Math 417 – Introduction to Abstract Algebra – Spring 2013

Lecturer:Rui Loja Fernandes
Email: ruiloja (at) illinois.edu
Office: 346 Illini Hall
Office Hours: Tuesdays and Thursdays, 11:00 am (or by appointment);
Class meets: TTh 9:30-10:50 am, 2 Illini Hall;
Prerequisites: Officially either MATH 416 or one of MATH 410, MATH 415 together with one of MATH 347, MATH 348, CS 373; or consent of instructor. In practice, ability to understand and write proofs.

In this page:

Announcements:

  • The grades for the final exam have been posted. You can view the scores on-line (please note that you will have to log in).
  • If you would like to take a look at your final exam you can find me in my office on Friday, May 10, between 2-3 pm.
  • Solutions to the Final Exam have been posted here.

Syllabus:

Chapters 1-6 of the recommended text, covering: Fundamental theorem of arithmetic, congruences. Permutations. Groups and subgroups, homomorphisms. Group actions with applications. Polynomials. Rings, subrings, and ideals. Integral domains and fields. Roots of polynomials. Maximal ideals, construction of fields.

Textbooks:

Recommended Textbook:

  • Frederick M. Goodman, Algebra: Abstract and Concrete (Edition 2.5), SemiSimple Press Iowa City, IA. [PDF file available for download free of charge]

Other Textbooks: (on hold in the Math Library)

  • Michael Artin, Algebra, (2nd edition) Prentice Hall, 1991. [some level as the recommended textbook with alternative approaches]
  • Garrett Birkhoff and Saunders MacLane, A survey of modern algebra , (4th Edition), Macmillan, 1977. [a classic book; more advanced than the recommended textbook]

Grading Policy and Exams

There will be weekly homework/quizzes, 2 midterms and a final exam. All exams/midterms will be closed book.

  • Homework and quizzes (25% of the grade): Homework problems are to be assigned once a week. They are due the following week, at the beginning of the Thursday class. No late homework will be accepted. The two worst homework grades will be dropped. If necessary, quizzes may be offered during the semester.
  • Midterms (each 20% of the grade): The midterms will take place on February 21 and April 11 (the dates are subject to change).
  • Final Exam (35% of the grade): You have to pass the final to pass the course. According to the non-combined final examination schedule it will take place 8:00-11:00 AM, Tuesday, May 7, in the regular classroom.

Homework Assignments and Sections covered so far:

  • Homework #1 (PDF): Goodman, Exercises 1.3.1, 1.3.2, 1.3.3, 1.4.1, 1.4.2, 1.4.3. [Important Note: In the textbook, the only symmetries consider are rigid motions, i.e., rotations+translations] and its solutions.
  • Homework #2 (PDF): Goodman, Exercises 1.5.1, 1.5.3, 1.5.6, 1.5.7, 1.5.10, 1.6.3, 1.6.5. [Important Note: For exercise 1.6.5 recall that the g.c.d(m,n) was defined in class as the unique natural number k satisfying the following two conditions: (i) k|m and k|n; (ii) if r is any natural number such that r|m and r|n then r|k;] and its solutions.
  • Homework #3 (PDF): Goodman, Exercises 1.6.11, 1.7.4, 1.7.5, 1.7.6, 1.7.7., 1.7.11, 1.7.12 and the following exercise: Let $n=d_k d_{k-1} \cdots d_2 d_1 d_0$ be the decimal representation of the integer $n$. Show that 9 divides $n$ if and only if 9 divides $d_0+ d_1 + d_2 +d_3 + \cdots +d_k$. Solutions.
  • Homework #4 (PDF): Goodman, Exercises 1.7.14 (c); 1.7.15; 1.7.16; 1.10.4, 1.10.5, 1.10.9, 1.10.10 and the following exercise: Which day of the week was March 15, 1800? [Important Note: In the current calendar, called the Gregorian calendar, years which are divisible by 4, but not by 100, or years which are divisible by 400, are leap years (e.g., 800 was a leap year, but 900, 1000 and 1100 were not leap years).] Solutions.
  • Sample 1st Midterm Exam and its Solutions.
  • 1st Midterm Exam and its Solutions.
  • Homework #5 (PDF): Goodman, Exercises 1.8.7, 1.8.8, 1.8.10, 1.11.3, 1.11.5, 1.11.8, 1.11.11. [Important Note: In the textbook, the invertible elements in a ring are also called units] Solutions.
  • Homework #6 (PDF): Goodman, Exercises 2.1.7, 2.1.10, 2.1.11, 2.2.4, 2.2.6, 2.2.9, 2.2.17, 2.2.19. and its solutions.
  • Homework #7 (PDF): Goodman, Exercises 2.3.6, 2.3.7, 2.4.5, 2.4.8, 2.4.14, 2.4.15, 2.4.17, 2.4.18. and its solutions.
  • Homework #8 (PDF): Goodman, Exercises 2.5.4, 2.5.6, 2.5.7, 2.5.8, 2.5.14, 2.6.3, 2.6.5, 2.7.7, 2.7.11. and its solutions.
  • Homework #9 (PDF): Goodman, Exercises 3.1.10, 3.1.11, 3.1.12, 3.1.13, 3.1.15, 3.2.2., 3.2.4, 3.2.6. and its solutions.
  • Sample 2nd Midterm Exam and its Solutions.
  • 2nd Midterm Exam and its Solutions.
  • Homework #10 (PDF): Goodman, Exercises 5.1.3, 5.1.4, 5.1.6, 5.1.8, 5.1.12, 5.1.13, 5.1.14. and its solutions.
  • Homework #11 (PDF): Goodman, Exercises 6.1.3, 6.1.11, 6.1.17, 6.2.2, 6.2.7, 6.2.9, 6.2.16, 6.2.19. and its solutions.
  • Homework #12 (PDF): Goodman, Exercises 6.3.6, 6.3.7, 6.3.8, 6.4.1, 6.4.4, 6.4.5, 6.4.6, 6.4.7, 6.4.13. and its solutions.
  • Review problems for the final exam: PDF.
  • Final Exam and its Solutions.

Sections of the recommended text covered: 1.1-1.11, 2.1-2.7, 3.1-3.2, 5.1-5.2, 6.1-6.5.

(PDF files can be viewed using Adobe Acrobat Reader which can be downloaded for free from Adobe Systems for all operating systems.)

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Last updated May 9, 2013