University of Illinois at Urbana-Champaign

Math 417 - Introduction to Abstract Algebra - Fall 2019

(section D13)

Algebra is the study of operations, rules and procedures to solve equations. The origin of the term 'Algebra' seems to go back to a IX Century treaty by an Arab mathematician with the title 'The Compendious Book on Calculation by al-jabr and al-muqabala'. The term al-jabr is used in this book to denote two procedures: (i) the sum of two positive quantities to both sides of an equation, in order to cancel negative terms and (ii) the multiplication of both sides of an equation by a positive number to cancel fractions. With the passage of time, the term al-jabr or algebra became synonymous of the general study of equations and operations on them.

Algebra is one of the pillars of Mathematics and this course gives an introduction to the basics of Algebra, including conceptual proofs of all main results.

Lecturer: Rui Loja Fernandes
Email: ruiloja (at)
Office: 346 Illini Hall
Office Hours: Mondays and Fridays 1.30-2.30 pm (or by appointment);
Class meets: MWF 11:00-11:50 am, 341 Altgeld 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:



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.


Recommended Textbook:

Other Textbooks: (first ref available on the web; last two refs on hold in the Math Library)

Grading Policy and Exams

There will be weekly homework/quizzes, 3 midterms and a final exam. All exams/midterms will be closed book.

Homework Assignments and Sections covered so far:

Sections of the book covered so far: 1.1-1.7, 1.10 (midterm 1 stops here), 2.1-2.7 (midterm 2 stops here), 3.1, 5.1, 5.2, 6.1-6.3 (midterm 3 stops here at the Isomorphism Theorem for Rings).

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

Frequently Asked Questions about Homework
  1. How many homework assignments will there be?
  2. At least 12, but eventually there will be more, depending on the weeks when there are midterms.
  3. How is the grades of the homework calculated?
  4. Only the ten highest grades will count for your total homework grade. The homework grade will be the average of the ten best grades.
  5. How is each homework assignment graded?
  6. Each homework assignment receives a grade in the range 0-10 (0 minimum, 10 maximum). The grader will only grade 3 or 4 problems from each homework set (the same problems for all students).
  7. Can I turn in late homework?
  8. No.
  9. Can I turn in homework via e-mail?
  10. No.
  11. What if I fall sick, or what if I decide to go to Las Vegas to get married, or... , and I cannot turn in homework on time?
  12. One of the reasons that only the 10 best grades will count is to accommodate for such situations.

Emergency information for students in Mathematics courses

For important emergency information related to fires, tornados or active threats, please look at the following leaflet.

Last updated November 11, 2019