Introduction to Abstract Algebra

Course Description and Grading Breakdown

The second term of Math 5 will be devoted to the study of rings and modules; including some advaced topics in linear algebra. The material corresponds roughly to Chapters 7 through 12 in the text for the course, Abstract Algebra by Dummit and Foote.

Topics includes: Introduction to rings and ideals; Isomorphism Theorems; Chinese Remainder Theorem;
Euclidean domains, Principal domains, Unique Factorization domains; Polynomial rings, Irreducibility criteria for polynomials. Introduction to modules; Free modules, Finitely generated modules; Classification of finitely generated modules over PIDs; Advanced Spectral theory. 


Grading: Roughly 40% Homework, 30% Midterm, and 30% Final.

Course Meeting Time and Location
Monday, Wednesday and Friday
9:00 - 9:55 am
387 Linde

Course Instructor Contact Information and Office Hours
Mondays 2:30-3:30pm in 375 Linde Hall

TA Contact Information and Office Hours
Wednesday 3-4pm Linde 289 (glass conference room near the staircase)

Office Hours start 2nd week. I will be away 2nd week and Elena will cover it.

Remark on grading, proof writing and office hours:
This year we decided to take a more systematic approach to the grading of proofs in the class. Now 20% of the points will be attached to good proof writing. Student are encouraged to come to one of the office hours to present a proof and figure out the best way to write it. I will keep a running log of proof writing mistakes and corrections I see (e.g. undeclared variables). Here is a suggested principle for good proof writing:
1. Set up notation.
2. Lay out the proof in steps, where each step is either obvious or directly follows from a previous step and mention which.
3. Being rigorous is not the same as being verbose! In fact being verbose can harm a proof. Do not write down irrelevant things for the sake of writing things down.
Refer to the question sheet and the posted solutions for one idea of concise but good proofs.

Course Schedule and Textbook

 DateTopic 
 1/15 Class notes (up to week 2)
  


Course Policies
HW sets are due Thursdays at 4pm, in the Ma5 mailbox. 
Solutions will be posted by the following Monday.

No late HW sets will be accepted, except in unusual circumstances and ONLY IF prior arrangements have been made with the Instructor and TA.


Assignments
 Date PostedAssignment Due Date 
 1/10 HW1 1/17
 1/16 HW2 1/24


Midterm and Final Exam
Midterm will be posted on February 1, 2019 due on THURSDAY February 7, at 4pm.
Final will be posted on March 13, 2019 due on TUESDAY March 18, at 4pm.

Collaboration Table
 HomeworkExams
You may consult:  
Course textbook (including answers in the back)YESYES
Other booksYESNO
Solution manualsNONO
InternetYESNO
Your notes (taken in class)YESYES
Class notes of othersYESNO
Your hand copies of class notes of othersYESYES
Photocopies of class notes of othersYESNO
Electronic copies of class notes of othersYESNO
Course handoutsYESYES
Your returned homework / examsYESYES
Solutions to homework / exams (posted on webpage)YESYES
Homework / exams of previous yearsNONO
Solutions to homework / exams of previous yearsNONO
Emails from TAsYESNO
You may:

Discuss problems with othersYESNO
Look at communal materials while writing up solutionsYESNO
Look at individual written work of othersNONO
Post about problems onlineNONO
For computational aids, you may use:

CalculatorsYES*NO
ComputersYES*NO

* You may use a computer or calculator while doing the homework, but may not refer to this as justification for your work.  For example, "by Mathematica" is not an acceptable justification for deriving one equation from another.  Also, since computers and calculators will not be allowed on the exams, it's best not to get too dependent on them.

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Elena Mantovan,
Jan 14, 2019, 12:43 PM
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Elena Mantovan,
Jan 16, 2019, 8:45 AM
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Elena Mantovan,
Jan 15, 2019, 10:06 AM
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Victor Zhang,
Jan 19, 2019, 12:37 AM