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Cheeger Constants Of Two Related Hyperbolic Riemann Surfaces, Ronald E. Hoagland

Masters Theses

This thesis concerns the study of the Cheeger constant of two related hyperbolic Riemann surfaces. The first surface R is formed by taking the quotient U²/Γ(4), where U² is the upper half-plane model of the hyperbolic plane and Γ(4) is a congruence subgroup of PSL2(Z), an isometry group of U² . This quotient is shown to form a Riemann surface which is constructed by gluing sides of a fundamental domain for Γ(4) together according to certain specified side pairings. To form the related Riemann surface R' , we follow a similar procedure, this time taking the …

Hidden Symmetries In Classical Mechanics And Related Number Theory Dynamical System, Mohsin Md Abdul Karim

Masters Theses

Classical Mechanics consists of three parts: Newtonian, Lagrangian and Hamiltonian Mechanics, where each part is a special extension of the previous part. Each part has explicit symmetries (the explicit Laws of Motion), which, in turn, generate implicit or hidden symmetries (like the Law of Conservation of Energy, etc). In this Master's Thesis, different types of hidden symmetries are considered; they are reflected in the Noether Theorem and the Poincare Recurrence Theorem applied to Lagrangian and Hamiltonian Systems respectively.

The Poincare Recurrence Theorem is also applicable to some number theory problems, which can be considered as dynamical systems. In …

An Exposition Of The Eisenstein Integers, Sarada Bandara

Masters Theses

In this thesis, we will give a brief introduction to number theory and prime numbers. We also provide the necessary background to understand how the imaginary ring of quadratic integers behaves.

An example of said ring are complex numbers of the form ℤ[ω] = {a+bω ∣ a, b ∈ ℤ} where ω² + ω + 1 = 0. These are known as the Eisenstein integers, which form a triangular lattice in the complex plane, in contrast with the Gaussian integers, ℤ[i] = {a + bi ∣ a, b ∈ …

Hyperbolic Geometry With And Without Models, Chad Kelterborn

Masters Theses

We explore the development of hyperbolic geometry in the 18th and early 19th following the works of Legendre, Lambert, Saccheri, Bolyai, Lobachevsky, and Gauss. In their attempts to prove Euclid's parallel postulate, they developed hyperbolic geometry without a model. It was not until later in the 19th century, when Felix Klein provided a method (which was influenced by projective geometry) for viewing the hyperbolic plane as a disk in the Euclidean plane, appropriately named the "Klein disk model". Later other models for viewing the hyperbolic plane as a subset of the Euclidean plane were created, namely the Poincaré disk model, …

A Glance At Tropical Operations And Tropical Linear Algebra, Semere Tsehaye Tesfay

Masters Theses

The tropical semiring is ℝ ∪ {∞} with the operations x ⊕ y = min{x, y}, x ⊕ ∞ = ∞ ⊕ x = x, x ⊙ y = x + y, x ⊙ ∞ = ∞ ⊙ y = ∞. This paper explores how ideas from classical algebra and linear algebra over the real numbers such as polynomials, roots of polynomials, lines, matrices and matrix operations, determinants, eigen values and eigen vectors would appear in tropical mathematics. It uses numerous computed examples to illustrate these concepts and explores the relationship between certain tropical matrices and graph …

Near Minimum Energy Distributions On The Sphere Using Voronoi Cells, Benedictus Sitou Mensah

Masters Theses

No abstract provided.

Of Music, Mathematics, And Magic: Why Math Is All Made Up And Why It Works So Well, Gregory A. Leach

Masters Theses

No abstract provided.

Casimir Effect In Quantum Physics, Matthew James Urfer

Masters Theses

No abstract provided.

Numerical Approximations Of Differential Equations And Applications In Maple, Joyce Zimmerman

Masters Theses

No abstract provided.

Computational Modeling Of Tumor Angiogenesis, Santanu Chatterjee

Masters Theses

No abstract provided.

Cyclic Rings, Warren K. Buck

Masters Theses

No abstract provided.

Practical Approach To Incorporating Maple Into The Finite Mathematics Course: 3 Modules And 8 Case Studies, Jonica Helene Craft-Mcbride

Masters Theses

No abstract provided.

Sums Of Powers And The Bernoulli Numbers, Laura Elizabeth S. Coen

Masters Theses

This expository thesis examines the relationship between finite sums of powers and a sequence of numbers known as the Bernoulli numbers. It presents significant historical events tracing the discovery of formulas for finite sums of powers of integers, the discovery of a single formula by Jacob Bernoulli which gives the Bernoulli numbers, and important discoveries related to the Bernoulli numbers. A method of generating the sequence by means of a number theoretic recursive formula is given. Also given is an application of matrix theory to find a relation, first given by Johannes Faulhaber, between finite sums of odd powers and …

A Comparison Of Ancient Mathematical And Calendrical Systems, Karen Schlauch

Masters Theses

No abstract provided.

The General Linear Group Related Groups, J. William Beck

Masters Theses

No abstract provided.

An Introduction To The Derivative Of A Polynomial, Floyd A. Miller

Masters Theses

No abstract provided.

Mathematicians And Royalty: A Historical Survey, Loren W. Pixley

Masters Theses

No abstract provided.

A Critical Analysis Of Several Product And Factoring Formulas, Herbert Wills

Masters Theses

No abstract provided.