# St. Bonaventure University Faculty Profiles

# Hill, Christopher

E-mail: chill@sbu.edu

*Undergraduate Instruction*

- MATH 107. Introduction to Statistics
- MATH 111. Mathematics for Elementary Education I
- MATH 112. Mathematics for Elementary Education II
- MATH 121. Finite Mathematics for Management and Social Sciences
- MATH 122. Calculus for Management and Social Sciences
- MATH 135. Quantitative Reasoning
- MATH 151. Calculus I
- MATH 152. Calculus II
- MATH 207. Discrete Mathematics I
- MATH 208. Discrete Mathematics II
- MATH 241. Linear Algebra
- MATH 251. Calculus III
- MATH 252. Differential Equations
- MATH 281. The Problem Solving Seminar
- MATH 312. Geometry
- MATH 322. Mathematical Probability
- MATH 323. Mathematical Statistics
- MATH 351. Introduction to Real Analysis I
- MATH 413. Number Theory
- MATH 453. Complex Variables
- MATH 486. Topology

*Graduate Instruction*

- MATH 500. Mathematics for Management

*Projects Mentored*

- Mentor for Joseph Posillico's 2016/2017 Senior Comprehensive Project:
*Resolving Hilbert's Third Problem*. - Mentor for Jordan Farnham's 2015/2016 Senior Comprehensive Project:
*A Look at Fractal Dimensions and the Importance of Fractals in Finance*. - Mentor for Mitch Kovacs' 2015/2016 Senior Comprehensive Project:
*Investigation into Consecutive Integers with Equally many Distinct Prime Divisors*. - Mentor for René Sandroni's 2014/2015 Senior Comprehensive Project:
*An Exploration of a Continuous but Nowhere Differentiable Function*. - Mentor for Levi Lewis's 2014 Senior Comprehensive Project:
*Hirchhorn's Proof of Jacobi's Four-Square Theorem*. - Mentor for Samantha Humphry's 2013/2014 Senior Comprehensive Project:
*Pascal's Triangle over Certain Finite Groups*. - Mentor for Daniel Winger's 2012/2013 Senior Comprehensive Project:
*The Fourier Inversion Theorem with an Application to Quantum Mechanics*. - Mentor for Jennifer Dempsey's 2011/2012 Senior Comprehensive Project:
*Representations of Graphs Modulo n*. - Mentor for Natalya Ghostlaw's 2010/2011 Senior Comprehensive Project:
*The Creation of Random Number Generators Using Number Theory*. - Mentor for John Postl's 2010/2011 Senior Comprehensive Project:
*Riemann's Rearrangement Theorem: Proof, Illustration, and Generalization.* - Mentor for Casey Krug's 2009/2010 Senior Comprehensive Project:
*Bounds for the Partition Function*. - Mentor for John Grillo's 2008/2009 Senior Comprehensive Project:
*Deriving the Leibniz Series Using Number Theory*. - Mentor for Jayne Pollard’s 2007/2008 Senior Comprehensive Project:
*Public Key Cryptosystems*. - Mentor for Shane Randolph’s 2007/2008 Senior Comprehensive Project:
*The Central Limit Theorem*. - Faculty examiner for Kaitlin Drago’s 2005/2006 honors project:
*An Econometric Analysis of the Determinants of Credit Ratings for the Issuers of Municipal Bonds*. - Field examiner for Lindsey Besch’s 2004/2005 honors project:
*A Proof that the Standard Normal Function Cannot Be Integrated in Finite Terms*.

- Ph.D. in Mathematics, University of Illinois at Urbana-Champaign.
- Research area: number theory.
- Dissertation: Uniform distribution,
*P2*Behrend sequences, and some spaces of arithmetic functions. Advisor: Dr. A. J. Hildebrand.

- M.S. in Mathematics, Colorado State University.
- B.S. in Mathematics with a Minor in Physics, Colorado State University.

- Assistant Professor of Mathematics, St. Bonaventure University: Aug. 2003–present.
- Assistant Professor, Grinnell College, Grinnell, Iowa: July 2001–Dec. 2002.
- Assistant Professor, Furman University, Greenville, South Carolina: Sept. 2000–May 2001.
- Lecturer, Grinnell College, Grinnell, Iowa: Aug. 1998–July 2000.

*Zometool Workshops, Geometry Barn Raisings, and Projects Organized*

- Two Zometool workshops during Creative Arts Day at Coudersport Jr. Sr. High School in Coudersport, PA, on February 24, 2017. High school students explored art and mathematics by building tessellations with Zometool.
- Zometool workshop at the Challenger Learning Center of the Twin Tier Region, during the "Space Dreamers" Science Camp for 3rd-6th graders on February 21, 2017. The students built, among other projects, a large geodesic dome which was incorporated into their "Moon base."
- "Zometool as a STEAM Educational Tool," a Zometool workshop at the 2016 Art Teacher Professional Development Day at the Quick Center for the Arts, St. Bonaventure University, October 6, 2016.
- The Zometool Club at Southern Tier Catholic School, fall 2016–spring 2017.
- Zometool Camp at SBU, June 27–30, 2016. Thirteen students, ages 10–13, made 2- and 3-dimensional challenges, worked together to construct a large geodesic dome, competed to see who could make the best “spinner,” worked together to assemble a 7,200-piece work of “mathematical art” called a cantellated hypericosahedron, and made splendid projects of their own design.
- A geometry barn raising with Allegany-Limestone Central School — Spring 2016. On May 20 and 24, 2016, Linda Dodd-Nagel's 66 8th-grade students built a three-dimensional "shadow" of a four-dimensional figure called a runcitruncated hypericosahedron.
- The Connect 4 Project, which involved 87 middle school students from the Allegany-Limestone, Hinsdale, Olean, and Portville school districts working together to build the world's first stage-6 Sierpinski tetrahedron made from Zometool. The structure stands 13 feet tall and contains 32,770 parts. The project was completed on the stage in the Quick Center for Arts on May 7, 2015.
- Zometool Workshop at the Challenger Learning Center of the Twin Tier Region, during the Space Dreamers Winter Camp for 4th-7th graders, February 17, 2015.
- The Zometool Club at Southern Tier Catholic School, fall 2014 and spring 2015.
- A Geometry Barn-Raising with Southern Tier Catholic School — Fall 2014. On October 25, 2014, 5th- and 6th-grade students built a three-dimensional "shadow" of a four-dimensional figure called a cantitruncated hypericosahedron.
- Mathematics sessions in the Olean School District's STEM Enrichment Summer Camp, July 28 and 30, 2014
- A Geometry Barn-Raising with Allegany-Limestone Central School, May 20, 2014.
- Mathematics Sessions in the Olean School District's STEM Enrichment Program, March 8 and 22, 2014.
- A Geometry Barn-Raising with Allegany-Limestone Central School, Spring 2013. The event was highlighted in the cover story for the May 2013 Allegany-Limestone Central School District Newsletter.
- Mathematics Session at St. Bonaventure's 2012 Summer STEM Camp.
- Zometool Workshop & Geometry Barn-Raising at St. Bonaventure, Fall 2011.

*Recent Talks*

- Banquet talk at the Spring 2013 Mathematical Association of America Seaway Section Meeting at SUNY Fredonia. “The
*abc*Conjecture and Beyond.”

*Grants*

- Martine Grant (with Jeff Peterson and Denny Wilkins):
*Development of Proposed Curricular Changes to Improve the Effectiveness of a Quantitative Reasoning Requirement at St. Bonaventure University*. Grant was for $3600. (2007/2008) - Martine Grant (with Jeff Peterson and Denny Wilkins):
*An Evaluation of the Effectiveness of the Quantitative Reasoning Requirement at St. Bonaventure University*. Grant was for $6000.(2006/2007)

*Additional Accomplishments*

- Hill, C. (July, 1999). Uniform distribution modulo one on subsequences,
*Proceedings of the American Mathematical Society*. *College of Liberal Arts and Sciences Award for Excellence in Undergraduate Teaching*, received as a graduate teaching assistant at the University of Illinois at Urbana/Champaign.*Departmental Award for Excellence in Teaching Mathematics*, received as a graduate teaching assistant at UIUC.

My goals as a teacher are to help students become independent thinkers and to help them develop the skills and the confidence needed to tackle challenging problems. Accordingly, my philosophy of teaching is characterized by the Socratic method, small-group work, and problem-solving strategies.

When the instructor poses questions to his or her students, be it in class or during office hours, the students become active, rather than passive, participants in their learning. During office hours, an instructor can tailor the questions to the needs of a particular student. The instructor’s queries can be designed so that it is the *student*who discovers the key that unlocks the problem at hand. I've observed again and again that students are capable of more than they realize.

An instructor can ask only so many questions during the lecture. Inevitably, most of the time most of the students are not involved in the discussion. Small-group work is a way for nearly all of the students to be active participants in their learning nearly all of the time. As students work together in groups of about three on a worksheet or project, they are providing themselves with examples, making mistakes without being penalized, talking mathematics, and meeting their classmates.

Every problem contains within it a lesson. Author Richard Bach puts it this way: *There is no such thing as a problem without a gift for you in its hands. You seek problems because you need their gifts.* The lessons lurking within a mathematics problem are the principles that we apply to solve the problem, whose utility extends to countless other problems. These “gifts” are called *problem-solving strategies*. Although students encounter a vast number of problems during a mathematics course, only a small number of problem-solving strategies, in conjunction with basic knowledge of course material, are required to tackle almost all of them. By unlocking so many problems simultaneously, problem-solving strategies help to demystify mathematics. I strive to point out key strategies as they arise in the problems that I work for my students.

I am deeply interested in community outreach. I have organized several Zometool workshops, "geometry barn raisings," and projects with middle school and high school students and am looking for opportunities to do more. For more information, please see my webpage of Zometool Resources.

To promote mathematical problem-solving at St. Bonaventure, I created and teach MATH 281. The Problem Solving Seminar, run the Bona's Bonus Problems Program, and act as the local supervisor for the Putnam Mathematics Competition and the University of Rochester Mathematical Olympiad.

Dr. Jeff Peterson, Dr. Denny Wilkins, and I have worked on an extended project on improving the quantitative literacy of students at St Bonaventure University. In particular, we studied the effectiveness of the quantitative reasoning requirement in the Clare College curriculum (the core curriculum of St. Bonaventure). Our project was funded by 2006/2007 and 2007/2008 Martine Grants. In the spring of 2013, we created a new course, MATH 135. Quantitative Reasoning, which is a foundational course in quantitative literacy.

I am deeply interested in community outreach. I have organized several Zometool workshops, "geometry barn raisings," and projects with middle school and high school students and am looking for opportunities to do more. For more information, please see my webpage of Zometool Resources.

I'm fascinated by the visual presentation of information, so I often pursue projects and activities that may be characterized in this way. For example, I organize the Arts & Sciences Exposition, I created and maintain the website for *The Laurel* (St. Bonaventure's campus literary magazine), and I'm the principal academic web editor for the university. I love cinema and I'm *gradually* learning American Sign Language.