University of Illinois at Urbana-Champaign

Math 417 - Introduction to Abstract Algebra - Spring 2017

(section B1)





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) illinois.edu
Office: 346 Illini Hall
Office Hours: M 10:00-10:50 am and Th 1.30-2.30 pm (or by appointment);
Class meets: MWF 09:00-09:50 am, 447 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.


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Syllabus:

Chapters 1-3 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:

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 lecture notes covered: 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 3.1, 4.1, 4.2.

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Emergency information for students in Mathematics courses

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Last updated April 29, 2017