Bob Milnikel

Prior to his 2002 arrival at Kenyon, Bob Milnikel studied at Carleton College and Cornell University and taught at Wellesley College. His research is focused on the mathematical analysis of logic as used in computer science. His teaching includes introductory-level courses across mathematics, CS and statistics, as well as intermediate and advanced courses in logic and proof and occasional team-teaching the Philosophy Department. He has been active in the Kenyon Educational Enrichment Program (KEEP) since 2016.

Milnikel is also active in several Kenyon and community musical ensembles, including the Kenyon Symphonic Wind Ensemble and the Knox Community Jazz Orchestra.

Areas of Expertise

Mathematical logic, justification logic, non-monotonic logic

Education

1999 — Doctor of Philosophy from Cornell University

1996 — Master of Science from Cornell University

1992 — Bachelor of Arts from Carleton College, Phi Beta Kappa

Courses Recently Taught

This course presents an introduction to computer programming intended both for those who plan to take further courses in which a strong background in computation is desirable and for those who are interested in learning basic programming principles. The course will expose the student to a variety of applications where an algorithmic approach is natural and will include both numerical and non-numerical computation. The principles of program structure and style will be emphasized. May be paired with COMP 218 or with any mathematics or statistics course to satisfy the natural science diversification requirement. No prerequisite. Offered every semester.

Our intuitions about sets, numbers, shapes and logic all break down in the realm of the infinite. Seemingly paradoxical facts about infinity are the subject of this course. We discuss what infinity is, how it has been viewed through history, why some infinities are bigger than others and how a finite shape can have an infinite perimeter. This very likely is quite different from any mathematics course you have ever taken. This course focuses on ideas and reasoning rather than algebraic manipulation, though some algebraic work will be required to clarify big ideas. The class is a mixture of lecture and discussion, based on selected readings. Students can expect essay tests, frequent homework and writing assignments. This course does not count toward any major requirement. Students who have credit for MATH 222 may not receive credit for this course. No prerequisite. Offered occasionally.

This course is a mathematical examination of the formal language most common in mathematics: predicate calculus. We examine various definitions of meaning and proof for this language and consider its strengths and inadequacies. We develop some elementary computability theory en route to rigorous proofs of Godel's Incompleteness Theorems. Concepts from model logic, model theory and other advanced topics are discussed as time permits. This counts toward the algebraic (column A) elective for the major. Prerequisite: MATH 222 or PHIL 201. Offered occasionally.

This is a team-taught course on philosophical issues in mathematics. We ask questions like "What is a number?", "What constitutes a mathematical proof?" and "How can we be certain of mathematical knowledge?" We look at the question of how something as abstract as mathematics can have any use or connection to reality. This course counts toward the epistemology requirement for the major. Permission of instructor is required. Contact either Professor Milnikel or Professor Richeimer. Prerequisite: PHIL 201 or some coursework in mathematics.

This course presents an introduction to computer programming intended both for those who plan to take further courses in which a strong background in computation is desirable and for those who are interested in learning basic programming principles. The course will expose the student to a variety of applications where an algorithmic approach is natural and will include both numerical and non-numerical computation. The principles of program structure and style will be emphasized. SCMP 118 may be paired with SCMP 218 or either may be paired with any mathematics or statistics course to satisfy the natural science diversification requirement. No prerequisite. Offered every semester.

This is a basic course in statistics. The topics covered are the nature of statistical reasoning, graphical and descriptive statistical methods, design of experiments, sampling methods, probability, probability distributions, sampling distributions, estimation and statistical inference. Confidence intervals and hypothesis tests for means and proportions are studied in the one- and two-sample settings. The course concludes with inference-regarding correlation, linear regression, chi-square tests for two-way tables and one-way ANOVA. Statistical software is used throughout the course, and students engage in a wide variety of hands-on projects. This counts toward the core course requirement for the major. Students with credit for STAT 116 cannot take STAT 106 for credit. No prerequisite. Offered every semester.