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Spr2008: MAS4301 3175 ABSTRACT.ALGEBRA.1 MWF6 LIT237

(abstract) Algebra 1 Algebra

Lyrics for The Klein Four – Finite Simple Group are:
The path of love is never smooth But mine's continuous for you You're the upper bound in the chains of my heart You're my Axiom of Choice, you know it's true But lately our relation's not so well-defined And I just can't function without you I'll prove my proposition and I'm sure you'll find We're a finite simple group of order two I'm losing my identity I'm getting tensor every day And without loss of generality I will assume that you feel the same way Since every time I see you, you just quotient out The faithful image that I map into But when we're one-to-one you'll see what I'm about 'Cause we're a finite simple group of order two Our equivalence was stable, A principal love bundle sitting deep inside But then you drove a wedge between our two-forms Now everything is so complexified When we first met, we simply connected My heart was open but too dense Our system was already directed To have a finite limit, in some sense I'm living in the kernel of a rank-one map From my domain, its image looks so blue, 'Cause all I see are zeroes, it's a cruel trap But we're a finite simple group of order two I'm not the smoothest operator in my class, But we're a mirror pair, me and you, So let's apply forgetful functors to the past And be a finite simple group, a finite simple group, Let's be a finite simple group of order two (Oughter: "Why not three?") I've proved my proposition now, as you can see, So let's both be associative and free And by corollary, this shows you and I to be Purely inseparable. Q. E. D.
Lyrics by Matt Salomone
The following came from Earliest Known Uses of Some of the Words of Mathematics.
ALGEBRA comes from the title of a work written in Arabic about 825 by al-Khowarizmi, al-jabr w'al-muqabalah, in which al-jabr means "the reunion of broken parts." When this was translated from Arabic into Latin four centuries later, the title emerged as Ludus algebrae et almucgrabalaeque.

In 1140 Robert of Chester translated the Arabic title into Latin as Liber algebrae et almucabala.

In the 16th century it is found in English as algiebar and almachabel, and in various other forms but was finally shortened to algebra. The words mean restoration and opposition.

In Kholâsat al-Hisâb (Essence of Arithmetic), Behâ Eddîn (c. 1600) writes, The member which is affected by a minus sign will be increased and the same added to the other member, this being algebra; the homogeneous and equal terms will then be canceled, this being al-muqâbala.

The Moors took the word al-jabr into Spain, an algebrista being a restorer, one who resets broken bones. Thus in Don Quixote (II, chap. 15), mention is made of un algebrista who attended to the luckless Samson. At one time it was not unusual to see over the entrance to a barber shop the words Algebrista y Sangrador [bonesetter and bloodletter] (Smith vol. 2, pages 389-90).

The earliest known use of the word algebra in English in its mathematical sense is by Robert Recorde in The Pathwaie to Knowledge in 1551: Also the rule of false position, with dyvers examples not onely vulgar, but some appertayning to the rule of Algeber.

The phrase an algebra is found in 1849 Trigonometry and Double Algebra by Augustus de Morgan: Ordinary langauge has methods of instantaneously assigning meaning to contadictory phrases: and thus it has stronger analogies with an algebra (if there were such a thing) in which there are preorganized rules for explaining new contradictory symbols as they arise, than with one in which a single instance of them demands an immediate revision of the whole dictionary [University of Michigan Historical Math Collection]. …

Welcome. Our Teaching Page has useful information for students in all of my classes. It has my schedule, LOR guidelines, and Usually Useful Pamphlets. One of them is the ChecklistThe checklist (pdf) which gives pointers on what I consider to be good mathematical writing. Further information is at our class-archive URL (I email this private URL directly to students).

Optional end-of-semester project

Available is the optional Home-E (pdf) project, to be done individually. It is due, slid u n d e r room 402 Little Hall my office door (Little Hall 402, Northeast corner) , by 2PM, Friday, 25Apr2008 The project must be carefully typed and carefully proofread.


At all times have a paper copy you can hand-in; I do NOT accept electronic versions. Print out a copy each day, so that you always have the latest version to hand-in; this, in case your printer or computer fails. (You are too old for My dog ate my homework.)

Please follow the guidelines on the Checklist Checklist (pdf, 3pages) to earn full credit.



In all of my courses, attendance is absolutely required (excepting illness and religious holidays). In the unfortunate event that you miss a class, you are responsible to get all Notes / Announcements / TheWholeNineYards from a classmate, or several. All my classes have a substantial class-participation grade.

As the semester progresses, you will also need to print-out a few pages of handouts that I have prepared for you.

We will cover some material that is not in our text; in particular, applications of group-theory for solving certain games and puzzles.


Our textbook is Contemporary Abstract Algebra (6th edition) .


Author: Joseph A. Gallian ISBN: 978-0-618-51471-7
Year: 2006 Publisher: Houghton Mifflin
Photo of text cover
It is available from the publisher as well as from online booksellers.

The various Math czars who help out.

E-Probs Phone-list Chalk Blackboard Time Computer
Jessi & Andrew Sebastian Ali John Phil Steven

Web Algebra on The Web

See also general math references.

Previous invocations of this Fine Course

Below is part of Autumn 2005, Algebra.

Our textbook is Contemporary Abstract Algebra (6th edition).

Here is the course syllabus and First Homework Assignment (txt).

Mr. Natan Milgram has been kindly recording the Extra Problems that we occasionally invent in class. (Anyone can invent an EP, not just the Prof.) Folks posting solutions usually earn chocolate, provided by the prof. If chocolate is not your thing, then you can earn gold ingots…

Here is Z-Home (pdf). Voila Z-InClass (pdf).

Here is Y-Home (pdf) Voila Y-InClass (pdf).

Here is X-Home (pdf)



From the Spring 2003, Algebra page.


The text is Contemporary Abstract Algebra (5th edition), by J. Gallian.

You can also study this material from other algebra texts. The Marston Science Library has many good algebra texts that you may check-out.

[Image: Steaming coffee cup] Exams and Projects (Algebra)

There will be some small number of exams as well as a final exam or project. There will also be some number of pop (surprise) quizzes. I may also ask (teams of) you to present homework problems at the board.

When(2003) ExamText
03Feb Here are the joyous A-home (pdf). and A-InClass (pdf), veritable walks-in-the-park.
31Mar For the wonderful B-home (pdf) the class wrote many good essays. Among them were the Dihedral essay and Coconut essay by Robert, Matt and Carmen.
Is everyone prepared for B-InClass (pdf)?
18Apr The poly-fabulous C-home (pdf) now exists. It is due, slid u n d e r room 402 Little Hall my office door (Little Hall 402, Northeast corner) , no later than 2PM on Friday, 25Apr2003.

JK Home page Goto jk HomePage

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Abstract Algebra