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Ewing, J. H.; And Others – American Mathematical Monthly, 1976
Ten recent results in pure mathematics are described, covering the continuum hypothesis, Diophantine equations, simple groups, resolution of singularities, Weil conjectures, Lie groups, Poincare conjecture, exotic spheres, differential equations, and the index theorem. Proofs are omitted, but references are provided. (DT)
Descriptors: Algebra, Calculus, College Mathematics, History
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Nardi, Elena – Educational Studies in Mathematics, 2000
Identifies and explores the difficulties in the novice mathematician's encounter with mathematical abstraction. Observes 20 first-year mathematics undergraduates and extracts sets of episodes from the transcripts of the tutorials and interviews within five topics in pure mathematics. Discusses issues related to the learning of one mathematical…
Descriptors: Abstract Reasoning, College Students, Higher Education, Mathematics Education
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Flesher, Tatyana; Holder, Eleanor – Mathematics and Computer Education, 2007
One of the main problems in undergraduate research in pure mathematics is that of determining a problem that is, at once, interesting to and capable of solution by a student who has completed only the calculus sequence. It is also desirable that the problem should present something new, since novelty and originality greatly increase the enthusiasm…
Descriptors: Computer Software, Graphs, Calculus, Algebra
Turner, Nura Dorothea Rains, Ed. – 1971
The essays in this booklet have been written by persons who had ranked in the top one percent of the 1958-60 Upstate New York Mathematical Association of America Contests. Personal accounts are given of the role of mathematics in the authors' education and career. The careers described include applied mathematics, computer research and programing,…
Descriptors: Accounting, Biology, Careers, Computers
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Fischer, Roland – For the Learning of Mathematics, 1992
Discusses the impact that the relationship between people and mathematics could have on the development of pure and applied mathematics. Argues for (1) a growing interest in philosophy, history and sociology of science; (2) new models in educational and psychological research; and (3) a growing awareness of the human factor in technology,…
Descriptors: Computer Uses in Education, Constructivism (Learning), Educational Trends, Elementary Secondary Education
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Lo, Bruce W. N. – Australian Mathematics Teacher, 1983
As a way to dispel negative feelings toward mathematics, a variety of quotations are given. They are categorized by: what mathematics is, mathematicians, mathematics and other disciplines, different areas of mathematics, mathematics and humor, applications of mathematics, and pure versus applied mathematics. (MNS)
Descriptors: Educational Philosophy, Mathematical Applications, Mathematicians, Mathematics Education
Olesen, Mogens Noergaard – Forum on Public Policy Online, 2010
In the history of mankind three important philosophical and scientific revolutions have taken place. The first of these revolutions was the mathematical-axiomatic revolution in ancient Greece, when the philosophers from Thales of Miletus to Archimedes built up the abstract deductive method used in pure mathematics. The second took place in the…
Descriptors: High Schools, Scientific Research, Educational Principles, Educational Change
Knoll, Eva; Ernest, Paul; Morgan, Simon – International Group for the Psychology of Mathematics Education, 2004
This paper presents the early results of an experiment involving a class of elementary student teachers within the context of their mathematics preparation. The motivation of the exercise centered on giving them an experience with mathematical research at their own level and ascertaining its impact on their attitudes and beliefs. The students…
Descriptors: Research Tools, Mathematics Instruction, Student Teachers, Teacher Education
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Hilton, Peter – Mathematics Teacher, 1984
Hilton describes the team of cryptanalysts who tried to decipher German and Japanese codes during the Second World War. The work of Turing, essentially developing the computer, is reported, as well as inferences about pure and applied mathematics. (MNS)
Descriptors: Biographies, Computers, Mathematical Applications, Mathematicians
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Prevot, K. J. – International Journal of Mathematical Education in Science & Technology, 2006
Offering mathematics majors the opportunity to engage in current, real-world applications can be an important enhancement to their undergraduate course curriculum. Instead of focusing on the traditional topic areas in pure and/or applied mathematics, one may structure a seminar course for senior mathematics majors by concentrating on a specific…
Descriptors: Majors (Students), College Mathematics, Seminars, Calculus
Bell, Max S., Ed. – 1967
This is a collection of articles dealing with mathematical applications for use by high school teachers and students. The articles are intended to illustrate several themes: (1) how mathematics is applied via construction of mathematical models; (2) the various types of activities in applied mathematics; (3) the role of pure mathematics in applied…
Descriptors: Curriculum, Instruction, Instructional Materials, Mathematical Applications
Australian Early Childhood Association, Inc., Watson. – 1981
Autobiographical sketches of four Australians living with physical handicaps are presented in this Australian early childhood resource booklet. Life experiences in school and out are reported by a blind man, a young woman who was brain damaged due to injuries in an automobile accident, a mother of a child with spina bifida, and a Doctor of…
Descriptors: Adults, Autobiographies, Coping, Disabilities
Blanford, Doris K.; Thornton, James E., Jr. – 1971
This guidebook specifies minimum course content covering number systems and bases, rational numbers and operations with rationals, and solving simple open sentences. Course goals are stated, then performance objectives, a course outline, references, and suggested teaching strategies are listed for each topic covered. Posttest items and a list of…
Descriptors: Behavioral Objectives, Curriculum, Instruction, Mathematics Education
Blanford, Doris K.; Thornton, James E., Jr. – 1972
This is the first in a series of three guidebooks on minimum course content for gifted grade seven students who will begin algebra in grade eight. The topics covered include integers, sets, number properties, open sentences, and graphing; concepts are stressed. Overall course goals are specified; a course outline, performance objectives, suggested…
Descriptors: Behavioral Objectives, Curriculum, Grade 7, Graphs
McClellan, Kathryn T. – 1984
Why mathematics should be learned is discussed. Its role as an important active force in the development of our civilization, and as the most useful subject taught in our schools, next to English, is noted. The primary objective of all mathematics work is to help man study nature, and some practical achievements of this connection are noted.…
Descriptors: Art, Cognitive Processes, Educational Philosophy, Engineering
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