Mathematics Commons^™

Problems With And Without … Problems!, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This book is addressed to College honor students, researchers, and professors. It contains 136 original problems published by the author in various scientific journals around the world. The problems could be used to preparing for courses, exams, and Olympiads in mathematics. Many of these have a generalized form. For each problem we provide a detailed solution.

I was a professeur coopérant between 1982-1984, teaching mathematics in French language at Lycée Sidi EL Hassan Lyoussi in Sefrou, Province de Fès, Morocco. I used many of these problems for selecting and training, together with other Moroccan professors, in Rabat city, of the …

Women In Mathematics: An Historical Account Of Women's Experiences And Achievement, Kendra D. Huff

CMC Senior Theses

For a long time, women have struggled to gain complete acceptance in the mathematics field. The purpose of this paper is to explore the history of women in the field of mathematics, the impact and experiences of current female mathematicians, and the common trends for women in the mathematics field, through literature review and personal interviews. This paper looks at the lives of four famous female mathematicians, as well as female mathematicians in the Claremont Colleges who were interviewed for this paper. Specifically this paper examines the discrimination they faced and how they overcame this discrimination, as well as the …

The Effects Of The Use Of Technology In Mathematics Instruction On Student Achievement, Ron Y. Myers

FIU Electronic Theses and Dissertations

The purpose of this study was to examine the effects of the use of technology on students’ mathematics achievement, particularly the Florida Comprehensive Assessment Test (FCAT) mathematics results. Eleven schools within the Miami-Dade County Public School System participated in a pilot program on the use of Geometers Sketchpad (GSP). Three of these schools were randomly selected for this study. Each school sent a teacher to a summer in-service training program on how to use GSP to teach geometry. In each school, the GSP class and a traditional geometry class taught by the same teacher were the study participants. Students’ mathematics …

Dynamic Web Tools For Trigonometry, Steven J. Wilson

Innovations in Math Technology

In the last 20 years, computer technology having mathematical capability has been developed, improved, and become widely available, but textbook presentations are still largely free of any discussion that might require technology. Technology could be used in mathematical instruction for student drill and practice, for instructor demonstrations that promote conceptual understanding, or for the exploration of mathematical ideas, but software is often designed to be pedagogically generic, leaving its use to the creativity of the instructor. Technological solutions for local machines can be quite extensive, but cost and time constraints then limit availability for student use. The internet has the …

When A Mechanical Model Goes Nonlinear, Lisa D. Humphreys, P. J. Mckenna

Faculty Publications

This paper had its origin in a curious discovery by the first author in research performed with an undergraduate student. The following odd fact was noticed: when a mechanical model of a suspension bridge (linear near equilibrium but allowed to slacken at large distance in one direction) is shaken with a low-frequency periodic force, several different periodic responses can result, many with high-frequency components.

Flowers Of Ice- Beauty, Symmetry, And Complexity: A Review Of The Snowflake: Winter's Secret Beauty, John A. Adam

Mathematics & Statistics Faculty Publications

(First paragraph) Growing up as a child in southern England, my early memories of snow include trudging home from school with my father, gazing at the seemingly enormous snowdrifts that smoothed the hedgerows, fields and bushes, while listening to the soft “scrunch” of the snow under my Wellington boots. In the country, snow stretching as far as I could see was not a particularly uncommon sight. The quietness of the land under a foot of snow seemed eerie. I cannot remember the first time I looked at snowflakes per se; my interests as a small child were primarily in their …

Mathematical Magic, Arthur T. Benjamin

All HMC Faculty Publications and Research

In this paper, we present simple strategies for performing mathematical calculations that appear magical to most audiences. Specifically, we explain how to square large numbers, memorize pi to 100 places and determine the day of the week of any given date.

Tree-Like Continua And 2-To-1 Maps, Jo Heath, Van C. Nall

Department of Math & Statistics Faculty Publications

It is not known if there is a 2-to-1 map from a continuum onto a tree-like continuum. In fact, it is not known if there is a 2-to-1 map onto a hereditarily decomposable tree-like continuum. We show that the domain of such a map would have to contain an indecomposable continuum.

A Unifying Field In Logics: Neutrosophic Logic Neutrosophy, Neutrosophic Set, Neutrosophic Probability (In Traditional Chinese), Florentin Smarandache, Feng Liu

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Algebra În Exercijii Şi Probleme Pentru Liceu, Florentin Smarandache, Ion Goian, Raisa Grigor, Vasila Marin

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

The Best Way To Knock 'M Down, Arthur T. Benjamin, Matthew T. Fluet '99

All HMC Faculty Publications and Research

"Knock 'm Down" is a game of dice that is so easy to learn that it is being played in classrooms around the world. Although this game has been effective at developing students' intuition about probability [Fendel et al. 1997; Hunt 1998], we will show that lurking underneath this deceptively simple game are many surprising and highly unintuitive results.

Bounds On A Bug, Arthur T. Benjamin, Matthew T. Fluet '99

All HMC Faculty Publications and Research

In the game of Cootie, players race to construct a "cootie bug" by rolling a die to collect component parts. Each cootie bug is composed of a body, a head, two eyes, one nose, two antennae, and six legs. Players must first acquire the body of the bug by rolling a 1. Next, they must roll a 2 to add the head to the body. Once the body and head are both in place, the remaining body parts can be obtained in any order by rolling two 3s for the eyes, one 4 for the nose, two 5s for the …

Asupra Unor Noi Functii În Teoria Numerelor, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Performantele matematicii actuale,ca si descoperirile din viitor isi au,desigur, inceputul in cea mai veche si mai aproape de filozofie ramura a matematicii, in teoria numerelor. Matematicienii din toate timpurile au fost, sunt si vor fi atrasi de frumusetea si varietatea problemelor specifice acestei ramuri a matematicii. Regina a matematicii, care la randul ei este regina a stiintelor, dupa cum spunea Gauss, teoria numerelor straluceste cu lumina si atractiile ei, fascinandu-ne si usurandu-ne drumul cunoasterii legitatilor ce guverneaza macrocosmosul si microcosmosul. De la etapa antichitatii, cand teoria numerelor era cuprinsa in aritmetica, la etapa aritmeticii superioare din perioada Renasterii, cand teoria …

Mathematical Rebuses, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Optimal Klappenspiel, Arthur T. Benjamin, Derek Stanford '93

All HMC Faculty Publications and Research

The game Klappenspiel ("flipping game") is a traditional German game of flipping tiles according to dice rolls. In this paper, we derive the optimal strategy for this game by using dynamic programming. We show that the probability of winning using the optimal strategy is 0.30%.

Problemes Avec Et, Sans Problemes!, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Linear Estimation: The Kalman-Bucy Filter, William Douglas Schindel

Graduate Theses - Mathematics

The problem of linear dynamic estimation, its solution as developed by Kalman and Bucy, and interpretations, properties and illustrations of that solution are discussed. The central problem considered is the estimation of the system state vector X, describing a linear dynamic system governed by

dx/dt = F(t)X(t) + G(t)U(t)

Y(t) = H(t)X(t) + V(t)

for observations of Y (system output), where V is a random observation-corrupting process, and U is a random system driving process.

An extension of the Kalman-Bucy filter to estimation in the absence of priori knowledge of the random process U and V is developed and illustrated.

History Of Applied Geometry, Evelyn Jackson

Electronic Thesis and Dissertation

Mathematics: Just what does the word mean to us? After a moment of thought many different meanings may present themselves to our minds. At first we are inclined to say that the word mathematics covers a vast field. We are justified in so thinking because mathematics embraces a wide scope of study. Were we to say that it is a science we should place it in its proper genius, for it is truly a science of numbers and space. However, could not the science be the art of calculation or the art of computation?

Some Contributions Of Pure Math To Science, Herbert B.E. Case

Student and Lippitt Prize essays

An examination of the connection between math and science through discoveries in the subjects of astronomy, mechanics, physics and chemistry.