MATH 440-01
Abstract Algebra
Syllabus for Fall 2011
Mon, Wed, & Fri, 10:00 – 10:50am
Gildemeister 326
Prerequisite: Technically just MATH210, though MATH310 helps a lot.
About This Course: This course develops the foundational ideas of groups and rings. It focuses on the algebraic structures that accompany sets with binary operations.
Expectations: Students who complete this course with a passing grade are expected to be able to demonstrate the following skills: (i) Mastery of prerequisite material, (ii) Demonstrate knowledge (i.e. memorization) of pertinent definitions and theorems, (iii) Construct valid proofs and reason in a variety of forms, (iv) Critical analysis of conjectures through examples and/or counter-examples, (v) Communicate mathematics correctly, clearly, and concisely.
Text: Abstract Algebra: Theory and Applications, Thomas Judson, 2011 edition (free download)
Course Website: http://course1.winona.edu/eerrthum/math440
Instructor: Dr. Eric Errthum Office: 124A Gildemeister
Winona Email Username: eerrthum Office Phone: 474-5775
Office Hours: See schedule on my home page. Or by appointment on any day.
Grading: Problem
Write-Ups (scaled as needed) 105
points----- 14.0%
Quizzes
(8 @ 15 points, drop lowest) 105
points------ 14.0%
Midterms (2 @ 100
points) 200
points------ 26.7%
Essay Reflections (3 @
30 points) 90 points------ 12.0%
Portfolio 50
points------- 6.6%
Final 200
points------ 26.7%
--------
750
points total
Grades: A = 90% (675 pts), B = 80% (600 pts), C = 70% (525 pts), D = 60% (450 pts). There will be no curving of individual exams, quizzes or assignments.
Problem Write-Ups: For each chapter, a collection of problems will be assigned (see WU links in the schedule below).
· These problems are to be typed and printed out to be handed in. No hand-written or email submissions will be allowed. Students can use LaTeX, Microsoft Word, or any other appropriate software. (Here are some LaTeX resources.)
· Proper punctuation, grammar, fonts, and formatting are expected (in other words, it should look like something from a textbook: important equations centered and on their own line, multi-line formulas or equalities properly aligned, variables italicized, standard notation, etc.). Write-ups should contain the problem numbers and statement of the problem in addition to the solution. For more details, refer to these Writing Guidelines.
· Problems will be worth 5 points apiece: 2 points for correct mathematical idea, 2 points for correct mathematical exposition, 1 point for formatting/grammar.
· Many of these problems are posed as “prove or disprove”. In the event of a “disproof”, students must adequately disprove the original statement. In addition, though, students can earn 1 extra credit point for rephrasing the statement into something true (if possible) and another 1 extra credit point for a correct proof of this revised statement.
· Students may submit up to 3 attempts on a problem; your final grade for the problem will be the average of all submissions. When you submit a revision, include any previous submissions.
· This work should be considered individual work and near-identical submissions will result in a score of zero for both students.
Portfolio: At the end of the semester, students will submit the drafts and final submission of 5 problem write-ups along with a reflection of what they learned from each problem and/or a narrative of how revising each problem changed their subsequent work. Students can choose any 5 problems from the semester, but no more than 2 problems from the same chapter. The rubric will be based on 10 points per problem: 2 for final mathematical correctness, 2 for exposition of solution, and 6 for depth of reflection. November 28th is the last day to hand in problems to be revised and returned before the last day of class. Portfolios are due (in the box outside my office) at 11am on Thursday, December 8.
Quizzes: We will have a short (approx. 15-minute) quiz periodically (about once a week, see schedule below). Each quiz will count for 15 points and the lowest quiz will be dropped from your grade. Quiz problems will be drawn solely from the Quiz Preparation (QP) questions from the Judson text listed in the schedule below (extra credit questions might not be). Students are encouraged to work together on these problems outside of class.
Exams: There will be two in-class exams and one comprehensive final exam, potentially with take-home portions. Exam dates are tentative until officially announced in class. The final exam is tentatively scheduled for Wednesday, December 7, 8:00am – 10:00am.
Essay Reflections: Students will write a 1-2 page (size 12 font, single spaced, 1” margins) reflection on each of three essays on current issues in mathematics:
• Essay 1: “In Math You Have to Remember, In Other Subjects You Can Think About It” by Keith Devlin
• Essay 2: “A Mathematician’s Lament” by Paul Lockhart.
• Essay 3: “Visions of Mathematics” by Ben Daley … and “Arthur Benjamin's formula for changing math education” by Art Benjamin
The due dates are given in the schedule below. Grades will be determined by the level and depth of your reflection as well as on readability/grammar. If you having trouble getting started, consider these optional prompts. However, the reflection is to be written as one coherent piece, not just answers to questions.
Late/Missed Work: Late homework or missed quizzes will result in a score of zero. Make-up quizzes and make-up exams before the time of the normal quiz or exam will be given at the discretion of the instructor. If you miss class, it is your responsibility to obtain notes and assignments from fellow students. If you have an unavoidable absence, please inform the instructor beforehand.
Desire2Learn: Many course materials can be found on D2L including solutions to quizzes and exams and approximate grades. If at any point during the semester you would like to know your exact grade, please email the instructor.
Resources: All students are advised to read these general Tips for Proof Writing. Also, you are encouraged to visit me in my office (see schedule on my home page, or by appointment on any day) or e-mail me.
Academic Dishonesty: Any type of academic dishonesty (cheating, copying, using solution manuals, etc.) will result in failure and will be reported to school authorities. If you are having trouble with an assignment, please see the instructor first.
Note: This syllabus is subject to change if deemed necessary by the instructor.
Tentative Schedule of Events – Math 440
(subject to change)
|
Week Beginning |
Monday |
Wednesday |
Friday |
|
8/22 |
Introductions 1.1 1.2 (pages 1 – 5) |
1.2, cont |
1.2, cont |
|
8/29 |
Quiz (Chapter 1) QP: 4-16, 20-22, 24-25 2.1 |
2.1, cont 2.2 |
2.2, cont. 3.1 (pages 31 – 32, 37 – 40) |
|
9/5 |
Labor Day |
Quiz (Chapter 2) QP: 1-6, 9-10, 15ab, 16, 18, 24-27 3.1, cont (pages 40 – 42) |
3.2 |
|
9/12 |
Group Activity |
3.2, cont 3.3 (pages 46 – 50) |
3.3, cont (pages 50 – 51) |
|
9/19 |
Quiz (Chapter 3) QP: 1, 3, 6-14, 24, 30-32, 40-42, 48-52 Exam Review |
Exam I |
Essay 1 Reflection Due 4.1 |
|
9/26 |
4.2 |
Quiz (Chapter 4) QP: 1, 3 – 6, 9 – 21, 23 – 27, 29 – 33, 39, 43 – 44 5.1 (pages 76 – 78) |
5.1, cont (pages 78 – 83) |
|
10/3 |
5.1, cont 5.2 (pages 84 – 90) |
Permutation Groups |
Quiz (Chapter 5) QP: 1 – 4, 6, 12 –
14, 16 – 24, 27, 30 – 35 (pages 94 – 96) |
|
10/10 |
6.1, cont 6.2, 6.3 pages (96 – 100) |
9.1 (pages 142 – 147) |
9.2 (pages 147 – 152) |
|
10/17 |
Cosets
and Isomorphisms |
WU: Chapter
6 & 9 ( tex
) Due Quiz
(Chapters 6 & 9) QP: (Chapter 6) 1 –
6, 11 – 12, 16 – 20 10.1 (pages 156 – 158) |
10.1, cont. (pages 158 – 159) 11.1 (pages 166 – 168) |
|
10/24 |
11.2 (pages 168 – 172) |
11.2
wrap-up |
Exam II |
|
10/31 |
Essay 2 Reflection
Due 16.1 (pages 240 – 243) |
16.2 (pages 243 – 246) |
16.3 (pages 246 – 248) |
|
11/7 |
16.3, cont (pages 248 – 253) |
WU: Chapter 16 ( tex ) Due Quiz (Chapter 16) QP: 1 – 13, 16 – 19, 21 – 22, 24 – 30, 34 – 35, 38 – 41 17.1 (pages 264 – 266) |
Veteran’s Day |
|
11/14 |
17.2, 17.3 (pages 269 – 278) |
Activity: Polynomial Factor Rings |
17.3, cont. (pages 273 – 278) |
|
11/21 |
WU: Chapter 17 ( tex ) Due Quiz (Chapter 17) QP: 1 – 7, 9 – 13,
15 – 18, 20 – 24(abcd), 25 – 28 20.1 |
Thanksgiving Break |
|
|
11/28 |
Essay 3 Reflection Due
|
Geometric Constructions (Activity?) |
Final Review |
Final Exam (i.e. Exam III + a tad more)
Wednesday, December 7
8:00am – 10:00am
Welcome to college math!
If this is your first math class
taken in college, there are some important things you need to know. College
math classes are run very differently from high school math classes. On the
surface it may seem they are similar as you listen to the lecture and take
notes, but there are significant underlying differences. Knowing these ahead of
time can help you make the most of this coming semester.
#1: College math classes
generally stay on the schedule in the syllabus. If there is one day allotted to
the topic that is probably all of the class time that will be spent on it, even
if “most” of the students “don’t get it.”
#2: It is expected that you will
read the text and do the problems in order to learn the material, even if no
one checks up on you. The instructor might never collect the homework, but that
doesn’t mean it doesn’t affect your grade.
#3: You will sometimes be
responsible for material in the textbook that is not covered in class. If there
is a text reading and/or homework problems covering a concept that was not
discussed in class, you are still expected to learn it. If you don’t understand
it, make an appointment with your instructor for help.
#4: Some material is covered only
in class, is not in the textbook, and may not have any homework problems on it.
If you miss class, you may miss content that you are responsible to know. If
you have an unavoidable absence, be sure to get the notes and any announcements
from a classmate.
#5: There will be test questions
that don’t look “just like the homework.” In college, you are expected to focus
on learning the concepts, not just memorizing how to do certain types of problems.
These concepts can – and will – appear in very different forms on tests and
quizzes.
#6: At times you will be expected
to be able to explain why a problem
is done a certain way in addition to being expected to do the problem. As you
work on problems in class and on homework, don’t be satisfied with getting the
correct answer; ask yourself why that method is logical, and how you could
explain that logic to someone else.
#7: Most importantly, you are
responsible for your own learning. If you attend class faithfully, get the
notes and announcements if you have an unavoidable absence, read the text, do
the homework and question yourself (as in #6), and still don’t understand
something, it is up to you to get the extra help you need. Visit the instructor
during office hours or make a special appointment to ask questions, form a
study group, etc. There are many resources and people willing and happy to
help, but you need to take the initiative and seek out the help you need.
Good luck on a happy and successful
semester!
Commitment
to Inclusive Excellence: WSU recognizes
that our individual differences can deepen our understanding of one another and
the world around us, rather than divide us. In this class, people of all
ethnicities, genders and gender identities, religions, ages, sexual
orientations, disabilities, socioeconomic backgrounds, regions, and
nationalities are strongly encouraged to share their rich array of perspectives
and experiences. If you feel your differences
may in some way isolate you from WSU’s community or if you have a need of any
specific accommodations, please speak with the instructor early in the semester
about your concerns and what we can do together to help you become an active
and engaged member of our class and community.
•
Student
Support Services, Krueger Library 219, 457-5465
(www.winona.edu/studentsupportservices/)
•
Inclusion
and Diversity Office, Kryzsko Commons Room 122,
457-5595 (www.winona.edu/culturaldiversity/)
•
Disability
Services, Maxwell 314, 457-5878 (www.winona.edu/disabilityservices/)
•
Counseling
and Wellness Services, Integrated Wellness Center 222, 457-5330
(www.winona.edu/counselingcenter/)
•
GLBTA
Advocate, contact Counseling and Wellness Services for name and number of the
current Advocate
•
Tutoring
Services, Krueger Library 220, 457-5680 (http://www.winona.edu/tutoring/)
•
Writing
Center, Minné Hall 348, 457-5505
(www.winona.edu/writingcenter/)
•
Math
Achievement Center, Tau 313, 457-5370
•
Advising
Services, Maxwell 314, 457-5878 (www.winona.edu/advising/)
•
Two good
places to help you find resources of all kinds on campus are Student Support
Services and the Inclusion and Diversity Office. Both offices are dedicated to helping
students of all races, ethnicities, economic backgrounds, nationalities, and
sexual orientations. They can facilitate
tutoring and point you to a wide range of resources. Student Support Services is in Krueger
Library 219, and they can be reached at 457-5465. The Inclusion and Diversity Office is in Kryzsko Commons Room 122, and they can be reached at
457-5595.
•
If you
have a disability, the Disability Services office can document it for your
professors and facilitate accommodation. Their office is in Maxwell Hall, 3rd
floor, and they can be reached at 457-5878.
If you have a documented disability that requires accommodation, please
let me know as soon as possible. If you suspect you may have a disability, you
are encouraged to visit Disability Services as soon as possible.
•
College
can be very stressful. The Counseling
Center is there to help you with a wide range of difficulties, ranging from
sexual assault, depression, and grief after the loss of a loved one to stress
management, anxiety, general adjustment to college, and many others. Their office is located in the Integrated
Wellness Center (room 222) and they can be reached at 457-5330.
•
For help
with understanding the concepts of a particular class or understanding the
requirements of an assignment, Tutoring Services offers three types of
tutoring: drop-in appointments, 1-on-1 tutoring, and group sessions. You can
visit them in the Library in room 220, or go on-line and use the TutorTrac program to schedule a session.
•
For help
specifically with writing and the development of papers, the English department
has a Writing Center available to students and staffed by trained graduate
students pursuing their Master’s degree in English. The Writing Center is located in Minné Hall 348. You
can make an appointment on the sign-up sheet on the door or call 457-5505.
•
For help
specifically with understanding math concepts and solving math problems, the
Math Achievement Center (MAC) is staffed with friendly undergraduate tutors who
will help you work through difficult material. The MAC is located in Tau
313 and provides free tutoring for all students in math, statistics, or math
education courses. The center is open 1pm-10pm Mon-Thurs, 1pm-5pm Fri,
and 4pm-8pm Sun.
•
The GLBTA
Advocate is responsible for documenting homophobic and transphobic
incidents on campus and working with the appropriate channels to get these
incidents resolved. In addition, the advocate can direct people to GLBT
resources on campus and in Winona.
The Standard Disclaimer
applies.