Department of Mathematics

Boston College

Chestnut Hill, MA 02467-3806

(617) 552-3758

gross@bc.edu

Position:

Associate Professor of MathematicsThis web page contains my educational history, employment history, information about my books, some publications, information about courses that I’m teaching this year (2022–2023), information about Ideas in Math: The Grammar of Numbers, a course that Michael Connolly and I taught in the spring of 1998, and other useful stuﬀ.

Education

A.B., 1979, Princeton University.

Ph.D., 1986, Massachusetts Institute of Technology. Thesis advisor: Joseph Silverman.

Position:

Associate Professor of Mathematics

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Massachusetts Institute of Technology Teaching Assistant 1979–1983 Northeastern University Instructor 1983 Boston College Instructor 1984–6 Boston College Assistant Professor 1986–93 Boston College Associate Professor 1993–present Boston University Visiting Associate Professor 1993–4, 2000–1 Back to top

Books

Summing It Up: From One Plus One to Modern Number Theory, with Avner Ash. Princeton University Press, 2016. Reviews and errata.

Elliptic Tales: Curves, Counting, and Number Theory, with Avner Ash. Princeton University Press, 2012. Reviews and errata.

Fearless Symmetry: Exposing the Hidden Patterns of Numbers, with Avner Ash. Princeton University Press, 2006, paperback 2009. Reviews and errata.

Getting Started with Mathematica®, with C-K. Cheung, G.E. Keough, and Charles Landraitis. Wiley, 2005.Contributor to

Standard Mathematical Tables and Formulæ, Thirty-ﬁrst Edition, Edited by Daniel Zwillinger, CRC Press, 2003, New York.Contributor to

Standard Mathematical Tables and Formulæ, Thirtieth Edition, Edited by Daniel Zwillinger, CRC Press, 1996, New York.

Papers

“Lattice Packing by Spheres and Eutactic Forms,” with Avner Ash,

Experimental Mathematics,31:1, 2022, 302–308. Click here for PDF format.“Frequencies of Successive Pairs of Prime Residues,” with Avner Ash, Laura Beltis, and Warren Sinnott,

Experimental Mathematics,20:4, 2011, 400–411. Click here for PDF format.“Frequences of Successive Tuples of Frobenius Classes,” with Avner Ash and Brandon Bate,

Experimental Mathematics,18:1, 2009, 55–63. Click here for PDF format.“Prime Specialization in Genus 0,” with Brian Conrad and Keith Conrad,

Transactions of the American Mathematical Society,360:6, June, 2008, 2867–2908. Click here for PDF format.“Generalized Non-abelian Reciprocity Laws: A Context for Wiles’s Proof,” with Avner Ash,

Bulletin of the London Mathematical Society,32, 2000: 385–397. Click here for PDF format.“A Generalization of a Conjecture of Hardy and Littlewood to Algebraic Number Fields,” with John H. Smith,

Rocky Mountain Journal of Mathematics,30:1, Spring, 2000: 195–215. Click here for PDF format.“

S-Integer Points on Elliptic Curves,” with Joseph Silverman,Paciﬁc Journal of Mathematics,167, 1995: 263–288. Click here for PDF format.“On the Integrality of Some Galois Representations,”

Proceedings of the American Mathematical Society,123:1, January, 1995: 299–301. Click here for PDF format.“A Note on Roth’s Theorem,”

Journal of Number Theory,36:1, September, 1990: 127–132. Click here for PDF format.“Antigenesis: A Cascade Theoretical Analysis of the Size Distribution of Antigen-Antibody Complexes: Applications of graphs in chemistry and physics,” with John Kennedy, Lou Quintas, and Martin Yarmush.

Discrete Applied Mathematics,19:1–3, 1988: 177–194.

Supplementary notes to the Harvard Calculus Text, covering inﬁnite series. Click here to get the ﬁle in PDF format. Other

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Current Courses

MATH2216.01:Introduction to Abstract MathematicsFall

This course is designed to develop the student’s ability to do abstract mathematics through the presentation and development of the basic notions of logic and proof. Topics include elementary set theory, mappings, integers, rings, complex numbers, and polynomials.

Class home page.

MATH4426:ProbabilitySpring

Prerequisite:MATH2202 or MATH2203, Multivariable Calculus.

This course provides a general introduction to modern probability theory. Topics include probability spaces, discrete and continuous random variables, joint and conditional distributions, mathematical expectation, the central limit theorem, and the weak and strong laws of large numbers.

Class home page.

MATH4470.01:Mathematical ModelingFall

Prerequisites: MATH2202 (Multivariable Calculus) and MATH2210 (Linear Algebra)

This course introduces students to methods of mathematical modeling. The emphasis is on ways to analytically represent and study today’s complex modeling problems, with cases from the natural and social sciences. Topics include the model building process, mathematical models of systems, and modeling data to discover properties and hidden characteristics. The calculus of ﬁnite diﬀerences and solutions to classes of diﬀerence equations will serve as the core mathematical theory taught in this course. The dynamics of certain linear and nonlinear models will be explored from various domains (e.g., population models, economic models, Markov models). The course will conclude with an introduction to mathematical graph theory and its application to modeling interacting and interdependent systems and networks.

Class home page.

The Grammar of NumbersIn the spring of 1998, Michael Connolly (the chair of the Department of Slavic and Eastern European Languages) and I taught a course called:

MT007/SL266Ideas in Mathematics: The Grammar of Numbers.It had no prerequisites, and was a core mathematics course for non-math and non-science majors. This one-semester course studied the role of numbers, number names, and number symbols in various cultures. Topics include number mysticism, symbolism in religion and the arts, elementary number theory, number representations, and calendars.

Texts:The Magic Numbers of Doctor Matrix,Martin Gardner.

Number Words and Number Symbols: A Cultural History of Numbers,Karl Menninger.

Click here for more information.

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My .emacsﬁle, for use withunixandemacs. Download.Back to top

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