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Curriculum Vitae June 2017

sarah-marie belcastro

231 W Franklin St
Holyoke, MA 01040
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 program MathILy-Er (MathILy, Earlier).

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

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

Research Associate, Smith College, Northampton, MA. June 2008--present
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.

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

Calculus I, Calculus II, Calculus III---taught up to three sections of the multisection Engineering Calculus course sequence each semester (roughly 170 students/term), using Stewart text and some cooperative learning in class. Assisted in mentoring teaching assistants. Also Calculus III Honors (single section, 25 students).

Linear Algebra---taught a section of the multisection 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; Salmagundi and Mélange covered combinatorics, graph theory, group theory, topology, and geometry at a sophomore mathematics major level and All Dimensions All the Time covered convex geometry with a focus on polytopes at a junior/senior mathematics major level.

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.

Visiting Assistant Professor, Mount Holyoke College, South Hadley, MA. Sept. 2009--May 2010

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.

Discrete Mathematics, Spring 2010---designed sophomore-level highly interactive course with focus on combinatorics and graph theory content as the context for learning to create and write proofs; readings amalgamated from several electronic and print texts; both in-class and take-home exams.

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).

Teaching Discussion Group, Mathematics Department, University of Northern Iowa, Spring 1999--2001

Members met once per month to discuss various aspects of teaching with a different focus each semester. The four semester foci were (a) studying teaching styles via structured visits to classes (b) working closely with a colleague (I worked with Linear Algebra) (c) active learning in the classroom and (d) assessment.

Mathematics Research Papers:

Edge-Kempe-equivalence graphs of class 1 k-regular graphs, with R. Haas, to appear, >Australasian J. Combinatorics.

Small snarks and 6-chromatic triangulations on the Klein bottle, Australasian J. Combinatorics, 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. (find it on the arXiv)

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.

Domino Tilings of 2 x n Grids (or Perfect Matchings of Grid Graphs) on Surfaces, preprint in revision.

Topological minor-closed classes of signed graphs, with D. C. Slilaty, in preparation (rough draft).

Hamilton Circuits and Grünbaum Colorings, with M. O. Albertson and R. Haas, in preparation (rough draft).

Parsimonious Edge Colorings on Surfaces, in preparation (rough draft).

Selected Additional Refereed or Invited Publications (complete list):

Knitting Torus Knots and Links, chapter for edited book, submitted.

Floor-quences and their Conse-quences, submitted.

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.

Student Handbook for Discrete Mathematics with Ducks: SRRSLEH (Student Reference, Review, Supplemental Learning, and Example Handbook), A K Peters/CRC Press 2015.

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.

Discrete Mathematics with Ducks, textbook, A K Peters (2012).

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

Constructing Regular n-gonal Twist Boxes, with T. Veenstra, Origami4, A K Peters (2009), 41--49.

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.

Active Learning in Abstract Algebra: An Arsenal of Techniques, with L. Burton and M. McDermott, in Innovations in Teaching Abstract Algebra, MAA Notes 60, MAA, 2002, 3--9.

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:

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.

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:

Counting Across Dimensions At Least Twice, June 2017
American Regions Mathematics League, Pennsylvania State University

A Big (graph) Cover-Up, February 2017
Harvard-MIT Mathematics Tournament

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

Floor-quences and their Conse-quences, June 2016
American Regions Mathematics League, Pennsylvania State University

Adding in Geometry (Minkowski Sums), February 2016
Harvard-MIT Mathematics Tournament

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

IBL Instructor Training and Support Materials, June 2015
Legacy of R.L. Moore IBL Conference, Austin, TX

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

Topological Graph Theory and YOU, April 2014
North Shore Undergraduate Research Conference Invited Address, Gordon College

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

Knitting Torus Knots and Links, January 2014
AMS Special Session on Mathematics and Mathematics Education in Fiber Arts                       
Joint Mathematics Meetings, Baltimore

Epistemological Culture and Mathematics, January 2012
MAA Session on the Philosophy of Mathematics and Mathematical Practice, Joint Mathematics Meetings, Boston

Counting Kempe-equivalence classes for 3-edge-colored cubic graphs, July 2011
Discrete Mathematics Days, St. Michael's College, VT

The Excess Range of Factorizations of Regular Graphs, January 2010
AMS Session on Discrete Mathematics, Joint Mathematics Meetings, San Francisco

An elementary enumeration of perfect matchings on 2 × n grid graphs on surfaces, May 2009
CanaDAM, Montréal Canada

Laban's Choreutics and Polyhedra, January 2009
MAA Session on Performing Mathematics, Joint Mathematics Meetings, Washington DC

Grünbaum Colorings of Toroidal Triangulations, June 2008
SIAM DM08, Burlington

Dancing mathematics and the mathematics of dance, January 2008
MAA Special Presentation, Joint Mathematics Meetings, San Diego

(and an additional 30 talks given since the start of 2008)

Fellowships and Awards:

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

Faculty Development Leave grant (competitive across Xavier), awarded but unfunded, October 2004

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:

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

Team-graded the Power Question (proofs) at the ARML competition, Junes 2008--2017

Refereed for Journal of Graph Theory and Australasian J. Comb, 2016

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

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

Refereed for Graphs and Combinatorics, 2012

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

Co-author of XU Mathematics Academic Program Review, Fall 2002

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 Comm. (Co-Chair 1999--2000 with T. Veenstra), 1998--2000
Colloquium Committee (Chair, 1998--2000), 1997--2000

Selected Additional Activities:

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)

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

Pre-Major Advisor and Research Mentor to a STRIDE student, Sept. 2006--August 2007

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:

AMS (since 1990)
AWM (since 1990)
MAA (since 1997)
SIAM (since 2008)

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