Abstract Algebra

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Announcements

12/18/03 Final course grades are now posted.
12/15/03 Grades to date are now posted.  A couple people have a little missing work, which needs to get to me ASAP (put it in the folder-holder in the hall outside my office if I'm not there).

The plow still hasn't come and I can't yet get out of my driveway.  If I can't make it in for the review session this afternoon, please feel free to call me at home-- 372-3743-- with any questions you may have.

12/9/03 Class Canceled, Wednesday, December 10.  I do have to report for Jury Duty.  There will be an (optional) extra review session on Monday, December 15, from 1:00 -2:30 to make up for the missed class.

12/1/03

!!!  EXTRA CREDIT ATTENDANCE TALK  !!!

Date: Monday, December 8, 2003

Time: 2:30 Ė 3:30

Location: Cheray 111, SMC campus

Title: A new direct construction method for block designs

Speaker: Gennian Ge, UVM CS department

(To get the extra credit, write a paragraph or two synopsis of the talk.)

More details at: http://academics.smcvt.edu/jellis-monaghan/Combo_Seminar/combo_seminar.htm#10-1-03 

11/21/03 Revised homework for chapters 10 and 11:

Chpt. 10:  9, 28, 37, 38, 47, 51, 52.  Chpt. 11: 3, 5, 6, 10, 19, 32.

11/20/03

Final Exam:  Take home part.  1.  Redo the Three Examples, using the theory you have learned as well as your own intelligence.  These should be pretty extensive by now.  Emphasis will be on the second and third examples.  Think factor groups for the second example, and direct products for the third.

 

2.  Write up the following exercises beautifully--presentation and clarity count!  Find as many non-isomorphic groups of order 12 as you can--you must say why each is not isomorphic to the others.  Pg. 224 #12.  Pg. 225 #24 (hint--use the N/C theorem on page 203).   You must work entirely on your own--no collaborating or discussing these problems in any way with anyone other than myself.

Take home part is due Wednesday, December 17, at the start of the final exam.

Inclass part:  This will consist of true/false from the Gallian website (to check your understanding of the theory), as well as basic computation examples.  Eg you should be able to find (quickly) gdcs, lcms, s and t for linear combinations, orders of various elements in various groups, subgroup lattices, permutations (multiply, invert, write as transpositions, find orders, know Sn and An), group tables, orders of subgroups and factor groups, elementary divisor and invariant factor forms, isomorphisms.  You should be very familiar with a wide range of common groups and their properties.  This portion is really to see that you are adept at the basic computation necessary to work small examples.  The inclass test will be on Wednesday, December 17, at 9:00-11:30.

You may use your study guide during the final exam.

11/19/03 Grades have been posted--please check them for accuracy and see me if you have any questions.
11/17/03 Caesar Ciphers and Secret Messages

Professor Susan Diesel

Norwich University

Julius Caesar is said to have sent messages in cipher by using a simple substitution, where the plaintext letter was replaced by the letter three places further along in the alphabet, so that A was replaced by D, and so on.

 The Caesar Cipher is one of the simplest monoalphabetic substitutions one may use, and it's also an easy one to break.

 Creating unbreakable ciphers, and trying to decrypt them, has occupied mathematicians, linguists, and others for a long time.  Find out about the Caesar cipher and other ciphers from history, and about the public key cryptography of today in this colloquium.

 Wednesday, December 3, 2003 at 12:00 P.M.

Cabot 295

Refreshments will be served.

 

11/10/03

EXCELLENT TALK OPPORTUNITY!!

This is a general audience talk from someone who has won awards for excellence in this field (graph coloring).

 

WEDNESDAY, November 12:

 

4:00 - 5:00pm†††† University Scholars Lecture

††††††††††††††††† "A Tale of Crayons and their Consequences: Why Four Colors Suffice"

††††††††††††††††† Speaker: Dan Archdeacon, Mathematics and Statistics

††††††††††††††††† Location: Memorial Lounge, Waterman Building

††††††††††††††††† REFRESHMENTS AT 3:45 AND AFTER SEMINAR

 

11/7/03

Add computer problems 2 and 3 to chapter 8.There will also be an RSA code assignment (see problem 5)

11/6/03

Study Sheets for chapters 0 through 8 are due Monday, Nov. 10.  You will be able to use these on the Final Exam, so the more thorough, the better.  They should include all theorems and definitions, with small examples attached to help you understand what is being said.  There is no page limit here, but if it is longer than 3 or 4 pages, you might want to come up with a system to let yourself find things easily during a test.

10/31/03

STUDENT SUMMER RESEARCH INTERNSHIPS AVAILABLE

Summer Research Opportunity--$3500 plus $1000 in supplies for May 15 - June 30.  I would be thrilled down to my toes to help you come up with a project and be your advisor.  Returning students only.

10/30/03

Some career resources:

Lots of people with exciting real jobs using Math, More people using Math,  Job Listing Services, Comprehensive resources from SIAM.

The department has (in George's office) a CD-ROM and videotape entitled Careers in Mathematics created by three major professional societies of mathematicians (AMS, MAA, and SIAM).  He also has video tapes of a panel and presentation by recent SMC math alums.

There is also this note from George:

"This summer I have been in contact with a number of St. Michael's mathematics alumni in a wide variety of careers, in such areas as statistical data analysis, actuarial consulting, software engineering and other computer-related fields, education (at the secondary and university levels), and even flying (specifically as a USAF pilot). These alumni are willing to be resource/contact people representing a variety of careers. If you wish to be in contact with an SMC alumnus from a particular mathematics-related field, then let me know and I will try to connect you with an appropriate person. I recently have given a few of my advisees e-mail addresses of mathematics alumni who are pursuing careers in an area of interest to them, and could do a similar service for any of you that are interested."

 

10/20/03

!!Required Attendance Talk!!

Talk Overheads

(This is more graph theoretic than algebraic, but consequently more likely to be accessible!  You will need to write a short paragraph or two synopsis of the talk.)

Date:†† Wednesday, October 29, 2003

Time:2:30 - 3:30 p.m.

Location: SMC campus, St. Edmunds, Room 113.

Title: Bar-visibility Graphs, Generalized and Specialized

Speaker:Alice Dean , Skidmore College

10/17/03

MIDTERM Reschedule--The inclass portion of the Midterm has been rescheduled to Monday, October 27.

10/6/03

MIDTERM:  Take home part.  1.  Redo the Three Examples, using the theory you have learned as well as your own intelligence.   2.  Write up the following exercises beautifully--presentation and clarity count!  pg 89-92, numbers 18, 24, 26, 32. pg 169-171 numbers 2, 6, 48, 52 (need that n>2).  You must work entirely on your own--no collaborating or discussing these problems in any way with anyone other than myself.

Take home part is due October 27.

Inclass part:  This will consist of true/false from the Gallian website (to check your understanding of the theory), as well as basic computation examples.  Eg you should be able to find (quickly) gdcs, lcms, s and t for linear combinations, orders of various elements in various groups, subgroup lattices, permutations (multiply, invert, write as transpositions, find orders, know Sn and An), group tables.  This portion is really to see that you are adept at the basic computation necessary to work small examples.  The inclass test will be on Friday October 24.

10/1/03

Here are some examples of using Maple to work with permutations:  permutation group.mws

9/30/03

Since several people are traveling, the homework for tomorrow is postponed until Friday.

9/24/03

!!!  EXTRA CREDIT ATTENDANCE TALK  !!!

Date:  Wednesday, October 1, 2003

Time: 2:30 pm

Location: Room 366, Jeanmarie, St. Michaels College Campus.

Title: Variations on Interval Graphs

 

Speaker: Richard Lundgren, Professor

Department of Mathematics

University of Colorado at Denver

(This is more graph theoretic than algebraic, but consequently more likely to be accessible!  To get the extra credit, write a paragraph or two synopsis of the talk.)

More details at: http://academics.smcvt.edu/jellis-monaghan/Combo_Seminar/combo_seminar.htm#10-1-03 

9/19/03

Just a reminder that we have a speaker coming from UC San Diego to talk about the difficulties of anonymous identity over the Internet, which has become so important in our networked society, two weeks from today (October 3).

Please pay attention to the second title and the disclaimer at the bottom which states you donít need any previous background to be able to learn something from the presentation. I encourage you to come and here about the research of this person who recently completed her PhD in Computer Science on the West Coast.

Prof. Trono

Anonymous Credentials with Biometrically-Enforced Non-Transferability

Designing Hand Stamps for the Digital World

Dr. Sara Miner More

University of California, San Diego

Friday, October 3rd 2003

3:45pm in St. Edís 104

ABSTRACT:

In this talk, we discuss digital non-transferable anonymous credentials, which allow individuals in a particular group to remain anonymous while demonstrating group membership. An analogous credential in the "real world" is a hand stamp one might obtain upon entering an establishment that serves alcohol. The individual uses his stamp to prove to the bartender that he is of legal drinking age, but the stamp alone does not reveal the individual's identity. Furthermore, this credential cannot be transferred to a different individual.

Specifically, we improve upon existing digital anonymous credential systems by developing a model and solution with stronger guarantees of non-transferability which do not sacrifice user anonymity. When anonymous credentials are implemented using only passwords or secret keys, for example, the credentials are easy to copy - users can simply tell their passwords to friends. In contrast, our model uses biometric authentication modules in tamper-resistant hardware to tie credentials directly to particular individuals, so credentials are essentially copy-resistant and useless if lent to others. Furthermore, despite the fact that the user cannot inspect the code inside the secure hardware, we ensure that the hardware cannot leak information about the user's identity without his knowledge when he displays the credential. Finally, we describe an extension which allows group members to be added to and removed from the group in a secure manner.

No background in cryptography or security is required, and light refreshments will be served. (This talk describes joint work with Russell Impagliazzo (UCSD)).

 

 

9/18/03

Math party moved!

Since it looks like rain on Friday, the party has been moved indoors to TownHouse 329.  Lasagna from Papa Franks!  We need to get a headcount to know how much to order, so please let me know asap if you can come.

 

9/16/03

Office Hours Change:  Office hours today have been moved to 1:15 to 2:15.

9/16/03

Math party!

What:†††††††††††††††††††††††††††††††† Mathematics Department Picnic/BBQ

When:††††††††††††††††††††††††††††††††††††††††††††††† Friday, September 19th, Starting Around 5:30 PM

Where:††††††††††††††††††††††††††††††† Between Townhouses 324 and 325

Come Meet Other Mathematics Majors and Students Interested in Mathematics.

Food and Entertainment will be provided

(and hardly any math).

Please RSVP to Patti Bodkin, Corinne Chick, or Aaron Desrochers if you plan to attend, so that the proper amount of food can be prepared.

 

9/11/03

Greetings,

The National office and Vermont Chapter of Sigma Xi, The Scientific Research Society, is once again offering Undergraduate Research Fellowships (URF) to interested undergraduates. Details can be found at:

Vermont Chapter: http://vtsigmaxi.smcvt.edu/URF/URFAppilications.htm; application due date: October 15th

National Chapter: http://www.sigmaxi.org/programs/giar/index.shtml; application due date: October 15th & March 15th.

Since the local Chapter offers its own version of the URF, students may apply to just the Vermont Chapter (following a similar format, procedure etc. as the National office, but the application review takes place locally). They may also apply to the National version, but this is separately reviewed and handled. Students can also apply to both if they choose. Since I am the SMC rep. for this, applications for the local Chapter should be directed to me.

Sandy

William Karstens

Assistant Professor of Physics

Saint Michael's College

Colchester, VT 05439

email: wkarstens@smcvt.edu

ph: (802) 654 - 2681

fax: (802) 654 - 2610

9/8/03

Note from John Trono about  upcominging talk:

I hope to see most of you there on Friday, as I think this will be a very entertaining and interesting presentation. Cookies and cider/soda will be available, and the talk should be 50 minutes or less.

Friday September 12th, 2003, 3:45pm, room is St. Edís 104:

Dr. Craig Wills, Worcester Polytechnic Institute (and a brief summary of his talk)

Inferring Relative Popularity of Internet Applications by Actively Querying DNS Caches

In this work, we propose a novel methodology that can be used to assess the relative popularity for any Internet application based on the data servers it uses. The basic idea is to infer popularity of data servers by periodically ``poking'' at local Domain Name servers (LDNSs) that service Domain Name System requests from a set of users running Internet applications and determining if LDNSs have cached resource records for the data servers. This approach allows us to measure the relative percentage of pokes that result in a cache hit as a coarse measure of the relative popularity of a particular data server among the users of a given LDNS.

 

9/2/03

A note from math dept chair Jim H:

Welcome back and hello,

For many years we've run math help sessions at night. These provide a chance for students in calculus classes, or in the 101 and 102 classes, to get somy help with their material on a drop-in basis. These sessions are staffed by students, so this is where you come in!

Are you interested in working one or two? We always pair people up, so you won't be lonely, and we get many people who have done it before that come back again, so it must be fun. If you have had through Calc III, and would be interested in making a little extra money (I am told, about $7-$8 per hour), working one or two nights in a one-on-one or small group setting, then I'd like to hear from you. Tell me what classes you've had, please, and what nights you could work.

Also, we are looking for folks who might be interested in grading homeworks or quizzes. You work with a faculty member, again in conjunction with a calculus, or 101, or 102 class. You will be grading quizzes or homework papers, following the instructions of the course instructor. If you are interested in this, please also write and tell me which classes you've had.

Thanks, Jim Hefferonjim@joshua.smcvt.edu 

8/21/03

Be sure to click 'refresh' when you visit this site to be sure you get the most recent changes.

8/21/03

The Student Resource Center runs excellent workshops every semester on study skills, time management, test-taking techniques, etc.  For details: SRC study skills  

8/21/03

The postings on this site have all been tested and all work.  If you have any difficulty getting material off this site, you can try any of the following:

1.  See if someone in your study group was able to print the file you want and make a photocopy of it.

2.  Try using one of the lab computers in case the problem is with how your own computer is configured.

3.  Using Explorer, right click on the link, select "save target as", then save the file to your home computer.  You should be able to open and print it from there.

4.  Contact Cynthia Kelley at 654-2756 or ckelley2@smcvt.edu.  She is the person for website trouble shooting.

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