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.
Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix.
MATH 252: ABSTRACT ALGEBRA II RESEARCH TOPICS The paper should be 6-8 pages in length; if your paper is slightly shorter or substantially longer, you will not be penalized. It should have an introduction and a conclusion, and clearly-written proofs and examples. Your target audience for the paper should be your peers; imagine.
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Understand fundamental properties of matrices including determinants, inverse matrices, matrix factorisations, eigenvalues and linear transformations. Solve linear systems of equations. Have an insight into the applicability of linear algebra. Synopsis. Lectures 1-20 cover the syllabus for the Preliminary Examination in Computer Science.
Make a 4-page paper and short presentation demonstrating the use of linear algebra in lossy audio compression, the modified discrete cosine transform (MDCT). Here's an undergraduate research project that may get you quickly into the topic, which has taken on more appeal since MP3 players have dominated the market, fueled by low-cost downloadable mp3 audio.