Sample Linear Algebra Applications abstracts
Economic Input Output Models
Anica Vujanic and Audrey Saunders
Abstract
The Leontief model is a model of inputs and outputs in an economy. In particular, it explores inter-industry demand and the interdependent nature manufacturing processes. The total production in an economy is the combination of internal consumption by different economic sectors and the public demand. The Leontief model like many economic models utilizes matrix algebra, with an emphasis on matrix inverses.
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Colour spaces
K.E.Raghav
Abstract:
A colour space is a method by which we can specify, create and visualise colour. As humans, we may define a colour by its attributes of brightness, hue and colourfulness. A computer may describe a colour using the amounts of red, green and blue phosphor emission required to match a colour. A colour is thus usually specified using three co-ordinates, or parameters. In order to use linear algebra tools to apply to color space, we model it as a vector space. An example of a color space is RGB space, where colors are represented the amount of red, green, and blue light they contain.
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Structural Engineering
Aaron Zaubi and Jacob Czaja
Abstract
Structural Engineering is a subdivision of civil engineering that specifically deals with systems designed to support loads, a load being a force or collection of forces that causes stress on the system. Linear algebra is an integral part of structural engineering. Linear algebra is predominantly used to solve systems of many linear equations. This presentation will focus on applications of linear algebra to bridges whose joints exhibit multiple linear equations describing the forces acting on them. By analyzing the equations of the forces acting on these bridges in terms of linear algebra, one can determine the stability of various designs.
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Linear Algebra Techniques in Cryptography
Janet Northey
Abstract
A cryptogram is a type of puzzle or code where messages are encoded by ciphers. From the game Cryptoquote, found in local newspapers, to secret messages used during war, examples of cryptography are plentiful. Focusing on encrypted text, I will examine the basic process of coding and decoding cryptograms by using basic linear algebra skills and theories.
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Gaussian Blur
Sarah Gilliland and Talon Holmes
Abstract
A Gaussian blur is applied to a picture to cause smoothing of edges and reduce sharpness. The Gaussian matrix will take another matrix, created out of a small portion of the image’s RGB (or black and white) values, and transform it in a circular pattern. This convolution will result in a blurring of that portion. This is repeated across the entire image. We will demonstrate the use of the Gaussian matrix with images of different size and complexity.
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Signal Transmissions
Sean Eggleston
Abstract
Signal transmissions are the subject of a hybrid field fed by electrical engineering, mathematics, and computer science where the focus is efficient and error free algorithms for data transfer. Emissions from antennae and satellites are both examples of mediums optimized by this coding theory. Not only is extraneous or duplicated information a target, but as is interference from a variety of sources. The focus will be with signal encoding then decryption once received, as well as Hamming code and error correction.
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Fourier Analysis and Wolfram Mathematica
Paige Hardie
Abstract
Fourier series and transforms were discovered and named after French mathematician Jean-Baptiste Fourier. The Fourier Transform is a mathematical procedure that transforms a function from the time domain to the frequency domain. This transform can break down notes, for example, into a linear combination of sines and cosines, using the orthogonatily relationship of sines and cosines. I will examine and demonstrate the breaking down of tones into its linear parts. I will focus on applications compatible with Wolfram Mathematica and its sound operations.
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Linear Algebra Applications in Physical Chemistry
Brianna Medrano
Abstract
Linear algebra is used a lot in chemistry, specifically physical chemistry. It is used to find Eigen values and symmetry operators. The symmetry operators are something I find to be fascinating. When these operators are taught to chemistry students we do not learn the matrices behind them. However, now that I know the operational matrices that are used in determining the symmetry, it makes much more sense. I will be covering what the matrices are and a little on determining the symmetry of a molecule and/or object and what implications this can have for chemists.
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Linear Algebra Tools for Educators
Rachel Spriggs
ABSTRACT
Throughout history, people have tried to understand the way that we, as humans, learn best, and from this, researches have tried to discern the single most effective way to teach. From these studies, they have found that there is not a single way to learn, and, therefore, not a single best approach to teaching, but most practicing teachers would agree that as concepts grow more abstract educators must relate these increasingly complex ideas to more concrete examples. In the study of linear algebra in particular, there are available for teachers and professors many premade calculators, interactive geometric and symbolic representations of linear systems, as well as games to give students a chance to think analytically about matrices and matrix algebra. I will examine a variety of tools made available for educators and their usefulness in the teaching and learning of linear algebra.
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The Hungarian Method
Tom Speulda and Micky Spiwak
Abstract
Let’s say there are four US agents with jet packs that need to deliver a bomb to four different places. They need to travel the minimum total distance because jet fuel is expensive. An easy way to figure this out is to use a Linear Algebra Application called the Hungarian Method. Not only can we use the Hungarian Method to solve for minimal distances, but also for finding things like bids and matching.
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Genetics and Markov Chains
Isaku Beggert
Abstract
A Markov chain or Markov process is a system that has a finite number of states and at any given observation period, for example the nth period, it is in one and only one of its states and the probability of the system being in a particular state depends on its state at the n-1 period. This applies to dominant and recessive genes because the probability that an offspring of the nth generation will have a certain combination of dominant and recessive traits can be modeled by a linear system, specifically it can be modeled by a Markov chain.