Open Access. Powered by Scholars. Published by Universities.®
- Discipline
-
- Discrete Mathematics and Combinatorics (7)
- Number Theory (5)
- Other Mathematics (5)
- Computer Sciences (4)
- Curriculum and Instruction (4)
-
- Education (4)
- Educational Methods (4)
- Analysis (3)
- Teacher Education and Professional Development (3)
- Algebraic Geometry (2)
- Applied Mathematics (2)
- Artificial Intelligence and Robotics (2)
- Geometry and Topology (2)
- Numerical Analysis and Scientific Computing (2)
- Science and Mathematics Education (2)
- Set Theory (2)
- Anatomy (1)
- Applied Statistics (1)
- Business (1)
- Cardiovascular Diseases (1)
- Cardiovascular System (1)
- Databases and Information Systems (1)
- Diseases (1)
- Dynamical Systems (1)
- Finance and Financial Management (1)
- Information Security (1)
- Junior High, Intermediate, Middle School Education and Teaching (1)
- Institution
- Keyword
-
- Graph theory (2)
- Abstract Algebra (1)
- Algebra (1)
- Category theory (1)
- Combinatorial analysis (1)
-
- Compositional approach (1)
- Convolutional neural network (1)
- Graphs (1)
- Group Theory (1)
- Human activity recognition (1)
- Machine learning (1)
- Mathematics (1)
- Number Theory (1)
- Partial differential equation (1)
- Pattern theory (1)
- Pollution diffusion (1)
- Sudoku (1)
- Video event understanding (1)
- Video-Based Instruction; Video Prompting; Mobile Technology (iPad); Students with Disabilities; At-Risk Students; Academic Supports; Individualized Intervention (1)
- Publication Year
- Publication
-
- Algebra Seminar (4)
- Professional Learning Day (3)
- Student Scholar Showcase (3)
- Annual Symposium on Biomathematics and Ecology Education and Research (2)
- Georgia State Undergraduate Research Conference (2)
-
- ATU Research Symposium (1)
- Celebration of Learning (1)
- Cybersecurity Undergraduate Research Showcase (1)
- Idaho Conference on Undergraduate Research (1)
- MODVIS Workshop (1)
- National Youth Advocacy and Resilience Conference (1)
- Student Research Symposium (1)
- The Summer Undergraduate Research Fellowship (SURF) Symposium (1)
- UNO Student Research and Creative Activity Fair (1)
- Undergraduate Research Conference (1)
- Undergraduate Student Research Internships Conference (1)
- File Type
Articles 1 - 25 of 25
Full-Text Articles in Algebra
Rsa Algorithm, Evalisbeth Garcia Diazbarriga
Rsa Algorithm, Evalisbeth Garcia Diazbarriga
ATU Research Symposium
I will be presenting about the RSA method in cryptology which is the coding and decoding of messages. My research will focus on proving that the method works and how it is used to communicate secretly.
Extensions Of Algebraic Frames, Papiya Bhattacharjee
Extensions Of Algebraic Frames, Papiya Bhattacharjee
Algebra Seminar
A frame is a complete lattice that satisfies a strong distributive law, known as the frame law. Frames are also known as Pointfree Topology, as every topology is a frame. Even though the concept of frames originated from topology, the idea has expanded to many other areas of mathematics and frames are now studied in their own merit. Given two frame L and M, we say M is an extension of L if L is a subframe of M. In this talk we will discuss different types of frames extensions, such as Rigid extension, r-extension, and r*-extension between two frames. …
The Vulnerabilities To The Rsa Algorithm And Future Alternative Algorithms To Improve Security, James Johnson
The Vulnerabilities To The Rsa Algorithm And Future Alternative Algorithms To Improve Security, James Johnson
Cybersecurity Undergraduate Research Showcase
The RSA encryption algorithm has secured many large systems, including bank systems, data encryption in emails, several online transactions, etc. Benefiting from the use of asymmetric cryptography and properties of number theory, RSA was widely regarded as one of most difficult algorithms to decrypt without a key, especially since by brute force, breaking the algorithm would take thousands of years. However, in recent times, research has shown that RSA is getting closer to being efficiently decrypted classically, using algebraic methods, (fully cracked through limited bits) in which elliptic-curve cryptography has been thought of as the alternative that is stronger than …
The Heisenberg Lie Algebra And Its Role In The Quantum Mechanical Harmonic Oscillator, Angelina Georg
The Heisenberg Lie Algebra And Its Role In The Quantum Mechanical Harmonic Oscillator, Angelina Georg
Algebra Seminar
No abstract provided.
Irreducible Representations Of Sl(2,C), Della Medovoy
Irreducible Representations Of Sl(2,C), Della Medovoy
Algebra Seminar
No abstract provided.
Lie Algebras And Lie Groups, Nhi Nguyen
Extension Of Fundamental Transversals And Euler’S Polyhedron Theorem, Joy Marie D'Andrea
Extension Of Fundamental Transversals And Euler’S Polyhedron Theorem, Joy Marie D'Andrea
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Unomaha Problem Of The Week (2021-2022 Edition), Brad Horner, Jordan M. Sahs
Unomaha Problem Of The Week (2021-2022 Edition), Brad Horner, Jordan M. Sahs
UNO Student Research and Creative Activity Fair
The University of Omaha math department's Problem of the Week was taken over in Fall 2019 from faculty by the authors. The structure: each semester (Fall and Spring), three problems are given per week for twelve weeks, with each problem worth ten points - mimicking the structure of arguably the most well-regarded university math competition around, the Putnam Competition, with prizes awarded to top-scorers at semester's end. The weekly competition was halted midway through Spring 2020 due to COVID-19, but relaunched again in Fall 2021, with massive changes.
Now there are three difficulty tiers to POW problems, roughly corresponding to …
Categorical Aspects Of Graphs, Jacob D. Ender
Categorical Aspects Of Graphs, Jacob D. Ender
Undergraduate Student Research Internships Conference
In this article, we introduce a categorical characterization of directed and undirected graphs, and explore subcategories of reflexive and simple graphs. We show that there are a number of adjunctions between such subcategories, exploring varying combinations of graph types.
The Wright Stuff: An Integrative Approach To Stained Glass, Cassandra Wissink Armstrong
The Wright Stuff: An Integrative Approach To Stained Glass, Cassandra Wissink Armstrong
Professional Learning Day
In this session we'll explore the scientific and mathematical influences behind the artistic stained glass creations of Frank Lloyd Wright, and use them to create our own Wright-inspired stained glass designs. This is a truly integrative lesson that touches on properties of glass, linear functions, and artistic design.
The Last Digits Of Infinity (On Tetrations Under Modular Rings), William Stowe
The Last Digits Of Infinity (On Tetrations Under Modular Rings), William Stowe
Celebration of Learning
A tetration is defined as repeated exponentiation. As an example, 2 tetrated 4 times is 2^(2^(2^2)) = 2^16. Tetrated numbers grow rapidly; however, we will see that when tetrating where computations are performed mod n for some positive integer n, there is convergent behavior. We will show that, in general, this convergent behavior will always show up.
An Anatomical And Functional Analysis Of Digital Arteries, Katie Highsmith
An Anatomical And Functional Analysis Of Digital Arteries, Katie Highsmith
Student Scholar Showcase
Blood flow to the tissue of the hands and digits is efficiently regulated by vasoconstriction and vasodilation. Through a series of cadaveric dissection, we examined arteries in the hands and digits, including ulnar artery, radial artery, palmar arteries, and digital arteries, for their distribution (branching) patterns and morphological parameters (e.g., thickness, length between branches, external and internal diameters). Using data directly collected from three female cadavers as input variables to our mathematical model, we simulated vasoconstriction (-20% and -10% diameter) and vasodilation (+10% and +20 diameter) to evaluate the extent of changes in blood volume and flow within the arteries. …
Group Theoretical Analysis Of Arbitrarily Large, Colored Square Grids, Brett Ehrman
Group Theoretical Analysis Of Arbitrarily Large, Colored Square Grids, Brett Ehrman
Student Scholar Showcase
In this research, we examine n x n grids whose individual squares are each colored with one of k distinct colors. We seek a general formula for the number of colored grids that are distinct up to rotations, reflections, and color reversals. We examine the problem using a group theoretical approach. We define a specific group action that allows us to incorporate Burnside’s Lemma, which leads us to the desired general results
Distributed Evolution Of Spiking Neuron Models On Apache Mahout For Time Series Analysis, Andrew Palumbo
Distributed Evolution Of Spiking Neuron Models On Apache Mahout For Time Series Analysis, Andrew Palumbo
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Predicting Locations Of Pollution Sources Using Convolutional Neural Networks, Yiheng Chi, Nickolas D. Winovich, Guang Lin
Predicting Locations Of Pollution Sources Using Convolutional Neural Networks, Yiheng Chi, Nickolas D. Winovich, Guang Lin
The Summer Undergraduate Research Fellowship (SURF) Symposium
Pollution is a severe problem today, and the main challenge in water and air pollution controls and eliminations is detecting and locating pollution sources. This research project aims to predict the locations of pollution sources given diffusion information of pollution in the form of array or image data. These predictions are done using machine learning. The relations between time, location, and pollution concentration are first formulated as pollution diffusion equations, which are partial differential equations (PDEs), and then deep convolutional neural networks are built and trained to solve these PDEs. The convolutional neural networks consist of convolutional layers, reLU layers …
A Game Of Monovariants On A Checkerboard, Linwood Reynolds
A Game Of Monovariants On A Checkerboard, Linwood Reynolds
Student Scholar Showcase
Abstract: Assume there is a game that takes place on a 20x20 checkerboard in which each of the 400 squares are filled with either a penny, nickel, dime, or quarter. The coins are placed randomly onto the squares, and there are to be 100 of each of the coins on the board. To begin the game, 59 coins are removed at random. The goal of the game is to remove each remaining coin from the board according to the following rules: 1. A penny can only be removed if all 4 adjacent squares are empty. That is, a penny cannot …
Session A-3: Three-Act Math Tasks, Lindsey Herlehy
Session A-3: Three-Act Math Tasks, Lindsey Herlehy
Professional Learning Day
Participants will engage in a Three-Act Math task highlighting the application of properties of geometrical figures. Developed by Dan Meyer, an innovative and highly regarded mathematics instructor, Three-Act Math tasks utilize pedagogical skills that elicit student curiosity, collaboration and questioning. By posing a mathematical problem through active storytelling, this instructional approach redefines real-world mathematics and clarifies the role that a student plays in the learning process. Participants will be given multiple resources where they can access Three-Act Math tasks appropriate for upper elementary grades through Algebra and Geometry courses.
Math And Sudoku: Exploring Sudoku Boards Through Graph Theory, Group Theory, And Combinatorics, Kyle Oddson
Math And Sudoku: Exploring Sudoku Boards Through Graph Theory, Group Theory, And Combinatorics, Kyle Oddson
Student Research Symposium
Encoding Sudoku puzzles as partially colored graphs, we state and prove Akman’s theorem [1] regarding the associated partial chromatic polynomial [5]; we count the 4x4 sudoku boards, in total and fundamentally distinct; we count the diagonally distinct 4x4 sudoku boards; and we classify and enumerate the different structure types of 4x4 boards.
Using Ipads And Video-Based Instruction To Teach Algebra To High School Students With Disabilities, Elias Clinton, Tom J. Clees
Using Ipads And Video-Based Instruction To Teach Algebra To High School Students With Disabilities, Elias Clinton, Tom J. Clees
National Youth Advocacy and Resilience Conference
This presentation targets a study in which four high school students with disabilities were taught to solve algebraic equations using iPads and video-based instruction. All students showed immediate increases in accurate responding following the introduction of the video-based intervention. This presentation provides practitioners with a flexible technology-based intervention for students with disabilities in need of grade-level academic instruction. The intervention could be used across a variety of subjects and academic tasks.
Generalizations And Algebraic Structures Of The Grøstl-Based Primitives, Dmitriy Khripkov, Nicholas Lacasse, Bai Lin, Michelle Mastrianni, Liljana Babinkostova (Mentor)
Generalizations And Algebraic Structures Of The Grøstl-Based Primitives, Dmitriy Khripkov, Nicholas Lacasse, Bai Lin, Michelle Mastrianni, Liljana Babinkostova (Mentor)
Idaho Conference on Undergraduate Research
With the large scale proliferation of networked devices ranging from medical implants like pacemakers and insulin pumps, to corporate information assets, secure authentication, data integrity and confidentiality have become some of the central goals for cybersecurity. Cryptographic hash functions have many applications in information security and are commonly used to verify data authenticity. Our research focuses on the study of the properties that dictate the security of a cryptographic hash functions that use Even-Mansour type of ciphers in their underlying structure. In particular, we investigate the algebraic design requirements of the Grøstl hash function and its generalizations. Grøstl is an …
Video Event Understanding With Pattern Theory, Fillipe Souza, Sudeep Sarkar, Anuj Srivastava, Jingyong Su
Video Event Understanding With Pattern Theory, Fillipe Souza, Sudeep Sarkar, Anuj Srivastava, Jingyong Su
MODVIS Workshop
We propose a combinatorial approach built on Grenander’s pattern theory to generate semantic interpretations of video events of human activities. The basic units of representations, termed generators, are linked with each other using pairwise connections, termed bonds, that satisfy predefined relations. Different generators are specified for different levels, from (image) features at the bottom level to (human) actions at the highest, providing a rich representation of items in a scene. The resulting configurations of connected generators provide scene interpretations; the inference goal is to parse given video data and generate high-probability configurations. The probabilistic structures are imposed using energies that …
Fan-Linear Maps And Fan Algebras, John Hull
Fan-Linear Maps And Fan Algebras, John Hull
Georgia State Undergraduate Research Conference
No abstract provided.
Polynomial Functions Over Finite Fields, John J. Hull
Polynomial Functions Over Finite Fields, John J. Hull
Georgia State Undergraduate Research Conference
No abstract provided.
Session D-3: Discrete Mathematics: A Great Curriculum Connector, Donald Porzio
Session D-3: Discrete Mathematics: A Great Curriculum Connector, Donald Porzio
Professional Learning Day
Many topics that fall under the umbrella of Discrete Mathematics cut across the traditional high school curriculum areas of algebra, geometry, and pre-calculus. Come try some classroom-ready hands-on Discrete Mathematics activities that illustrate the true interconnectedness of mathematics.
Solids Of Revolution About The Line Y=Mx, Harvey Marquis Iii
Solids Of Revolution About The Line Y=Mx, Harvey Marquis Iii
Undergraduate Research Conference
No abstract provided.