IMMERSE 2009

Schedule of Classes (pdf)

Algebra		Analysis
Syllabus	( pdf )
Historical Introduction Beamer	( pdf | tex )	Complex Numbers	( pdf | tex )
Historical Introduction Timeline	( pdf )	Solutions	( pdf | tex )
I. Rings & Ideals	( pdf | tex )
Homework I	( pdf | tex )	Fourier Series	( pdf | tex )
Solutions	( pdf | tex )	Solutions	( pdf | tex )
II. PIDs, UFDs, & Euclidean Domains	( pdf | tex )
Homework II	( pdf | tex )	Hilbert Spaces & Orthonormal Bases	( pdf | tex )
Solutions (missing 1, 7, 8)	( pdf | tex )	Solutions	( pdf | tex )
III. Noetherian Rings, Atomicity & Elasticity	( pdf | tex )
Homework III	( pdf | tex )	Fourier Transform	( pdf | tex )
Solutions (missing 2, 6, 8)	( pdf | tex )	Solutions	( pdf | tex )
Countable Sets	( pdf | tex )
IV. Algebraic Extensions & Algebraic Closures	( pdf | tex )
Homework IV	( pdf | tex )
Solutions (missing 3, 6, 7, 9, 10, 11)	( pdf | tex )
V. Modules	( pdf | tex )
Homework V	( pdf | tex )
VI. Localization, Local Rings & Integral Closure	( pdf | tex )
Homework VI	( pdf | tex )
Solutions (missing 4)	( pdf | tex )
VII. Krull Dimension & Fractional Ideals	( pdf | tex )
Homework VII	( pdf | tex )
Solutions (missing 4)	( pdf | tex )
VIII. Dedekind Domains & Discrete Valuation Domains	( pdf | tex )
Homework VIII	( pdf | tex )
Solutions	( pdf | tex )

Elasticity for integral-valued polynomials: Presentations
Lemma 1.1 and Proposition 1.2	( pdf )
Theorem 1.3	( pdf )
Propositions 1.4 and 1.5	( pdf )
Theorem 1.6	( pdf )
Corollary 2.2 and Example 2.3	( pdf )
Example 2.8	( pdf )
Lemma 3.1	( pdf )
Theorem 3.2	( pdf )

Algebra Guest Speaker: Scott Chapman, Sam Houston State University

Lectures: Basic Factorization (Part 1) ( pdf )

Basic Factorization (Part 2) ( pdf )

Numerical Semigroups ( pdf )

Grad School and Mathematical Careers ( link )