Math 572: Algebra 2 - Revision history

AAEmpty at 14:51, 16 March 2015

2015-03-16T14:51:05Z

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2013-03-29T20:52:33Z

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Ls5 at 20:51, 29 March 2013

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Ls5: Created page with "== Catalog Information == === Title === Algebra 2. === Credit Hours === 3 === Prerequisite === Math 671. === Description === == Desired Learning Outcomes == === Prerequ..."

2013-03-29T20:36:22Z

Created page with "== Catalog Information == === Title === Algebra 2. === Credit Hours === 3 === Prerequisite === Math 671. === Description === == Desired Learning Outcomes == === Prerequ..."

New page

== Catalog Information ==

=== Title ===
Algebra 2.

=== Credit Hours ===
3

=== Prerequisite ===
[[Math 671]].

=== Description ===

== Desired Learning Outcomes ==

=== Prerequisites ===
[[Math 571]] is a prerequisite for this course. In particular, students should have a deep knowledge of groups, rings, and modules. Students should be able to prove difficult theorems on their own.

=== 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;">
#Linear Algebra
#*Basic theory (including infinite dimensional spaces)
#*Dual vector spaces
#*Determinants
#Modules over PID's
#*Fundamental Theorem
#*Applications to Rational and Jordan Canonical Forms of matrices
#Galois Theory
#*Field Extensions
#*Algebraic, separable, and inseparable extensions
#*Splitting fields
#*Algebraic closures
#*Cyclotomic extensions
#*Fundamental Theorem of Galois theory
#*Finite fields and their Galois groups
#*Composite extensions
#*Simple extensions
#*Kronecker-Weber Theorem (Statement)
#*Galois groups of polynomials
#*Transcendental extensions
#*Infinite Galois groups

</div>
=== Textbooks ===

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

*

=== Additional topics ===
If students in the class have not seen module theory, the module theory in [[Math 571]] should be considered a requirement. As time permits, additional topics may be covered. These may include Group representation theory, commutative algebra, homological algebra, lie algebras, or other topics chosen by the instructor.

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

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

← Older revision		Revision as of 14:51, 16 March 2015
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	=== Credit Hours ===		=== Credit Hours ===
	3		3
		+
		+	=== Offered ===
		+	W

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

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 === Prerequisite ===
-[[Math 571]].
+[[Math 571: Algebra 1]].
 === Description ===

@@ Line 2: / Line 2: @@
 === Title ===
-Algebra 2(formerly Math 672)
+Algebra 2 (formerly Math 672)
 === Credit Hours ===

@@ Line 15: / Line 15: @@
 === Prerequisites ===
-[[Math 571]] is a prerequisite for this course.  In particular, students should have a deep knowledge of groups, rings, and modules.  Students should be able to prove difficult theorems on their own.
+[[Math 571: Algebra 1]] is a prerequisite for this course.  In particular, students should have a deep knowledge of groups, rings, and modules.  Students should be able to prove difficult theorems on their own.
 === Minimal learning outcomes ===

@@ Line 51: / Line 51: @@
 === Additional topics ===
-If students in the class have not seen module theory, the module theory in [[Math 571]] should be considered a requirement.  As time permits, additional topics may be covered.  These may include Group representation theory, commutative algebra, homological algebra, lie algebras, or other topics chosen by the instructor.
+If students in the class have not seen module theory, the module theory in [[Math 571: Algebra 1]] should be considered a requirement.  As time permits, additional topics may be covered.  These may include Group representation theory, commutative algebra, homological algebra, lie algebras, or other topics chosen by the instructor.
 === Courses for which this course is prerequisite ===