Math 571: Algebra 1 - Revision history

AAEmpty at 14:49, 16 March 2015

2015-03-16T14:49:35Z

Ls5: /* Minimal learning outcomes */

2014-09-29T20:22:46Z

‎Minimal learning outcomes

Ls5: /* Title */

2013-03-29T20:47:02Z

‎Title

Ls5: /* Courses for which this course is prerequisite */

2013-03-29T20:38:30Z

‎Courses for which this course is prerequisite

Ls5: /* Additional topics */

2013-03-29T20:38:09Z

‎Additional topics

Ls5 at 20:37, 29 March 2013

2013-03-29T20:37:26Z

Ls5: Created page with "== Catalog Information == === Title === Algebra 1. === Credit Hours === 3 === Prerequisite === Math 372 or equivalent. === Description === == Desired Learning Outcomes =..."

2013-03-29T20:34:48Z

Created page with "== Catalog Information == === Title === Algebra 1. === Credit Hours === 3 === Prerequisite === Math 372 or equivalent. === Description === == Desired Learning Outcomes =..."

New page

== Catalog Information ==

=== Title ===
Algebra 1.

=== Credit Hours ===
3

=== Prerequisite ===
[[Math 372]] or equivalent.

=== Description ===

== Desired Learning Outcomes ==

=== Prerequisites ===
[[Math 372]] is a prerequisite for this course. In particular, students should be familiar with the concepts of groups and rings, and they should understand constructions of quotient groups and quotient rings. By this point in their mathematical career, students should be skilled at proving theorems by themselves.

=== Minimal learning outcomes ===
Students should achieve an advanced mastery of the topics listed below. This means that they should know all relevant definitions, correct statements and proofs of the major theorems (including their hypotheses and limitations), and examples and non-examples of the various concepts The students should be able to demonstrate their mastery by solving difficult problems related to these concepts, and by proving theorems about the below concepts, even if the theorems go beyond the material in the text.
<div style="-moz-column-count:2; column-count:2;">
#Group Theory
#* Axioms and Examples
#* Homomorphisms and Isomorphisms
#* Subgroups
#* Centralizers and Normalizers
#* Cyclic gorups and subgroups
#* Quotient Groups
#* Lagrange's Theorem
#* Isomorphism theorems
#* Group Actions
#* Permutation Representations
#* Cayley's Theorem
#* The class equation
#* Sylow theorems
#* Direct and semidirect products
#* Solvable and Nilpotent groups
#Ring Theory
#* Definitions and Examples
#* Homomorphisms and quotient rings
#* Ideals
#* Rings of fractions
#* Chinese remainder theorem
#* Euclidean Domains, PID's and UFD's
#* Polynomial Rings
#Module Theory
#* Definitions and Examples
#* Quotient modules and homomorphisms
#* Direct sums
#* Free Modules
#* Tensor Products
#* Exact Sequences
#* Projectives, Injectives, Flats

</div>
=== Textbooks ===

Possible textbooks for this course include (but are not limited to):

*

=== Additional topics ===
Most additional topics in this course will be covered in the second course of the sequence, [[Math 572]]. Depending on time constraints, some or all of the module theory listed here may be moved to the beginning of [[Math 572]]

=== Courses for which this course is prerequisite ===

[[Category:Courses|671]]
This course is a prerequisite for [[Math 572]], which is a prerequisite for [[Math 663]], [[Math 675R]], [[Math 676]], and [[Math 677]],

← Older revision		Revision as of 14:49, 16 March 2015
Line 6:		Line 6:
	=== Credit Hours ===		=== Credit Hours ===
	3		3
		+
		+	=== Offered ===
		+	F

	=== Prerequisite ===		=== Prerequisite ===

@@ Line 65: / Line 65: @@
 === Courses for which this course is prerequisite ===
-[[Category:Courses|571]]
+[[Category:Courses|571: Algebra 1]]
-This course is a prerequisite for [[Math 572]], which is a prerequisite for [[Math 663]], [[Math 675R]], [[Math 676]],  and [[Math 677]],
+This course is a prerequisite for [[Math 572: Algebra 2]], which is a prerequisite for [[Math 663]], [[Math 675R]], [[Math 676]],  and [[Math 677]],

@@ Line 25: / Line 25: @@
 #* Subgroups
 #* Centralizers and Normalizers
-#* Cyclic gorups and subgroups
+#* Cyclic groups and subgroups
 #* Quotient Groups
 #* Lagrange's Theorem
@@ Line 54: / Line 54: @@
 </div>
 === Textbooks ===

@@ Line 2: / Line 2: @@
 === Title ===
-Algebra 1.
+Algebra 1 (formerly Math 671)
 === Credit Hours ===

@@ Line 61: / Line 61: @@
 === Additional topics ===
-Most additional topics in this course will be covered in the second course of the sequence, [[Math 572]].  Depending on time constraints, some or all of the module theory listed here may be moved to the beginning of [[Math 572]]
+Most additional topics in this course will be covered in the second course of the sequence, [[Math 572: Algebra 2]].  Depending on time constraints, some or all of the module theory listed here may be moved to the beginning of [[Math 572: Algebra 2]]
 === Courses for which this course is prerequisite ===