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Curriculum Vitae January 2024

sarah-marie belcastro

Drexel Hill, PA
Citizenship: United States


(if you want more than is here, just ask; this is the short version...)


Ph.D. The University of Michigan, Ann Arbor, MI, May 1997

M.S. The University of Michigan, Ann Arbor, MI, May 1993

B.S. Haverford College, Haverford, PA, May 1991

Professional Experience:

Director, MathILy (serious Mathematics Infused with Levity),    February 2013--present

Designed 5-week intensive residential summer program for excellent secondary mathematics students, with focus on applicable pure mathematics and core curriculum of linear algebra, combinatorics, and graph theory. Created website, outlined curriculum, and wrote inquiry-based learning instructor training materials.
Annually: write new Exam Assessing Readiness, recruit students and staff, evaluate applications, teach college- and graduate-level courses for 7 hours/day for 5 weeks, coordinate mathematical visitors, mentor Apprentice Instructors and students and alumni, write program reports, write narrative evaluations of students and staff, and update website. Envision and coordinate program enhancements, expansions, finances, and outreach. Facilitate and contribute to administration of the companion programs MathILy-Er (MathILy, Earlier) and the MathILy-EST (MathILy, Early Scholarly Training) REU.
Falls 2021--23: Taught online topics course for program alumns (topological graph theory, groups and rings, tilings and patterns).

Instructor, The Art of Problem Solving Online School, Sept 2012--present

Introduction to Counting and Probability, Introduction to Number Theory, Intermediate Counting and Probability, Intermediate Number Theory, Calculus---classes are taught by inquiry in a text chat room, using Art of Problem Solving curriculum.

Visiting Assistant Professor/Lecturer, Mount Holyoke College, South Hadley, MA. Falls 2020, 2017, Sept. 2009--May 2010

Discrete Mathematics, Fall 2020, Spring 2010---highly interactive course with focus on combinatorics and graph theory content as the context for learning to create and write proofs; intensive online synchronous course in 2020.

Graph Theory, Fall 2017---used fundamental questions of graph theory to motivate student-driven explorations, supplemented with Trudeau and Wilson texts.

Calculus II, Fall 2009, Spring 2010---supplemented Stewart text with sections of Calculus in Context and Hughes-Hallett texts and Mathematica labs; frequent in-class cooperative learning; both individual and group homework.

Lecturer, University of Massachusetts-Amherst, Amherst, MA, Fall 2019, Fall 2018, 2015--16, and Jan. 2011--Aug. 2012

Calculus I, Calculus II, Calculus III---ttaught 55-student sections of the multisection Engineering Calculus course sequence each semester, using Stewart text and some cooperative learning in class. Assisted in mentoring teaching assistants. Wrote coursewide exam rubrics. Also Calculus III Honors (single section, 25 students).

Linear Algebra---taught 55-student sections of the course, using Lay text and cooperative learning in class.

Mathematics Triple---part of the UMass Summer College pilot program. Designed and taught two 2-credit courses for gifted high-school students at the mathematics major level.

Research Affiliiate, Smith College, Northampton, MA. June 2008--2025
Visiting Assistant Professor / Lecturer, Smith College
, Northampton, MA, Spring 2017, Feb. 2006--June 2008
Associate Director, Center for Women in Mathematics, Smith College, July 2007--June 2008

Modern Algebra, Spring 2017---used Judson's text for group and ring theory, with frequent in-class inquiry-based and cooperative learning; take-home exams.

Linear Algebra, Springs 2006, 2007, 2008---used cooperative learning in class; in-class and take-home exams; focus on building proof-writing skills with examples and exercises taken from applications; frequent student presentations required; Mathematica and web applets for computation.

The Mathematics of Knitted Objects, Interterm 2008---introduced the differential geometry, rubber-sheet and algebraic topology, and knot theory necessary to describe knit constructions for topological and curved surfaces.

Calculus II, Fall 2006, Fall 2007---used Calculus in Context for students who took Calculus I in high school; curriculum includes differential equations, dynamical systems, series approximations, and techniques of integration.

Topics in Algebra, Spring 2007---student-driven seminar investigating rings, modules, vector spaces, tensor products, exact sequences; significant project and regular presentations required.

Discovering Mathematics: Dimensionality, Spring 2007---mathematical fiction (Flatland, Sphereland, and Spaceland) used to launch discussion of the mathematics of spaces of various dimensions.

Critical Reading and Discussion: Sexing the Body: Gender Politics and the Construction of Sexuality by Anne Fausto-Sterling, Interterm 2007---five discussion sessions plus a reaction essay and a critical essay.

Number Theory, Fall 2006---exploration-based class using Silverman's A Friendly Introduction to Number Theory along with Mathematica for data collection; significant student project and presentation required.

Guest Instructor, Sarah Lawrence College, Bronxville, NY, 2013--14, Spring 2013, Fall 2010 and 2008--09
Sarah Lawrence courses incorporate independent projects (2 credits) with the usual class structure (3 credits).

Calculus I, Fall 2010, Spring 2014---used Hughes-Hallett text with frequent in-class cooperative learning, take-home exams, and derivative gateway exam. Projects included pharmacokinetics of morphine, repeated prime gaps, mathematical dressmaking, plane isometries, and translation of a mathematics paper from Japanese.

Multivariable and Vector Calculus, Spring 2014---used Colley text with frequent in-class cooperative learning, computer algebra systems, and take-home exams. Projects included differential geometry, mathematical modeling, and architecture.

Discrete Mathematics, Fall 2013---used Discrete Mathematics with Ducks to focus on proofwriting, combinatorics, and graph theory, with frequent in-class inquiry-based and cooperative learning, and take-home exams. Projects included coding/cryptography, abstract algebra, probability, and mathematics of Alice in Wonderland.

Calculus II, Spring and Fall 2013---used Calculus in Context (for differential equations, power series, integration, and numerical approximation) with frequent in-class cooperative learning, computer labs, and take-home exams.  Projects included crystallography, a narrative mathematical film, combinatorics, and modeling a roller coaster.

Linear Algebra, Spring 2009---as at Smith College, but with no in-class exams or formal student presentations. Projects included knot theory, mathematical choreography, number theory, and integer programming.

Dimensionality, Fall 2008---as at Smith College. Projects included classification and knitting of topological surfaces, Kempe's false proof of the Four Color Theorem, geometric matrix transformations, and basic fractals.

Visiting Faculty, Clark University, Worcester, MA, Fall 2012

Calculus I---taught two of five class sections, using Hass/Weir/Thomas text and cooperative learning in class.

Co-Director, Hampshire College Summer Studies in Mathematics, Amherst, MA. August 2004--March 2009
Senior Staff, Hampshire College Summer Studies in Mathematics,
Amherst, MA, Summers 1999--2009

Taught 100+ hours of college-level mathematics over six summer weeks at program for very talented high-school students. Content of the 3-week introductory workshop ranged from group theory to combinatorics to number theory to complex analysis to infinite set theory. Designed Polytopes and More, a 3-week course on convex geometry, Graphs on Surfaces, a 3-week course on topological graph theory, and Recent Papers and Lebesgue Integration short courses; co-designed Polyhedra and Friends, a 3-week course on convex geometry and origami mathematics, and Knot Theory and Convex Hulls short courses. Gave hour lectures ranging from Sets with no SETs to Computing Simplicial Homology Groups. As Co-Director, worked with David Kelly of Hampshire College to recruit, screen, mentor, and evaluate both students and staff, to write a new Interesting Test for the applications process each year, to maintain advisory relationships with alumni, and to write grant proposals to help fund the Summer Studies.

Assistant Professor, Xavier University, Cincinnati, OH, Sept. 2002--June 2006

Student Research---supervised seven students in mathematical research projects, 2004--2006.

Graph Theory, Springs 2003, 2005---used fundamental questions of topological graph theory to motivate student-driven explorations, including classifying surfaces, supplemented with Trudeau and Wilson texts.

Mathematical Perspectives: Dimensionality, Springs 2004, 2005---as at Sarah Lawrence College.

Mathematical Perspectives: Devilish Number Investigations, Spring 2005---used statements in The Number Devil as a springboard for making conjectures, investigating examples, and creating basic proofs.

Topology, Spring 2005 (ind. study)---did point-set (Munkres) and basic homotopy/homology (Hatcher).

Elements of Calculus, Falls 2002 - 2004, Spring 2003---used the LaTorre, Kenelly, et. al text; cooperative learning both in- and outside class; graphing calculators used; real-world project required.

Elementary Linear Algebra, Fall 2004---as at Smith College, with some group homework assignments as well.

Mathematical Perspectives: Knots, Surfaces, and other Visual Mathematics, Spring 2004---used a discovery-based text and classroom activities to discuss graph theory, surface theory, and knot theory.

Real Analysis, Spring 2004---students read one section of the Marsden text per class session, then discussed the text and exercises in class; take-home exams.

Abstract Algebra, Falls 2002, 2003---used exploratory and discovery-based activities as well as collaborative learning with Gallian's text; take-home exams; paper/project required. (Abstract Algebra II covered ring theory through Galois theory as an independent study Spring 2003.)

Visiting Assistant Professor, Bowdoin College, Brunswick, ME, Sept. 2001--June 2002

Calculus II , Fall 2001 and Spring 2002, and Calculus II Advanced, Fall 2001---used Hughes-Hallett text and weekly Mathematica labs; substantial cooperative learning; gateway exam and short paper required.

Real Analysis, Spring 2002---Marsden text supplemented by the Rosenlicht text; in-class discussions supplemented by selected worksheets (W. Barker); take-home exams.

Assistant Professor, University of Northern Iowa, Cedar Falls, IA, Aug. 1997--June 2002

Standard Courses: Real Analysis I and II (twice each, Marsden text), Analysis for Business Students (twice, Crauder/Evans/Noell text), Linear Algebra (four times, Leon, Andrilli/Hecker texts), Abstract Algebra I and II (once each, Gallian text), Calculus II (twice, Hughes-Hallett text).

Differential Geometry, Fall 1999---designed and conducted interactive-lecture class using four texts of various levels; covered theory of manifolds in general dimension with examples from dimensions 1, 2, 4.

Geometric Transformations, Fall 1998---designed and facilitated discussion-style class on plane transformational geometry and physics-oriented differential geometry with informal texts (Farmer, two by Rucker).

Mathematics Research Publications:

Domino Tilings of 2 x n Grids (or Perfect Matchings of Grid Graphs) on Surfaces, Journal of Integer Sequences Vol. 26 (2023), Article 23.5.6.

Grünbaum colorings extended to non-facial 3-cycles, with R. Haas, Electronic Journal of Graph Theory and Applications, 10(1) (2022), 199--212. (open access)

Color-induced subgraphs dual to Hamilton cycles of embedded cubic graphs, Australas. J. Combin. 81(2) (2021), 319--333. (open access)

Color-induced subgraphs of Grünbaum colorings of triangulations, with R. Haas, Australas. J. Combin. 79(3) (2021), 461--475. (open access)

Parsimonious edge colorings on surfaces, Electronic Journal of Graph Theory and Applications, 6(2) (2018), 306--309. (open access)

Edge-Kempe-equivalence graphs of class 1 k-regular graphs, with R. Haas, Australas. J. Combin. 69(2) (2017), 197--214. (open access)

Small snarks and 6-chromatic triangulations on the Klein bottle, Australas. J. Combin., 65(3) (2016), 232--250. (open access)

An Elementary Computation of the Conway Polynomial for (m,3) and (m,4) Torus Links, with D. Rowland, Journal of Combinatorial Mathematics and Combinatorial Computing, 96 (February 2016), 159--170.

Triangle-free Uniquely 3-Edge Colorable Cubic Graphs, with R. Haas, Contributions to Discrete Math. 10(2) (2015), 39--44. (open access)

Counting edge-Kempe-equivalence classes for 3-edge-colored cubic graphs, with R. Haas, Discrete Mathematics, 325 (28 June 2014), 77--84. (open archive)

1-factor Covers of Regular Graphs, with M. Young, Discrete Applied Mathematics, 159(5) March 2011, 281--287. (open archive)

Grünbaum Colorings of Toroidal Triangulations, with M. O. Albertson, H. Alpert, and R. Haas, Journal of Graph Theory, 63(1) January 2010, 68--81. (find it on the arXiv)

Every Topological Surface Can Be Knit: A Proof, Journal of Mathematics and the Arts, 3(2) June 2009, 67--83.

Families of Dot-Product Snarks on Orientable Surfaces of Low Genus, with J. Kaminski, Graphs and Combinatorics. 23(3) June 2007, 229--240.

Modelling the Folding of Paper into Three Dimensions, with T.C. Hull. Linear Algebra and Its Applications. 348 (2002), 273--282. (open archive)

Picard Lattices of Families of K3 Surfaces, Communications in Algebra. 30(1) , 61--82 (2002). (find it on the arXiv)

A Mathematical Model for Non-Flat Origami, with T.C. Hull, in Origami3: Third International Meeting of Origami, Science, Mathematics and Education, A K Peters, Ltd. (2002), 39--51. (also appears in the Japanese edition; not all papers were included.)

Classifying Frieze Patterns Without Using Groups, with T.C. Hull. The College Mathematics Journal, 33(2) March 2002, 93--98.

Counting Centralizers in Finite Groups, with G. J. Sherman. Mathematics Magazine 67 (1994), 366--374.

Minor-closed classes of signed graphs, with D. C. Slilaty, preprint.

Selected Additional Refereed or Invited Publications (complete list):

Introduction to the special issue on mathematics and fibre arts, with C. Yackel, Journal of Mathematics and the Arts, 17(1--2), 2023, 1--8. Co-edited special issue of 10 articles.

Discrete Mathematics with Ducks, textbook, 2nd ed. CRC Press (2018); 1st ed. A K Peters (2012); Student Handbook for Discrete Mathematics with Ducks: SRRSLEH (Student Reference, Review, Supplemental Learning, and Example Handbook), A K Peters/CRC Press 2015.

Figuring Fibers, book, assistant editor; chief editor C. Yackel, AMS (2018).
Knitting Torus Knots and Links, chapter.

Ask Questions to Encourage Questions Asked, PRIMUS, 27(2), 2017, 171--178.

Do the Twist! (on polygon-base boxes), with T. Veenstra, The College Math J., 47(5) November 2016, 340--345.

Symmetric Colorings of Polypolyhedra, with T. Hull, Origami6 1: Mathematics, AMS (2015), 21--31.

Adventures in Mathematical Knitting. American Scientist, 101(2), March-April 2013, 124--133; reprinted in The Best Writing on Mathematics 2014, Ed. Mircea Pitici, Princeton University Press, pp. 128--143.

The Continuing Saga of Snarks. The College Math. J., 43(1) January 2012, 82--87; reprinted in Martin Gardner in the Twenty-First Century, ed. Michael Henle and Brian Hopkins (2012), 65--71.

Dancing Mathematics and the Mathematics of Dance, with K. Schaffer. Math Horizons, February 2011, pp. 16--20; reprinted in The Best Writing on Mathematics 2012, Ed. Mircea Pitici, Princeton University Press, pp. 79--92.

Crafting by Concepts, book edited with C. Yackel, A K Peters (2011).

Generalized Helix Striping, chapter
Group Actions in Cross-stitch, chapter with M. Shepherd and C. Yackel
Spherical Symmetries of Temari, chapter with C. Yackel

Making Mathematics with Needlework, book edited with C. Yackel, A K Peters (2007).

Introduction (survey of the field), with C. Yackel
Only Two Knit Stitches Can Create a Torus, chapter
(K)Not Cables, Braids, chapter with A. Szczepanski and C. Yackel
Stop Those Pants!, chapter with C. Yackel

Interpretations of Feminist Philosophy of Science by Feminist Physical Scientists, with J. M. Moran, NWSA Journal, 15 (1) Spring 2003, 20--33.

A Teaching Discussion Group in Your Department---It Can Happen, with D. Shaw and D. Thiessen, College Teaching. 50 (1),Winter 2002, 29--33.

The Cantor Set Contains 1/4? Really?, with M. Green, The College Mathematics Journal, 32 (1) 2001, 60--61.

Additional Works In Progress:

Floorquences and their Consequences, in revision.

Tablets versus IV---What's the Dose?, in preparation (rough draft).

Laban's Choreutics and Polyhedra, in preparation (rough draft).

Coloring Duality for Polypolyhedra, with T. Hull, in preparation (draft).

How to Classify Regular Polytopes, with E. Peters, preprint; Convex Realizable Polytopes, in preparation (rough draft).

Why are there 3n cubes in the n-cube? with T. C. Hull, preprint.

Intervening Discourse about Feminist Physical Sciences and Mathematics, preprint.

Selected Recent Presentations:

Tetris-y Tilings, February 2024
Harvard-MIT Mathematics Tournament

Enumerating domino tilings of 2 × n grids on surfaces, January 2024
AMS Special Session on Serious Recreational Mathematics, JMM, San Francisco CA

Drawing Networks on Doughnuts, February 2023
Harvard-MIT Mathematics Tournament

Curvature within knitted blanket squares, January 2023
AMS Special Session on Mathematics and Fiber Arts, Joint Mathematics Meetings, Boston MA

Secrets (well, not any more) of the MathILy-EST REU, April 2022
SIGMAA Special Session on Programs that Support Student Research, JMM, online

Topological Graph Theory and YOU,
Junior Seminar, California State University, Fresno, online, March 2022
Colloquium, Hofstra University, online, March 2022
Colloquium, Valparaiso University, online, September 2021
Colloquium, San Jose State University, online, April 2021

Colorful Polyhedral Skeleta, February 2020
Harvard-MIT Mathematics Tournament

Identifying very strong high-school students + An early-college REU, January 2020
AMS Special Session on How to Discover and Train Gifted Students, JMM, Denver CO

A Slice of a Slice of Topological Graph Theory, November 2019
Smith College Lunch Talk + visit to Dialogues class

Illustrating topology and geometry (but mostly topology) with knitting, September 2019
Computational Textiles Working Group, ICERM Illustrating Mathematics Semester, Providence RI

Symmetries of Wall Trim, May 2019
American Regions Mathematics League, Pennsylvania State University

Color-induced subgraphs of Grünbaum colorings of triangulations,
AMS Special Session on Topology, Structure and Symmetry in Graph Theory, JMM, Baltimore MD, January 2019
Discrete Mathematics Day, University of Rhode Island, September 2018

Tiles on Surfaces / Matchings on Grids, March 2018
Colloquium, Loyola University Chicago

Does Inclusivity Matter in Mathematical Practice?, January 2018
MAA Session on Philosophy of Mathematics as Actually Practiced, JMM, San Diego CA

Grünbaum colorings extended to non-facial 3-cycles, January 2017
AMS Contributed Paper Session, Joint Mathematics Meetings, Atlanta GA

Branching out within IBL: Guides to Support Experimentation , January 2016
MAA Contributed Paper Session on Inquiry-Based Teaching and Learning, JMM, Seattle

Scheduling the Week of Chaos (co-given with Max Engelstein, Jonah Ostroff, and Thomas Hull) , January 2016
MAA CPS on Math Experiences and Projects in Business, Industry, Government, JMM, Seattle

Stories about Snarks (Plenary Speaker), March, 2015
Forty-Sixth Southeastern Intl. Conf. on Comb., Graph Theory, and Computing, Boca Raton, FL

Ask questions to encourage questions asked, January 2015
MAA Contributed Paper Session on Teaching Inquiry, Joint Mathematics Meetings, San Antonio

Symmetric Colorings of Polypolyhedra, August 2014
The 6th International Meeting on Origami in Science, Mathematics and Education, Tokyo, Japan

Small snarks and 6-chromatic triangulations on the Klein bottle, June 2014
Minisymposium on Variations in Chromatic Graph Theory, SIAM DM14, Minneapolis MN

Snark Attack!: visualizations of 'uncolorable' graphs on surfaces, January 2014
MAA Invited Address, Joint Mathematics Meetings, Baltimore

(and an additional 37 talks given since the start of 2014)

Fellowships and Awards:

PI on NSF-REU grants DMS-1851842 and DMS-2149647 for the MathILy-EST REU, April 2019--February 2025

AWM Service Award to the EvenQuads Project Management Committee, 2022

AWM-NSF Travel Grant for participation in the 6th International Meeting on Origami in Science, Mathematics and Education, Tokyo, Japan, August 2014

AWM-NSF Travel Grant for participation in 2012 AMS Fall Eastern Sectional Meeting, June 2012

Tensor Foundation Grant for recruiting/enhancement of HCSSiM, Feb. 2007

UNI 2000 Summer Fellowship---internally competitive grant supported research, June 2000

Project NExT Fellow---one of 70 young mathematicians chosen nationally by the MAA to participate in extensive discussions on teaching and pedagogy at three national conferences, July 1997 - Aug. 1998

Selected Professional Service:

Chair of AWM playing card project Management Committee, August 2019--present
Co-organized JMM 2024 AWM Special Session on EvenQuads: Live and in person: The honorees and the games

Steering Committee Member, Summer Mathematics Programs Consortium, August 2022--present

Co-edited (with C. Yackel) Special Issue of Journal of Mathematics and the Arts, 2022--2023

Organized (with C. Yackel) AMS Special Sessions, Joint Mathematics Meetings, Jans. 2005, 2009, 2014, 2023
Mathematics and Mathematics Education in Fiber Arts / Mathematics and Fiber Arts (2005 pages; 2009 pages; 2014 pages; 2023 pages)
We also organized accompanying exhibits; the 2009, 2014, and 2023 exhibits were juried.

Participated in Rutgers AWM student chapter career Q&A, April 2021

Team-graded the Power Question (proofs) at the ARML competition, Junes 2008--2019

Associate Editor for The College Mathematics Journal, Jan. 2003--2019

Refereed for Journal of Graph Theory, 2016, 2017, 2018

Organized (with M. Ellingham) MAA Invited Paper Session, Joint Mathematics Meetings, January 2014
MAA IPS on Graphs don't have to lie flat: the shape of topological graph theory 

Refereed for Journal of Mathematics and the Arts, 2013 and 2014

Advisory Board member for Math Horizons, June 2003--Jan. 2008

Organized (with R. Haas) Discrete Math Day (DMD-NE) Conference, April 2008

Consultant to Project NExT 2004 cohort, January 2005--present

Organized (with D. Kelly) Yellow Pig Math Days conference, Oct. 2005--July 2006

Supervised four XU mathematics major Senior Projects, Fall 2004--Spring 2006

Re-visioning XU Core (Gen. Ed.) Mathematics Task Force; created six new courses, 2003

Organized (with R. Favro and K. Moore) CPW Panel Discussion, Joint Math Meetings January 2003
Improving the persistence of women in graduate school.

Chair of XU Mathematics Task Forces: Fall 2002--Spring 2003
Teaching Evaluations, Advisor/Advisee Matchings, Placement Test Revisions

Organized (with D. Sabo) MAA-Project NExT Panel Discussion, Joint Math Meetings, January 2002
Introduction to the hiring process: Preparation, execution, and follow-up.

Mathematical Association of America Committee on the Participation of Women, Jan. 2000--Jan. 2003

Selection Committee for AWM Alice T. Shafer Prize (Chair in 2002), Oct. 2000--Oct. 2002

Selected UNI Mathematics Department Committees:
Mathematics Position Search Committee (Co-Chair 1999--2000 with T. Veenstra), 1998--2000
Colloquium Committee (Chair, 1998--2000), 1997--2000

Selected Additional Activities:

Choreographed 2 min. solo included as video (2012+) and performed live (2024) in Karl Schaffer's modern dance piece The Daughters of Hypatia: Circles of Mathematical Women, February 2012, January 2024

Six knitted/crocheted mathematical objects displayed in four juried art exhibits, Jan. 2012--July 2012
JMM 2012 (Boston), Lafayette Art Gallery (PA), SMI 2012 (TX), ATMCS5 (UK)

Faculty Advisor to XU Sexual Health And Reproductive Education student group, Feb. 2003--Dec. 2004

UNI Women's Studies Undergraduate Program Advisory Board, Sept. 1998--May 2001

Member of UNI Orchesis Dance Company (choreography co-chair 1999--2000), Sept. 1997--May 2001

Faculty Advisor to UNI-Lesbian Gay Bisexual Transgender Alliance, April 1998--May 2001

Professional Organizations:


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