Math 686R: Topics in Algebraic Number Theory. - Revision history

Dmd54 at 22:20, 11 July 2016

2016-07-11T22:20:42Z

AAEmpty at 15:20, 16 March 2015

2015-03-16T15:20:16Z

AAEmpty at 15:19, 16 March 2015

2015-03-16T15:19:07Z

AAEmpty at 15:16, 16 March 2015

2015-03-16T15:16:54Z

AAEmpty at 15:16, 16 March 2015

2015-03-16T15:16:27Z

AAEmpty at 15:15, 16 March 2015

2015-03-16T15:15:52Z

AAEmpty at 15:14, 16 March 2015

2015-03-16T15:14:59Z

AAEmpty: /* Textbooks */

2014-10-01T15:37:57Z

‎Textbooks

AAEmpty at 15:35, 1 October 2014

2014-10-01T15:35:14Z

Roundy: /* Minimal learning outcomes */

2011-05-04T03:46:41Z

‎Minimal learning outcomes

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 === Minimal learning outcomes ===
-These cannot be specified uniquely for a topics course. Past topics have included "Primes of the form <i>x<sup>2</sup>+Ny<sup>2</sup></i>," "The Proof of Fermat's Last Theorem," and "Computational Algebraice Number Theory." The following example gives a clear indication of the level of difficulty appropriate to the course. Students should know the technical terms, and be able to implement the methods taught in the course to work associated problems, including proving results of suitable accessibility.
+These cannot be specified uniquely for a topics course. Past topics have included "Primes of the form <i>x<sup>2</sup>+Ny<sup>2</sup></i>," "The Proof of Fermat's Last Theorem," and "Computational Algebraic Number Theory." The following example gives a clear indication of the level of difficulty appropriate to the course. Students should know the technical terms, and be able to implement the methods taught in the course to work associated problems, including proving results of suitable accessibility.
 <div style="-moz-column-count:2; column-count:2;">

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 == Desired Learning Outcomes ==
-To gain familiarity with working in general settings, e.g. elliptic curves over number fields, and not just over rationals.
+Gaining mastery over an advanced area of algebraic number theory of interest in research.
 === Prerequisites ===
 Math 372 and permission of the Instructor.  In general, the prerequisites will depend on the material covered.

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 === Minimal learning outcomes ===
-These cannot be specified uniquely for a topics course. The following example gives a clear indication of the level of difficulty appropriate to the course. Students should know the technical terms, and be able to implement the methods taught in the course to work associated problems, including proving results of suitable accessibility.
+These cannot be specified uniquely for a topics course. Past topics have included "Primes of the form <i>x<sup>2</sup>+Ny<sup>2</sup></i>," "The Proof of Fermat's Last Theorem," and "Computational Algebraice Number Theory." The following example gives a clear indication of the level of difficulty appropriate to the course. Students should know the technical terms, and be able to implement the methods taught in the course to work associated problems, including proving results of suitable accessibility.
 <div style="-moz-column-count:2; column-count:2;">
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 === Additional topics ===
 === Courses for which this course is prerequisite ===
 [[Category:Courses|686]]

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 <div style="-moz-column-count:2; column-count:2;">
-# Primes of the form <it>x<sup>2</sup>+Ny<sup>2</sup></it>
+# Primes of the form <i>x<sup>2</sup>+Ny<sup>2</sup></i>
 #* Classical Topics
 #** Equivalence of binary quadratic forms

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 <div style="-moz-column-count:2; column-count:2;">
-# Primes of the form <it>x<sup>2</sup>+Ny<sup>2</sup>
+# Primes of the form <it>x<sup>2</sup>+Ny<sup>2</sup></it>
 #* Classical Topics
 #** Equivalence of binary quadratic forms

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 # Primes of the form <it>x<sup>2</sup>+Ny<sup>2</sup>
 #* Classical Topics
-#* Equivalence of binary quadratic forms
+#** Equivalence of binary quadratic forms
-#* Composition of Binary quadratic forms
+#** Composition of Binary quadratic forms
-#* Relation between binary quadratic forms and ideal class groups of quadratic fields
+#** Relation between binary quadratic forms and ideal class groups of quadratic fields
-#* Representations of integers by binary quadratic forms
+#** Representations of integers by binary quadratic forms
-# Class field theory
+#* Class field theory
-#* Artin Reciprocity and the Artin Map
+#** Artin Reciprocity and the Artin Map
-#* The Existence and Conductor Theorems
+#** The Existence and Conductor Theorems
-#* Cebotarev Density Theorem
+#** Cebotarev Density Theorem
-#* Identifying Ray Class Fields and Ring Class Fields
+#** Identifying Ray Class Fields and Ring Class Fields
-# Complex Analytic Techniques
+#* Complex Analytic Techniques
-#* Elliptic Functions
+#** Elliptic Functions
-#* Properties of the Weierstrass p-function
+#** Properties of the Weierstrass p-function
-#* Invariants of Lattices
+#** Invariants of Lattices
-#* Modular forms--definitions and properties
+#** Modular forms--definitions and properties
-#* Singular values of modular forms
+#** Singular values of modular forms
-#* The modular equation
+#** The modular equation
-#* Computing generators for ring class fields
+#** Computing generators for ring class fields
 </div>

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 Possible textbooks for this course include, (but are not limited to):
-#* D. Marcus, Number Fields (Universitext)
+* D. Marcus, Number Fields (Universitext)
-#* D. Cox, Primes of the form x^2+Ny^2
+* D. Cox, Primes of the form x^2+Ny^2
-#* H. Cohen, A course in computational number theory
+* H. Cohen, A course in computational number theory
-−
-−
 === Additional topics ===

← Older revision		Revision as of 15:35, 1 October 2014
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	Possible textbooks for this course include, (but are not limited to):		Possible textbooks for this course include, (but are not limited to):
	#* D. Marcus, Number Fields (Universitext)		#* D. Marcus, Number Fields (Universitext)
		+	#* D. Cox, Primes of the form x^2+Ny^2
		+	#* H. Cohen, A course in computational number theory

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 #* The class number formula - the formula which relates the residue of the Dedekind zeta function of a number field at s=1 to its class number, regulator and discriminant
 </div>
 === Textbooks ===