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Physical Sciences and Mathematics Commons™

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Mathematics

Journal

Georgia Academy of Science

Articles 1 - 12 of 12

Full-Text Articles in Physical Sciences and Mathematics

An Experiential Report On The Thayer Method Of Teaching Across College-Level Chemistry, Biology, Math, And Physics Courses, Kevin P. O'Halloran, Sairam Tangirala, Fengjie Sun, Leonard E. Anagho, Gerald Agbegha, Clay Runck, David Roth, Amy H. Erickson Apr 2020

An Experiential Report On The Thayer Method Of Teaching Across College-Level Chemistry, Biology, Math, And Physics Courses, Kevin P. O'Halloran, Sairam Tangirala, Fengjie Sun, Leonard E. Anagho, Gerald Agbegha, Clay Runck, David Roth, Amy H. Erickson

Georgia Journal of Science

The Thayer method of instruction is a little-known active learning technique that dates back to 1817 at the U.S. Military Academy. This study describes the implementation and statistical evaluation of an adaptation of the Thayer method in a variety of college science and math courses. All courses had five characteristics in common: (i) students were given a daily reading schedule and instructed to prepare before class, (ii) each class started with a question and answer session, (iii) class time minimized the use of lecture, (iv) class time maximized the use of active learning, and (v) students were frequently quizzed. A …

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Using Well-Known Probability Density Functions To Evaluate Certain Integrals In Calculus, Stacy Pitman, Andreas Lazari Jul 2017

Using Well-Known Probability Density Functions To Evaluate Certain Integrals In Calculus, Stacy Pitman, Andreas Lazari

Georgia Journal of Science

A major source of anxiety for engineering and science majors who must take calculus is the topic of integration. The techniques of integration necessary for solving practical problems in the sciences are lengthy and complex. In this paper, we are introducing a method that minimizes the algebra as well as the number of computations for certain types of integrals. It is important to note that we are not suggesting that the conventional methods for teaching techniques of integration be replaced with the innovation we are proposing. Rather, the new approach we suggest is to be presented only after the traditional …

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The Fascinating Mathematical Beauty Of Triangular Numbers Jun 2017

The Fascinating Mathematical Beauty Of Triangular Numbers

Georgia Journal of Science

The abstract is available under additional files below.

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The Mathematical Magic Of Perfect Numbers Jun 2017

The Mathematical Magic Of Perfect Numbers

Georgia Journal of Science

Mathematicians have been fascinated for centuries by the properties and patterns of numbers [2]. They have noticed that some numbers are equal to the sum of all of their factors (not including the number itself). Such numbers are called perfect numbers. Thus a positive integer is called a perfect number if it is equal to the sum of its proper positive divisors. The search for perfect numbers began in ancient times. The four perfect numbers 6, 28, 496, and 8128 seem to have been known from ancient times [2]. In this paper, we will investigate some important properties of perfect …

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Properties Enjoyed By The Highest Digit In A Base Other Than The Base 10, Sudhir Goel, Kathy Simons Jun 2017

Properties Enjoyed By The Highest Digit In A Base Other Than The Base 10, Sudhir Goel, Kathy Simons

Georgia Journal of Science

The number nine in base ten enjoys some nice arithmetic properties. In this paper, we show that these properties are not intrinsic to the number nine; in fact, they are true for the largest digit in any base b. Four properties involving the final sums of all the digits of a number in a non-decimal base are explored and proofs of these properties are given in the appendix.

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Principle Components For Diagnosing Dispersion In Multivariate Statistical Process Control, Terrance E. Murphy, Mary Mcshane-Vaughn, Kwok Leung-Tsui Jun 2017

Principle Components For Diagnosing Dispersion In Multivariate Statistical Process Control, Terrance E. Murphy, Mary Mcshane-Vaughn, Kwok Leung-Tsui

Georgia Journal of Science

We provide an easily implemented procedure to help data analysts systematically diagnose which quality characteristics may be driving the dispersion of a multivariate process out of control. Multivariate statistical process control commonly uses Hotelling's T2 statistic to indicate when a multivariate observation goes out-of-control. Several techniques currently exist that accurately diagnose which specific variables are driving the T2 statistic out-of-control. For subgroups of independently and identically distributed multivariate normal observations, we advocate decomposing the overall T2 into independent T2 statistics for separate monitoring of location and dispersion. We propose a procedure based on principle components to …

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The Importance Of Mathematical Wording By Math Instructors, Sudhir Goel, Denise Reid Jun 2017

The Importance Of Mathematical Wording By Math Instructors, Sudhir Goel, Denise Reid

Georgia Journal of Science

At times we the math instructors in a classroom are not careful enough to use proper Mathematical wording, e.g. sin2 + cos2 = 1 without any reference to the angle. Improper Mathematical wording can be confusing to a student at any level, especially at high school and/or at a college freshman or sophomore level. It may hinder the students’ progress in the present and the subsequent math courses.

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Connecting Algebra And Geometry For Extraneous Roots, Sudhir Goel, Iwan Elstak Jun 2017

Connecting Algebra And Geometry For Extraneous Roots, Sudhir Goel, Iwan Elstak

Georgia Journal of Science

Extraneous roots are an unsolved mystery for our freshmen level college math students. The students are often confused and wonder what extraneous roots are and how do they suddenly appear while solving an algebraic equation. In this paper we clarify the idea of extraneous roots and connect the algebra and geometry behind extraneous roots.

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Been There Done That Can We Connect?, Sudhir Goel, Patricia Bezona Jun 2017

Been There Done That Can We Connect?, Sudhir Goel, Patricia Bezona

Georgia Journal of Science

A standard topic in a College Algebra course is to find the coordinates of the midpoint of a line segment connecting two points. In the early twentieth century [1] and [2], in a few texts, this idea was extended to find the coordinates of a point that divides a line segment in any given ratio. In this paper, we present a neat application of this extended idea, and further use it to find the co-ordinates of the centroid of a triangle with vertices A(x1, y1), B(x2, y2) and …

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Leslie Matrices And Women Population In The United States Of America, Brittney Nelson, Denise T. Reid, Antonija Tangar, Jose A. Velez-Marulanda Jun 2017

Leslie Matrices And Women Population In The United States Of America, Brittney Nelson, Denise T. Reid, Antonija Tangar, Jose A. Velez-Marulanda

Georgia Journal of Science

This research tests the accuracy of the Leslie matrix, which is a discrete age-structured method that uses fertility and survival rates, as a tool for predicting women population. Based on available data for the year 2000, we have constructed a Leslie matrix that predicts female population in the United States for every five years from the years 2000 to 2020. To test the accuracy of this method, we compare the aforementioned obtained projected data for the year 2010 with the actual data for women population in the United States obtained by the 2010 U.S. Census.

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College Algebra - Large Section Versus Traditional Size, Andreas Lazari, Denise Reid Jun 2017

College Algebra - Large Section Versus Traditional Size, Andreas Lazari, Denise Reid

Georgia Journal of Science

The economic crisis facing our nation forced many companies and universities to downsize and learn to operate with smaller budgets. Valdosta State University (VSU) was not immune to this economic crisis. To deal with this crisis VSU started offering large sections of core area courses, including College Algebra (MATH 1111). It is clear from a financial point of view that large sections will benefit the university during this financial crisis. What was not clear was the impact to student learning and success in College Algebra. In the fall 2010 and fall 2011 terms, VSU offered the first large sections of …

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Connecting Algebra And Geometry To Find Square And Higher Order Roots, Iwan R. Elstak, Sudhir Goel Jun 2017

Connecting Algebra And Geometry To Find Square And Higher Order Roots, Iwan R. Elstak, Sudhir Goel

Georgia Journal of Science

Unfortunately, the repeat rate for all core curriculum courses including calculus-I and II, and also math education courses is too high. K-12 students are barely able to do estimation, an important part of Mathematics, whether it is adding fractions or finding roots, or for that matter, simple percent problems. In this paper we present geometric ways to reason about approximation of square roots and cube roots that are not accessible with simple routine techniques. We combine graphical methods, the use of a geometry software (sketch pad) and convergence of sequences to find higher order roots of positive real numbers and …

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