Annalisa Crannell Carmie L. and Beatrice J. Creitz Professor of Mathematics
Why I Teach Mathematics
I started teaching math for the very geeky reason that I love doing math, and I doubly love doing math with other people.
Once I got started though, I was inspired by some amazing people to broaden my outlook. Bob Moses (Civil Rights activist and developer of the Algebra Project) argued that a strong mathematical education is essential for economic justice. Master teachers Jaime Escalante and Uri Treisman transformed traditional (that is, failing) classrooms full of Latinx and African American students into communities of high-performing prowess, and in so doing they opened all our eyes to the chances to serve our own students better. I have also learned first-hand how important it is to be willing to fail wisely, to learn from those failures, and to persevere. I've come to want my role to be one that empowers all of my students--whoever that might be and whatever background they bring--as best I can, so that they can be gritty problem solvers, effective communicators, and adroit builders of community.
Mathematical Interests
I received my PhD from Brown University, writing my dissertation in the area of non-linear partial differential equations. For many years after that, I published in the area of discrete topological dynamical systems, with particular interest in quasi-continuous functions.
But my current research is much more accessible and visual. Together with students and with research colleagues, I ask questions about the applications of projective geometry to perspective art: specifically, how the heck do we project our three-dimensional world into a two-dimensional canvas?
Teaching Interests
I teach classes ranging from Calculus to Projective Geometry to Analysis, and I also enjoy including students in independent studies and research.
I have two books on the mathematics of perspective art, co-authored with my friends/colleagues Marc Frantz and Fumiko Futamura:
- Perspective and Projective Geometry (an IBL intro to proofs course for math majors)
- Viewpoints: Mathematical Perspsective and Fractal Geometry in Art (for a first year seminar)
My work on Writing within the Mathematics Curriculum includes numersous talks, articles, and the MAA book (coauthored with Elyn Rykken, Tommy Ratliff, and Gavin LaRose): Writing Projects for Mathematics Courses: Crushed Clowns, Cars, and Coffee to Go.
I am exceedingly fond of using Inquiry Based Learning in my teaching. Some of the worksheets I use in my class appear in these Course Materials pages listed below.
Talks and Presentations
- Gaining perspective on homographies (every non-affine homography is like a perspective map, and this has applications for anamorphism.)
- Math and Art: the good, the bad, and the pretty (an introduction to the geometry of perspective and viewing distance)
- In the Shadow of Desargues (part 1: background and definitions, with a hint of the proof)
- In the Shadow of Desargues (part 2: applications, including kite shadows and beach towels)
- Drawing Conclusions from Drawing a Square
- How to grade 300 Math Essays (and survive to tell the tale)
- Four and a Half Useful Methods for Grading Writing
- (Speaking in Favor of) Redundancy, Inefficiency, Extravagance, and Waste
- On Being Exquisitely Organized
- Inquiry, Encouragement, Home Cooking, and other boundary value problems (2016 Leitzel Lecture)
Videos
- Calculus II: "I'll Integrate!" (flash mob) [5:10]
- My math/art challenge problem (from the MAA) [2:30]
- Math & Art: the Good, the Bad, and the Pretty (@ St. John's U.) [52:10]
- Shadow of Desargues (@ St. John's U.) [47:58]
- Portrait of a Mathematician (by F&M) [4:00]
- Vimeo clip (by F&M) [1:43]
By my students
- Yanlin Yang '18, Summer research on Undrawable Spirals [10:42]
- Anton Arapin '19, Independent study on the Shape of a Mirror [12:39]
- Yike Gong '19, Summer research on Two-slit Cameras [9:21]
- Ellie Burkett, '20, Independent study on Hyperbola deconstructions [5:15]
- Patricia Anika, '24, Independent Study on Multiview Geometry [12:48]
Writing Projects in Math Classes
For more information, see Crannell, Annalisa, "How to Grade 300 Mathematical Essays and Survive to tell the Tale," PRIMUS 4, 3 (1994), 193-201.
Below, you can find sets of projects and solutions for PreCalculus, Calculus I, and Calculus II. Please feel free to use these materials with proper citation. If you do adopt or adapt any of these, please let me know at annalisa.crannell@fandm.edu.
Course Materials
Perspective and Projective Geometry (an IBL intro to proofs course for math majors)
Perspective and Projective Geometry
Perspective and Projective Geometry (an IBL intro to proofs course for math majors)
Perspective and Projective Geometry is an inquiry-based course designed for sophomore- and junior-level mathematics majors. The book -- developed as a collaborative project by Marc Frantz in Indiana, Fumiko Futamura in Texas, and Annalisa Crannell in Pennsylvania -- come from a project supported by NSF TUES Grand DUE-1140135, so thank you for your tax dollars! It's available from Princeton University Press.
Each worksheet in the completed book has
- a one-page picture that is also a math/art puzzle,
- a module with IBL-style in-class worksheet, and
- a homework set (with short exercises, an art project, and a proof/counter-example).
The Instructors' Manual comes with
- an instructor's section, with a guide to using the module, and
- answers to the module / homework questions.
For Instructors' Manuals, please email exam_copy@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").
Viewpoints: Mathematical Perspsective and Fractal Geometry in Art
Viewpoints: Mathematical Perspsective and Fractal Geometry in Art (for a first year seminar)
For Instructors' Manuals, please email exam_copy@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").
- Course-Follow-up Blog for Perspective Geometry
- Instrutor's Materials for a First Year Seminar on the math of art
Student Co-authors
I enjoy working with students. Not all Independent Studies result in published papers, but some do. Below are papers I have co-published with F&M students:
- with Ojima Abraham, Jihang Dai, Yike Gong, Rebecca McClain, Nithya Ramaswamy, Charles Reisner, Evan Shinn, & Shen Wang, "Perspectives Through a Two-Slit Camera'', Mathematics Intelligencer, (2022), DOI 10.1007/s00283-022-10238-2, open access via https://rdcu.be/c1H8Q.
- with Stephanie Douglas (`12), ``Drawing on Desargues,'' Mathematics Intelligencer, 34:2 (2012) 7--12.
- with M. Sohaib Alam (`07), ``Quasicontinuous functions with totally discontinuous iterates,'' Real Analysis Exchange, 33:1 (2008) 159-164.
- with Martina Mincheva ( `07), ``Reflections on Spheres,'' Math Horizons, (November 2007) 22--26.
- with Lindsay Hilbert (`04) and Stephen May ( `04), ``Shifts of Finite Type and Fibonacci Harps”, Applied Math Letters, 20:2, (2007) 138--141.
- with Jack Stewart ( `03), ``The Band around a (non)Convex Set,'' The College Mathematics Journal, 34:5 (2003) 377--379.
- with Brian Habecker ( `02), ``Using Fractals to Motivate Linear Algebra'', Undergrad. Math. and its Applications, 25:1 (2004) 47--82.
- by Melissa Shearer and Hayley Rintel ( ’00),``Math and Architecture'', JOMA 1:2, http://www.joma.org/ (2001).
- with Ben Shanfelder (`98), ``Chaotic Results for Triangular Maps of the Square,'' Mathematics Magazine, 73 (2000) 13--20.
Professional Service
I am active in several national mathematical societies, including the
- The Mathematical Association of America
- The Association for Women in Mathematics
- The American Mathematical Society
I have served on the Board of Governors of the MAA and on the Executive Council of the AWM. I've long been a mentor/consultant for early-career mathematicians through the MAA's Project NExT program.
Two of my most relevant publications for professional service include
- Applying for Jobs: Advice from the Front (and the Rear), AMS employment pages
- Starting Our Careers: A Collection of Essays and Advice on Professional Development from the Young Mathematicians' Network, co-edited with Curtis Bennett, AMS: Rhode Island (1999).
Contact Me
Mailing Address
Annalisa Crannell
F&M Mathematics
Box 3003
Lancaster, PA 17604-3003