For more than 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 and statistics have 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, 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.
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 SCMP 118.
Students wanting to continue the study of mathematics beyond one year, either by pursuing a major or minor in mathematics 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 who want to take more than one math course may choose to begin with STAT 106 and 206 or SCMP 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. 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. 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 will be expected to use appropriate computer software in many of the mathematics and statistics 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.
Use the major requirements found in the archived course catalog.
There are three different areas of emphasis within the mathematics 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:
Beyond the core requirements, there 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.
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 at 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 will sign 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 336 Probability |
MATH 347 Mathematical Modeling |
STAT 206 Data Analysis |
| MATH 435 Abstract Algebra II | MATH 441 Real Analysis II |
MATH 236 Random Structures |
MATH 258 Mathematical Biology | STAT 436 Mathematical Stats |
| MATH 327 Number Theory | MATH 360 Topology | MATH 328 Coding Theory |
SCMP 218 Data Structures |
STAT 416 Linear Regression |
| MATH 328 Coding Theory | MATH 230 Geometry | MATH 327 Number Theory |
MATH 333 Applied Differential Equations | STAT 216 Nonparametrics |
| MATH 322 Mathematical Logic | MATH 352 Complex Functions | MATH 227 Combinatorics |
MATH 324 Applied Linear Algebra |
|
| MATH 336 Probability | MATH 368 Design and Analysis of Algorithms |
MATH 348 System and Software Design | ||
| MATH 330 Principles of Applied Math | ||||
Additionally, (only) one of the following courses offered outside of the Department of Mathematics and Statistics may be counted towards Column D:
The math major's choice of column determines both the area of emphasis and the area of focus within the mathematics major.
1. Classical Mathematics
To earn a math major with an emphasis in classical mathematics, the student must choose an area of focus residing within Category 1 in the above table. So, for example, a math major taking three courses from the first column would be a math major with 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 residing in column D. Applied mathematics will also be the area of focus for this student.
3. Statistics
To earn a math major with an emphasis in statistics, the student must take three courses from column E. Statistics will also be the area of focus for this student.
Majors are expected to attain a depth of study within mathematics. To this end, every major must take at least two courses at or above the 300 level. At least one of these 300- or 400-level courses must reside 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 at least two different columns that are not the area of focus. (These courses must not also be listed within the area of focus.) Additionally, every major must take at least one course from Category I and one course from Category II.
For instance, a student that is pursuing a mathematics 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 reside in Category II. Neither of these two additional courses can be Probability (MATH 336) because the course resides 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 (including the Senior Seminar), three courses in an area of focus and two additional courses outside the area of focus and spanning Categories I and II. Students with IB or AP credit can place out of some of the introductory core coursework, and this will decrease the number of required courses to a number less 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. While seniors will be studying their topics individually, all must be enrolled in the Senior Seminar during this fall semester as it will provide the structure and a timeline for completing the paper. Juniors are encouraged to begin thinking about possible topics before they leave for the summer. Students are required to take the Major Field Test in Mathematics produced by the Educational Testing Service. Evaluation of the Senior Capstone is based on the student's performance on the paper and the standardized exam. Detailed information on the Senior Capstone is available on the mathematics 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 SCMP 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 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 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 the following:
To earn honors in mathematics, a student must:
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 minor 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:
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 approved 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.
Transfer credit from other institutions, and the applicability of this credit to the major or minor, must be approved by the department chair.
The following course is cross-listed in biology and will satisfy the natural science requirement: