Instructor: Timothy Riley
Lectures: Mondays,
Wednesdays & Fridays
1:25pm–2:15pm
in MLT 251
Office hours: Mondays
2:15pm–4:15pm in MLT 401
Textbook: A first course in abstract algebra,
by J.J. Rotman, Third Edition, Prentice Hall,
ISBN-10: 0131862677
Math 4320 is an introduction to abstract algebra. It includes groups, rings, fields, factorization of polynomials and integers, congruences, and the structure of finitely generated abelian groups. Euclidean domains and Sylow's theorems may be discussed, time allowing.
Math 4320 is a 4–credit course. The course catalogue states that students may not receive credit for both this course and MATH 4340 (Honors Introduction to Algebra), and that the prerequisite is at least one of
MATH 3320 — Introduction to Number Theory
MATH 3360 — Applicable Algebra
MATH 4310 — Linear Algebra
MATH 4330 — Honors Linear Algebra
or permission of the instructor.
My interpretation of this is that the primary prerequisite is "mathematical maturity." What I have in mind here is that you should be able to read and write proofs, you should be willing to persevere on a hard problem, and you should be willing to learn things on your own once in a while. (Hat tip to Ken Brown.)
Undergraduates who plan to attend graduate school in mathematics should take MATH 4330 and MATH 4340 instead of MATH 4310 and MATH 4320.
Grades will be computed according to the following point break–down:
Prelim
25%
Final exam
40%
Homework
35%.
Cornell's code of academic integrity applies to this and all other courses. In particular, academic misconduct of any kind may result in a grade penalty or the assignment of a failing grade.
Prelim Part I 3/12/12 & Part II 3/14/12 in class covering sections through 2.5
Final 2:00pm–4:30pm, 5/18/12 MLT 406 comprehensive
Exams will be taken without the aid of any textbooks or notes.
Calculators will NOT be allowed for the exams. Cell phones, MP3 players and other electronic devices (aside from watches) will NOT be allowed in the exam room, not even as time–keeping devices.
Accommodations may be made in the event of illness, a clash with another examinations, a conflict with religious observances, or other serious circumstances — please contact your instructor as early as possible. Students who miss exams and then present excuses that could have been given in advance will not be looked upon favorably. Do not make travel plans that conflict with the exams.
If you have been approved for extended–time or special–condition exams by Cornell Student Disability Services, notify your instructor in the first two weeks of the semester.
Due 2/1:
1.46 (vi, vii, x), 1.49, 1.50, 1.54, 1.55, 1.60, 1.64, 1.67
Due 2/8:
1.68, 1.72, 1.73, 1.81, 1.83, 1.87
Due 2/15:
1.89, 1.92. 1.97, link to questions on RSA, 2.1, 2.18
Due 2/22:
2.21 (ii, iv, x), 2.22, 2.24 (i), 2.26, 2.32, 2.34, 2.35 (see p. 119 for background)
Due 2/29:
2.36 (i, v, vi, vii, ix), 2.39, 2.40, 2.42, 2.44, 2.47, 2.50
Due 3/7:
2.52 (i, iv, v, x, xi), 2.57, 2.58, 2.63, 2.64 (vi, vii, viii). 2.68, 2.71, 2.75
3/14, 3/21:
no homework
Due 3/28:
2.86, 2.95 (ii, iv, v, vi, ix), 2.99, 2.104, 2.106, 2.109, 2.113Due 4/4:
2.114 (ii, iii, v, vii, xiv), 2.120, 2.121, 2.125, 2.132
Due 4/11:
2.141, 3.1 (ii, iii, vi, vii), 3.9, 3.13, 3.15, 3.17 (ii, v, vi, vii), 3.20, 3.21, 3.23
Due 4/18:
3.29 (i, iv, v, vi), 3.30, 3.33, 3.39, 3.40, 3.41 (iii, v, vi). 3.42, 3.46, 3.55
Due 4/25:
3.56 (i, ii, iii, vi), 3.58, 3.66, 3.75, 3.81, further questions
Due 5/4:
3.77, further question and comments, 3.85, 3.87 (iii, vi, viii, ix, x), 3.89, 3.91, 3.103, 3.105
MATH 4320 is a four–credit course, so you should plan on spending at least twelve hours a week working on it.
Homework is the most important part of MATH 4320 since mathematics is really learnt by doing it.
Homework assignments will be due in class on Wednesdays. Papers should be stapled and your name clearly indicated. Late homework will not be accepted. If you have a medical excuse or other serious circumstances, allowences will be made; contact your instructor at the earliest opportunity. The lowest score across the semester will be dropped (as everyone has a bad week sometime).
I expect homework to be graded and returned within a week. Due to constraints on resources, not all problems may be graded.
Collaborating. You may collaborate with other students on homework. I believe, however, that for maximum benefit, you should try hard to do all the problems yourself before consulting others. What you turn in should represent your own solutions expressed in your own words, even if you arrived at these solutions with others. Remember, you are doing the homework to learn the material; do not try to defeat its purpose. Copying someone else's homework and presenting it as your own will be treated as a violation of Cornell's Academic Integrity Code, as will copying solutions that you might find on the internet or elsewhere.
In keeping with the good practice of acknowledging all contributors to a piece of work, if you do collaborate, please give the names of your collaborators so on your homework. (Your grade will not be affected.)
Writing well. Mathematics is not mere computation; arguments and abstract concepts must be communicated. Use complete sentences with proper spelling, grammar, and punctuation. Write linearly down the page rather than scattering words, symbols and equations around. Explain your reasoning carefully. Indicate the significances of and relationships between any calculations which contribute to your answers. Define and employ clear and concise notation. State clearly any results (from lectures or from the textbook) to which you appeal in your solutions. Imagine your fellow-students as your readers — ask yourself whether they would they be able to follow your arguments.
Support. The Mathematics Support Center in Malott 256 provides free tutoring. Details of my office hours and those of the T.A. are on the course homepage.
In addition to our main text, Dummit & Foote, the following are recommended.
P. Aluffi, Algebra: Chapter 0, AMS, 2009
T. W. Hungerford, Algebra, 1974
I. M. Isaacs, Algebra, a graduate course, 1994
N. Jacobson, Basic algebra, two volumes, 2nd edition, 1985–1989
S. Lang, Algebra, 3rd edition, 2002
J. J. Rotman, Advanced Modern Algebra, AMS, 2010
B. L. van der Waerden, Algebra, two volumes, 1991 reprinting
There are copies on reserve in the library. You can find a huge number of other books on algebra there (start browsing around QA150).