Other Mathematics Commons^™

Linear Algebra, Daniel Scully

Math Faculty Publications

Table of Contents:

1. Systems of Linear Equations and Matrices

• Systems of Linear Equations
• Elementary Row Operations
• Row Reduction and Reduced Row-Echelon Form
• Solutions of Systems of Linear Equations
• Matrix Operations
• Matrix Inverses

2. Euclidean 2-Space and 3-Space

• Vectors in the Plane and in Space
• The Dot Product
• Cross Product
• Lines in Space
• Planes in Space

3. Determinants

• The Definition of Determinant
• Elementary Row Operations and the Determinant
• Elementary Matrices and the Determinant
• Applications of the Determinant

4. Vector Spaces and Subspaces

• Vector Spaces
• Subspaces
• Linear Dependence and Independence
• Basis and Dimension

5. Linear Transformations

• Definition of Linear Transformation
• The …

A Fast-Slow Analysis Of The Dynamics Of Rem Sleep, Victoria Booth, Cecilia G. Diniz Behn

Math Faculty Publications

Waking and sleep states are regulated by the coordinated activity of a number of neuronal population in the brainstem and hypothalamus whose synaptic interactions compose a sleep-wake regulatory network. Physiologically based mathematical models of the sleep-wake regulatory network contain mechanisms operating on multiple time scales including relatively fast synaptic-based interations between neuronal populations, and much slower homeostatic and circadian processes that modulate sleep-wake temporal patterning. In this study, we exploit the naturally arising slow time scale of the homeostatic sleep drive in a reduced sleep-wake regulatory network model to utilize fast-slow analysis to investigate the dynamics of rapid eye movement …

Codes From Riemann-Roch Spaces For Y2 = Xp - X Over Gf(P), Darren B. Glass, David Joyner, Amy Ksir

Math Faculty Publications

Let Χ denote the hyperelliptic curve y2 = xp - x over a field F of characteristic p. The automorphism group of Χ is G = PSL(2, p). Let D be a G-invariant divisor on Χ(F). We compute explicit F-bases for the Riemann-Roch space of D in many cases as well as G-module decompositions. AG codes with good parameters and large automorphism group are constructed as a result. Numerical examples using GAP and SAGE are also given.