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J.S. Milne

The theory of groups of finite order may be said to date from the time of Cauchy. To him are due the first attempts at classification with a view to forming a theory from a number of isolated facts. Galois introduced into the theory the exceedingly important idea of a [normal] sub-group, and the corresponding division of groups into simple and ...

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J.S. Milne

www.jmilne.org

author={Milne, James S.}, title={Group Theory (v3.13)}, year={2013}, ... GAP is an open source computer algebra program, emphasizing computational group theory.

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Algebraic Number Theory - James Milne

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An algebraic number field is a finite extension of Q; an algebraic number is an element of an algebraic number field. Algebraic number theory studies the arithmetic of algebraic

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Algebraic Geometry - James Milne

www.jmilne.org

Introduction There is almost nothing left to discover in geometry. Descartes, March 26, 1619 Just as the starting point of linear algebra is the study of the solutions of systems of

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J.S. Milne

www.jmilne.org

Group Theory J.S. Milne S3 r D 1 2 3 2 3 1 f D 1 2 3 1 3 2 Version 3.10 September 24, 2010. A more recent version of these notes is available at www.jmilne.org/math/

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Algebraic Groups - James Milne

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but the most serious students. By considering only schemes algebraic over a field, we avoid many of the technicalities that plague the general theory.

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Shimura Varieties and Moduli - James Milne

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Shimura Varieties and Moduli J.S. Milne April 30, 2011, v2.00 Abstract Connected Shimura varieties are the quotients of hermitian symmetric domains

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Motives — Grothendieck's Dream

www.jmilne.org

Motives — Grothendieck’s Dream James S. Milne April 24, 2012; v2.04 Abstract Grothendieck introduced the notion of a “motif” in a letter to Serre in 1964.

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J.S. Milne: Elliptic Curves

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Preface In early 1996, I taught a course on elliptic curves. Since this was not long after Wiles hadprovedFermat’sLast TheoremandI promisedto explainsome ofthe

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The tikz package

www.jmilne.org

The tikz package This is a general purpose graphics package. To load it for this document, I used: \usepackage{tikz} \usetikzlibrary{matrix,arrows,decorations.pathmorphing}

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Modular functions and modular forms - James Milne

www.jmilne.org

PREREQUISITES The algebra and complex analysis usually covered in advanced undergraduate or first-year graduate courses. REFERENCES A reference monnnnn is to question nnnnn on mathoverflow.net.

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