Math 321: Modern Algebra and the Theory of Equations I
Spring 2017, Section 01, CRN 809

Schedule: MWF 10:00pm-10:50pm
Location: Fitzelle Hall 246
Text: Abstract Algebra: A First Undergraduate Course , by Hillman and Alexanderson (5th edition).

Professor: Jonathan Brown
Office: Fitzelle Hall 260
Email: jonathan.brown@oneonta.edu
Phone: 436-3720
Office Hours: Wednesday 1:00-1:50, Thursday 11:00-11:50, Friday 1:00-1:50, or by appointment
Course website: http://employees.oneonta.edu/brownjs/f14/321

Catalog Description: Introductory concepts of modern algebra and their applications to the solution of polynomial equations over various fields. Elementary properties of groups, rings, integral domains, fields, and vector spaces; introductory Galois theory and applications including Abel's theorem and compass-straightedge constructions.
Prerequisites: MATH 174 and MATH 205 each with a grade of C or better.

Course Goals and Objectives: The goals of the algebra sequence MATH 321-322 include giving the student an appreciation and understanding of the ideas and results of modern algebra including number theoretic results and properties of the algebraic structures of modern algebra and linear algebra; providing connections between modern algebra and other areas of mathematics such as number theory, linear algebra, and geometry; providing historical perspectives into the development of the ideas of modern algebra, where appropriate; and giving the student experience in constructing mathematical proofs and in applying the ideas of modern algebra to the solution of polynomial equations and compass/straightedge constructions. Objectives of the course designed to achieve these goals include presentation and discussion of the topics included in the catalog description and completion of homework assignments and exams by the students.

Course Content: We will cover Chapters 1 and 2, and most of Chapter 3 from the textbook.

SUNY General Education Attributes: LA

Grades:
Homework: 18%
3 in class exams: 18% each
Final: 28%

Your letter grade will be determined from the following heuristic:
A : 93 - 100
A-: 90 - 92.99
B+: 87 - 89.99
B : 83 - 86.99
B-: 80 - 82.99
C+: 77 - 79.99
C :73 - 76.99
C-: 70 - 72.99
D+: 67 - 69.99
D : 63 - 66.99
D-: 60 - 62.99
E : 0 - 59.99


Homework: Problem sets will be assigned periodically. These will be collected and graded.
Homework from the text will be assigned regularly. This homework will not be collected or graded, however it is essential that you do these problems. Learning, development, and growth require time and sustained effort. Most of the knowledge and skills you obtain from this course will come from the time you spend with these problems. Furthermore the exam problems will sometimes closely resemble (or even be copied from) the problems from the text.

Tentative Exam Schedule:
Exam 1: 2/17
Exam 2: 3/24
Exam 3: 4/21

Final Exam Schedule:
Wednesday May 10, 8:00am - 10:30am.

Calculators: Calculators may occasionally be usefule while doing the homework, however they are not allowed to be used during exams.

Attendance Policy: Missing class is a very bad idea. Anyone who misses more than 25% of classes starting in week 2 may be removed from the course.

Emergency Evacuation Procedures: In the event of an emergency evacuation, classes meeting in this building are directed to reassemble in the IRC Lobby so that all persons can be accounted for. Complete details of the College's emergency evacuation, shelter-in-place, and other emergency procedures can be found at http://www.oneonta.edu/security/.

ADA (American with Disabilities Act): Students Diagnosed with a Disability, all individuals who are diagnosed with a disability are protected under the Americans with Disabilities Act, and Section 504 of the Rehabilitation Act of 1973. As such, you may be entitled to certain accommodations within this class. If you are diagnosed with a disability, please make and appointment to meet with Student Disability Services, 209 Alumni Hall, ext. 2137. All students with the necessary supporting documentation will be provided appropriate accommodations as determined by the SDS Office.

Getting Help
You are expected to spend anywhere between 6 and 12 hours per week outside of class on the material. The amount of time necessary to pass, or obtain the grade you expect, depends heavily from person to person. Typically, a student spending less than 6 hours per week outside the class should expect to earn a "C" or worse.

If you are struggling with the material, be aware that you have options:
(1) Struggle a bit. Part of the learning process is the internal struggle of trying to understand how all of the pieces fit together. It can be frustrating, but it can also be rewarding. If you make progress, however slow, then it is time well spent. If you feel that your time is not productive, then you should talk to me, or other students, about how you can make better use of your study time.
(2) Visit my office hours. It is part of my job to be available to help you understand the material. There is not enough time in the classroom to get everything across, and you are not expected to do it all on your own.
(3) Find alternate instructional material online. Different people have different styles, and while you might have found my way of discussing something to be confusing, there may be someone else out there who can discuss it in a away that makes sense to you. There are a number of free text books, lessons, and video lectures available online. Feel free to ask me about other sources.
(4) Talk to your fellow students who are taking or who have taken the class. Learning is a social activity; you are not expected to do it all on your own.
(5) If after availing yourself of the above options, you still find that you are struggling regularly to understand the material, find a regular tutor. If you are in this situation, you will likely have to spend significant extra time on the material to ensure a passing grade.

Tentative Schedule
Date Section Topic Suggested Textbook Problems
1/18 1.1 Mathematical Induction p. 8 #1, 3, 7, 11, 13
1/20 1.2 Multiples, Divisors, and Prime Numbers p. 12 #1, 3, 7, 9, 11, 13, 15, 19, 21
1/23
1/25 		1.3 The Division Algorithm p. 19 #1, 3, 5, 7, 9, 11, 13, 17
1/27
1/30 		1.4 Common Divisors p. 23 #1, 3, 5, 7, 11, 13, 15, 23, 25
2/1 1.5/1.6 Euclid's Algorithm/Common Multiples p. 33 #1, 2, 3, 5, 7, 9, 15, 16, 17
2/3 1.7 Unique Factorization p. 37 #1, 3, 7, 9, 13, 17, 19, 21, 23, 25
2/6 2.1 Permutations p. 44 #1, 2, 3, 5, 7, 9, 11, 13, 15
2/8 2.2 Multiplication of Permutations p. 49 #1,3,5,7,9
2/10
2/13
2/15 		2.3 Abstract Groups p. 57 #3, 5, 7, 9, 11, 13, 15, 23, 25
2/20
2/22 		2.4 Cycle Notation p. 66 #1, 3, 5, 7, 9, 13, 15, 19, 21, 23, 27, 29
2/24
2/27 		2.5 Subgroups p. 72 #1, 3, 5, 7, 9, 11, 13, 15, 19, 21, 23, 27
3/1
3/3 		2.6 Modular Arithemetic p. 79 #1-6, 11, 15, 17, 21
3/13
3/15 		2.7 Cyclic Groups p. 86 #1-25odd, 39, 40, 41, 49, 51
3/17 2.8 Even and Odd Permutations p. 93 #1, 5, 7, 9, 10, 13
3/20
3/22 		2.9 Groups of Symmetries p. 98 #1-5, 7, 11, 13, 18
3/27 2.10 The Alternating Group p. 103 #1-5, 7, 13, 15, 19, 23
3/29
3/31 		2.11 Cosets p. 108 #1, 3, 5, 9, 13, 15, 17, 19, 20, 21, 25
4/3
4/5
4/7 		2.12 Quotient Groups p. 116 #1, 2, 3, 5, 7, 9, 11, 13
4/10
4/12 		2.13 Solvable Groups p. 121 #1, 2, 3, 5, 6, 7, 13
4/14 3.1 Mappings p. 139 #1-7, 13
4/17
4/19 		3.2 Isomorphisms p. 146 #1-4, 7, 9-12, 15, 17, 19
4/24 3.3 Homomorphisms p. 154 #1, 2, 3, 7, 9, 17
4/26 3.4 Cayley's Theorem p. 160 #1, 2, 3, 5
4/28 3.6 Cartesian and Direct Products p. 171 #5, 6, 8, 9, 10, 15, 18, 19, 20