## Research Papers Abstract Algebra

The *Journal of Algebra* is a leading international journal and publishes papers that demonstrate high quality research results in **algebra** and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.

The **Computational Algebra** Section

The Computational Algebra section has been introduced to provide an appropriate forum for contributions which make use of computer calculations and to broaden the scope of the Journal.

The following papers are particularly welcome in the Computational Algebra section of the Journal of Algebra:

• Results obtained by computer calculations - to be suitable for publication such results must represent a major advance of mathematics. It is not sufficient to extend previous computations by means of higher computer power. Rather the contribution has to exhibit new methods and mathematical results to be accepted.

• Classifications of specific algebraic structures (in form of tables, if appropriate), which are not easily obtained and are useful to the algebraic community.

• Description and outcome of experiments, to put forward new conjectures, to support existing conjectures, or to give counter examples to existing conjectures.

• Papers emphasizing the constructive aspect of algebra, such as description and analysis of new algorithms (not program listings, nor, in the first instance, discussions of software development issues), improvements and extensions of existing algorithms, description of computational methods which are not algorithms in the strict sense (since, e.g., they need not terminate).

• Interactions between algebra and computer science, such as automatic structures, word problems and other decision problems in groups and semigroups, preferably, but not necessarily, with an emphasis on practicality, implementations, and performance of the related algorithms.

• Contributions are welcome from all areas of algebra, including algebraic geometry or algebraic number theory, if the emphasis is on the algebraic aspects.

Contributions describing applications of algebraic results or methods, for example in **coding theory**, **cryptography**, or the algebraic theory of **differential equations** are highly welcome. An important general criterion for the publication of a paper in the Computational Algebra section is its emphasis on the constructive aspects.

This journal has an Open Archive. All published items, including research articles, have unrestricted access and will remain permanently free to read and download 48 months after publication. All papers in the Archive are subject to Elsevier's user license.

Hide full Aims & Scope### Including number theory, algebraic geometry, and combinatorics

We have large groups of researchers active in number theory and algebraic geometry, as well as many individuals who work in other areas of algebra: groups, noncommutative rings, Lie algebras and Lie super-algebras, representation theory, combinatorics, game theory, and coding. A number of members of the algebra group belong to the Research Training Group in Representation Theory, Geometry and Combinatorics, which runs activities and supports grad students and postdocs in its areas of interest.

## Courses

### Undergraduate upper division courses

**Math 110** (and honors version, **Math H110**). Linear algebra.**Math 113** (and honors version, **Math H113**). Introduction to abstract algebra.**Math 114.** Second course in abstract algebra. (Instructor's choice; usually Galois Theory)**Math 115.** Introduction to number theory.**Math 116.** Cryptography.**Math 143.** Elementary algebraic geometry.**Math 172.** Combinatorics.

The Mathematics Department also offers, at the undergraduate level, courses which may include algebraic topics along with others: Problem Solving (H90), Experimental Courses (191), a Special Topics course (195), and several courses of directed and independent individual and group work (196-199).

### Graduate courses

**Math 245A.** General theory of algebraic structures.**Math 249.** Algebraic combinatorics.**Math 250A.** Groups, rings and fields.**Math 250B.** Multilinear algebra and further topics.**Math 251.** Ring theory.**Math 252.** Representation theory.**Math 253.** Homological algebra.**Math 254A-254B.** Number theory.**Math 255.** Algebraic curves.**Math 256A-256B.** Algebraic geometry.**Math 257.** Group theory.

## Seminars

### 2008-2009

**Math 290**. Seminar - Commutative algebra and algebraic geometry, *David Eisenbud***Math 290**. Seminar - Number theory, *Kenneth Ribet*

*Spring 2009*

**Math 274**. Topics in Algebra - Tropical geometry, *Bernd Sturmfels***Math 274**. Topics in Algebra - Infinitesimal geometry, *Mariusz Wodzicki*

*Fall 2008*

**Math 290**. Seminar - Algebraic geometry, *David Eisenbud and Daniel Erman***Math 290**. Seminar - Discrete mathematics, *Bernd Sturmfels***Math 290**. Seminar - Representation theory, geometry and combinatorics, *Mark Haiman and Nicolai Reshetikhin***Math 290**. Seminar - Student arithmetic geometry seminar, *Martin Olsson***Student Seminar**. Student algebraic and arithmetic geometry seminar, *David Brown, Daniel Erman and Anthony Varilly*

### 2007-2008

**Math 270**. Hot Topics - Derived algebraic geometry and topology, *Peter Teichner***Math 290**. Seminar - Commutative algebra and algebraic geometry,*David Eisenbud***Math 290**. Seminar - Representation theory, geometry and combinatorics, *Mark Haiman and Nicolai Reshetikhin*

*Spring 2008*

**Math 274**. Topics in Algebra - Real p-adic analysis,*Robert Coleman*

*Fall 2007*

**Math 274**. Topics in Algebra - Locally finite lie algebras and their representations with a view toward open problems, *Ivan Penkov***Math 290**. Seminar - Student representation theory, geometry and combinatorics, *Vera Serganova and Peter Tingley***Math 290**. Seminar - Number theory, *Kenneth Ribet***Math 290**. Seminar - Perverse sheaves, *Joel Kamnitzer and Xinwen Zhu*

Earlier years, from 2006-2007

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