Conference Presentations by Randy K Schwartz
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A course module that uses concepts of modeling, trigonometry, differential equations, and feature... more A course module that uses concepts of modeling, trigonometry, differential equations, and features of the graphing calculator.
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A course module that uses concepts of linear algebra, calculus, and differential equations, and f... more A course module that uses concepts of linear algebra, calculus, and differential equations, and features of the graphing calculator.
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A course exercise in business optimization using concepts of calculus and features of the graphin... more A course exercise in business optimization using concepts of calculus and features of the graphing calculator.
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Talks by Randy K Schwartz
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Papers by Randy K Schwartz
Math Horizons, 2003
Page 1. Have you ever noticed that "circle" and "circus" sound very much alik... more Page 1. Have you ever noticed that "circle" and "circus" sound very much alike? Or that "radius" and "radio" differ only a little? Word Wise Circles Around, About, Across, & Through Rheta N. Rubenstein University of Michigan-Dearborn Randy K. Schwartz Schoolcraft College ...
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This brief article recalls the life of the English weaver-turned-mathematician Thomas Simpson (Au... more This brief article recalls the life of the English weaver-turned-mathematician Thomas Simpson (Aug. 20, 1710 – May 14, 1761), whose name became attached to Simpson’s Rule for the numerical approximation of integrals. The article takes special note of the fact that during this era, mathematics had special appeal among certain circles of working-class men and upper-middle class women.
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This article shows how the possible roots of a polynomial with integer coefficients are constrain... more This article shows how the possible roots of a polynomial with integer coefficients are constrained by combinatorial principles. Knowledge of properties of Pascal’s Triangle can enable one to infer information about the roots from a few known facts about the polynomial.
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This article, with accompanying exercises for student readers, explores the mathematics of Mendel... more This article, with accompanying exercises for student readers, explores the mathematics of Mendel’s Laws of Inheritance, and shows how such calculations are used to solve practical problems arising in biology, horticulture, and agriculture.
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This article, with accompanying exercises for student readers, explores the Binomial Theorem and ... more This article, with accompanying exercises for student readers, explores the Binomial Theorem and its generalization to arbitrary exponents discovered by Isaac Newton.
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This article, with accompanying exercises for student readers, describes the efforts carried out ... more This article, with accompanying exercises for student readers, describes the efforts carried out by Leonardo da Vinci and other early-modern scientists to rectify the area of a circle by pizza-like dissection, and to use circle area calculations to understand the geometry of tree-branching in nature.
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This report summarizes some representative talks presented at the 12th Maghreb Colloquium on the ... more This report summarizes some representative talks presented at the 12th Maghreb Colloquium on the History of Arab Mathematics (COMHISMA12), held on May 26-28, 2016, at Cadi Ayyad University in Marrakesh, Morocco. This rich and diverse colloquium series, the longest-running and still leading international conference on the overall history of Arab mathematics, is part of the effort to uncover and disseminate the mathematical contributions of Arab and other Islamic cultures.
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Malaria has been humanity's worst public health problem throughout recorded history. Mathematical... more Malaria has been humanity's worst public health problem throughout recorded history. Mathematical methods are needed to understand which factors are relevant to the disease and to develop countermeasures against it. This article and the accompanying exercises provide examples of those methods for use in lower-or upper-level courses dealing with probability, statistics, or population modeling. These can be used to illustrate such concepts as correlation, causation, conditional probability, and independence. The article explains how the apparent link between sickle cell trait and resistance to malaria was first verified in Uganda using the chi-squared probability distribution. It goes on to explain that the incidence of sickle cell within a given population is an example of an asymptotically stable equilibrium determined by the selective pressure of malaria. It summarizes the impact of malaria on human history in order to explain why this equilibrium has varied over time and space. Finally, the article summarizes how linkage analysis and other statistical modeling techniques are being used as an important step in developing genomic pharmaceuticals to combat such diseases.
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سيدي عمر عسالي، جامعة عمار ثليجي بالأغواط – الجزائر :
الميادين التطبيقية لهندسة الإسقاطات العر... more سيدي عمر عسالي، جامعة عمار ثليجي بالأغواط – الجزائر :
الميادين التطبيقية لهندسة الإسقاطات العربية: مثال تسطيح الكرة على سطح الأسطرلاب
BEBBOUCHI Rachid : Astronomie –Astrologie : complémentarité ou symbiose ?
CALVO Emilia : Un exemple de l’application des mathématiques à l’astronomie: Les instruments trigonométriques et leurs applications aux calculs astronomiques.
DÍAZ - FAJARDO Montse : Les techniques dans l'astrologie: la table de force d'une planète d'Ibn Azzuz al-Qusantini.
MARTOS QUESADA Juan : Le mathématicien andalous Ibn Mu'adh.
SCHWARTZ Randy, Al-qibla and the New Spherical Trigonometry: The Examples of al-Bīrūnī and al-Marrākushī
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Dick Jardine and Amy Shell-Gellasch, eds.,Mathematical Time Capsules: Historical Modules for the Mathematics Classroom (MAA Notes series), Chapter 5 (pp. 29-37) , 2011
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Conference Presentations by Randy K Schwartz
Talks by Randy K Schwartz
Papers by Randy K Schwartz
الميادين التطبيقية لهندسة الإسقاطات العربية: مثال تسطيح الكرة على سطح الأسطرلاب
BEBBOUCHI Rachid : Astronomie –Astrologie : complémentarité ou symbiose ?
CALVO Emilia : Un exemple de l’application des mathématiques à l’astronomie: Les instruments trigonométriques et leurs applications aux calculs astronomiques.
DÍAZ - FAJARDO Montse : Les techniques dans l'astrologie: la table de force d'une planète d'Ibn Azzuz al-Qusantini.
MARTOS QUESADA Juan : Le mathématicien andalous Ibn Mu'adh.
SCHWARTZ Randy, Al-qibla and the New Spherical Trigonometry: The Examples of al-Bīrūnī and al-Marrākushī
الميادين التطبيقية لهندسة الإسقاطات العربية: مثال تسطيح الكرة على سطح الأسطرلاب
BEBBOUCHI Rachid : Astronomie –Astrologie : complémentarité ou symbiose ?
CALVO Emilia : Un exemple de l’application des mathématiques à l’astronomie: Les instruments trigonométriques et leurs applications aux calculs astronomiques.
DÍAZ - FAJARDO Montse : Les techniques dans l'astrologie: la table de force d'une planète d'Ibn Azzuz al-Qusantini.
MARTOS QUESADA Juan : Le mathématicien andalous Ibn Mu'adh.
SCHWARTZ Randy, Al-qibla and the New Spherical Trigonometry: The Examples of al-Bīrūnī and al-Marrākushī
"In this outstanding article, Randy K. Schwartz gives a historical perspective of the development of the meter as a precise form of measurement beginning his account in the wake of the French Revolution. The birth of this unit of measurement was not without its pains. Amidst the political turmoil of the 1790s, a heated debate ensued from the decision to replace over 250,000 different weights and measures with a system of measurement that would not be arbitrary. The author verses readers in the mathematical arguments as to how a meter should be defined – as a unit related to the swing of a pendulum or proportional to the size of the Earth. Readers see how each idea was implemented in its turn and learn the mathematical challenges inherent in each. The author explains the motion of a pendulum clock and why it does not lead to the desired universal measurement. Readers also learn about the French surveying project, the complications associated with it, and its ultimate success. In each step of the article, readers are exposed to wonderful descriptions of how mathematical tools, ranging from trigonometry to differential equations, were used to define the meter."