Arthur Hobbs

Arthur Hobbs, Professor

 Photo shows me in PhD robes of the University of Waterloo 
My office is Room 218 in Milner Hall.


My mailing address is:


Prof. Arthur M. Hobbs      	    AMS Classification 05C
Department of Mathematics  	    Also interested in 05B35, 01-XX 
Texas A&M University
College Station, TX 77843


Office phone:  (979)-845-3250


Home phone:    (979)-846-9376


e-mail:         hobbs@math.tamu.edu

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FRIENDS AND FAMILY

Here are my wife, Barbara, and myself at a new years party:

I have been very fortunate in the many friends I have had. The following photograph shows me between two of them. The one on my left is my thesis advisor, the outstanding graph and matroid theorist, William T. Tutte. The one on my right was one of the most prolific mathematicians who ever lived and was the founder of several branches of mathematics, Paul Erdos. (There should be a Hungarian umlaut above the o of Erdos's name, but I don't know how to produce one in html.) So here we are, from left to right, Paul Erdos, Arthur Hobbs, and William T. Tutte. The picture was taken at Western Michigan University at the Quadrennial conference on May 7, 1980, by my mother, Helen Hobbs.

VIGRE COURSE, Math 662, Section 601, Fall 2002.

Prof. Borosh and I taught a course in the intersection of graph theory and number theory. We taught enough of the elements of our specialties that students could read a research paper including elements of both subjects. Then students were asked to select a paper from a list we provided, read it, and report on it to the class. An important aspect of the course was gaining a feeling for the discovery process involved in research. We asked about each idea presented, "Are there questions that are not addressed here? Can these ideas be extended in ways the authors did not discuss?" There was a test on each of number theory and graph theory just after the lectures on that topic, and the grade was based on the results of those tests and on the presentations made. The homework assignments were as shown.

COMBINATEXAS

The eighth annual Texas combinatorics conference, called CombinaTexas, will be held on February 24 at Texas A&M University, College Station. Click on the title above for more information. COMBINATEXAS was held at Texas A&M University on March 31 through April 2, 2000, for the first time. It has continued as an annual event, changing venue from year to year.

COMBINATORICS AT TAMU

The web page of the Algebra and Combinatorics Group contains announcements of interest in this area. Moreover, the Group runs a weekly seminar . Take a look at the seminar offerings.

TAMU AAUP CHAPTER

I was President of our AAUP chapter in 2001-2002. The chapter has slightly revised the New Faculty Brochure originally distributed to all new faculty in 2000. The revised brochure was distributed to the new faculty of 2001 and 2002. We worked on the rewrite of System Policy 12.01 (academic freedom and tenure) proposed by the System attorneys. The Faculty Senate formed a committee to prepare an alternative rewrite, and faculty members from throughout the System had a role in formulating the final document.

THE SPECIAL ISSUE OF DISCRETE MATHEMATICS IN MEMORY OF PAUL CATLIN:

Paul Catlin, 1948-1995, painting by Ying Wu, Univ. of West Virginia

Prof. Hong-Jian Lai of West Virginia University and I prepared a special issue of Discrete Mathematics in honor of the memory of Paul Catlin . It appeared as volume 230 in 2001.

A STORY

ls Texas is rather hotter than the part of the world where I grew up (northern Indiana) and got my PhD (Ontario, Canada). To understand just how much hotter, the following story, which was written during the 1996 heat wave, will help. Why I was Late .

COURSE INFORMATION

During the summer sessions of 2008 I am teaching MATH 304 from the Seventh edition of Leon's "Linear Algebra with Applications". The homework assignments are as shown, and a previous assignment list (which is similar to, but not exactly the same as, this semester's list) appears at the end of the current assignments.
THE CLASSROOM FOR MATH 304 THIS SEMESTER IS BLOCKER 120..

OFFICE HOURS:
Every day from 2 pm to 3 pm, and by appointment. In fact, if you need to see me at another time, give me a call at 846-9376 or 845-3250 and make an appointment. The surest way of talking to me is to call 846-9376 between 7:30 and 8 am almost any morning.

THE FINAL EXAM will be from 1 pm to 3 pm on August 6..
My office is 218 Milner Hall.

THE PUTNAM EXAM

The William Lowell Putnam mathematics competition is a national undergraduate mathematics compentition of the highest order. Preparing for it and taking it are valuable learning experiences. All students interested in mathematics should give it a try. The names of winners and of high scoring students are published, and being on that list is a valuable reference for those who succeed. Check out the latest information about the Putnam contest.

PROJECT TO PROVIDE ANSWERS TO FREQUENTLY ASKED QUESTIONS

On Monday, January 12, 1998, the Faculty Senate approved the Answers to Frequently Asked Questions as finally submitted to it, and during the following months the Executive Committee of the Faculty Senate agreed to adopt the official name of "TAMU Faculty Facts: Answers to Questions About Faculty Roles and Responsibilities at Texas A&M University" for these papers. They have been revised since then, and the revision was approved by the Faculty Senate at its meeting on September 14, 1998. The following file contains the complete second edition of "Faculty Facts:"

TAMU Faculty Facts: Answers to Questions About Faculty Roles and Responsibilities at Texas A&M University

This document is now out of date. I hope another faculty member will someday update it and get it published again.

Personal

Brazos Valley Chorale

here is a nice picture of a night launch as photographed by my friend Tom Dow. For more from Tom Dow, see some of Tom's home page. In 1999, I completed 6 years on the Faculty Senate of Texas A&M University. I am married to Barbara J. Hobbs and have two children, Melissa Howlett and Patty Hobbs . We attend St. Andrew's Episcopal Church. I am a member of TACT and of AAUP.

Square Dancing, round dancing, and Contra

Circle Squares, which meets regularly on the first and third Thursday of each month at the A&M Methodist Church starting at 7 pm. Members of the group also often have dance lessons at the same time and place on the second and fourth Thursdays. Wayne Morvant is the caller.
Levis and Lace, which meets regularly on the second and fourth Tuesdays of each month at 8 pm in the cafeteria of the school in Gause. This is a plus club. Larry Astle is its caller.
CONTRA: Often dancing to live music, we have a fine time from 3 until 6 pm on the second Saturday of each month. We meet in the Unitarian Fellowship Hall at 305 Wellborn Road, College Station. First time dancers enter free; we ask a $5 donation (students $3) of other dancers. One of the nicer things about contra is that you don't have to have a partner to participate, and you don't have to already know how to dance contra. The dance has many appealing traditional elements. We form in facing lines, and if the dance is "proper," women are in one line and men in the other. ("Improper" dances have the men and women alternating in each line.) We are walked through the figure two or three times until we have understood it, and then the music starts and we dance for awhile. It's great fun and great exercise.

Among my favorite callers are the callers for my clubs, Larry Astle and Wayne Morvant, but I think very highly of Jim and Fae Park from Michigan. I was extremely fond of Johnnie Wykoff and his wife Star, but sadly Johnnie died suddenly in May, 2000. For those who also loved his calling, Star has prepared a list of Johnnie's records.
Education
- B.S. University of Michigan 1962
- Ph.D. University of Waterloo 1971.
Research Interests
- Graph Theory. My research before entering graduate school was on thickness of graphs. In graduate school and for 10 years after that, I concentrated on Hamiltonian cycles, particularly in squares and higher powers of graphs. I then spent a couple of years working on the Gyarfas and Lehel conjecture that n trees of orders 1 through n can always be packed into K_n. After working on a textbook in linear algebra (Hartfiel and Hobbs, Elementary Linear Algebra, PWS Publishers, STILL AVAILABLE), I began working with packings of graphs with trees and covering by trees. I did this work with several co-authors, including Paul Catlin, Jerrold W. Grossman, and Hong-Jian Lai. We defined the fractional arboricity of a graph as $$\gamma(G) = max_{H \subseteq G}({|E(H)}|\over{|V(H)| - \omega(H)}),$$ where $\omega(H)$ is the number of components of H and the maximum is taken over all subgraphs H for which the denominator is not zero. We also defined the strength of a graph (following Cunningham) as $$\eta(G) = min_{S \subseteq E(G)}({|S|}\over{\omega(G-S)-\omega(G)}),$$ where the maximum is taken over all subsets S of E(G) for which the denominator is not zero. A graph is uniformly dense if eta and gamma are equal. We have characterized uniformly dense graphs. We note that a uniformly dense graph is particularly survivable, and so we are interested in constructing such graphs. We have found several classes of uniformly dense graphs and several ways of constructing such graphs.
- Matroid Theory. Both eta and gamma are easily expressed in matroid terms, and so uniformly dense matroids are defined. Many of our results in this subject are most naturally expressed in matroid terms, and so our papers are often papers in matroid theory.
- Selected Publications available.
Annual reports for 1996 , 1997 , 1998 , 1999 , 2000 , 2001 , 2002 , 2003 , 2004 , 2005 , available.
ESSAY ON READING RESEARCH PAPERS
I have written an essay on how to read research papers that some people have found interesting. To see that paper, click here , and to download it in AMSTeX, click here .
Interesting Links
Math Reviews 2000 subject classifications
Electronic Research Announcements of the AMS
MAA
Go to here for a graph drawing system.
A list of hundreds of graph theorists and other information is available together with links to other useful information.
The travelling salesman problem bibliography is a useful source of information on this problem.
The newsletter "Concerns of Young Mathematicians" newsletter is interesting to more than just young mathematicians. It talks about jobs, meetings, and how to do one's job. The archives are worth examining.
The Texas A&M System Policy on Tenure is interesting in relation to the preceeding item. See particularly paragraphs 2.3 and 4.3.
Powell's Technical Books , a really great used book store with lots of used advanced mathematics books for sale.
The Paul Erdos page tells about the Erdos number and names the people who are involved in it. There is also a link to an excellent obituary of Paul, who died on September 20, 1996.
Photos of the asteroid Eros taken by NEAR are very interesting.
Novaspace Galleries sells paintings and prints related to space. The pictures at this site are fantastic!
Abby's Menagerie home page presents an interesting idea, and it has links to a lot of other comic book home pages.
Read Shakespeare's works , complete with on-line glossary (of mixed value).
Some neat archaeological home pages are listed.
A very nice list of the academic genealogies of people in mathematical fields related to computer science, such as in combinatorics. Take a look.
A fascinating spoof by Prof. Sokal together with his explanation can be found aat this web site.
Mathcamp is a really good experinece for a bright high school student. Check it out.

Last updated: January 17, 2001.