Math 448 Syllabus – Fall 2019

  • Course: Modern Algebra I
  • Term: Fall 2019
  • Time: TR 6:00-7:15
  • Location: LSC 329

Office Hours:  T-Th 5:15-6:00pm, 7:15-8:00pm and beyond (or following the end of Math 448, whichever comes last) and by appointment or email.

[Note: Office hours may be held in either LSC 329, HYL 102, or LSC 311. Check all three locations.]

Textbook: Hungerford, T.; Abstract Algebra, 3rd edition,  ISBN:1111569622

Course Prerequisites: Math 299 and Math 351

Course Objective: To provide the student with an understanding of the major topics of modern algebra. This will be accomplished by covering the topics given in Chapters 1-7 of the textbook along with any supplementary material provided by the instructor.  Students should strive to obtain a mastery of the subject matter by 1) developing both the technical skill necessary to solve problems and 2) demonstrate a deeper understanding of the underlying theory by reading and writing proofs.  The assignments and exams will attempt to ascertain if each of these objectives have been met.

Attendance Policy: Class attendance is highly encouraged. Should you miss a class for any reason, you are still responsible for all announcements made and all material presented during that class.   Missed quizzes or exams due to absence cannot be made up.

Abstract Algebra

Email and the Web: All students in this course are required to have a university email account and are expected to check their email frequently for announcements and other information I may send to you. I will use email and the internet quite extensively in the course. Each student is also expected to be able to access any information that I post on the web that is related to your course.  Contact the Help Desk if you need assistance.

Homework: I will post your homework assignments on our course web page. Due to the large volume of homework I assign, I must require that all homework satisfies the following criteria.  Each assignment will specify if you can hand it in handwritten on paper or if you have to hand it in typeset in LaTeX (no MS Word!)

  1. All paper homework must be done on 8.5″x11″ paper.  The paper must have straight smooth edges, not the jagged edges that are obtained when paper is removed from a “spiral bound” notebook. The paper should not be folded.
  2. All homework that consists of more than a single sheet of paper must be stapled in the upper left hand corner. Corners should not be folded or “dog eared”.
  3. All homework must have the following information in the upper right hand corner of the first page:
    1. Name
    2. Assignment number (this is the assignment number given on the homework assignment web page, not the number of assignments you have handed in).
  4. All individual problems should be clearly labeled by writing both the problem number and the problem itself at the top of the problem.  For proofs, put only one problem per sheet of paper, unless they are exceptionally tiny proofs.  Do not write the problem number so that the staple will obscure it.  Do not write or print on both sides of the paper.
  5. All proofs must be semi-formal proofs. In particular they must have only one statement per line and each line that is not an assumption or declaration must be justified with a reason.  Subproofs should be indented.  Line numbers and references to premises are optional unless it is not obvious what the premises for a particular certain reason is or you want to improve the clarity of the proof.
  6. Problems must occur in the assignment in the same order that they are assigned, e.g. problem #3 must appear before problem #4 which must appear before problem #7, etc.
  7. Some assignments must be typeset. For those assignments, in addition to meeting the criteria above, you must also use some form of LaTeX to typeset your work. This can be done with raw LaTeX code, or by using a program such as LyX or Scientific Workplace which produce LaTeX output. You cannot use Microsoft Word under any circumstance. Typeset assignments do not have to be printed on paper, but instead can be directly sent to me in .pdf format through a mechanism we will discuss in lecture.

Thus, the first page of every homework assignment should look like this:

Homework Format

(The course name and time are optional since you are my only course that hands in assignments.) Any homework that does not conform to the above format may be ignored!

The homework that you hand in may not be returned to you, so if you want to keep a copy for yourself you should make a copy before handing it in, or keep a backup copy of your original file. If you are handing in more than one Assignment number on a single day, each assignment must be stapled and labeled separately!  Failure to follow these procedures may result in you not getting credit for all of your assignments.

Late Assignments: Don’t even think about it.  I have yet to accept one and don’t want to spoil my record.  You will receive no credit for late assignments.  I also will not accept EARLY assignments.  Assignments must be handed in, on the day they are due, during the first three minutes of class.  You may not place paper homework assignments under my office door or hand it to me in the hall or mail it to me or have an uncle deliver it to my house. You can have another student hand in your assignment for you during the first three minutes of class on the day it is due if you cannot make it to class for some reason. Electronic assignments must be time-stamped before the start of class on the day they are due.

Missed assignments: In order to allow for sickness, bad days, other exams, scheduling conflicts, etc. I will compute the average number of problems graded in each assignment and quiz at the end of the term and drop this number of points from the total possible points when computing your homework average (this is similar to “dropping” one homework assignment for everyone).

Collaboration: All questions on each assignment can be done either individually or collaboratively as teams of two or more. If you discuss a problem with another student, that student becomes your collaborator on that question and you must write their name at the start of your solution like this:

#5 (Team: John Doe, Mary Smith)

This indicates that you spoke to John Doe, and Mary Smith about problem #5 (do not include your own name in the ‘Team:’ list, since your name is on the top of the assignment).  Similarly, John and Mary would list you, and each other, on their problem #5 as team members.  Note that it does not matter how much or how little you discuss on a particular problem.  Whether you work out the solution entirely together and read each other’s write ups, or simply ask for a small hint from another student, each of you must list the other as a collaborator on that problem.  When working on a problem as a team, each member of the team must still write up their own solution in their own words and notation.  Credit for a correct problem that is selected to be graded will be shared equally among all members of the team (see grading policy below).

Thus, it is in your best interested to follow the following guidelines regarding doing your homework.  If you can get a question entirely correct on your own, you should do so without talking to anyone else, otherwise your credit for that question will be divided by the number of members on your team. However, if two or more students are really stuck on a question and are not going to be able to get it by themselves and want to team up to try to answer it together, then it would be in their best interest to do so since they would receive at least some partial credit instead of no credit at all.  So if you can get it by yourself, you should, and if you can’t, find someone else who can’t and work together.

You should attempt to do all assigned problems completely on your own (or with members of your team) without using any outside resources beyond our book and course materials. In every case you should write your own solution in your own words and symbols.

For homework assignments that are handed in electronically, please name your file:

Assignment nlastname

where n is the assignment number and lastname is your last name.  No two students should send me the same .pdf file or use the same LaTeX file. Just like paper assignments, you should each do your own write ups even if you collaborate.

Any acts of cheating on assignments or exams which come to my attention will be dealt with in the most severe manner possible under University guidelines. Plus I will be really upset!

Quizzes:  There may be unannounced quizzes in some classes which will consist of problems from the homework you are handing in on that day.  These quizzes will be graded the same way as the homework assignments, except that you cannot collaborate with other team members on the quizzes.

Grading:  There will be a midterm exam and a final exam unless I determine that it is in the best interests of your education to not have them. There will be a lot of homework which will not be graded, and a lot of quizzes. Quizzes can either be in-class or a random selection from the homework handed in on that day and will consist of zero or more problems selected randomly by Maple or intentionally by me from the homework assignments that you hand in, or a problem or two that I give you in class to work on. When selected at random, the selection process will be as follows: a random sequence of problem numbers will be selected (this sequence can contain duplicates) and graded in the order they appear on the list. If a problem has more than one part the part will then be selected by a second random sequence of part letters.  Which problems are are on the quiz will not be announced before you hand in the homework assignment, thus you should strive to get all of the homework problems correct. There will also be some bonus problems assigned which you can solve for extra credit. I will keep a tally of the number of these optional problems that you solve during the semester and take that into account when determining your final course grade. Each part of each quiz problem will be worth 1 points, with points awarded as follows:

Points awarded Awarded if:
$100/n$ Your response is complete and correct and there are n members on your team.
10 You made a significant attempt at the problem which is either incomplete or incorrect, and you clearly write (or type) “NOT CORRECT” at the very top of your solution.
0 Your response is either incomplete or incorrect.

There will be no partial credit for any solution, especially on proofs (but I do sometimes give a score of ‘+1ce’ which means ‘plus one point because you were close enough’). Exam problems will also be graded the same way that quiz problems are graded. Thus you should strive to get as many problems entirely correct as possible rather than wasting your time trying to get partial credit on a lot of problems but have them all be wrong.

At the end of the term I will compute your grade as follows:

Let $x$ be a student.

Let $p(x)$ be the total number of points earned by $x$ on all exams and quizzes.

Let $T$ be the total number of points possible.

Let $D$ be the number of points I drop for everyone in order to account for sickness and excused absence.

Let $K$ be a constant (the curve) to be determined by me at the end of the semester.

Let $G(x)$ be the student’s final grade.

Then $G(x)$ is computed by:  $$G(x) = \frac{p(x)}{T-D}+K$$ and this number is converted to a letter grade in accordance with the following table:

Conversion between numeric
and letter grades
If your numeric grade
is greater than
or equal to …
Your letter grade
will be at least …
93A
89A-
85B+
82B
78B-
74C+
70C
67C-
63D+
60D
0F

Remember that the best way to learn mathematics by doing it yourself.

I hear and I forget.

I see and I remember.

I do and I understand

– Chinese Proverb

Adaptability: I retain the right to modify or change any of the policies stated in this syllabus during the term if I feel it is in the best interests of the students and the course. That includes the right to give letter grades which are not consistent with the numerical grades computed above.