This course is an introduction to the main ideas of abstract algebra. The focal points are the concepts of groups, rings and fields. The course emphasizes abstract reasoning which is at the core of modern mathematics and many of its applications to the real world. Proofs - understanding them and developing them on your own - play a central role.
It will benefit you a lot to read the corresponding sections of the text before each lecture. There is a lot of material in the text that can't be covered in class, and you will need to read and understand this on your own, starting with Chapters 0 and 1. Always feel free to ask questions to your instructor and grader.
Final Exam, Wednesday, Dec 10, 5:30-8:00pm, in Library E4315
The Final is cumulative, covering the full semester of material roughly equally. There are 10 problems on the exam, with 4-5 on group theory, 5-6 on rings and fields. The exam covers material up to and including Ch. 22. (This is a change from an earlier statement if you saw that).
As before, prepare by doing many problems to test your understanding. In addition to previous exercises below and HW problems, try some of the following. One of them will be on the exam.
Supplementary Exercises, p 341-: 1, 2, 8, 23, 31
(to be continued - maybe)
Midterm II, Tuesday, Nov 18, in class.
Material on Midterm II:
Rings: Chapters 12 - 17
Fields: Chapter 20
Topics you may skip:
Ch. 17, statement only of Thms. 17.2, 3, 4, skip Corollary p. 310, and p.313 on, but know statement of Theorem 17.6
Ch. 18 - all
Ch. 20, p.360-366, but know statement of uniqueness of splitting fields, p.362.
Topics to read, not covered in class
There is no formal practice midterm exam, but have a look at the midterms for MAT 313 for Fall 13 and Fall 09; these are indicative for this exam. As before, in general do as many problems/exercises as you can: below are some concrete suggestions.
Supplementary Exercises, p. 276-: 8, 19, 24, 31, 39
Supplementary Exercises, p. 341-: 7, 11, 19, 21, 23
Midterm I: Tuesday, Oct 7, in class.
Material: Group theory, Chapters 1-11
Topics to read, not covered in class:
Ch. 0 and Ch. 1
Ch. 5, even and odd permuations, alternating group
Ch. 6, automorphisms and inner automorphisms
Ch. 9, internal direct products
Topics you can skip:
Ch.4, Theorem 4.4 and Corollary, p.80
p. 185(bottom) - p. 188 (top)
Practice Exam Look at the Midterm I exams for MAT 313, Fall 13 and Fall 09. (Find the link for the websites for these courses via the undergrad course webpages on the math dept site). Some of the problems for Fall 13 are too hard, but most are at the level of this exam; all of the Fall 09 exam is fine.
In general, do as many problems as you can to practice for the Midterm. Here are some concrete suggestions:
Supplemental Problems, Ch.9-11, p.230: 7, 18, 19, 22
Supplemental Problems, Ch.5-8, p.174: 10, 24, 25, 29
Supplemental Problems, Ch.1-4, p.91: 2, 16, 33, 34
Final Exam: Wednesday Dec 10, 5:30-8:00pm, Library E4315
11:30am - 12:50pm
Instructor: Michael Anderson
Office Location: 4-110 Math Tower
Email: anderson at math.sunysb.edu
Web site: http://www.math.sunysb.edu/~anderson
Office hours: M/W 1:30-3pm & by appointment in 4-110 Math Tower
Grader: Mu Zhao
Email: mu.zhao at stonybrook dot edu
Office hours: TBD
If you do buy or have bought the 8th Edition of the text, that's fine. It will serve as a text perfectly well.
Contemporary Abstract Algebra, 7th Edition, by Joseph A. Gallian, Brooks/Cole, 2010.
However, HW problems will be assigned from the 7th Edition
There will be weekly HW assignments, generally due in class on Tuesdays.
Check the course schedule below regularly (at least weekly) for the assignments.
Note that minimal solutions to odd numbered problems are at the back of the textbook. You should nonetheless try and solve these problems without recourse to the answer key. In case odd numbered problems are assigned as HW, you should write up the solution carefully in your own words, even if you consulted the book for the final answer. You must always show your work to receive credit.
It is OK to discuss HW problems with other students. However, each student must write up homework solutions individually in his/her own words, rather than merely copying from someone else.
Although only a random selection of problems on each homework will be graded by your TA, it is important that you do all the HW problems (or at least as many as possible). You should not expect to do well on the exams without the work and experience that goes into solving the HW problems.All policies regarding HW and your grades for this part of the course are decided first by your grader. If you remain unsatisfied after discussion with the grader, then take it up with me (your instructor). At the end of the semester, I will drop your lowest homework.
Grades will be computed according to the following percentages:
Midterm I, Tuesday, Oct. 7, in class
Midterm II, Date TBD, in class
Final Exam, Wednesday, Dec 10, 5:30-8:00pm Library E4315
No make-up exams will be given. If a midterm exam is missed because of a serious (documented) illness or emergency, your semester grade will be determined on the basis of other work done in the course. Exams missed for other reasons will be counted as failures.
Resources: If you have questions regarding the course material at any time during the semester, you are encouraged to visit your instructor or TA during office hours, or make a separate appointment if necessary. Your instructors will also reply to email, within reason. Another excellent source of help is the Mathematics Learning Center (S240A in the Math Building - basement level), which is staffed by advanced math majors, graduate students and faculty daily. For a schedule of their hours, check their website.
Americans with Disabilities Act: If you have a physical, psychological, medical, or learning disability that may impact on your ability to carry out assigned course work, please contact Disability Support Services at (631) 632-6748 DSS . DSS office: EEC (Educational Communications Center) Building, Room 128. DSS will review your concerns and determine, with you, what accommodations, if any, are necessary and appropriate. All information and documentation is confidential. Arrangements should be made early in the semester so that your needs can be accommodated.
Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and DSS. For procedures and information go to the DSS website above.
Academic Integrity: Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another persons work as your own is always wrong. Faculty are required to report any suspected instances of academic dishonesty to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website here.
Critical Incident Management: Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of University Community Standards any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits the students' ability to learn. Further information about most academic matters can be found in the Undergraduate Bulletin, the Undergraduate Class Handbook and the Faculty-Employee Handbook.
Schedule of Topics
Remember, HW assignments are from 7th edition.
Ch. 2, 3
Read Ch. 0, Ch. 1
Ch.2: 2, 5, 8, 18, 26
Ch.3: 8, 10, 14, 18, 19
Ch.4: 2, 4, 14, 22, 34
Ch.5 : 4, 10, 17, 24, 36
Ch.6: 4, 18, 19, 20, 32
Ch.7: 6, 8, 10, 12, 19
Ch. 7: 26, 28
Ch. 8: 6, 17, 28, 34
Ch. 9: 4, 6, 7, 11, 22
Ch. 10: 6, 8, 22, 24, 29
At least one problem will be on Midterm
Tuesday, Oct 7
Ch.12: 2, 6, 26, 40, 47
Ch.13: 4, 8, 9, 10, 39, 53
Ch.13: 11, 20, 30, 27, 35, 38 (see Exercise 11) TYPO: This should be Ch 14
Ch.14: 10, 13, 14, 26 TYPO: This should be Ch 15
Ch. 15: 45, 46
Ch 16: 2, 13, 14,(see 17), 18, 30, 42
Ch. 16: 25, 41
Ch. 17: 6, 8, 12, 14, 33, 34
Ch. 20: 2, 4, 7, 8(no mult. table), 10, 27
One problem will be on midterm
Ch.21: 14, 17, 19, 24
Ch.22: 3, 4, 11, 33, 35