math3140-fall2018
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说明: 抽象代数,2018年秋季,科罗拉多大学,博尔德
(Abstract Algebra, Fall 2018, University of Colorado, Boulder)
文件列表:
homework/ (0, 2018-12-02)
homework/pdf/ (0, 2018-12-02)
homework/pdf/hw01.pdf (73523, 2018-12-02)
homework/pdf/hw02.pdf (72471, 2018-12-02)
homework/pdf/hw03.pdf (68522, 2018-12-02)
homework/pdf/hw04.pdf (86717, 2018-12-02)
homework/pdf/hw05.pdf (87919, 2018-12-02)
homework/pdf/hw06.pdf (100282, 2018-12-02)
homework/pdf/hw07.pdf (74034, 2018-12-02)
homework/pdf/hw08.pdf (71758, 2018-12-02)
homework/pdf/hw09.pdf (119022, 2018-12-02)
homework/pdf/hw10.pdf (132217, 2018-12-02)
homework/pdf/hw11.pdf (65972, 2018-12-02)
homework/pdf/hw12.pdf (96064, 2018-12-02)
homework/tex/ (0, 2018-12-02)
homework/tex/hw01.tex (4789, 2018-12-02)
homework/tex/hw02.tex (3798, 2018-12-02)
homework/tex/hw03.tex (3798, 2018-12-02)
homework/tex/hw04.tex (20809, 2018-12-02)
homework/tex/hw05.tex (4172, 2018-12-02)
homework/tex/hw06.tex (4985, 2018-12-02)
homework/tex/hw07.tex (3419, 2018-12-02)
homework/tex/hw08.tex (2877, 2018-12-02)
homework/tex/hw09.tex (9752, 2018-12-02)
homework/tex/hw10.tex (5260, 2018-12-02)
homework/tex/hw11.tex (3387, 2018-12-02)
homework/tex/hw12.tex (15097, 2018-12-02)
misc/ (0, 2018-12-02)
misc/ConstructionOfNaturalNumbers.pdf (199939, 2018-12-02)
misc/CyclicGroupAnswers.pdf (96561, 2018-12-02)
misc/CyclicGroupSupplement.pdf (175173, 2018-12-02)
misc/Definitions.pdf (93444, 2018-12-02)
misc/G-sets.pdf (64421, 2018-12-02)
misc/GeneralAlgebraNotes.pdf (290061, 2018-12-02)
misc/GenerationOfSubgroups.pdf (73114, 2018-12-02)
misc/images/ (0, 2018-12-02)
misc/images/Dixon.jpeg (16318, 2018-12-02)
misc/images/Herstein.jpeg (2582, 2018-12-02)
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# Math 3140: Abstract Algebra I -- Fall 2018
**Lecture Time and Location.** MWF 9:00--9:50pm in MUEN D439.
**Final Exam Date, Time and Location.** Wednesday, December 19, 1:30--4pm in MUEN D439.
**Course Webpage:** http://github.com/williamdemeo/math3140-fall2018 (this page!)
---
**Instructor:** Dr. William DeMeo
**Email:** [williamdemeo@gmail.com](https://github.com/williamdemeo/math3140-fall2018/blob/master/mailto:williamdemeo@gmail.com)
**Office:** MATH, Room 202
**Office hours:** Mondays and Wednesdays, 10:15--11:30am
It is helpful, but not required, to send the instructor an email in advance
to notify him of your intention to attend office hours.
---
## Contents
- [Introduction](https://github.com/williamdemeo/math3140-fall2018/blob/master/#introduction)
- [Overview](https://github.com/williamdemeo/math3140-fall2018/blob/master/#overview)
- [Learning Outcomes](https://github.com/williamdemeo/math3140-fall2018/blob/master/#learning-outcomes)
- [Prerequisites](https://github.com/williamdemeo/math3140-fall2018/blob/master/#prerequisites)
- [Textbook Information](https://github.com/williamdemeo/math3140-fall2018/blob/master/#textbook-information)
- [Homework](https://github.com/williamdemeo/math3140-fall2018/blob/master/#homework)
- [Exams](https://github.com/williamdemeo/math3140-fall2018/blob/master/#exams)
- [Make-up Policy](https://github.com/williamdemeo/math3140-fall2018/blob/master/#make-up-policy)
- [Computing](https://github.com/williamdemeo/math3140-fall2018/blob/master/#computing)
- [Questions and Online Discussions](https://github.com/williamdemeo/math3140-fall2018/blob/master/#questions-and-online-discussions)
- [Disabilities Statement](https://github.com/williamdemeo/math3140-fall2018/blob/master/#disabilities-statement)
- [Other References](https://github.com/williamdemeo/math3140-fall2018/blob/master/#other-references)
-------------------------------------------
## Introduction
You are now reading the main course webpage (which is simply a README.md
file in a GitHub repository called math3140-fall2018).
The paragraphs below serve as the syllabus for Math 3140.
*This page and the subdirectories of this repository (see links above) will
be updated throughout the semester, and students are expected to visit this
page routinely.*
For this class the CU D2L system will be used only for recording grades.
--------
## Overview
Basic theory of groups and other algebraic structures, with an emphasis on writing proofs.
+ Introduction to algebraic and relational structures.
+ Brief introduction to a few special structures: groupoids, semigroups, monoids, graphs, posets, lattices.
+ Elementary theory of groups: subgroups, cyclic groups, permutation groups, cosets.
+ Isomorphisms, quotient groups, homomorphisms; group isomorphism theorems.
+ Group actions, Sylow theorems.
+ Introduction to rings (time permitting).
--------
## Learning Outcomes
Develop skill in communicating mathematics. Develop competence in writing proofs.
Construct proofs about the following mathematical structures and concepts: groups,
lattices, homomorphisms, quotient groups, group actions, rings.
--------
## Prerequisites
The most important prerequisite for this class is Math 2001. If you did well in
Math 2001, you should be able to do well in this course. Although you are not
expected to be highly skilled at constructing your own original proofs upon entering
this course, you should be familiar with basic methods of proof---such as induction,
proof-by-contradiction---and what it means to prove a proposition or to prove
the negation of a proposition; you should also know what words like "converse" and
"contrapositive" mean.
During the first few lectures, we will review some of the required background.
If this early material seems unfamiliar and difficult to you, then it is likely
that you will find the course very challenging.
--------
## Textbook Information
[Abstract Algebra: theory and applications](https://github.com/williamdemeo/math3140-fall2018/blob/master/http://abstract.ups.edu/)
by Tom Judson
See also the [other references](https://github.com/williamdemeo/math3140-fall2018/blob/master/#other-references) below.
--------
## Homework
**Homework is worth 30%** of the course grade and will be assigned slightly less than
once per week. Students must solve many homework problems in order to do well
in the course.
Homework is announced in lecture approximately once per week, and is
usually due the week after it is announced (with exact due dates specified
in lecture).
I will do my best to keep [our homework page](https://github.com/williamdemeo/math3140-fall2018/blob/master/homework) updated with
a list of the problems that are due each week, but it is the students'
responsibility to show up for lecture to stay current with the course agenda.
Although many homework problems will be assigned, only a limited number from
each assignment will be graded. Therefore,
[solutions to many of the homework problems](https://github.com/williamdemeo/math3140-fall2018/blob/master/homework/solutions) will
be made available, with the expectation that students will read the correct
solutions, compare them with their own, and understand the differences.
Students are not required to turn in corrected solutions, but
would do well to keep up with the corrections since these can be very
useful when preparing for exams.
-----
## Exams
**Two Midterm Exams each worth 20%** of the course grade will be given during the
semester; the exact dates will be announced soon after the course begins.
The **Final Exam is worth 30%** of the course grade.
In accordance with university policy, the final exam must be taken by all
students at the scheduled time. *There are no make-up exams.*
+ **MIDTERM EXAM 1** (focus: Ch 1--5)
**DATE:** Wednesday, October 10
**LOCATION:** MUEN D439
+ **MIDTERM EXAM 2** (focus: Ch 6, 9--11, 19)
**DATE:** Monday, November 12
**LOCATION:** MUEN D439
+ **FINAL EXAM** (cumulative)
**DATE:** Wedensday, December 19
**TIME:** 1:30--4pm
**LOCATION:** MUEN D439
-----------------------------------
## Make-up Policy
**No late homework will be accepted for any reason.** If you fail
to submit homework on time, this will not necessarily hurt
your final course grade since the lowest homework score will be dropped.
Generally speaking, there are no make-up exams. However,
if you must miss an exam for one of the legitimate reasons listed below,
and if you contact the professor at least five days before the exam date,
then you might be able to take a make-up exam *before the scheduled exam time*.
To request a make-up exam, a student must provide documented evidence of
one of the following:
+ Documented medical excuse - student's own medical emergency.
+ Documented medical excuse - a member of the student's family has a medical emergency.
+ Extra curricular activity sponsored University of Colorado.
+ Armed forces deployment (military duty).
+ Officially mandated court appearances, including jury duty.
+ A conflict with another exam or if you have three or more final exams on a
given day. (In each case the exam with the fewest students must arrange the make-up exam.)
If you miss an exam due to some unforeseen circumstance, you must contact the
professor within one class meeting after the missed test and provide an
explanation. If your excuse is accepted, the missed test score may be replaced
with 80% of your final exam score. For example, if your excuse is accepted and
you score a 90% on the final, then you will receive a 72% for the missed test
(0.80*0.90 = 0.72).
---
## Computing
No prior programming experience is required for this course, and the amount of
computing done in this class will be left up to the students. I encourage, but
do not require, all students to use the computer to help develop intuition about
the algebraic structures that we will study, and I will provide some guidance in
this regard.
**Sage:**
One of the best ways to develop a deeper understanding of many mathematical
subjects (abstract algebra in particular) is to use the computer to experiment
with and apply the theory. For this purpose I recommend the open source math
software called [Sage](https://github.com/williamdemeo/math3140-fall2018/blob/master/http://www.sagemath.org). Sage essentially provides a
nice browser-based interface to a [vast array][] of well developed and powerful
open source mathematical software.
Getting started with Sage is very easy. You don't even need to install any
software. By using Sage though a web browser you can and do all your computing,
and store all your Sage worksheets, in the cloud.
It's also possible to download and install Sage on your own computer. Sage is free
and open source, and it is typically not *too* hard to install.
Here are some things you might try to get started with Sage:
1. Go to http://www.sagemath.org/ and click [Try Sage Online](https://github.com/williamdemeo/math3140-fall2018/blob/master/http://cloud.sagemath.com/).
2. Check out the web page at
[http://abstract.ups.edu/sage-aata.html](https://github.com/williamdemeo/math3140-fall2018/blob/master/http://abstract.ups.edu/sage-aata.html).
It is [a Sage companion to our textbook!](https://github.com/williamdemeo/math3140-fall2018/blob/master/http://abstract.ups.edu/sage-aata.html)
3. Browse some of the [Sage Thematic Tutorials](https://github.com/williamdemeo/math3140-fall2018/blob/master/http://www.sagemath.org/doc/thematic_tutorials/index.html)
If you've used Sage before and just need a quick refresher, you might
check out the [Sage Quick Start Guides](https://github.com/williamdemeo/math3140-fall2018/blob/master/http://www.sagemath.org/doc/prep/quickstart.html).
---
## Questions and Online Discussions
You are welcome to ask lots of questions in this class (during lecture, in
office hours, via email, etc.). You are especially encouraged to use a public
forum to ask questions so that all students can benefit.
The discussion forum that we will use for this class has yet to be determined, but will likely be Piazza.
Please consider posting to the
[class wiki pages](https://github.com/williamdemeo/math3140-fall2018/blob/master/https://github.com/williamdemeo/math3140-fall2018/wiki)
when you want to ask a question, or raise an issue, or start an online dialog
with the prof and/or your classmates. If you have any trouble editing
the class wiki pages, please [notify the professor](https://github.com/williamdemeo/math3140-fall2018/blob/master/mailto:williamdemeo@gmail.com).
---
## Disabilities Statement
If you believe that you have a disability that qualifies under the
Americans with Disabilities Act and Section 504 of the Rehabilitation
Act and requires accommodations, you should contact the [Student Disability
Resources Office](https://github.com/williamdemeo/math3140-fall2018/blob/master/https://www.colorado.edu/disabilityservices/) for information on appropriate policies and procedures.
The next step is to talk to the instructor who will be happy to assist with accommodations, but **will not
provide them retroactively** (so file the appropriate requests and paperwork
before the first exam!)
---
## Other References
[Our textbook](https://github.com/williamdemeo/math3140-fall2018/blob/master/http://abstract.ups.edu/) should cover everything we need for
this course. However, there are many other books that provide alternative
expositions of the same topics, and some are particularly good and might be
worth a look. Below are a few of your instructor's favorites, along with some
comments about them, but first, here's a list of some free online resources:
+ [Algebra: Abstract and Concrete](https://github.com/williamdemeo/math3140-fall2018/blob/master/http://homepage.divms.uiowa.edu/~goodman/algebrabook.dir/download.htm) by Frederick Goodman
+ [Wikibook](https://github.com/williamdemeo/math3140-fall2018/blob/master/https://en.wikibooks.org/wiki/Abstract_Algebra)
**Jacobson**, *Basic Algebra I* -- covers roughly the same material as our textbook,
but at a higher level of sophistication; used, for example, as a textbook for
advanced undergraduates and beginning graduate students.
**Herstein**, *Topics in Algebra* -- covers roughly the same material as our
textbook, but at a slightly higher level of sophistication; used, for example,
in an undergraduate honors abstract algebra course.
**Rose**, *A Course on Group Theory* -- We will spend a significant portion of our
time in this class studying *group theory*, and this book is an excellent
(and inexpensive) introduction to the subject. Our textbook provides a
sufficient treatment of group theory for our purposes, and Rose covers much more
than we will. However, you might find Rose's book useful if/when you are not
satisfied with our textbook's (or professor's) presentation of a particular topic.
**Dixon**, *Problems in Group Theory* -- our homework assignments should give you
plenty of practice solving problems in group theory; if you want more, I highly
recommend the book by Dixon.
-----------------------
[vast array]: http://en.wikipedia.org/wiki/Sage_(mathematics_software)#Software_packages_contained_in_Sage
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