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 also bridges math and CS, including algebra and calculus courses as well as logic and introductory programming.

Bob is also active in several of Kenyon's musical ensembles. His Chicago area roots engendered an enduring fondness for good pizza and hapless baseball teams.

### 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

INDS 100

## Data Analysis: Seeing w/ Data

#### INDS 100

In this course, students will gain experience analyzing, interpreting, and critiquing quantitative claims and communicating results and conclusions using graphical representations of data. Examples will be drawn from across the natural and social sciences, with context provided for each data set, so that students from any disciplinary background can participate in and benefit from this course. This course has no pre-requisites. It will be taught at a level accessible to all Kenyon students. Excellent preparation for further work on quantitative topics, this course will hone students' ability to apply mathematical techniques including graphing, statistics, linear and non-linear regression, and modeling the graphical behavior of mathematical functions to understanding and interpreting data. Students will practice these skills by engaging in critical reading of primary sources, oral presentation of quantitative data, and expression of analytic ideas in writing. Assessment will be based on in-class assignments, monthly quizzes, and oral reports on data-driven projects selected in consultation with the instructor.

MATH 105

## Surprises at Infinity

#### MATH 105

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 will 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 will be 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 will be a mixture of lecture and discussion, based on selected readings. Students can expect essay tests, frequent homework and writing assignments. No prerequisite. Generally offered every other year.

MATH 111

## Calculus I

#### MATH 111

The first in a three-semester calculus sequence, this course covers the basic ideas of differential calculus. Differential calculus is concerned primarily with the fundamental problem of determining instantaneous rates of change. In this course we will study instantaneous rates of change from both a qualitative geometric and a quantitative analytic perspective. We will cover in detail the underlying theory, techniques and applications of the derivative. The problem of anti-differentiation, identifying quantities given their rates of change, also will be introduced. The course will conclude by relating the process of anti-differentiation to the problem of finding the area beneath curves, thus providing an intuitive link between differential calculus and integral calculus. Those who have had a year of high school calculus but do not have advanced placement credit for MATH 111 should take the calculus placement exam to determine whether they are ready for MATH 112. Students who have 0.5 units of credit for calculus may not receive credit for MATH 111. Prerequisite: solid grounding in algebra, trigonometry and elementary functions. Offered every semester.

MATH 112

## Calculus II

#### MATH 112

The second in a three-semester calculus sequence, this course has two primary foci. The first is integration, including techniques of integration, numerical methods and applications of integration. This study leads into the analysis of differential equations by separation of variables, Euler's method and slope fields. The second focus is the notion of convergence, as manifested in improper integrals, sequences and series, particularly Taylor series. Prerequisite: MATH 111 or AP score of 4 or 5 on Calculus AB exam or an AB subscore of 4 or 5 on the Calculus BC exam or permission of instructor. Offered every semester.

MATH 222

## Foundations

#### MATH 222

This course introduces students to mathematical reasoning and rigor in the context of set-theoretic questions. The course will cover basic logic and set theory, relations — including orderings, functions and equivalence relations — and the fundamental aspects of cardinality. The course will emphasize helping students read, write and understand mathematical reasoning. Students will be actively engaged in creative work in mathematics. Students interested in majoring in mathematics should take this course no later than the spring semester of their sophomore year. Advanced first-year students interested in mathematics are encouraged to consider taking this course in their first year. Students wanting to do so should contact a member of the mathematics faculty. Prerequisite: MATH 213 or permission of instructor. Offered every spring semester.

MATH 322

## Mathematical Logic

#### MATH 322

This course is a mathematical examination of the formal language most common in mathematics: predicate calculus. We will examine various definitions of meaning and proof for this language and will consider its strengths and inadequacies. We will 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 will be discussed as time permits. Prerequisite: MATH 222 or PHIL 201 or permission of instructor. Offered occasionally.

MATH 498

## Senior Honors

#### MATH 498

This course will consist largely of an independent project in which students read several sources to learn about a mathematical topic that complements material studied in other courses, usually an already completed depth sequence. This study will culminate in an expository paper and a public or semi-public presentation before an audience consisting of at least several members of the mathematics faculty as well as an outside examiner. Permission of department chair required. Prerequisite: Senior standing and at least one "depth sequence" completed.

PHIL 391

PHIL 493

## Individual Study

#### PHIL 493

Individual studies are offered to those students who are highly motivated in a specific area of inquiry and who are judged responsible and capable enough to work independently. Such courses might be research oriented, but more usually are readings-oriented, allowing students to delve in greater depth into topics that interest them or which overlap or supplement other courses of the philosophy department. Students must seek permission of the instructor and department chair before enrolling. They are urged to do this in the semester prior to the one in which they hope to be enrolled. Individual study is at the discretion of the instructor, and schedules may limit such an addition. An individual study cannot duplicate a course or area being concurrently offered. Exceptions to this rule are at the discretion of the instructor and chair. Individual study is usually considered an advanced course. Required work should be viewed as on a par with a seminar or a 300- or 400-level course. The instructor and student(s) should establish and agree upon the extent and nature of the work expected. The work may take one of the following forms: several short papers, one long paper, one in-depth project, a lengthy general outline and annotated bibliography, public presentation(s), etc. An individual study can apply to the major or to the minor with permission of the department. Individual studies may be taken for either 0.25 or 0.50 credits. This decision must be agreed upon with the instructor. The student(s) and instructor will meet on a regular basis. The frequency of contact hours is to be determined by the instructor in consultation with the student. Because students must enroll for individual studies by the end of the seventh class day of each semester, they should begin discussion of the proposed individual study preferably the semester before, so that there is time to devise the proposal and seek departmental approval before the established deadline.\n

STAT 106

## Elements of Statistics

#### STAT 106

This is a basic course in statistics. The topics to be 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 will be 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 will be used throughout the course, and students will be engaged in a wide variety of hands-on projects. No prerequisite. Offered every semester.

### Academic & Scholarly Achievements

Forthcoming

"Group Activities for Math Enthusiasts," coauthored with Judy Holdener, *PRIMUS*.

2015

"A New Angle on an Old Construction," *Mathematics Magazine*, 88:4, October 2015.

2014

"The Logic of Uncertain Justifications," *Annals of Pure and Applied Logic*, 165:1, January 2014.

2013

"The Logic of Uncertain Justifications" (preliminary report), Proceedings of the International Symposium on the Logical Foundations of Computer Science, January 2013.

2012

"Conservativity in Logics of Justified Belief: Two Approaches," Annals of Pure and Applied Logic, 163:7, July 2012.

2009

"Conservativity in Logics of Justified Belief," Presented at LFCS '09, Spring Verlag series LNCS 5407, 2009.

2007

"Derivability in the Logic of Proofs is $\Pi^p_2$-complete," *Annals of Pure and Applied Logic*, 145:3, 223-239, March 2007.

2005

"Sequent Calculi for Skeptical Reasoning in Predicate Default Logic and Other Nonmonotonic Systems," *Annals of Mathematics and Artificial Intelligence* 44:1, 1-34, 2005.

2004

"A Sequent Calculus for Skeptical Reasoning in Autoepistemic Logic," Presented at the 10th International Symposium on Nonmonotonic Reasoning, June 2004.

2003

"Embedding Modal Nonmonotonic Logics into Default Logic," *Studia Logica*, 75, 377-382, 2003.

2003

"The Complexity of Predicate Default Logic Over a Countable Domain," *Annals of Pure and Applied Logic,* 120, 151-163, April 2003.

2003

"A Sequent Calculus for Skeptical Reasoning in Predicate Default Logic" (extended abstract), Presented at ECSQARU 2003, Proceedings Springer-Verlag LNCS 2711.

2001

"Skeptical Reasoning in FC-Normal Logic Programs is $\Pi^1_1$-Complete," *Fundamenta Informaticae,* 45, 237-252, 2001.