The curricular value of mathematics in non-mathematics degree

Higher education should provide the acquisition of skills and abilities that allow the student to play a full and active role in society. The educational experience should offer a series of conceptual, procedural and attitudinal contents that encourage “learning to know, learning to do, learning to be and learning to live together”. It is important to consider the curricular value of mathematics in the education of university undergraduates who do not intend to study mathematics but for whom the discipline will serve as an instrumental. This work discusses factors that form part of the debate on the curricular value of mathematics in non-mathematics degrees.

Do first-year university students understand the language of mathematics?

The aim of the project is to determine if the understanding of the language of Mathematics of students starting university is propitious to the development of an appropriate cognitive structure. The objective of this current work was to analyse the ability of first-year university students to translate the registers of verbal or written expressions and their representations to the registers of algebraic language. Results indicate that students do not understand the basic elements of the language of Mathematics and this causes them to make numerous errors of construction and interpretation. The students were not able to associate concepts with definitions and were unable to offer examples.

Earth’s Rotation: A Challenging Problem in Mathematics and Physics

A suitable knowledge of the orientation and motion of the Earth in space is a common need in various fields. That knowledge has been ever necessary to carry out astronomical observations, but with the advent of the space age, it became essential for making observations of satellites and predicting and determining their orbits, and for observing the Earth from space as well. Given the relevant role it plays in Space Geodesy, Earth rotation is considered as one of the three pillars of Geodesy, the other two being geometry and gravity. Besides, research on Earth rotation has fostered advances in many fields, such as Mathematics, Astronomy and Geophysics, for centuries. One remarkable feature of the problem is in the extreme requirements of accuracy that must be fulfilled in the near future, about a millimetre on the tangent plane to the planet surface, roughly speaking. That challenges all of the theories that have been devised and used to-date; the paper makes a short review of some of the most relevant methods, which can be envisaged as milestones in Earth rotation research, emphasizing the Hamiltonian approach developed by the authors. Some contemporary problems are presented, as well as the main lines of future research prospected by the International Astronomical Union/International Association of Geodesy Joint Working Group on Theory of Earth Rotation, created in 2013.

Mathematics notebook, ca. 1714-1718

This heavily illustrated notebook contains extensive notes on spheric triangles and spheric angles. These include rules and examples with their solutions.

Mathematics notebook, ca. 1714-1718, with chronology of the reign of Augustus

The first two pages of this notebook contain a comparative chronology of the reign of Augustus, outlined in two columns. One column outlines the chronology according to ecclesiastical scholar Laurence Echard, and the other column outlines the chronology according to William Cave. The rest of the notebook contains extensive entries on the following subjects, with related rules, problems, and illustrations: fractions, decimals, arithmetical progression, geometrical progression, "disjunct proportion, or ye Golden Rule," signs and symbols, integers, geometrical definitions, and Euclidian geometry.

Mathematics notebook : manuscript, 1782

With sections on numeration, surveying, trigonometry and other topics, accompanied by diagrams and hand-colored illustrations.

Mathematics notebook : manuscript, 1785-1789

Sections on numeration, interest, square root, geometry and surveying with accompanying diagrams.

Treatise on mathematics and astronomy: written about the year 1680, in Boston

Bound volume containing a late 17th century handwritten mathematical and astronomical text in one hand. The text is separated into mathematical and astronomical sections with rules, instructions for performing calculations, tables, and drawings. The subjects include arithmetic, geometry, astronomy, and trigonometry, and segments have titles such as "Subtraction," "A decimal table of English coince," "Logarithes & their use," and "To find the true place of the sun." The text is undated and unattributed but references Briggs, Oughtred, Ramus, and Apollonius. Certain tables are calculated from latitudinal and longitudinal numbers associated with Boston, and many of the examples use dates in the 1670s and 1680. The manuscript pages are mounted onto unruled pages, and some of the manuscript pages are fragments.

Algebra, or universal mathematics: revived 1738 with notes and additions : manuscript, [after 1738]

Instructional book in algebra with exercises.

Muqaddimah fī al-shudūd al-ḥarīr al-khāliṣah wa-bayʻihā li-man yalbasuhā / lil-Shaykh ʻUmar ibn Yūsuf al-Ḥanafī : manuscript, 1760

Unbound.

Dhikr maʻrifat aḥzāb al-Qurʼān wa-anṣāfihi wa-arbāʻih : manuscript, undated

Title from caption (fol. 1v).

Hādhihi Risālat Jāmiʻat al-funūn fī afḍalīyat Qāsiyūn / li-jāmiʻihā al-faqīr Muḥammad al-Shaṭṭī ibn al-Shaykh Ḥasan al-Shaṭṭī : manuscript, 1859

بسم الله الرحمن الرحيم الحمد لله الذي اختار لنبيه المصطفى دمشق الشام وجعلها عزا ومحشرا ومنعة وذكرا كما... :Incipit

Kitāb al-Barāhīn al-jalīyah fī ʻilm al-kalām / li-jāmiʻihā al-ʻabd al-ḥaqīr Muḥammad Rashīd Qazīhā al-shahīr bi-Ibn Sinān : manuscript, 1896

Paginated 1-32.

Arbaʻūn ḥadīthan maʻa sharḥihā ʻalá muqtaḍá mashrab al-Ṣūfīyah : manuscript, 1608 or 9

Written in 1017 [1608 or 1609].