Curriculum Vitae January 2012

sarah-marie belcastro

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

Education:

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

• Major Area---Algebraic Geometry (Surfaces and Toric Varieties)
• Dissertation Title---Picard Lattices of Families of K3 Surfaces
• Thesis Advisor---Dr. Igor Dolgachev

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

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

• Majors in Mathematics and Astronomy; graduated with Honors in Mathematics
• Advisor---Dr. Curtis Greene

Professional Experience:

Lecturer, University of Massachusetts-Amherst, Amherst, MA, Jan. 2011–May 2012

Calculus I, Calculus II, Calculus III---taught three sections of the multisection Engineering Calculus course sequence each semester (roughly 170 students/term), using Stewart text and some cooperative learning in class.

Guest Instructor, Sarah Lawrence College, Bronxville, NY, Fall 2010 and Sept. 2008–May 2009
Sarah Lawrence courses incorporate independent projects (2 credits) with the usual class structure (3 credits).

Calculus I, Fall 2010---using Hughes-Hallett text with frequent in-class cooperative learning, take-home exams, and derivative gateway exam. Projects include pharmacokinetics of morphine, systems of differential equations in population biology, investigating repeated prime gaps, and translation of a mathematics paper from Japanese.

Linear Algebra, Spring 2009---taught using cooperative learning in class; take-home exams; focus on building proof-writing skills with examples and exercises taken from applications; Mathematica and web applets for computation. Projects included knot theory, mathematical choreography, number theory, and integer programming.

Dimensionality, Fall 2008---mathematical fiction (Flatland, Sphereland, and Spaceland) used to launch discussion of the mathematics of spaces of various dimensions. Projects included classification and knitting of topological surfaces, Kempe’s false proof of the Four Color Theorem, geometric matrix transformations, and basic fractals.

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.

Research Associate, Smith College, Northampton, MA. June 2008–present
Visiting Assistant Professor, Smith College, Northampton, MA, Feb. 2006 - June 2008
Associate Director, Center for Women in Mathematics, Smith College, July 2007 - June 2008

Linear Algebra, Springs 2006, 2007, 2008---as at Sarah Lawrence, plus in-class exams and student presentations.

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---as at Sarah Lawrence College.

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.

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 - 2008

HCSSiM is a six-week intensive residential program for very talented high-school students. In class hours, I taught the equivalent of two college courses each summer. Content of the 3-week introductory workshop ranged from group theory to combinatorics to classification of surfaces to number theory to complex analysis to infinite set theory. 3-week maxi courses are equivalent to upper-level undergraduate semester courses. I designed Polytopes and More, a maxi course on convex geometry, Graphs on Surfaces, a maxi course on topological graph theory and Recent Papers and Lebesgue Integration mini courses; I co-designed Polyhedra and Friends, a maxi course on convex geometry and origami mathematics and Knot Theory and Convex Hulls mini courses. My numerous hour lectures ranged from Sets with no SETs to Computing Simplicial Homology Groups. As Co-Director, I worked with David Kelly of Hampshire College to recruit, screen, mentor, and evaluate both students and staff. In addition to these activities, we wrote a new Interesting Test for the applications process each year, maintained advisory relationships with alumni, and wrote 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:

An Elementary Computation of the Conway Polynomial for (m,3) and (m,4) Torus Links, with D. Rowland, submitted.

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

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

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.

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, in revision.

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

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

Hamilton Circuits and Grünbaum Colorings, with M. O. Albertson and R. Haas, in preparation.

Counting Kempe-equivalence classes for 3-edge-colored cubic graphs, with R. Haas, in preparation.

Parsimonious Edge Colorings on Surfaces, in preparation.

Selected Additional Refereed or Invited Publications (complete list):

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

The Continuing Saga of Snarks. The College Math. J., 43(1) January 2012, 82--87.

Cutting Space into Regions with Four Planes. Wolfram Demonstrations Project

Dancing Mathematics and the Mathematics of Dance, with K. Schaffer. Math Horizons, February 2011, pp. 16--20.

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.

Knitting Hyperbolic Pants, Wolfram Demonstrations Project.

A Conversation with Erik Demaine, with T. Hull, Math Horizons February 2009.

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

To include more students, don't focus on contests---prepare for mathematics!, February 2004 Mathematics Teacher, Vol. 97 Issue 2, 84--86.

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

The Devil is in the Culture: Why You Should Read The Number Devil and other Musings on Mathematical Education and Culture, with A.Howard, Math Horizons November 2002, 16--20 +29.

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.

Laban’s Choreutics and Polyhedra, in preparation.

How to Classify Regular Polytopes, with E. Peters, in revision.

Folding Rectangles into Regular Polygons, and Let’s fold polygonal-base twist boxes! with T. Veenstra, in revision.

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

Intervening Discourse about Feminist Physical Sciences and Mathematics, in revision.

Selected Recent Presentations:

Counting Kempe-equivalence classes for 3-edge-colored cubic graphs, January 2012
AMS Special Session on Recent Trends in Graph Theory, Joint Mathematics Meetings, Boston

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

Counting Across Dimensions At Least Twice, June 2011
American Regions Mathematics League, Pennsylvania State University

Lightweight Trees and How to Find Them---Fast, February 2011
Harvard–MIT Mathematics Tournament

Topological Graph Theory and YOU, April 2010
Abramson Colloquium at Pi Mu Epsilon induction ceremony, Bridgewater State College

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

Braid words in generalized helix stripe patterns, January 2009
AMS Special Session on Mathematics and Mathematics Education in Fiber Arts Joint Mathematics Meetings, Washington DC

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

Edge-Coloring Graphs on Surfaces: Recent Progress on Grünbaum's Conjecture, March 2008
Bi-College Mathematics Colloquium, Haverford College

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

Knitting Topological Surfaces, January 2006
AMS Session on Topology, Joint Mathematics Meetings, San Antonio

Embedding Snarks on Orientable Surfaces of Low Genus, with... the Petersen graph, May 2005
Graph Theory with Altitude (in honor of Joan Hutchinson’s 60th birthday), Denver

Using Class Time---How and Why I Developed My Classroom Style, August 2004
Invited panel participant at Project NExT (orange dots), Providence

(and an additional 20 talks given since the start of 2004)

Fellowships and Awards:

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

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

XU Information Fluency Initiative grant for Elements of Calculus; with D. Otero, J. Snodgrass, Summer 2003

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

AWM Workshop, Joint Mathematics Meeting, San Diego, January 1997

Selected Professional Service:

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

Team-graded the Power Question (written proofs) at the American Regions Mathematics League competition, Junes 2008–2011

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

AWM Mentor Network---one undergraduate mentee, 2002--2004, 2009

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

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

Splash Math Program instructor (5 hours of class at MIT, for high-school students), November 2006

Graduate and Career Advisor for Smith mathematics majors, Sept. 2006--Sept. 2007

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:

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

Organized (with J. Blue and L. Van Zee) and presented at Haverford College Reunion, May 2006
Women in Science and Mathematics: From Haverford Towards Tenure

Member of XU Africana Studies Minor Committee, Spring 2005

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

UNI WS Programming Committee/Women's Studies Social Action Project, Sept. 1997--May 2000

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)