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Physical Sciences and Mathematics Commons™
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- $j$-invariant (1)
- Algebraic geometry (1)
- Chebyshev Polynomials (1)
- Convex (1)
- Elliptic curve (1)
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- Finite field (1)
- Geometry (1)
- Inequality (1)
- Irregular Dice (1)
- Isoperimetric (1)
- Latin Square (1)
- Local Warming (1)
- Magic Square (1)
- Order of an elliptic curve (1)
- Probability (1)
- Siam Construction (1)
- Siam Method (1)
- Symmetric Polynomials; Analytic Number Theory; Distinct Prime Factors; Dirichlet Series; Divisor Sums; Multiplicative Number Theory (1)
- Time Series Analysis (1)
- Trigonometric Identities (1)
- Trirectangular Tetrahedron (1)
- Twists (1)
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Articles 1 - 7 of 7
Full-Text Articles in Physical Sciences and Mathematics
Sums Involving The Number Of Distinct Prime Factors Function, Tanay Wakhare
Sums Involving The Number Of Distinct Prime Factors Function, Tanay Wakhare
Rose-Hulman Undergraduate Mathematics Journal
We find closed form expressions for finite and infinite sums that are weighted by $\omega(n)$, where $\omega(n)$ is the number of distinct prime factors of $n$. We then derive general convergence criteria for these series. The approach of this paper is to use the theory of symmetric functions to derive identities for the elementary symmetric functions, then apply these identities to arbitrary primes and values of multiplicative functions evaluated at primes. This allows us to reinterpret sums over symmetric polynomials as divisor sums and sums over the natural numbers.
Local Warming In Low Latitude Locations: A Time Series Analysis, Ryan Pittman
Local Warming In Low Latitude Locations: A Time Series Analysis, Ryan Pittman
Rose-Hulman Undergraduate Mathematics Journal
Global warming is a well-known and well-studied phenomenon pertaining to a gradual increase of average global temperatures over time. Many global warming mathematical models make certain assumptions regarding the factors that impact global temperature. These assumptions include effects from increased global carbon dioxide levels in the atmosphere and the melting ice sheets, among others. This paper draws conclusions about temperature changes without the assumptions needed for the global warming mathematical models. Instead of using computer models to project temperatures on a global scale, 33 low-latitude locations in the southern United States were individually studied to see if each one has …
Partial Sum Trigonometric Identities And Chebyshev Polynomials, Sarah Weller
Partial Sum Trigonometric Identities And Chebyshev Polynomials, Sarah Weller
Rose-Hulman Undergraduate Mathematics Journal
Using Euler’s theorem, geometric sums and Chebyshev polynomials, we prove trigonometric identities involving sums and multiplications of cosine.
Probabilities Involving Standard Trirectangular Tetrahedral Dice Rolls, Rulon Olmstead, Doneliezer Baize
Probabilities Involving Standard Trirectangular Tetrahedral Dice Rolls, Rulon Olmstead, Doneliezer Baize
Rose-Hulman Undergraduate Mathematics Journal
The goal is to be able to calculate probabilities involving irregular shaped dice rolls. Here it is attempted to model the probabilities of rolling standard tri-rectangular tetrahedral dice on a hard surface, such as a table top. The vertices and edges of a tetrahedron were projected onto the surface of a sphere centered at the center of mass of the tetrahedron. By calculating the surface areas bounded by the resultant geodesics, baseline probabilities were achieved. Using a 3D printer, dice were constructed of uniform density and the results of rolling them were recorded. After calculating the corresponding confidence intervals, the …
A Proof Of The "Magicness" Of The Siam Construction Of A Magic Square, Joshua Arroyo
A Proof Of The "Magicness" Of The Siam Construction Of A Magic Square, Joshua Arroyo
Rose-Hulman Undergraduate Mathematics Journal
A magic square is an n x n array filled with n2 distinct positive integers 1, 2, ..., n2 such that the sum of the n integers in each row, column, and each of the main diagonals are the same. A Latin square is an n x n array consisting of n distinct symbols such that each symbol appears exactly once in each row and column of the square. Many articles dealing with the construction of magic squares introduce the Siam method as a "simple'' construction for magic squares. Rarely, however, does the article actually prove that the …
On Orders Of Elliptic Curves Over Finite Fields, Yujin H. Kim, Jackson Bahr, Eric Neyman, Gregory Taylor
On Orders Of Elliptic Curves Over Finite Fields, Yujin H. Kim, Jackson Bahr, Eric Neyman, Gregory Taylor
Rose-Hulman Undergraduate Mathematics Journal
In this work, we completely characterize by $j$-invariant the number of orders of elliptic curves over all finite fields $F_{p^r}$ using combinatorial arguments and elementary number theory. Whenever possible, we state and prove exactly which orders can be taken on.
The Convex Body Isoperimetric Conjecture In The Plane, John Berry, Eliot Bongiovanni, Wyatt Boyer, Bryan Brown, Paul Gallagher, David Hu, Alyssa Loving, Zane Martin, Maggie Miller, Byron Perpetua, Sarah Tammen
The Convex Body Isoperimetric Conjecture In The Plane, John Berry, Eliot Bongiovanni, Wyatt Boyer, Bryan Brown, Paul Gallagher, David Hu, Alyssa Loving, Zane Martin, Maggie Miller, Byron Perpetua, Sarah Tammen
Rose-Hulman Undergraduate Mathematics Journal
The Convex Body Isoperimetric Conjecture states that the least perimeter needed to enclose a volume within a ball is greater than the least perimeter needed to enclose the same volume within any other convex body of the same volume in Rn. We focus on the conjecture in the plane and prove a new sharp lower bound for the isoperimetric profile of the disk in this case. We prove the conjecture in the case of regular polygons, and show that in a general planar convex body the conjecture holds for small areas.