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Topic: The Problems of Mathematics

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	Math Forum: Famous Problems in the History of Mathematics
		Mathematics has been vital to the development of civilization; from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy.
		Included are problems that are suitable for middle school and high school math students, with links to solutions, as well as links to mathematicians' biographies and other math history sites.
		The Problem of Points - An age-old gambling problem led to the development of probability by French mathematicians Pascal and Fermat in the seventeenth century.
	mathforum.org /isaac/mathhist.html (370 words)

	Hilbert's problems - Wikipedia, the free encyclopedia
		Hilbert's problems are a list of 23 problems in mathematics put forth by German mathematician David Hilbert at the Paris conference of the International Congress of Mathematicians in 1900.
		The problems were all unsolved at the time, and several of them turned out to be very influential for 20th century mathematics.
		The "24th problem" (in proof theory, on a criterion for simplicity and general methods) was rediscovered in Hilbert's original manuscript notes by German historian Rüdiger Thiele in 2000.
	en.wikipedia.org /wiki/Hilbert's_problems (1690 words)

	Connected Mathematics (Site not responding. Last check: 2007-11-02)
		If students spend a majority of their mathematics time practicing paper-and-pencil computations, they come to believe that mathematics is about calculating answers to arithmetic problems as quickly as possible.
		On the other hand, if the purpose of studying mathematics is to understand concepts and procedures and be able to solve a variety of problems, then students should spend most of their mathematics time solving problems.
		If time is spent solving problems, reflecting on solution methods, examining why the methods work, comparing methods, and relating methods to those used in previous situations, then students are likely to build more robust understandings and strategies and to view mathematics as a valuable tool for making sense of and solving interesting problems.
	www.mth.msu.edu /cmp/StudentMaterials/ProblemCentered.htm (844 words)

	Unsolved problems in mathematics - Wikipedia, the free encyclopedia
		Unsolved problems in : Note: Use the unsolved tag: {{unsolvedFX}}, where "F" is any field in the sciences: and "X" is a concise "explanation" with or without links.
		This article describes some currently unsolved problems in mathematics.
		List of links to unsolved problems in mathematics, prizes and research.
	en.wikipedia.org /wiki/Unsolved_problems_in_mathematics (186 words)

	Learning Disabilities OnLine: LD In-Depth: Mathematics and Dyslexia (Site not responding. Last check: 2007-11-02)
		Mathematical terms such as numerator and denominator, prime numbers and prime factors, and carrying and borrowing may also be problematic.
		Additionally, the instructor needs to have an understanding of the mathematics curriculum; the ability to use a variety of instructional techniques that are simultaneously multisensory and which provide for explicit instruction that is systematic, cumulative, diagnostic, and both synthetic and analytical- as well as a knowledge of current research in mathematical instruction.
		This requires an understanding of mathematical knowledge, both conceptual (relationships constructed internally and connected to already existing ideas) and procedural (knowledge of symbols used to represent mathematics, and the rules and procedures that are used to carry out mathematical tasks).
	www.ldonline.org /ld_indepth/math_skills/ida_math_fall98.html (1459 words)

	Focus on Student-Centered Learning: Technology in Mathematics Instruction
		Mathematics teachers were early users and champions of technology because much of the initial software that was available to schools assisted in the teaching of basic mathematics skills.
		Mathematical power is defined as "an individual's abilities to explore, conjecture, and reason logically, as well as the ability to use a variety of mathematical methods effectively to solve non-routine problems.
		This is based on the recognition of mathematics as more than a collection of concepts and skills to be mastered; it includes methods of investigating and reasoning, means of communication, and notions of context.
	www.ncrel.org /tplan/handbook/foc6.htm (313 words)

	Geometric and algebraic problems (from history of mathematics) -- Encyclopædia Britannica
		The outstanding mathematical event of the year, of the decade, and perhaps even of the century was the announcement in June 1993 of a proof for Fermat's last theorem by Andrew Wiles (see BIOGRAPHIES)--a quiet, rather diffident Englishman working at Princeton University.
		Because mathematics has served as a model for rational inquiry in the West and is used extensively in the sciences, foundational studies have far-reaching consequences for the reliability and extensibility of rational...
		Mathematics is often defined as the study of quantity, magnitude, and relations of numbers or symbols.
	www.britannica.com /eb/article-65971 (849 words)

	Careers in Mathematics
		Mathematics is among the most fascinating of all intellectual disciplines, the purest of all art forms, and the most challenging of games.
		The study of mathematics is not only exciting, but important: mathematicians have an opportunity to make a lasting contribution to society by helping to solve problems in such diverse fields as medicine, management, economics.
		Applied mathematics draws heavily on analysis, differential equations, and linear algebra to solve problems in statics (making sure the beams are strong enough to hold up the bridge), mechanics (describing how a pendulum moves), electricity and magnetism (calculating the magnetic field induced by an electric current), and many other areas.
	math.usask.ca /document/netinfo/careers.html (4678 words)

	International Mathematics Olympiad
		The Bay Area Mathematical Olympiad (BAMO) is a contest for high school students sponsored jointly by the Mathematical Sciences Research Institute (MSRI), the American Institute of Mathematics (AIM), the University of California at Berkeley (UCB), and the University of San Francisco (USF).
		The Olimpíada Matemática Argentina (OMA) is the Argentinian Mathematics Olympiad.
		The goal of the Saturday Mathematics School is to teach students basic methods of solving math problems, concentrating (also) on research-type problems within the scope of grades 7-12.
	olympiads.win.tue.nl /imo (2157 words)

	Mathematics Problems
		The fact that these numbers are so close is one of the many amazing coincidences that arise in mathematics.
		His proof is a masterpiece and ranks as one of the finest proofs in mathematics.
		There are other proofs which are also interesting in their own right, and Proofs From The Book gives six of them.
	dspace.dial.pipex.com /town/way/po28/maths/problems.htm (301 words)

	History of Mathematics Home Page (Site not responding. Last check: 2007-11-02)
		Later some of this mathematics was translated into Latin and became the mathematics of Western Europe.
		There are other places in the world that developed significant mathematics, such as China, southern India, and Japan, and they are interesting to study, but the mathematics of the other regions have not had much influence on current international mathematics.
		There is, of course, much mathematics being done these and other regions, but it is not the traditional math of the regions, but international mathematics.
	aleph0.clarku.edu /~djoyce/mathhist/mathhist.html (278 words)

	Mathematics - Wikiquote
		W.S. Anglin, in Mathematics and History, elucidating the symmetry between the creative and logical aspects of mathematics.
		"Mathematics is not yet capable of coping with the naïveté of the mathematician himself." --Abraham Kaplan
		"Mathematics, rightly viewed, possesses not only truth, but supreme beauty —a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.
	en.wikiquote.org /wiki/Mathematics (1189 words)

	POP Mathematics
		Our aim is to present Mathematics to as wide as possible an audience, and to give an impression for mathematics of the objects of study of mathematics, the methodology of mathematics, the successes and applications of mathematics, the enjoyment of mathematics, and the wider context of mathematics.
		This archive is part of the Mathematical MacTutor system developed at the School of Mathematical and Computational Sciences of the University of St Andrews for learning and experimenting with mathematics.
		Mathematics Awareness Week is held in late April each year to increase public understanding of and appreciation for mathematics.
	archives.math.utk.edu /popmath.html (2425 words)

	Alex Lopez-Ortiz' Home Page
		We revisited algorithms for set operations and proposed an adaptive algorithm and shows that its running time is within a constant factor of optimal with respect to a natural measure of the difficulty of an instance.
		Consider the problem of scheduling airplanes and gates in an airport.
		A set of heuristics dealing with these types of problems have been proposed within the field of Artificial Intelligence, where it is known as constraint programming.
	db.uwaterloo.ca /~alopez-o (831 words)

	Math Forum: Famous Problems in the History of Mathematics
		As a result, the history of mathematics has become an important study; hundreds of books, papers, and web pages have addressed the subject in a variety of different ways.
		The purpose of this site is to present a small portion of the history of mathematics through an investigation of some of the great problems that have inspired mathematicians throughout the ages.
		Famous Paradoxes - In the history of mathematical thought, several paradoxes have challenged the notion that mathematics is a self-consistent system of knowledge.
	www.mathforum.org /isaac/mathhist.html (370 words)

	Focus on Learning Problems in Mathematics: Trends in the degree of importance assigned to the NCTM's Standards by ... (Site not responding. Last check: 2007-11-02)
		Eggleton, T.J. Evolution of a mathematical philosophy: the story of one secondary mathematics preservice teacher.
		The use of concept mapping in qualitative research: Multiple case study in mathematics education.
		Mathematics education reform and mathematics education research: Opportunities, obstacles, and obligations.
	www.findarticles.com /p/articles/mi_m0NVC/is_2_24/ai_93211023/pg_6 (756 words)

	Wolfram Research, Inc.
		Twenty-one girls and twenty-one boys took part in a mathematical contest.
		For each girl and each boy, at least one problem was solved by both of them.
		Prove that there was a problem that was solved by at least three girls and at least three boys.
	imo.wolfram.com /problemset (186 words)

	nrich.maths.org::Mathematics Enrichment::NRICH Home Page
		Welcome to the NRICH website where the mathematical theme this month is Scale.
		Certainly the problems on NRICH this month focus on scale in terms of both these aspects.
		NRICH is part of the family of activities in the Millennium Mathematics Project, which also includes the Plus and Motivate sites.
	www.nrich.maths.org.uk /public/index.php (405 words)

	86.06.03: Mathematics:Problems on Coal and Energy
		Energy Problems It is not known when or by whom coal was first used.
		Measure the length of each side of the block that you used in problem 2 by using your bicycle and compare with the answers you obtained in problem 2.
		The power plant burns the coal described in the proceeding problem of a rate of 35 metric tons per hour, and it is operated 7800 hours per year.
	www.cis.yale.edu /ynhti/curriculum/units/1986/6/86.06.03.x.html (5626 words)

	Saturday Mathematics School, (Site not responding. Last check: 2007-11-02)
		The goal of the Saturday Math School is to teach students basic methods of solving math problems.
		We think that although olympiads are important in studying mathematics, a much more important thing is research.
		If you are not a member of the School but have a solution of one of the research problems, please send e-mail with your solution to the director.
	www.math.unl.edu /~msapir/school (211 words)

	Mathematics and Statistics Solutions
		This is your one stop shop to virtually any mathematic or science related problems you may have.
		Mathematics-Statistics-Solutions.com was designed by scholars who understand how difficult it is to learn mathematics, statistics and natural science when a teacher or professor cannot, or is unwilling to clearly explain the subject he/she is teaching.
		With this site you can simply send us your mathematical, statistical, financial or scientific assignments and our experts will solve the problems giving you the correct answers and also showing you all the work so you can see how they are done.
	www.mathematics-statistics-solutions.com (444 words)

	Hilbert’s Problems (PRIME) (Site not responding. Last check: 2007-11-02)
		eciding which outstanding problems in mathematics are the most important is to decide the course of mathematics’ future development.
		This problem was solved (in the affirmative) independently by Gelfond (1934) and Schneider (1935).
		This “decidability” problem is kin to the larger problem pursued by the logicist program of decidability of theories in general.
	www.mathacademy.com /pr/prime/articles/hilbert_prob (627 words)

	Amazon.ca: Books: Berkeley Problems in Mathematics (Site not responding. Last check: 2007-11-02)
		It is an ideal means for students to strengthen their foundation in basic mathematics and to prepare for graduate studies.
		The problem with the contents of this book is that they are mostly standard, or require a simple trick.
		Many problems also require quite a bit of knowledge in higher mathematics, which may be good if you want to test that.
	www.amazon.ca /exec/obidos/ASIN/0387008926 (522 words)

	Amazon.com: Berkeley Problems in Mathematics: Books: Paulo N. de Souza,Jorge-Nuno Silva,Paulo Ney de Souza (Site not responding. Last check: 2007-11-02)
		Problems in Mathematical Analysis II (Student Mathematical Library, Vol.
		It is an ideal means for students to strengthen their foundation in basic mathematics and to prepare for graduate studies.
		The problem with the contents of this book is that they are mostly standard, or require a simple trick.
	www.amazon.com /Berkeley-Problems-Mathematics-Paulo-Souza/dp/0387008926 (1208 words)

	Mathematics Archives - K12 Internet Sites
		The Hub is an Internetworked resource for mathematics and science education funded by the Eisenhower Regional Consortia and operated by TERC on behalf of the Regional Alliance for Mathematics and Science Education Reform.
		It is a facility at the University of Regina Department of Mathematics and Statistics and is maintained by mathematics and education students and faculty.
		Mathematics in Context (MiC) is an NSF-funded, comprehensive middle-school mathematics curriculum for grades 5-8 that reflects the philosophy and pedagogy of the NCTM standards.
	archives.math.utk.edu /k12.html (9883 words)

	Elementary Problem of the Week (Site not responding. Last check: 2007-11-02)
		The website also offers good advice to a teacher or parent for each problem.
		Good problems in the archive but no new problems in a long while.
		Problems for all age groups, with a link to the most current problem.
	www.wits.ac.za /ssproule/elem_pow.html (62 words)

	FOCUS--The RCML Quarterly Journal
		FOCUS--On Learning Problems in Mathematics is an inter-disciplinary journal, edited jointly by the Research Council on Mathematics Learning (RCML) and the Center for Teaching/Learning of Mathematics (CT/LM).
		The objective of FOCUS is to make available the current research, methods of identification, diagnosis, and remediation of learning problems in mathematics.
		Contributions from the fields of education, psychology, mathematics and medicine having the potential for impact on classroom or clinical practice are valued.
	www.unlv.edu /RCML/focus.html (300 words)

	Ole Miss Problem of the Week Contests (Site not responding. Last check: 2007-11-02)
		The Problem of the Week is an educational web site that originates at the University of Mississippi.
		All the prizes are generously donated by CASIO electronics.
		All contest winners are chosen randomly from the pool of contestants that successfully solve that week's problem.
	www.olemiss.edu /mathed/problem.htm (43 words)

	Egyptian mathematics
		But although there is a large body of papyrus literature describing their achievements in medicine, there is no records of how they reached their mathematical conclusions.
		The conventions for reading and writing numbers is quite simple; the higher number is always written in front of the lower number and where there is more than one row of numbers the reader should start at the top.
		Math Problems, which illustrate the benefit of using algebra.
	www.eyelid.co.uk /numbers.htm (358 words)

	Millennium Prize Problems
		The Board of Directors of CMI designated a $7 million prize fund for the solution to these problems, with $1 million allocated to each.
		During the Millennium Meeting held on May 24, 2000 at the Collège de France, Timothy Gowers presented a lecture entitled The Importance of Mathematics, aimed for the general public, while John Tate and Michael Atiyah spoke on the problems.
		The rules for the award of the prize have the endorsement of the CMI Scientific Advisory Board and the approval of the Directors.
	www.claymath.org /millennium (256 words)

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