# Math 351: Algebra I - Spring 2015 #
* * * * *
GO TO:
- [**Homework**](#homework) (Last updated: 04/24 - 5:10pm)
- [Latest Homework Assigned](#lhw)
- [Solutions to Selected HW Problems](#solutions-to-selected-hw-problems) (Last updated: 04/27 - 4:20pm)
- [Instructor and General Info](#instructor-and-general-information):
- [Instructor (office, phone, e-mail)](#instr)
- [Office Hours](#oh)
- [Textbook](#text)
- [Prerequisites](#pre)
- [Class Time and Room](#class)
- [Exams Dates](#exams)
- [Grade Calculation](#grade)
- [Course Description and Information](#course-description-and-information)
- [Course Content](#course-content)
- [Chapters and Topics](#chapters-and-topics)
- [Homework Policy](#homework-policy)
- [E-Mail Policy](#e-mail-policy)
- [Blackboard and Feedback](#blackboard-and-feedback)
- [Additional Bibliography](#additional-bibliography)
- [Legal Issues](#legal-issues)
- [Conduct](#conduct)
- [Disabilities](#disabilities)
- [Sexual Harassment and Discrimination](#sexual-harassment-and-discrimination)
- [Campus Syllabus](#campus-syllabus)
- [Problems Likely To Be Assigned](#problems-likely-to-be-assigned)
- [Links](#links)
- [Handouts](#handouts)
* * * * *
## Instructor and General Information ##
|------:|:-----|
| **Instructor:** | [Luís Finotti](http://www.math.utk.edu/~finotti/) |
| **Office:** | Ayres Hall 251 |
| **Phone:** | 974-1321 (don't leave messages! -- [e-mail](mailto:finotti@math.utk.edu) me if I don't answer!) |
| **e-mail:** | |
| **Office Hours:** | MW 9-10 or by appointment. |
|------:|:-----|
| **Textbook:** | J. Rotman, ["A First Course In Abstract Algebra"](http://www.pearsonhighered.com/educator/product/First-Course-in-Abstract-Algebra-A/9780131862678.page), 3rd Edition, Prentice Hall, 2006.|
| **Prerequisite:** | Math 300/307 (and 251/257). |
| **Class:** | MWF 10:10-11:00 at Ayres Hall 121. (Section 1.) |
| **Exams:** | Midterms: 02/18 (Wed), 04/01 (Wed) |
| | [Final:](http://registrar.tennessee.edu/academic_calendar/Spring_2015_Exam.pdf) 04/29 (Wednesday) from 8am to 10am, in our regular classroom. |
| **Grade:** | 25% for HW + 20% for each midterm + 35% for the Final. |
| | **Note the weight of the HWs!** |
Back to the [TOP](#math-351-algebra-i---spring-2015).
* * * * *
## Course Description and Information ##
### Course Content ###
This course is a one-semester introduction to
[Abstract Algebra](http://en.wikipedia.org/wiki/Abstract_algebra). (Math
455/456 and 457/458 are year long courses on the same subject, and
hence cover much more.) The emphasis will be given to
[integers](http://en.wikipedia.org/wiki/Integers) and
[polynomials](http://en.wikipedia.org/wiki/Polynomial_ring), which are
examples of
[commutative rings](http://en.wikipedia.org/wiki/Commutative_ring). The
other main topic to be covered (at least superficially) is
[groups](http://en.wikipedia.org/wiki/Group_(mathematics)).
This course might be a bit of a shock to many students, as up to now
most will not have dealt with
[discrete](http://en.wikipedia.org/wiki/Discrete_mathematics), rather
than continuous (in the calculus sense) structures and proofs, which
is what you usually deal with in calculus, differential equations, and
when working with real numbers. So, it might take a little time for
you to get use to the ideas and techniques used in this course.
Being an upper level course for math majors, most of the course will be
spent on proofs (as in Math 300), and you will have to read and write
many. *I will assume you are comfortable doing both.* We will also deal
with induction and set theory (again from Math 300.) Other than that,
there is really very little in terms of background knowledge necessary.
### Chapters and Topics ###
The goal is to cover the following: Sections 1.3 to 1.5 (1.1 and 1.2
are prerequisites), 3.1 to 3.7 (likely skipping some parts) and 2.1
to 2.5. Note that we will cover Chapter 3 (Ring Theory) before
Chapter 2 (Group Theory), as I find it would be better to make sure we
have enough time to cover rings well. (Our text was designed to allow
that.)
### Homework Policy ###
Homeworks will be posted regularly at the section [Homework](#homework) of
this page. No paper copy of the HW assignments will be distributed in
class. **It is your responsibility to check this page often!**
The HWs will be collected on Wednesdays. Each HW will have problems from
the previous week (Monday, Wednesday and Friday lectures). The problems
to be turned in, as well as due dates, will be clearly posted here. Note
that not all of the problems turned in will be graded, but you won't
know which until you get them back.
[Problems likely to be assigned](#problems-likely-to-be-assigned) are
posted below, but are subject to change. So, you can always start
early, even if the assignment is not posted. (The list is likely
incomplete, but chances of changing an assigned problem are small.)
Note that I might sometimes get too ambitious in posting problems, i.e.,
I might think we will cover a section during the week, put exercises
from it in the next assignment, and then end up not being able to finish
it. In this case I might have to take a few problems off the assignment.
The bottom line is the following: *the assignment is not final until I
remove the "More to come" from it*. (If you've done problems which were
removed, just saved them for the following week.)
Finally, if there is still a "More to come" in an assignment on a
Friday, please [write me](mailto:finotti@math.utk.edu) right away so
that I can update it. If I delay in replying, you can proceed with the
[Problems Likely To Be Assigned](#problems-likely-to-be-assigned).
No late HWs will be accepted, except in extraordinary circumstances
which are properly documented.
**It is your responsibility to keep all your graded HWs and Midterms!**
It is very important to have them in case there is any problem with your
grade.
In my opinion, doing the HW is one of the most important parts of the
learning process, so the weight for them is greater than the weight of
a single midterm, and I will assume that you will work very hard on
them.
Also, you should try to come to my office hours if you are having
difficulties with the course. I will do my best to help you. Please try
to come during my *scheduled* office hours, but feel free to make an
appointment if that would be impossible.
### E-Mail Policy ###
**I will assume you check your e-mail at least once a day.** I will use
your e-mail (given to me by the registrar's office) to make
announcements. (If that is not your preferred address, please make sure
to [forward](http://oit2011.utk.edu/helpdesk/kb/entry/1623/) your
university e-mail to it!) I will assume that any message that I sent via
e-mail will be read in less than twenty four hours, and it will be
considered an *official* communication.
### Blackboard and Feedback ###
In [Blackboard](https://bblearn.utk.edu/) you will be able to ask
questions, answer surveys and send me feedback.
There are forums where you can post questions about math or the course
structure. (I've created a different forum for each. Please use the
appropriate one!) All other students will also be able to read these
and offer help. **I strongly recommend you subscribed to all, to
receive email updates when a new post appears!** Things of interest to
all might appear there.
I'd much prefer you'd ask your questions there than e-mailing me
directly. Of course, some topics cannot or should not be discussed in
a public forum! But in other instances, please use the appropriate
forum instead of writing me, as others might also benefit from the
answer.
You can ask for math help there, but, of course, nothing like *"How do
I do problem X.X?"*. You can ask for hints or suggestions, though.
Lastly, there is also a link for (general) Feedback. (Please, also
subscribe to it.) Please, post all comments and suggestions there as
often as you want. (I really appreciate your input.) *These can be
posted anonymously (or not).* Just make sure to check the option before
posting! **Others students and myself will be able to respond and
comment.** If you prefer to keep the conversation private (between us),
you can send me an [e-mail](mailto:finotti@math.utk.edu), but then, of
course, it won't be anonymous.
To subscribe to the forums, go to
[Blackboard](https://bblearn.utk.edu), click on each of the three
forums ("Q&A (Math Related)", "Q&A - Course Structure" and
"Feedback"), click on the link to the forum and then "Subscribe".
This way you will get e-mail notifications when new questions/comments
are posted.
Back to the [TOP](#math-351-algebra-i---spring-2015).
* * * * *
## Additional Bibliography ##
Here are some other books you might find helpful:
- J. Fraleigh ["A First Course in Abstract
Algebra"](http://www.pearsonhighered.com/educator/academic/product/0,1144,0201763907,00.html),
7th Ed., 2002. Addison Wesley.
- J. Gallian, ["Contemporary Abstract
Algebra"](http://www.cengage.com/search/productOverview.do?Ntt=gallian||9780547165097&Ntk=all||P_Isbn13&N=+16),
7th Ed., 2009. Brooks Cole.
- M. Artin.
["Algebra"](http://www.pearsonhighered.com/educator/product/Algebra/9780132413770.page),
2nd Ed.,2011. Pearson.
- I. Herstein, ["Topics in
Algebra"](http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010901.html),
2nd Ed., 1975. Wiley.
The first two books are considered "easier" books. The Artin's book is
of a bit higher level (and has a slightly different focus). The last
one is a "standard" text for a first course in abstract algebra, but
have a higher level of difficulty than the previous two. It's been
used for the honors section of the undergraduate algebra course here
at UT.
Back to the [TOP](#math-351-algebra-i---spring-2015).
* * * * *
## Legal Issues ##
### Conduct ###
All students should be familiar and maintain their *Academic Integrity*:
from [Hilltopics](http://dos.utk.edu/publications/hilltopics/), pg. 46:
> **Academic Integrity**
>
> *The university expects that all academic work will provide an honest
> reflection of the knowledge and abilities of both students and faculty.
> Cheating, plagiarism, fabrication of data, providing unauthorized help,
> and other acts of academic dishonesty are abhorrent to the purposes for
> which the university exists. In support of its commitment to academic
> integrity, the university has adopted an Honor Statement.*
>
All students should follow the *Honor Statement*: from
[Hilltopics](http://dos.utk.edu/publications/hilltopics/), pg. 16:
> **Honor Statement**
>
> *"An essential feature of The University of Tennessee is a commitment
> to maintaining an atmosphere of intellectual integrity and academic
> honesty. As a student of the University, I pledge that I will neither
> knowingly give nor receive any inappropriate assistance in academic
> work, thus affirming my own personal commitment to honor and
> integrity."*
You should also be familiar with the [Classroom Behavior
Expectations](http://www.math.utk.edu/Courses/Expectations.pdf).
***We are in a honor system in this course!***
### Disabilities ###
Students with disabilities that need special accommodations should
contact the [Office of Disability Services](http://ods.utk.edu/) and
bring me the appropriate letter/forms.
### Sexual Harassment and Discrimination ###
For
[Sexual Harassment](http://oed.utk.edu/complaints/sexual-harrassment/)
and [Discrimination](http://oed.utk.edu/statement/) information,
please visit the
[Office of Equity and Diversity](http://oed.utk.edu/).
### Campus Syllabus ###
Please, see also the [Campus Syllabus](http://www.math.utk.edu/~finotti/files/campus_syllabus.pdf).
Back to the [TOP](#math-351-algebra-i---spring-2015).
* * * * *
## Links ##
- [UT Knoxville Home](http://www.utk.edu)
- [UTK's Math Department.](http://www.math.utk.edu)
- My course page for
[Math 351 (Fall 2009)](http://www.math.utk.edu/~finotti/f09/m351/M351.html).
- Videos (from old
[Math 457](http://www.math.utk.edu/~finotti/f13/m457/M457.html)
course, but still relevant):
* [What Is Algebra?](https://www.youtube.com/watch?v=9iRXkLKqyjA).
Similar to what I've talked in class, but a few more details.
Here are the
[slides](http://www.math.utk.edu/~finotti/files/algebra/whats_alg-slides.pdf).
*
[Algebraic Structures](https://www.youtube.com/watch?v=NRDtfVquLX0).
Description of a few Algebraic Structures, some of which we will
*not* see in this course. (We *will* see Groups, Rings and
Fields.) Here are the
[slides](http://www.math.utk.edu/~finotti/files/algebra/alg_str-slides.pdf).
- [Blackboard](https://bblearn.utk.edu/) -- Announcements, feedback
and grades for this course.
- [Services for Current Students](http://www.utk.edu/currentstudents/)
and [MyUTK](http://myutk.utk.edu/) (registration, view your grades,
etc.).
- [Office of the Registrar](http://registrar.tennessee.edu/)
- [Academic
Calendars](http://registrar.tennessee.edu/academic_calendar/index.shtml),
including dates for add and drops, other deadlines, final exam
dates, etc.
- [Hilltopics](http://dos.utk.edu/publications/hilltopics/).
- [Office of Disability Services](http://ods.utk.edu/)
- [Office of Equity and Diversity](http://oed.utk.edu/) (includes
sexual harassment and discrimination).
- [Catalog](http://catalog.utk.edu/) and [Course
Descriptions](http://catalog.utk.edu/content.php?catoid=1&navoid=104).
- [Student Success Center](http://studentsuccess.tennessee.edu/).
- [My homepage](http://www.math.utk.edu/~finotti/).
Back to the [TOP](#math-351-algebra-i---spring-2015).
* * * * *
## Handouts ##
- [Campus Syllabus](http://www.math.utk.edu/~finotti/files/campus_syllabus.pdf).
- **Midterm 1:** [in-class part](exam1.pdf) and
[solutions](exam1_sols.pdf), and [take-home part](th1.pdf) and [solutions](th1_sols.pdf).
- **Midterm 2:** [take-home](th2.pdf) and [solutions](th2_sols.pdf).
- **Final:** [final (in-class)](final.pdf) and [solutions](final_sol.pdf).
Back to the [TOP](#math-351-algebra-i---spring-2015).
* * * * *
## Solutions to Selected HW Problems ##
**Please read:** I will *try* to post here a few solutions. The new
solutions will be added to this same file.
**Disclaimer:** I will have to put these solutions together rather
quickly, so they are subject to typos and conceptual mistakes. (I expect
you to be a lot more careful when doing your HW than I when preparing
these.) You can contact me if you think that there is something wrong
and I will fix the file if you are correct.
[Solutions to Selected HW Problems](sols.pdf) (Click on "Refresh" or
"Reload" if you don't see the changes!)
**CHANGE LOG:**
- **04/27 - 4:20pm:** Added solutions for sections 3.4, 2.2-4.
- **03/27 - 5:15pm:** Added solutions for sections 3.1 to 3.3.
- **02/16 - 5:55pm:** Added solutions for sections 1.4 and 1.5
(excpet 1.78(v) and 1.95).
- **02/06 - 4:20pm:** Added solutions for section 1.3.
Back to the [TOP](#math-351-algebra-i---spring-2015).
* * * * *
## Problems *Likely* To Be Assigned ##
This list is subject to change without prior notice. The official
assignments will be posted [below](#homework).
**Section 1.3:** 1.46, 1.47, 1.50, 1.53, 1.55(i), 1.57, 1.58, 1.60, 1.62.
**Section 1.4:** 1.68, 1.69(i), 1.70(i), 1.71, 1.75.
**Section 1.5:** 1.77, 1.78(ii), (iii), (iv), 1.79, 1.81, 1.82(i), 1.85, 1.86, 1.87, 1.88, 1.91, 1.95.
**Section 3.1:** 3.1 except (v) and (viii), 3.3(i) and (iii), 3.5, 3.6,
3.12, 3.13.
**Section 3.2:** 3.17 except (v) and (vi), 3.19, 3.20, 3.26.
**Section 3.3:** 3.29, 3.30, 3.32, 3.35 (if you are not familiar with
complex numbers, replace them with real numbers, i.e., take alpha to be
real), 3.37 (you can use 3.36 without proving it).
**Section 3.5:** 3.56(i)-(vii), 3.58, 3.62, 3.64, 3.67.
**Section 3.7:** 3.86 except (i), 3.87 except (ii), (v), (vii), (viii),
3.90(i), 3.91.
**Section 2.2:** 2.21, 2.22, 2.23, 2.25, 2.26, 2.27, 2.34. (Note that I
took off 2.29, which is too long.)
**Section 2.3:** **More to come!**
Back to the [TOP](#math-351-algebra-i---spring-2015).
* * * * *
## Homework ##
**HW1** - Due on **Wednesday 01/21**:
**Section 1.3:** 1.46(i)-(vii), 1.47, 1.50, 1.57.
**HW2** - Due on **Wednesday 01/28**:
**Section 1.3:** 1.58, 1.60, 1.62.
**HW3** - Due on **Wednesday 02/04**:
**Section 1.3:** 1.46(viii)-(x), 1.53, 1.55(i).
**HW4** - Due on **Wednesday 02/11**:
**Section 1.4:** 1.68, 1.69(i), 1.70(i), 1.71, 1.75.
**HW5** - Due on **Wednesday 02/18**:
**Section 1.5:** 1.77, 1.78(ii), (iii), (iv), 1.79, 1.81, 1.82(i),
1.85, 1.86, 1.87, 1.88, 1.91.
**HW6** - Due on **Wednesday 02/25**:
**Section 1.5:** 1.78(v), (vi), 1.92, 1.95.
**HW7** - Due on **Wednesday 03/11**:
**Section 3.1:** 3.1 except (v) and (viii), 3.3(i) and (iii), 3.5, 3.6,
3.12, 3.13.
**HW8** - Due on **Wednesday 03/25**:
**Section 3.2:** 3.17 except (v) and (vi), 3.19, 3.20, 3.26.
**HW9** - Due on **Wednesday 04/01** (**DO NOT TURN IN!** Just
practice for the exam.):
**Section 3.3:** 3.29 (except (i)), 3.30, 3.32, 3.35 (if you are not familiar with
complex numbers, replace them with real numbers, i.e., take alpha to be
real), 3.37 (you can use 3.36 without proving it).
**HW10** - Due on **Wednesday 04/08**:
**Section 3.5:** 3.56(i)-(vii), 3.58, 3.62, 3.64, 3.67.
**HW11** - **Do not turn in!** Just practice for the
final:
**Section 2.2:** 2.21, 2.22, 2.23, 2.25, 2.26, 2.27, 2.34.
**Section 2.3:** 2.36(i-v) and (viii), 2.37, 2.38, 2.40.
**Section 2.4:** 2.52(i-iii), 2.55.
**PLEASE, HIT "REFRESH" (OR "RELOAD") IN YOUR BROWSER WHEN
VISITING THIS PAGE!!!!!!!** I usually get messages asking for the update
in the HW when it has already been updated. Since I change this page
often, some times the browser don't see the changes. But, if you hit
refresh and there is still problems missing, feel free to write me.
If it is already **Friday** afternoon and there still is a "More to
come" after the HW assignment due on the coming Wednesday, write me an
e-mail at , and I'll update it and let you know.
Back to the [TOP](#math-351-algebra-i---spring-2015).
* * * * *