Grading and Policies

Homework Assignments

MATH3100 Modern Algebra I

Course Outline

Course Description: Integer Arithmetic, Modular Arithmetic, Rings and Fields, Isomorphisms, Polynomials over a Field, Ideals, Homomorphisms and Quotient Rings, Prime and Maximal Ideals

Course Goals: 

  1. Students will understand the basic structure of rings, fields and ideals.
  2. Students will strengthen their ability to construct rigorous proofs to the level appropriate for advanced undergraduate courses in mathematics.
  3. Students will develop an appreciation for the aesthetics of abstract mathematics.

Course Objectives: Upon satisfactory completion of this course a student will:

  1. Understand the basic properties of arithmetic in Z and Z modulo n.
  2. Understand the basic properties of rings and fields.
  3. Identify and define isomorphisms of rings.
  4. Understand the basic properties of Polynomial rings.
  5. Understand the basic properties of ideals and quotient rings and how these ideas unite all of the course material.
  6. Construct rigorous proofs of theorems involving these topics.

 

Course Outline:

Text and Materials: Hungerford, Thomas W.; Abstract Algebra: An Introduction, 2nd Edition, Saunders College Publishing, 1997.

Prerequisite: A grade of C or better in MATH3090 or consent of the instructor.

Course Requirements: The Mathematics Department has established minimal standards for satisfactory completion of this course. These are a passing average on at least three major tests and a comprehensive final exam. Each instructor may have additional requirements for satisfactory completion of his/her course.

 

It is the policy of NSU to accommodate students with disabilities, pursuant to federal law, state law, and the University’s commitment to equal educational opportunities. Any student with a disability, who needs accommodation, for example in seating placement or in arrangements for examinations, should inform the instructor at the beginning of the course. Students with disabilities are encouraged to contact the Office of Disabled Student Services, which is located in Kyser Hall, Room 237, telephone 357-6950 or (TTD) 357-4393 or disability@nsula.edu

 

Information for MATH3100

MWF 11:00 - 11:50 Kyser 425

Tests:

Test Chapters Covered Approximate Date
1 1 - 2 September 26
2 3 - 4  November 7
3 5 - 6 December 8
Final Comprehensive December 15, 11:00 AM

Homework:

I will assign homework each day. Usually these will be individual assignments, but several will be group projects. I will collect these problems at the next class meeting. Your solutions should be written out fully in paragraph form using complete sentences and correct punctuation. Chronic lateness of homework assignments will negatively affect your grade. I will also give brief quizzes at the beginning of class over definitions and the statements of theorems; these will count as a homework assignment. I will drop your lowest 5-6 grades when computing your average. Regular completion of homework is essential for success in this class. If you fail to complete 10 or more assignments, you will be penalized one letter grade for the course. For every 5 missing assignments after that, I will deduct an additional letter grade.

Grading:

Each of the tests, the Final, and your homework average count for 20% of your grade. The approximate grading scale will be:

90-100 A
80-89 B
70-79 C
60-69 D
00-59 F

I reserve the right to curve the grades in your favor.

Class Policies:

If your Final Exam score is higher than your lowest test score, I will drop that score and your Final will count for 40% of your grade. If you miss a test and have an excuse, I will drop the test in the same manner. If, however, you miss a test with no excuse, you will receive a 0. If you know ahead of time that you will miss a test, I will be glad to let you take it early.

Cheating will not be tolerated. If you are caught cheating on a test, you will receive a 0 on that test. If you are caught cheating on the Final, you will receive an F in the course.

Attendance is mandatory. If you miss a class, you should submit a written excuse to me within 3 days of your return to class. If you miss more that 3 classes, it will negatively affect your grade.

Homework Assignments (tentative)

  1. 1.1    4, 5, 7 
  2. 1.2    3, 4, 6, 7
  3. 1.2    1ac, 15ac, 26, 28
  4. 1.3    6, 16, 21, BONUS: 23
  5. 1.4    5, 6, 12
  6. 2.1    1, 6, (a,b) = 1, if and only if, ax + by =1 for some x,y in Z       
  7. 2.1    20, 27, 31
  8. 2.2    2, 7, 10
  9. 2.3    4, 7, 8
  10. 3.1    11, 18, 36
  11. 3.1    5, 8, 31
  12. 3.2    6, 11, 23 
  13. 3.3    5, 6, 10
  14. 3.3    19, 28, 33
  15. 4.1     5, 6, 11, 16            BONUS: 17, 18, 19
  16. 4.2    5ad, 6ad, 14
  17. 4.3    1, 5, 10
  18. 4.3    16 [NOTE: p(x) is non-constant], 20, 25
  19. 4.4    4, 13, 24
  20. 5.1    4, 8, 10
  21. 5.2    1, 7, 9
  22. 5.3    4, 5, 6
  23. 6.1    1, 2, 13
  24. 6.1    25, 32, 41
  25. 6.2    12, 14, 24
  26. 6.3    10, 11, 17

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