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Mathematical Practice
Mathematical practice comprises the working practices of professional mathematicians: selecting theorems to prove, using informal notations to persuade themselves and others that various steps in the final proof are convincing, and seeking peer review and publication, as opposed to the end result of proven and published theorems. Philip Kitcher has proposed a more formal definition of a mathematical practice, as a quintuple. His intention was primarily to document mathematical practice through its historical changes. Historical tradition The evolution of mathematical practice was slow, and some contributors to modern mathematics did not follow even the practice of their time. For example, Pierre de Fermat was infamous for withholding his proofs, but nonetheless had a vast reputation for correct assertions of results. One motivation to study mathematical practice is that, despite much work in the 20th century, some still feel that the foundations of mathematics remain unclear a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Woman Teaching Geometry
A woman is an adult female human. Prior to adulthood, a female human is referred to as a girl (a female child or adolescent). The plural ''women'' is sometimes used in certain phrases such as "women's rights" to denote female humans regardless of age. Typically, women inherit a pair of X chromosomes, one from each parent, and are capable of pregnancy and giving birth from puberty until menopause. More generally, sex differentiation of the female fetus is governed by the lack of a present, or functioning, SRY-gene on either one of the respective sex chromosomes. Female anatomy is distinguished from male anatomy by the female reproductive system, which includes the ovaries, fallopian tubes, uterus, vagina, and vulva. A fully developed woman generally has a wider pelvis, broader hips, and larger breasts than an adult man. Women have significantly less facial and other body hair, have a higher body fat composition, and are on average shorter and less muscular than men. Througho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A-Level
The A-Level (Advanced Level) is a subject-based qualification conferred as part of the General Certificate of Education, as well as a school leaving qualification offered by the educational bodies in the United Kingdom and the educational authorities of British Crown dependencies to students completing secondary or pre-university education. They were introduced in England and Wales in 1951 to replace the Higher School Certificate. A number of Commonwealth countries have developed qualifications with the same name as and a similar format to the British A Levels. Obtaining an A Level, or equivalent qualifications, is generally required across the board for university entrance, with universities granting offers based on grades achieved. Particularly in Singapore, its A level examinations have been regarded as being much more challenging than the United Kingdom, with most universities offering lower entry qualifications with regard to grades achieved on a Singaporean A level cer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Informal Mathematics
Informal mathematics, also called naïve mathematics, has historically been the predominant form of mathematics at most times and in most cultures, and is the subject of modern ethno-cultural studies of mathematics. The philosopher Imre Lakatos in his ''Proofs and Refutations'' aimed to sharpen the formulation of informal mathematics, by reconstructing its role in nineteenth century mathematical debates and concept formation, opposing the predominant assumptions of mathematical formalism.Imre Lakatos, ''Proofs and Refutations'' (1976), especially the Introduction. Informality may not discern between statements given by '' inductive reasoning'' (as in approximations which are deemed "correct" merely because they are useful), and statements derived by ''deductive reasoning''. Terminology ''Informal mathematics'' means any informal mathematical practices, as used in everyday life, or by aboriginal or ancient peoples, without historical or geographical limitation. Modern mathematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Foundations Of Mathematics
Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics. In this latter sense, the distinction between foundations of mathematics and philosophy of mathematics turns out to be quite vague. Foundations of mathematics can be conceived as the study of the basic mathematical concepts (set, function, geometrical figure, number, etc.) and how they form hierarchies of more complex structures and concepts, especially the fundamentally important structures that form the language of mathematics (formulas, theories and their models giving a meaning to formulas, definitions, proofs, algorithms, etc.) also called metamathematical concepts, with an eye to the philosophical aspects and the unity of mathematics. The search for foundations of mathematics is a central question of the philosophy of mathe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Practice
Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of abstract objects that consist of either abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to prove properties of objects, a ''proof'' consisting of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Mathematical Olympiad
The International Mathematical Olympiad (IMO) is a mathematical olympiad for pre-university students, and is the oldest of the International Science Olympiads. The first IMO was held in Romania in 1959. It has since been held annually, except in 1980. More than 100 countries, representing over 90% of the world's population, send teams of up to six students, plus one team leader, one deputy leader, and observers. The content ranges from extremely difficult algebra and pre-calculus problems to problems on branches of mathematics not conventionally covered in secondary or high school and often not at university level either, such as projective and complex geometry, functional equations, combinatorics, and well-grounded number theory, of which extensive knowledge of theorems is required. Calculus, though allowed in solutions, is never required, as there is a principle that anyone with a basic understanding of mathematics should understand the problems, even if the solutions req ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
British Mathematical Olympiad
The British Mathematical Olympiad (BMO) forms part of the selection process for the UK International Mathematical Olympiad team and for other international maths competitions, including the European Girls' Mathematical Olympiad, the Romanian Master of Mathematics and Sciences, and the Balkan Mathematical Olympiad. It is organised by the British Mathematical Olympiad Subtrust, which is part of the United Kingdom Mathematics Trust. There are two rounds, the BMO1 and the BMO2.http://www.bmoc.maths.org/home/bmo.shtml, BMO website, list of papers BMO Round 1 The first round of the BMO is held in November each year, and from 2006 is an open entry competition. The qualification to BMO Round 1 is through the Senior Mathematical Challenge. Students who do not make the qualification through the Senior Mathematical Challenge may be entered at the discretion of their school for a fee of £40. The paper lasts 3½ hours, and consists of six questions (from 2005), each worth 10 marks. The exa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doctoral
A doctorate (from Latin ''docere'', "to teach"), doctor's degree (from Latin ''doctor'', "teacher"), or doctoral degree is an academic degree awarded by universities and some other educational institutions, derived from the ancient formalism '' licentia docendi'' ("licence to teach"). In most countries, a research degree qualifies the holder to teach at university level in the degree's field or work in a specific profession. There are a number of doctoral degrees; the most common is the Doctor of Philosophy (PhD), awarded in many different fields, ranging from the humanities to scientific disciplines. In the United States and some other countries, there are also some types of technical or professional degrees that include "doctor" in their name and are classified as a doctorate in some of those countries. Professional doctorates historically came about to meet the needs of practitioners in a variety of disciplines. Many universities also award honorary doctorates to individuals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Post-graduate
Postgraduate or graduate education refers to academic or professional degrees, certificates, diplomas, or other qualifications pursued by post-secondary students who have earned an undergraduate (bachelor's) degree. The organization and structure of postgraduate education varies in different countries, as well as in different institutions within countries. While the term "graduate school" or "grad school" is typically used in North America, "postgraduate" is often used in countries such as ( Australia, Bangladesh, India, Ireland, New Zealand, Pakistan, South Africa, and the UK). Graduate degrees can include master's degrees, doctoral degrees, and other qualifications such as graduate certificates and professional degrees. A distinction is typically made between graduate schools (where courses of study vary in the degree to which they provide training for a particular profession) and professional schools, which can include medical school, law school, business school, and oth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Textbook
A textbook is a book containing a comprehensive compilation of content in a branch of study with the intention of explaining it. Textbooks are produced to meet the needs of educators, usually at educational institutions. Schoolbooks are textbooks and other books used in schools. Today, many textbooks are published in both print and digital formats. History The history of textbooks dates back to ancient civilizations. For example, Ancient Greeks wrote educational texts. The modern textbook has its roots in the mass production made possible by the printing press. Johannes Gutenberg himself may have printed editions of ''Ars Minor'', a schoolbook on Latin grammar by Aelius Donatus. Early textbooks were used by tutors and teachers (e.g. alphabet books), as well as by individuals who taught themselves. The Greek philosopher Socrates lamented the loss of knowledge because the media of transmission were changing. Before the invention of the Greek alphabet 2,500 years ago, knowledge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Undergraduate
Undergraduate education is education conducted after secondary education and before postgraduate education. It typically includes all postsecondary programs up to the level of a bachelor's degree. For example, in the United States, an entry-level university student is known as an ''undergraduate'', while students of higher degrees are known as '' graduate students''. Upon completion of a number of required and elective courses as part of an undergraduate program, the student would earn the corresponding degree. (In some regions, individual "courses" and the "program" collection are given other terms, such as "units" and "course", respectively.) In some other educational systems, undergraduate education is postsecondary education up to the level of a master's degree; this is the case for some science courses in Britain and some medicine courses in Europe. Programs Africa Nigerian system In Nigeria, undergraduate degrees (excluding Medicine, Medical Laboratory Science, Nursing, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General Certificate Of Secondary Education
The General Certificate of Secondary Education (GCSE) is an academic qualification in a particular subject, taken in England, Wales, and Northern Ireland. State schools in Scotland use the Scottish Qualifications Certificate instead. Private schools in Scotland may choose to use GCSEs from England. Each GCSE qualification is offered in a specific school subject (English literature, English language, mathematics, science, history, geography, art and design, design and technology, business studies, classical civilisation, drama, music, foreign languages, etc). The Department for Education has drawn up a list of preferred subjects known as the English Baccalaureate for England on the results in eight GCSEs including English, mathematics, the sciences (physics, chemistry, biology, computer science), history, geography, and an ancient or modern foreign language. Studies for GCSE examinations take place over a period of two or three academic years (depending upon the subject, scho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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