MATH 407-01 [3357], Spring 2019
Modern Algebra
Course information
| Course: | MATH 407-01 [3357]:
Modern Algebra |
| Time/Place: | TuTh 2:30pm-3:45pm, Sondheim 113
|
| Instructor: | Dr.
Jacob Kogan
|
Grader: |
Kayla McAdoo
|
| Office: |
MP 426 |
|
|
| Phone: | 410-455-3297 |
| Email: |
kogan at math.umbc.edu |
|
kaylam2@umbc.edu
|
| Office hours: |
TuTh 4:45 PM-5:30 PM, and by appointment
|
|
|
Textbook
Abstract Algebra,
by Beachy and Blair, 2006
Additional textbooks you may want to consult:
-
Basic Algebra I, 2nd edition by N. Jacobson
-
Abstract Algebra, 3rd edition by Dummit and Foote
Course Description
Much of modern algebra concerns the study of sets (such as the natural numbers
ℕ, the integers
ℤ, or the set of functions from a set X to itself) equipped with one or more binary
operations (such as addition, multiplication or composition). We will be concerned with:
-
Rules imposed upon these operations such as associativity, commutativity or
(when there are two operations) distributivity.
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Consequences of these rules.
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Deeper explorations of commonly occuring examples of sets with binary operations.
We begin the course with a brief review of sets, relations, and functions. We
briefly present Peano's Axioms for the non-negative integers from the Appendix.
Altogether we cover A.1-A.4 and Sections 2.1-2.2 before turning our attention to
Chapter 1 on the Integers and basic Number Theory.
Next we will proceed to Section 2.3 on Permutations,
Chapter 3 on Groups,
Chapter 4 on Polynomials and
as much as we have time for Chapter 5 on Commutative Rings.
Depending on time we may cover more (or delete) topics.
Learning Goals
The aim of this course is to introduce you to the basic ideas of modern
algebra, including those that appear in elementary number theory.
To strengthen your skills in abstract mathematical reasoning,
formal proofs, and mathematical writing.
By the end of the class one should:
-
understand the key ideas, concept, definitions, and results,
-
be able to apply results to material realted problems.
To succeed in the class one should:
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preview each section before it is covered in class,
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actively participate in each class,
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form and participate in a study group,
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to work out each problem, discuss it in study group if needed;
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do and hand in each assignment on time.
Homework, Project, and Grading
Homework
-
Weekly homework will be assigned on Thursday and collected the following
Thursday.
Classes will generally begin with presentation by 1 - 2 students of solved problems
from the preceding week's material.
-
All homework must be typed pdf files to be uploaded through the
homework form (if you need to convert your file to pdf you may
consider using
zamzar).
If you want credit, then
please upload your homework on time.
-
No late homework will be accepted.
Grading
The final grade will be based on
homework grades (50% of the final grade), and the project grade (50% of the final grade).
Letter grade cutoffs are expected to be the following:
| Percentage |
≥ 90% |
89% ≥ and ≥ 80% |
79% ≥ and ≥ 70% |
69% ≥ and ≥ 60% |
59% ≥ |
| Letter Grade |
A |
B |
C |
D |
F |
Remember: Mathematics is NOT a spectator sport.
Read through the relevant section of the text (and look over
all
the assigned problems) before each lecture.
project
Homework assignments
-
homework assignment
and
solutions
-
homework assignment
and
solutions
-
homework assignment
and
solutions
-
homework assignment
and
solutions
-
homework assignment
and
solutions
-
homework assignment
and
solutions
and
Matthew Thompson Totient Proof
-
homework assignment
and
solutions
and
Matthew Thompson problem 5 solution
-
homework assignment
and
solutions
The Official UMBC Honors Code
By enrolling in this course, each student assumes the responsibilities
of an active participant in UMBC's scholarly community in which
everyone's academic work and behavior are held to the highest standards
of honesty. Cheating, fabrication, plagiarism, and helping others to
commit these acts are all forms of academic dishonesty, and they are
wrong. Academic misconduct could result in disciplinary action that
may include, but is not limited to, suspension or dismissal.
To read the full Student Academic Conduct Policy, consult the UMBC Student
Handbook, the Faculty Handbook, the UMBC Integrity webpage
www.umbc.edu/integrity, or the Graduate School website
http://www.umbc.edu/gradschool/procedures/integrity.html.