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An Inquiry-Based, workbook style, introduction to projective geometry via perspective art puzzles, for mathematics majors.
Each chapter begins with a drawing puzzle that leads to geometric definitions and explorations, and concludes with a trifecta of short-answer exercises, proofs/ counter-examples, and drawing/photography assignments.
A comprehensive instructor's manual is available upon request; see below for more information.
Coauthored with Marc Frantz and Fumiko Futamura
An undergraduate textbook devoted exclusively to relationships between mathematics and art, Viewpoints is ideally suited for math-for-liberal-arts courses and mathematics courses for fine arts majors. The textbook contains a wide variety of classroom-tested activities and problems, a series of essays by contemporary artists written especially for the book, and a plethora of pedagogical and learning opportunities for instructors and students.
A comprehensive instructor's manual is available upon request; see below for more information.
Coauthored with Marc Frantz
For Instructors' Manuals for the books above, please email textbooks@press.princeton.edu with the subject line “Solution Manual Request.” Please include your name, institution, a complete university shipping address, course name, enrollment, and semester, along with the book’s title, ISBN and/or author (e.g., "Viewpoints: Mathematical Perspective and Fractal Geometry in Art, ISBN 9780691125923" or "Perspective and Projective Geometry, ISBN 9780691196565").
Suitable for a wide range of undergraduate mathematics courses, from a survey of mathematics to differential equations.
The stories are sometimes fanciful and sometimes grounded in standard scientific applications. Students see these problems as 'real' in a way that textbook problems are not, even though many of the characters involved (e.g. detectives and CEOs) are obviously fictional.
Coauthored with Elyn Rykken, Tommy Ratliff, and Gavin LaRose; published by the MAA Press and available from the AMS bookstore
This “how-to” book addresses all aspects of a young mathematician's early career development: How do I get good letters of recommendation? How do I apply for a grant? How do I do research in a small department that has no one in my field? How do I do anything meaningful if all I can get is a series of one-year jobs?
Co-edited with authored with Curtis Bennett; available from the AMS bookstore
Journal Articles
Journal Articles
Mathematics and Art
Mathematics and Art
“Perspectives Through a Two-Slit Camera”, with 8 students: Ojima Abraham, Ji-hang Dai, Yike Gong, Rebecca McClain, Nithya Ramaswamy, Charles Reisner, Evan Shinn & Shen Wang, The Mathematical Intelligencer (2022), DOI 10.1007/s00283- 022-10238-2 open access via https://rdcu.be/c1H8Q
“Factoring a Homography to Analyze Projective Distortion,” with F. Futamura and M. Frantz, Journal of Mathematical Imaging and Vision, 61(7), 967–989, (2019) DOI 10.1007/s10851-019-00881-4
An (Isometric) Perspective on Homographies, with F. Futamura and M. Frantz, Journal for Geometry and Graphics 23 (2019), No. 1, 065–083
“Looking Through the Glass”. In: Sriraman B. (eds) Handbook of the Mathematics of the Arts and Sciences, Springer, Cham (2019) https://doi.org/10.1007/978-3-319-70658-0_41-1
“The image of a square” with F. Futamura and M. Frantz, The American Mathematical Monthly; 124:2 (2017), pp. 99-115;
also http://dx.doi.org/10.4169/amer.math.monthly.124.2.99
“The cross ratio as a shape parameter for Dürer’s solid” with F. Futamura and M. Frantz, Journal of Mathematics and the Arts, 8:3–4 (2014) 111-119; also online at http://dx.doi.org/10.1080/17513472.2014.974483.
“Durer: disguise, distance, disagreements, and diagonals!” with F. Futamura and M. Frantz, Math Horizons (November 2014) 8–11.
This article was selected for inclusion in the annual series The Best Writing on Mathematics, Mircea Pitici, ed., The Princeton University Press: Princeton, N.J. (2015) 132–140.
“Drawing on Desargues” with Stephanie Douglas (F&M ‘12), Mathematics Intelligencer, 34:2 (2012) 7–12.
“Review of the 2012 Mathematical Meetings Exhibition on Mathematical Art”, Journal of Mathematics and Art, 6:4 (Dec. 2012) 211–217.
“The Shad-Fack Transom Window Problem”, College Mathematics Journal, 42:4 (September 2011) 309–316.
“Perspective in Math and Art”, Inside Higher Ed, July 18, 2011 at http://www.insidehighered.com/views/2011/07/18/essay on using art to teach mathematics
“Perspective drawings of reflective spheres”, Journal of Mathematics and the Arts, 5:2 (2011), 71–85.
“Reflections on Spheres” with Martina Mincheva (F&M ‘07), Math Horizons, (November 2007) 22–26.
“Three-point perspective and plane geometry” with Marc Frantz, Journal of Mathematics and the Arts, 1:4 (2007) 213–223, https://doi.org/10.1080/17513470701884180
“Where the Camera Was, Take Two”, Mathematics Magazine, 79:4 (2006) 306–308. “Hands-On Perspective”, Marc Frantz, Annalisa Crannell, Dan Maki, and Ted Hodgson, NCTM’s Mathematics Teacher, 99:8 (2006), 554–559.
“Mathematics and Baseball and Art”, an invited submission to the National Math Awareness Month web pages, http://mathforum.org (April 2003).
Topological Dynamics
Topological Dynamics
“Quasicontinuous functions with totally discontinuous iterates”, with M. Sohaib Alam (F&M ‘07), Real Analysis Exchange, 33:1 (2008) 159-164.
“Shifts of Finite Type and Fibonacci Harps”, with Lindsay Hilbert (F&M ‘04) and Stephen May (F&M ‘04), Applied Math Letters, 20:2, (2007) 138–141.
“Closed Relations and Equivalence Classes of Quasicontinuous Functions”, with Marc Frantz and Michelle LeMasurier, Real Analysis Exchange, 31:2, (2006) 409–424.
“The Band around a (non)Convex Set” with Jack Stewart (F&M ‘03), The College Mathematics Journal, 34:5 (2003) 377–379.
“Set-wise semicontinuity and Pi-related Topologies” with Ralph Kopperman, Real Analysis Exchange, 26: 2 (2000/01) 609–622.
“Chaotic Results for Triangular Maps of the Square” with Ben Shanfelder (F&M ‘98), Mathematics Magazine, 73 (2000) 13–20.
“Dynamics of Quasicontinuous Systems” with Mario Martelli, Journal of Difference Equations and Applications, 6 (2000) 351–361.
“A Chaotic, Non-mixing subshift”, Proceedings of the International Conference on Dynamical Systems and Differential Equations, an added volume to“Discrete and Continuous Dynamical Systems,” Southwest Missouri State University I (1998) 195– 202.
“Periodic Orbits from Non Periodic Orbits on the Interval”, with Mario Martelli, Applied Mathematics Letters, 10: 6 (1997) 45–47.
“The Role of Transitivity in Devaney’s Definition of Chaos”, American Mathematical Monthly, 102 (1995) 788–793.
“The Existence of Many Periodic, Non-traveling Solutions to the Boussinesq Equation”, J. Differential Equations, 126: 2 (April 1996) 169–183.
Pedagogy
Pedagogy
“(Speaking in favor of) Redundancy, Inefficiency, Extravagance, and Waste, MAA FOCUS, 28:2 (2008), 21–23.
[This was the text of my invited talk upon the receipt of the Haimo Teaching Award.]
“A Course on Size and Structure”, PRIMUS, 13: 3 (2004) 209–222.
“Using Fractals to Motivate Linear Algebra”, with Brian Habecker (F&M ‘02), Undergrad. Math. and its Applications, 25:1 (2004) 47–82.
“Assessing Expository Mathematics: Grading Journals, Essays, and Other Vagaries”, Assessment Practices in Mathematics, MAA Notes 49 (1999) 113–115.
“Collaborative Oral Take-Home Exams”, Assessment Practices in Mathematics, MAA Notes 49 (1999) 143–145.
“How to Grade 300 Math Essays and Survive to Tell the Tale”, PRIMUS, 4: 3 (1994) 193–204.
“How to Grade 300 Math Essays and Survive to Tell the Tale”, reprinted in Instructor’s Resource Manual for Calculus (from Graphical, Numerical, and Symbolic Points of View), Harcourt Brace and Company, Osterbee and Zorn, eds (1996) 97–108.
In service to the profession
In service to the profession
"Mathematicians and Money Management," Math Values blog, https://www.mathvalues.org/masterblog/mathematicians-and-money-management, (August 15, 2024).
“Applying for Jobs: Advice from the Front (and the Rear)”, EIMS, AMS, and at http://www.ams.org/employment/job-articles.html (October 2004).
“Career Information” in Encyclopedia of Math. Ed., Louise Grinstein and Sally J. Lipsey (eds), Rutledge Flamer, New York (2001) p. 103–7.
“Graduate Students, Young Faculty, and Temporary Positions: A Tangled Issue”, in January/February 1998 issue of AAUP Academe.
Preparing for Careers in Mathematics [co-editor with Allyn Jackson], a video distributed by the AMS, Providence (1996).
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