This page serves as the root for all documents in my directories, but only a small attempt has been made to make it fancy. Few special features are used to avoid shutting out those using older browsers.

Here is another picture taken by C. J. Mozzochi at the Workshop on Combinatorial and Additive Number Theory in May 2004.

I have now retired, but I was on the faculty of the Mathematics Department on the New Brunswick/Piscataway Campus of Rutgers University from September 1960 to June 2010.

From 1991 to 1995, I was editor of the *Problems and
Solutions* section of the American Mathematical
Monthly.

I also belong to the TeX Users Group. At the meeting in August 2001, I learned about some amazing things that can be created in TeX for viewing in the PDF format. If you have version 4 (or newer) of the Acrobat Reader (version 3 won't work since a javascript interface is used), take a look at this calculator.

I was a fellow of Livingston College and represented the College on the New Brunswick Faculty Council. This has been compounded in two ways: (1) I became Faculty Council webmaster for the 2003-2004 academic year and continued in that role through June 2009; (2) I was chair of the Livingston College Executive Council of Fellows for the 2005-2006 and 2006-2007 academic years. While Livingston College no longer has an Assembly of Fellows following the reorganization of the New Brunswick/Piscataway Campus, I remained on the Faculty Council as a representative of the Livingston Campus Community for 2007-2009. I was also elected to represent SAS on the University Senate for a 3 year term starting Fall 2007.

Form September 2008 to May 2010, I was the Head Undergraduate Advisor for the Mathematics Department.

As department computer
coordinator, I was prepared to assist members of the department with
all computer-related questions, although an official help desk now exists.
General computing
support provided by our support staff can be found on
the Department computing page. A new addition
to our system is **jsMath**. Here is a sample page illustrating its abilities. A newer
system that seems to work better is
MathJax. Here is a
sample. We also have
documentation on our system.

There is a new Rutgers letterhead that we should use for all official correspondence. Unfortunately, it was only made available for a popular system that few of us use. To remedy this, a LaTeX class was created that is installed on our system as rutgersletter.cls. There is currently no documentation other than comments in the file (use "rutgersletter.cls" to find it), but some information about the use of the same class can be found on a Physics Department page.

Other items that catch my attention will be shared. Here is a modification of an article entitled How to listen to a maths lecture posted by T. W. Körner of the University of Cambridge. I changed the fonts changed to Times, but the original A4 paper size was retained.

As suggested by the image (stolen from a site devoted to web design), I encouraged the use of W3 standards on the pages that I maintain. In addition to this page, I served as webmaster for the Faculty Council and maintained several pages for courses in the mathematics department.

Slides from a talk in the *New York Number Theory seminar* in February 2012, entitled "Introduction to Hausdorff measures and dimension".

Slides from a talk in the *AMS Special
Session on Continued Fractions* in January 2009, entitled "Quadratics,
continued fractions and divided cells". This continues joint work with
Mary
Flahive.

Slides from a talk given in the *New
York Number Theory seminar* and the *Logic and Games
seminar* at the CUNY graduate Center in March 2006. The talk was
based on my paper with Erik Ellentuck, "Finitely additive measures and
the first digit problem" that appeared Fundamenta Mathematicae 65
(1969).

Slides from a talk in the *AMS Special
Session on Continued Fractions* in January 2006, and later at the
*New York Number Theory seminar*. entitled "Resurrecting the
divided cell algorithm for inhomogeneous Diophantine approximation".
(joint work with
Mary
Flahive). A revised version was presented at a
conference in Japan in March 2007. It was then prepared for
publication in the proceedings of the conference with the title "The
divided cell algorithm and the inhomogeneous Lagrange and Markoff
spectra". Here is a preprint

An article entitled Hand computation of matrix exponentials, based on some course notes is in a form that can be shown, although I intend further revision before submitting it for publication.

There is now a posted version of
*Sums of four squares *from *Number Theory: New
York Seminar 1991-1995 *(ISBN 0-387-94826-0).

A copy of *Computing Endpoints in Markoff Spectra *from
*number theory with an emphasis on the Markoff spectrum *(ISBN
0-8247-8902-4) has been located, but minor reformatting will be
required for posting.

Earlier publications are unlikely to be available. However, the following short papers were scanned.

- Modules which are isomorphic to submodules of
each other, published in
*Archiv der Mathematik*, XVI (1965), 184-185. - An inequality for perimeters in a subdivided triangle, published in
*Univ. Beograd. Publ. Elektrotetehn. Fak.*Ser. Mat. Fiz. No. 602-633 (1978) 191-193. - 29 is not equal to 29,
published in
*The Australian Mathematical Society Gazette*(ISSN 0311-0729), 4 (1977), 19-21. - Interactive computation of homology of finite
partially ordered sets (with E. Cooper and D. M. Latch),
published in
*SIAM J. Computing*, 4 (1975) 321-325. - A problem with telephones, published in
*SIAM J. Alg. Disc. Meth.*, 2 (1981) 13-18. - Hausdorff dimensions of sets arising in number
theory, published in
*Number Theory: New York 1983-1984*, Lecture Notes in Mathematics 1135, Springer . - The continued fraction algorithm approached
through quadratic forms, published in
*Ranchi University Mathematical Journal*, 22 (1991), 1-24.

I have participated in the New York Number Theory Seminar since its founding in 1982.

Material more than five years old will be removed unless it has some unique feature. Direct links to more recent material will also be removed if it can be reached through a more recent version of the same course.

Sakai has used for most of my courses since its introduction at Rutgers in Fall 2005. Individual section pages may not have been created if there is no need for public supplements. Links to the department course page will be given in those cases.

- 356 selected course material, Fall 1998. There is no more recent version of this course, so it will be retained.
- 135 course material, Fall 2001. This course used both prepared slides and "surveys" of examples that were handwritten in lecture and transcribed later using dvipdfm to produce some colorful pdf files. Direct computer displays in enhanced classrooms have since replaced these transparencies and surveys for most courses, but it is interesting to preserve an earlier way of organizing lectures. Also, there is no more recent version of this course, so it will be retained.
- 252 course material, Spring 2002. There are differences in style between the two Differential Equations courses (244 and 252), so this will be retained.
- 373 course material, Fall 2003. There is no more recent version of this course, so it will be retained.
- 574 course material, Spring 2004. A course on Diophantine Approximation not likely to be repeated, so it will be retained.
- 250 course material, Spring 2007
- 311 course material, Spring 2007
- 103H course material, Fall 2007
- 454 course material, Fall 2007
- 151 course material, Fall 2008
- 321 course material, Fall 2008
- 550 course material, Summer 2009. This page contains a chain of links to pages from the summers of 1999, 2000, 2001, 2002, 2003, 2004, 2006, 2007 and 2008 (I did not teach the course in 2005). Material is similar over those years, but the supplementary material is revised each year
- 250C course material, Fall 2009
- 351 course material, Fall 2009
- 421 course material, Spring 2010

Archives can be generally located by selecting "Course Materials" from the Mathematics Department Home Page, and following links to the appropriate course and section.

Mail to: bumby@math.rutgers.edu

This file was last modified on
Monday November 29, 2021.