Goto: Prof. King's page at Univ. of Florida.
Or: JK Homepage.

Page:
http://squash.1gainesville.com/Include/thispage.shtml

Aut2022: MAS4301 3249 (14949) Abstract.Algebra.1 MWF7 [13:55-14:45] LIT235 (NE)

Little 235

Little 235

A bout of Nostalgia? See
past Abstract Algebra courses.

.
Our Teaching Page
has important information for my students.
(It has the
Notes, Exams and Links
from all of my previous courses.)

The *Teaching Page* has **my schedule**,
LOR guidelines,
and Usually Useful Pamphlets.
One of them is the
*Checklist* (pdf)
which gives pointers on competant mathematical writing.
Further information is at our
class-archive URL
(I email this private URL directly to students).

Quantifiers ∀ and ∃ (“for all”

and“there exists”) are like nitroglycerin, in that one little mis-step leads to the whole thing blowing up in your face.There is no partial credit when it comes to Explosives and Quantifiers.

-JLF King

The various Math czars who help out.

Extra-Probs | Computer&Projector | Time | Memory/Telepathy | Blackboard |
---|---|---|---|---|

?? | Brandon D. | everyone | ? | everyone |

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 responsibleto get all Notes / Announcements / TheWholeNineYards from a classmate, or several. All my classes have a substantial class-participation grade.

- In one convenient location:
All 3
Alg quizzes so far (pdf),
[Wednesday, 14Sep2022]

*In this*quizzes

link, please have read the binomial/multinomial conventions on page 2, together with Operations on Sets. - Fall2022 Abstract Alg. syllabus. [Friday, 16Sep]
- A useful reference is
Group Notes (pdf).
[Thursday, 21Nov2019]
See also Burnside's lemma (W) and its application to Counting necklaces (W).

We will discuss commutator of two elements (W) in a group.

The Euclidean algorithm can be presented in table-form; I call this form the Lightning-bolt algorithm (pdf), because the update-rule looks like a lightning-bolt (used thrice). Here is a practice sheet for LBolt (pdf).

The first page of Algorithms in Number Theory (pdf), uses LBolt iteratively to compute the GCD of a list of integers, together with its list of Bézout multipliers. Page 2 uses LBolt to solve linear congruences:

Find all

*x*where 33*x*is mod-114 congruent to 18.- Prof. Gallian's home page. Has links to a modular-arithmetic calculator.
- In order to facilitate for students posting solns to our Archive,
in addition to Gallian, we
*may*use Abstract Algebra: Theory and Applications by Thomas Judson (2016 Edition), an online text made publicly available by its author. Students can post solns both from Gallian and the Judson text, as well as any interesting algebra problems that students create. - An Introduction to Isomorphism, via Gambling. And a A solution to Gambling!
- [For the extraordinarily ambitious student]
Finite fields have cyclic multiplicative groups (pdf).
This also proves the
*Primitive Root Thm*, and*Korselt's Thm*characterizing the Carmichael numbers. - Nostalgia?: See
past Abstract Algebra incarnations.
This will help you decide if my teaching-style is the right style for you.

- First week of class:
*Memorize*the Math-Greek alphabet (pdf). which we will use in class frequently. - First week of class: Read and throughly understand Set-builder notation (up through “Equivalent predicates...”).
- First week of class: Work through this Practice-prereq (pdf) to see what you need to review.

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

Our textbook is
Contemporary Abstract Algebra
9^{th} edition.
RS

Author: | Joseph A. Gallian | ISBN: | 9781305657960 |

Year: | 2017 | Publisher: | Houghton Mifflin |

It is available from the publisher as well as from online booksellers.

The various Math czars who help out.

Computer&Projector | Time | Memory/Telepathy | Blackboard | E-Probs |
---|---|---|---|---|

?? |

The Web

- Alg. T/F at Gallian's website.
- Group Explorer. I have not reviewed this.

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

...will be due, slid u n d e r my office door (Little Hall 402, Northeast corner) , no later than 2PM, Thursday, 7Dec2022

*The IOP must be carefully typed*,
but diagrams may be hand-drawn.

For the typesetting, one possibility
is the (free)
mathematics-typesetting language
.

**At all times** have a **paper copy** you can hand-in; I do
** NOT** accept
electronic versions.
Print out a copy

My dog ate my homework.)

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