Curriculum Vitae May 2008

sarah-marie belcastro

 

Dept. of Mathematics and Statistics   11 Jewett Street
Smith College   Northampton, MA 01060
Northampton, MA 01063   (413) 341-1373
(413) 585-3791 Fax: 585-3786   Citizenship: United States 

smbelcas(at)toroidalsnark.net
(if you want more than is here, just ask; this is only for the past few years...)

Education:

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:

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---taught using cooperative learning in class; take-home and in-class exams; focus on building proof-writing skills with examples and exercises taken from applications.

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, Falls 2006, 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 Friendly along with Mathematica for data collection; significant student project and presentation required.

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

Student Research---supervised seven students in mathematical research projects during the school year
and summers, 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---used mathematical fiction (Flatland, Sphereland, and Spaceland) to launch discussion of the mathematics of spaces of various dimensions.

Mathematical Perspectives: Devilish Number Investigations, Spring 2005---used unjustified mathematical 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---cooperative learning in class; individual and group homework; take-home and in-class exams; student presentations required; focus on proofs; used Mathematica and Maple.

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 dis- cussed 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 Harvard Consortium 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, Harvard 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).

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

HCSSiM is a six-week residential program for very talented high-school students. Content of the 3-week introductory workshop ranges 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 range from Sets with no SETs to Computing Simplicial Homology Groups. As Co-Director, I work with David Kelly of Hampshire College to recruit, screen, mentor, and evaluate both students and staff.

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.

Graduate Student Instructor, The University of Michigan, Sept. 1993 - May 1997

Calculus I (thrice), Calculus II (twice)---used cooperative learning and graphing calculators; full responsibility
for the course. One Calculus I was an all-female class for for the Women In Science and Engineering program.

 

Mathematics Research Papers:

Grünbaum Colorings of Toroidal Triangulations, with M. O. Albertson, H. Alpert, and R. Haas, submitted. preprint

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

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, Morikita Publishing Co., Ltd., ISBN 4-627-01691-3; 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.

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

An Elementary Approach to the Conway Polynomial for (m,3) and (m,4) Torus Links, with D. Rowland, in preparation.

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

Parsimonious Edge Colorings on Surfaces, in preparation.

Additional Refereed or Invited Publications:

Every Topological Surface Can Be Knit: A Proof, submitted.

Generalizing twist boxes, with T. Veenstra, to appear in Origami4 proceedings volume.

The Seven-Colored Torus: mathematically interesting and nontrivial to construct, with C. Yackel, in Homage to a Pied Puzzler, ed. by Ed Pegg, Jr., Alan H. Schoen, and Tom Rodgers, to appear A K Peters (2008).

A Conversation with Erik Demaine, with T. Hull, to appear in Math Horizons November 2008.

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

About Knitting, with C. Yackel, Math Horizons November 2006, pp. 24-27+39.

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.

Book Review: Feminist Science Studies: A New Generation, AWM Newsletter, 32 (4) July-August 2002, 7 - 12.

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:

Knitting Topological Surfaces, in preparation.

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

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

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

N-gonal boxes from one piece of paper, with T. Veenstra, in preparation.

 

Selected Recent Presentations:

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

College “Calculus" for students who have already had some Calculus, January 2008
MAA Session on Serving Students Who Have Taken Calculus in High School, Joint Mathematics Meetings, San Diego

Knitting Uniformly Curved Pants, January 2008
MAA Session on Mathematics and the Arts, Joint Mathematics Meetings, San Diego

Surprising Binary Sequences and Mysterious Expanding Tilings, June 2007
American Regions Mathematics League, Pennsylvania State University

Undergraduate Teaching which Leads to Undergraduate Research, January 2007
MAA Session on Research and Other Mathematical Experiences for Students Outside the Classroom
Joint Mathematics Meetings, New Orleans

Topological Graph Theory and YOU, Spring 2006
Student Colloquium at Smith College, Mount Holyoke College, and Amherst College

Merging Mathematics and Motion, April 2006
Lecture/Demonstration for Merging Minds and Motion dance class, Hampshire College

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

How the way we ‘see’ mathematics changes mathematics, January 2006
MAA Session on Philosophy of Mathematics, 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

How NOT to Prove Grünbaum's Conjecture on the Torus, October 2003
Miami University Annual Conference: Discrete Mathematics and Its Applications

A Conjecture about... Feminist Mathematics? January 2003
MAA Session on Philosophy of Mathematics, Joint Mathematics Meetings, Baltimore

(and an additional 6 talks given since the start of 2003)

 

Professional Service:

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

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

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

Organized (with R. Haas, J. Henle) Smith Alumnae Mathematics Conference, September 2007

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

Organized (with C. Yackel) AMS Special Session, Joint Mathematics Meetings January 2005
AMS Special Session on Mathematics and Mathematics Education in Fiber Arts

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

AWM Mentor Network---one undergraduate mentee, Nov. 2002 - Fall 2004

Updated and maintained Xavier University Mathematics web pages, Fall 2002 - Fall 2005

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

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

 

Fellowships and Awards:

Faculty Development Leave proposal (competitive across Xavier), recommended for funding but not funded, October 2004

XU Information Fluency Initiative---grant to integrate information fluency proficiencies into a general education course (Elements of Calculus); with D. Otero, J. Snodgrass, Summer 2003

UNI 2000 Summer Fellowship---internally competitive grant supports 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---one of twelve graduate students chosen nationally to present a poster on dissertation research, January 1997

Professional Organizations:
AMS (since 1990)
AWM (since 1990)
MAA (since 1997)