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Mathematics 31

Topics in Algebra

General Information

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According to the ORC: "This course will provide an introduction to fundamental algebraic structures, and may include significant applications. The majority of the course will consist of an introduction to the basic algebraic structures of groups and rings. Additionoal work will consist of development of further algebraic structures or applications of the previously developed theory." So this will definitely be included in our goals for the course.

Other goals include, but are certainly not limited to:

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Labs will take place every week, usually during the X-hour. You will not receive any credit for a lab you are not present for, but you will be able to drop your two lowest lab scores from your final grade. Labs will vary in nature, but they will always be self contained in the 50 minute X-hour. In other words, you will not be expected to prepare anything, nor have any extra homework related to a lab.

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There will be a quiz the first ten minutes of class each Monday. These quizzes are not designed to "stump" you, they are meant to keep everyone up to speed with the course. The questions will ask you to state a definition we learned in the previous week, make a simple calculation, or give an example. Attending class, and perhaps a short review of your lecture notes before the quiz, should be enough to get you 100% every time. Like labs, you will not receive any credit for a quiz you are not present for, but your two lowest quiz scores will be dropped from your final grade. Note that quizzes take place at the beginning of class, I suggest being on time.

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There will be one midterm exam and a final at the end. Portions of the exams may be of the take-home type, if it is decided that this is the best way to test certain material. If that is the case your homework load will reflect this decision. If you have a conflict with the time or date for the midterm exam, you must meet with the instructor at least a week in advance to schedule a make-up time. If you do not take the exam with the rest of the class, or during your scheduled make-up time, you will receive no credit for the exam. The registrar schedules our final exam time, so I can not make special arrangements to accommodate your winter break travel plans.

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There will be a final project due at the end of the term. Each student will research and learn about one or more applications of abstract algebra, and write a paper summarizing and explaining their chosen topic. I will give you ideas of applications, but lists of suggested reading are at the end of each chapter of the text, and many of them would make excellent paper topics. Topic suggestions, grading specifics, and a timeline of due dates will be available early in the term.

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Grades will be out of 1000 points according to the table below. I will keep a numerical total of your points throughout the term, but will not assign a letter grade until after the final exam is graded.

If you ever have a question about the grading policy, or about your standing in the course, please feel free to consult with me.

Dartmouth students are expected to adhere to the honor principle. In this course that means:

**On Homework**:
Working together is permitted and encouraged, but no copying. You are welcome to work in
groups to discuss ideas and specific problems (also feel free to
talk with your instructors, tutors, and anyone else you may find). However, **each student is expected to produce the final written
homework set individually and independently.**
This means you
cannot simply copy down the solution arrived at by the group, even if
you were a member of the group. If you do work in a group or
receive help from a tutor or friend, state that on your homework and
include their names if they are in the class.

On Labs: Each week's lab will have different rules regarding collaboration, allowable resources, and final product responsiblilty. These rules will be stated clearly on the lab assignment.

On Quizzes and Exams: No help will be given nor received from any person other than the instructor. Different exams may have different rules regarding the resources allowed. These rules will be printed on the exams themselves and stated in class before the exam, with enough time to prepare or study the appropriate resources.

On Final Projects: The details of how the honor principle will apply to your final project will be clearly stated on the official assignment sheet.

If you have any questions as to whether some action would be acceptable under the Academic Honor Code, please speak to me, and I will be glad to help clarify things. This is a case in which it is definitely better to ask permission rather than forgiveness.

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This section will contain links to interesting websites, files, or papers relavant to the course. If you find something interesting, please let me know so that I can post it here.

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Mathematics 31

Topics in Algebra

General Information

Course Info | Text | Goals |

Homework | Labs | Quizzes |

Exams | Final Project | Grades |

Honor Principle | Links | Other Issues |

Instructor | Class Meetings |
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Sarah Wright Office: 211 Kemeny Hall | MWF 12:30 - 1:35 X-Hour Tues 1:00 - 1:50 |

Office Hours: M: 3-4, T: 2-4, W: 10-11, F: 2-3 | Classroom: Kemeny Hall 108 |

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Contemporary Abstract Algebra (Sixth Edition) Joseph A. Gallain Houghton Mifflin Publishing Avaliable at Wheelock Books |

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According to the ORC: "This course will provide an introduction to fundamental algebraic structures, and may include significant applications. The majority of the course will consist of an introduction to the basic algebraic structures of groups and rings. Additionoal work will consist of development of further algebraic structures or applications of the previously developed theory." So this will definitely be included in our goals for the course.

Other goals include, but are certainly not limited to:

- Development and understanding of mathematical proof: what it means to prove something, methods of proof, how to write a proof well, etc.
- Work with peers to understand difficult concepts and solve problems.
- Explore and understand the connections between pure mathematical structures and the real world.
- HAVE FUN!!!

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## I hate homeworkHomework, oh homework I hate you, you stink. - Shel Silverstein | Homework will be assigned every day of lecture, and collected at the beginning of class on the next Wednesday. You can find the details of the assignment, and when it will be due HERE. No late homework assignment will be accepted without prior permission from the instructor. Your lowest homework grade will be dropped from your final grade. The grades for homework will be based on accuracy and completeness. Because of the size of the class, and in an effort to get graded homework returned to you in a timely manner, it may become necessary to only grade and comment on a few homework problems. In this case your entire assignment will be checked for completeness, and your accuracy score will be based on those few problems. Solutions to the homework will be posted, and you are encouraged to visit office hours to discuss your solutions if you have questions. You are encouraged to work with your classmates on homework assignments. However, anything you write down to turn in should be your own thoughts in your own words. So, take a few notes on the problem while you're working with the group, then use those notes while you're alone to write-up your final solution. Include the names of the students you worked with. |

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Labs will take place every week, usually during the X-hour. You will not receive any credit for a lab you are not present for, but you will be able to drop your two lowest lab scores from your final grade. Labs will vary in nature, but they will always be self contained in the 50 minute X-hour. In other words, you will not be expected to prepare anything, nor have any extra homework related to a lab.

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Quizzes |
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There will be a quiz the first ten minutes of class each Monday. These quizzes are not designed to "stump" you, they are meant to keep everyone up to speed with the course. The questions will ask you to state a definition we learned in the previous week, make a simple calculation, or give an example. Attending class, and perhaps a short review of your lecture notes before the quiz, should be enough to get you 100% every time. Like labs, you will not receive any credit for a quiz you are not present for, but your two lowest quiz scores will be dropped from your final grade. Note that quizzes take place at the beginning of class, I suggest being on time.

Top

There will be one midterm exam and a final at the end. Portions of the exams may be of the take-home type, if it is decided that this is the best way to test certain material. If that is the case your homework load will reflect this decision. If you have a conflict with the time or date for the midterm exam, you must meet with the instructor at least a week in advance to schedule a make-up time. If you do not take the exam with the rest of the class, or during your scheduled make-up time, you will receive no credit for the exam. The registrar schedules our final exam time, so I can not make special arrangements to accommodate your winter break travel plans.

Midterm | Friday, October 31 12:30 - 1:35 |
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Final | Monday, December 8 3-6 pm |

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Final Projects |
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There will be a final project due at the end of the term. Each student will research and learn about one or more applications of abstract algebra, and write a paper summarizing and explaining their chosen topic. I will give you ideas of applications, but lists of suggested reading are at the end of each chapter of the text, and many of them would make excellent paper topics. Topic suggestions, grading specifics, and a timeline of due dates will be available early in the term.

Top

Grades will be out of 1000 points according to the table below. I will keep a numerical total of your points throughout the term, but will not assign a letter grade until after the final exam is graded.

Number Graded | Points Each | Total | |
---|---|---|---|

Homework | 9 - 1 = 8 | 25 | 200 |

Labs | 10 - 2 = 8 | 5 | 40 |

Quizzes | 10 - 2 = 8 | 20 | 160 |

Exams | 2 | 200 | 400 |

Final Project | 1 | 200 | 200 |

Total | 1000 |

If you ever have a question about the grading policy, or about your standing in the course, please feel free to consult with me.

Dartmouth students are expected to adhere to the honor principle. In this course that means:

On Labs: Each week's lab will have different rules regarding collaboration, allowable resources, and final product responsiblilty. These rules will be stated clearly on the lab assignment.

On Quizzes and Exams: No help will be given nor received from any person other than the instructor. Different exams may have different rules regarding the resources allowed. These rules will be printed on the exams themselves and stated in class before the exam, with enough time to prepare or study the appropriate resources.

On Final Projects: The details of how the honor principle will apply to your final project will be clearly stated on the official assignment sheet.

If you have any questions as to whether some action would be acceptable under the Academic Honor Code, please speak to me, and I will be glad to help clarify things. This is a case in which it is definitely better to ask permission rather than forgiveness.

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Interesting Links |
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This section will contain links to interesting websites, files, or papers relavant to the course. If you find something interesting, please let me know so that I can post it here.

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Disabilities and Religious Observances |
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Students with disabilities enrolled in this course and who may need disability-related classroom accommodations are encouraged to make an appointment to see me before the end of the second week of the term. All discussions will remain confidential, although the Student Accessibility Services office may be consulted to discuss appropriate implementation of any accommodation requested.

Whether or not you have a disability, the Academic Skills Center is an excellent place to visit. Take some time to look at their videos and other resources. Would you benefit from some of the planning tools? Do you think you could improve your note-taking skills? Is stress eating your life? You're the only one who knows what might benefit you, and it doesn't hurt to look.

I realize that some students may wish to take part in religious observances that fall during this academic term. Should you have a religious observance that conflicts with your participation in the course, please come speak with me before the end of the second week of the term to discuss appropriate accommodations.Top