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 wordsAlgebrista 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 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).
Available is the optional Home-E (pdf) project, to be done individually. It is due, slid u n d e r 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 (pdf, 3pages) to earn full credit.
Here are a few questions as practice for Class-D (pdf). Voila the actual Class-D (pdf).
Home-D (pdf) was jumpin' with interesting Algebra. Post your solutions for Fun And Profit…
The actual Class-C (pdf) brought actual chocolate to the classroom, as well as actual colored pencils. It was preceded by the Practice Class-C (pdf) exam.
The fascinating and colorful Home-C (pdf) was cheerfully handed-in on Friday, 28Mar2008.
Most astonishingly, genuine class participation points are earned by posting nicely-written solutions (to any of these three) to our archive. Genuine joint solutions are allowed; indeed, encouraged. The minor extra-credit Cl-C problem was to Burnside the edges of cube, with K colors.
Chuckles of appreciation met Class-B (pdf) ("The Permutation Exam"), with a wink and a nod at the similarity of these problems with those of the take-home.
General gaity and acclaim greeted the taut Home-B (pdf) with its clean lines, and minimalistic mostly-black-and-white format. It was due: noon on Thursday, 14Feb2008.
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 (6^{th} edition) .
Author: | Joseph A. Gallian | ISBN: | 978-0-618-51471-7 |
Year: | 2006 | Publisher: | Houghton Mifflin |
The various Math czars who help out.
E-Probs | Phone-list | Chalk | Blackboard | Time | Computer |
---|---|---|---|---|---|
Jessi & Andrew | Sebastian | Ali | John | Phil | Steven |
The Web
Below is part of Autumn 2005, Algebra.
Our textbook is Contemporary Abstract Algebra (6^{th} 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 (5^{th} 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.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.
(2003) | |
---|---|
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 my office door (Little Hall 402, Northeast corner) , no later than 2PM on Friday, 25Apr2003. |