
- Maintain a GPA in mathematics courses of at least 3.6
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.
There are two minors in mathematics and statistics. Each deals with core material of a part of the discipline, and each reflects the logically structured nature of the subject through a pattern of prerequisites. A minor consists of satisfactory completion of the following courses:
- The calculus sequence MATH 111, 112, 213 or the equivalent
- Four other courses offered by the Department of Mathematics and Statistics. COMP 118 and/or COMP 218 may also be used toward this requirement. Of these four other courses, students may count at most one at the 100 level.
- STAT 106: Elements of Statistics, STAT 116: Statistics in Sports
or an equivalent introductory statistics course
- STAT 206: Data Analysis
- Three courses from the following:
- MATH 258: Mathematical Biology
- MATH 336: Probability
- STAT 216: Nonparametric Statistics
- STAT 226: Statistical Computing with R
- STAT 306: Topics in Statistics
- STAT 416: Linear Regression Models
- STAT 436: Mathematical Statistics
- Students may count at most one statistics course from another department. ECON 205 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.
Deviations from the list of approved minor courses must be approved by the department. Students considering a minor in mathematics or statistics are urged to speak with a member of the department about the selection of courses.
Transfer credit from other institutions, and the applicability of this credit to the major or minor, must be approved by the department chair. Majors may count off-campus studies courses toward the major, with approval of the department chair. Ordinarily, no more than one unit of such credit is allowed. Moreover, OCS transfer credit ordinarily does not count as one of the two 300- or 400-level courses required for the depth requirement or the area of focus.
The following course is cross-listed in biology and satisfies the natural science requirement:
- MATH 258: Mathematical Biology