Model Theory Of Groups And Monoids, 2020 The Graduate Center, City University of New York

#### Model Theory Of Groups And Monoids, Laura M. Lopez Cruz

*All Dissertations, Theses, and Capstone Projects*

We first show that arithmetic is bi-interpretable (with parameters) with the free monoid and with partially commutative monoids with trivial center. This bi-interpretability implies that these monoids have the QFA property and that finitely generated submonoids of these monoids are definable. Moreover, we show that any recursively enumerable language in a finite alphabet X with two or more generators is definable in the free monoid. We also show that for metabelian Baumslag-Solitar groups and for a family of metabelian restricted wreath products, the Diophantine Problem is decidable. That is, we provide an algorithm that decides whether or not a given ...

"Fireworks And Quadratic Functions”, 2020 Illinois Mathematics and Science Academy

#### "Fireworks And Quadratic Functions”, Kelly W. Remijan

*Teacher Resources*

No abstract provided.

"Sheet Metal And Polynomials At Work”, 2020 Illinois Mathematics and Science Academy

#### "Sheet Metal And Polynomials At Work”, Kelly W. Remijan

*Teacher Resources*

No abstract provided.

"Dancing Fountains”, 2020 Illinois Mathematics and Science Academy

"American Football: Field Goals And Quadratic Functions”, 2020 Illinois Mathematics and Science Academy

#### "American Football: Field Goals And Quadratic Functions”, Kelly W. Remijan

*Teacher Resources*

No abstract provided.

“Product Development: Model Rockets As Toys”, 2020 Illinois Mathematics and Science Academy

#### “Product Development: Model Rockets As Toys”, Kelly W. Remijan

*Teacher Resources*

No abstract provided.

"Crash Reconstruction: Stopping Distance”, 2020 Illinois Mathematics and Science Academy

#### "Crash Reconstruction: Stopping Distance”, Kelly W. Remijan

*Teacher Resources*

No abstract provided.

The Distribution Of The Greatest Common Divisor Of Elements In Quadratic Integer Rings, 2020 CUNY Bernard M Baruch College

#### The Distribution Of The Greatest Common Divisor Of Elements In Quadratic Integer Rings, Asimina S. Hamakiotes

*Student Theses*

For a pair of quadratic integers *n* and *m* chosen randomly, uniformly, and independently from the set of quadratic integers of norm *x* or less, we calculate the probability that the greatest common divisor of (*n,m*) is *k*. We also calculate the expected norm of the greatest common divisor (*n,m*) as *x* tends to infinity, with explicit error terms. We determine the probability and expected norm of the greatest common divisor for quadratic integer rings that are unique factorization domains. We also outline a method to determine the probability and expected norm of the greatest common divisor of ...

"Tracker Software And Matchbox Car Jumps”, 2020 Illinois Mathematics and Science Academy

#### "Tracker Software And Matchbox Car Jumps”, Kelly W. Remijan

*Teacher Resources*

No abstract provided.

"Human Cannonball Stunts And Quadratic Functions”, 2020 Illinois Mathematics and Science Academy

#### "Human Cannonball Stunts And Quadratic Functions”, Kelly W. Remijan

*Teacher Resources*

No abstract provided.

"Straw Rockets And Parabolas”, 2020 Illinois Mathematics and Science Academy

#### "Straw Rockets And Parabolas”, Kelly W. Remijan

*Teacher Resources*

No abstract provided.

"Car Darts And Parabolas”, 2020 Illinois Mathematics and Science Academy

"Matchbox Stunts And Simulations”, 2020 Illinois Mathematics and Science Academy

#### "Matchbox Stunts And Simulations”, Kelly W. Remijan

*Teacher Resources*

No abstract provided.

Singular Value Decomposition, 2020 Coastal Carolina University

#### Singular Value Decomposition, Krystal Bonaccorso, Andrew Incognito

*Honors Theses*

A well-known theorem is Diagonalization, where one of the factors is a diagonal matrix. In this paper we will be describing a similar way to factor/decompose a non-square matrix. The key to both of these ways to factor is eigenvalues and eigenvectors.

Beginning Algebra Made Useful, 2020 Grand Valley State University

#### Beginning Algebra Made Useful, Charlene E. Beckmann

*Open Textbooks*

*Beginning Algebra Made Useful* addresses the needs of learners to make sense of algebra by quantifying and generalizing everyday occurrences such as commuting to work, buying gas or pizza, and determining the better deal. It requires learners to actively engage with algebraic concepts through physical and thought experiments in ways that help them connect ideas, representations, and contexts, and solve problems that arise in their daily lives. The text* *helps learners grow their brains and develop growth mindsets as they learn algebra conceptually. Problem sets continue the process, extending work begun in each lesson, applying new understandings to new contexts ...

Gray Codes In Music Theory, 2020 University of Maine

#### Gray Codes In Music Theory, Isaac L. Vaccaro

*Electronic Theses and Dissertations*

In the branch of Western music theory called serialism, it is desirable to construct chord progressions that use each chord in a chosen set exactly once. We view this problem through the scope of the mathematical theory of Gray codes, the notion of ordering a finite set X so that adjacent elements are related by an element of some specified set R of involutions in the permutation group of X. Using some basic results from the theory of permutation groups we translate the problem of finding Gray codes into the problem of finding Hamiltonian paths and cycles in a Schreier ...

"American Football, Quarterbacks, And Parabolas”, 2020 Illinois Mathematics and Science Academy

#### "American Football, Quarterbacks, And Parabolas”, Kelly W. Remijan

*Teacher Resources*

No abstract provided.

"Volleyball And Parabolas”, 2020 Illinois Mathematics and Science Academy

"Birds And Polynomial Functions”, 2020 Illinois Mathematics and Science Academy

#### "Birds And Polynomial Functions”, Kelly W. Remijan

*Teacher Resources*

No abstract provided.

"Bouncing Balls And Linear Functions”, 2020 Illinois Mathematics and Science Academy

#### "Bouncing Balls And Linear Functions”, Kelly W. Remijan

*Teacher Resources*

No abstract provided.