Math 311 (Fall 2009)
- Instructor: Byung-Jay Kahng
- Email: kahngb@canisius.edu
- Office: 304B Wehle Technology Center
- Office Phone: (716) 888-2493
- Office Hours: TuTh 10:00--12:00, MWF 10:00--10:50, also by appointment
Course Schedule: Weekly topics,
Exam dates, ...
OVERVIEW:
Nowadays, (abstract) algebraic methods and terminologies are used almost everywhere
in Pure and Applied mathematics, as well as Computer science, Physics, Coding
theory, etc. This course introduces the students the axiomatic/abstract definitions
of various algebraic structures, including "rings", "ideals", "fields", "groups".
The main goals of the course are: (1) to explore the basic properties of these
algebraic structures; (2) to learn about their uses in different settings in
mathematics; and at the same time, (3) to develop the ability to work with such
abstract concepts in formulating proper mathematical arguments.
Naturally, a strong emphasis will be given to writing logically proper proofs.
For this, the students should learn to work with abstract axioms, and in addition,
be able to convert heuristic and conceptual statements into logical and
mathematically rigorous arguments.
Homework Assignments: Will be announced here weekly.
- HW#1 [Due 9/2]: (§ 1.1)[p6]: 1(d)(f),6,9;
(§ 1.2)[p12]: 1(b)(d),3,6,8,15(b)(d),17,18,21,25,29
- HW#2 [Due 9/9]: (§ 1.3)[p18]: 1(b),2,4,12,15,17;
(§ 1.4)[p22]: 1,2,3,6,7,8
- HW#3 [Due 9/16]: (§ 2.1)[p29]: 1,5,8(a)(b),9,10,11(d),14,20,23;
(§ 2.2)[p35]: 2(b)(d),3,8;
(§ 2.3)[p39]: 1(a)(b),4
- HW#4 [Due 9/23]: (§ 13.1)[p410]: 8,12,14;
(§ 2.3)[p39]: 5,8;
(§ 3.1)[p50]: 1,2,5,6,9,13(b),14,16,20,29;
(§ 3.2)[p62]: 2
- HW#4(b) [Due 10/2]: (§ 3.2)[p62]: 4,8,11,12,15,19,23
- Exam 1 [9/29 (Tue)]
- HW#5 [Due 10/9]: (§ 3.3)[p76]: 6,7,10,11,12,13,16,20,23,28
- HW#6 [Due 10/16]: (§ 3.3)[p76]: 25,29;
(§ 4.1)[p88]: 1,5,6,12,13;
(§ 4.2)[p93]: 1,2,5(b)(c)(d),6(b)(c)(d)
- HW#7 [Due 10/21]: (§ 4.1)[p88]: 3,18;
(§ 4.2)[p93]: 3,7,14,15;
(§ 4.3)[p98]: 3,6,10,14,22;
(§ 4.4)[p104]: 6
- HW#8 [Due 10/28]: (§ 4.4)[p104]: 3(c)(d),10,13,14,15;
(§ 4.5)[p113]: 5,7,8,12,13;
(§ 4.6)[p93]: 3
- HW#9 [Due 11/4]: (§ 5.1)[p122]: 1(a)(b),3,8,10,11;
(§ 5.2)[p128]: 1,4,9,14
- Exam 2 [11/3 (Tue)]
- HW#10 [Due 11/11]: (§ 5.3)[p132]: 1,2,6,9,11
- HW#11 [Due 11/18]: (§ 6.1)[p141]: 3,4,7,12,13,14,15,16,18,35,38;
(§ 6.2)[p151]: 2,3,4,8,10,14,15,21
- Exam 3 [12/1 (Tue)]
- Final Exam Date & Time: TBA
Additional Information
- Pre-requisites: Should have taken (and passed) Math 230, 219. In particular, you
should be
comfortable working with Equivalence relations, Mathematical induction, and some of the
methods used in Linear algebra.
- Last day to drop/add classes is 8/29; Last day to withdraw from a course is 11/13.
- Due to the nature of the subject matter, we will be working with a lot of proof problems
(in homeworks, as well as in exams). When writing mathematical proofs, you should make
an effort to use complete English sentences, proper English/Math grammar, spelling and
punctuation. Leave enough room for me to write comments/feedback on your proofs.
- In the below are a (very short, not full) list of some books on introductory
abstract algebra,
and in the case of the last three, some graduate level books:
(*) J. Gallian, Contemporary Abstract Algebra
(*) D. Dummit and R. Foote, Abstract Algebra
(*) J. Fraleigh, A First Course in Abstract Algebra
(*) I. Herstein, Topics in Algebra
(*) N. Jacobson, Basic Algebra I, II
(*) S. Lang, Algebra
(*) T. Hungerford, Algebra
- If you have a disability for which accommodations and support are necessary,
please let me know. Also contact the office of Disability Support Services
at (716) 888-3748.
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