| INSPIRATION. Video title lettering for Math Magic, a video plus book course by human calculator and math evangelist Scott Flansburg. STORY. I first met Scott in 1996 when we were both presenting at the annual MathCounts award ceremony. MathCounts is a national mathematics competition for middle school students that culminates in an event where every state sends four students and adult chaperones to compete in a national playoff. Wanting to impress Scott, I wrote his name so it inverted into "The Human Calculator." The animation above morphs the digits 0 through 9 into the title. It appears at the beginning and end of the video. Originally I used the numbers 1 through 10, which is more familiar to most people, but Scott is insistent that the proper way to think about counting is to focus on the ten digits 0 through 9, so I redid it to match his wishes. The lettering style is based on medieval calligraphy, which is appropriate for the theme of magic and wizardry. The morphs of the ten numbers start in rapid sequence with considerable overlap, to create an effect that makes visual sense but is impossible to fully comprehend. |
Tuesday, September 8, 2009
Math Magic
What is MathMagic?
MathMagic is a K-12 telecommunications project developed in El Paso, Texas by Alan A. Hodson. It provides strong motivation for students to use computer technology while increasing problem-solving strategies and communications skills. MathMagic posts challenges in each of four categories (k-3, 4-6, 7-9 and 10-12) to trigger each registered team to pair up with another team and engage in a problem-solving dialog. When an agreement has been reached, one solution is posted for every pair.
Return to Mathmagic Main Page
MathMagic has received wide ideological acceptance by hundreds of past FidoNet users (spearheaded by Carol Hooper), because it addresses most of the National Council of Teachers of Mathematics standards. A modified format expanded into the Internet and has been available via regular e-mail or via the World Wide Web (WWW) since 1993.
Who can participate?
K-12 teachers and students, but higher education teachers, librarians, technology coordinators, computer teachers, and even home-schoolers are joining to act as facilitators.
What is needed?
Any teacher with access to electronic mail via the Internet can participate. AllInternet Service Providers (AOL, Compuserve, FlashNet, PrimeNet, etc.) now offer e-mail gateways and other Internet services. MathMagic is best suited to schools that use computers with modems and/or have direct Internet access.In some areas, a local Bulletin Board System (BBS) or a Net user (such as a parent with net access) may have to act as a go-between. Please ask about special arrangements.
Return to Mathmagic Main Page
Sunday, September 6, 2009
Math Division Tricks 1.0
With Math Division Tricks enter a number, and find out if it can be divided by a number that comes between two and twelve. In addition learn the division rules from two to twelve.Math Division Tricks will allow you to know about numbers and division rules.
CNET Editor's Note: The "Download Now" link directs you to the iTunes App Store, where you must continue the download process. You must have iTunes installed in order to open the link, and you must have an active iTunes account to download the application. This download may not be available in some countries.
Mental Math Tricks
Have you always wanted to be lightning-fast at math? Did you wish you can do fast math in your head?
Have you wondered why some people have an almost unnatural ability to solve math problems in their heads faster than you can do them on a calculator?
The truth is, anybody can learn how to calculate very quickly with just a few math tricks. The techniques do not take long to lean, and with just a little practice, you can become a seemingly mathematical wizard!
These math tricks are taught to you very clearly in “Fun With Figures”. You can quickly learn these tricks and impress your family, friends, and coworkers:
- How to multiply any 2-digit numbers together in your head within seconds!
- The magic phrase you can use to instantly check your change.
- How to calculate naturally – from left to right!
- How to double-check your bills by using a single number.
- The easiest method ever for dealing with fractions!
- A brand new approach to multiplication.
- 11 little words to instantly overcome the most-feared mental math sum of them all: long division.
These techniques are for everybody – especially kids!
The methods taught in this book are FUN! And they will inspire a love for math in kids which is important in order for them to do well in their studies of the sciences.
Beat the Calculator - Squaring
Squaring a 2-digit number
- Take a 2-digit number beginning with 1.
- Square the second digit
(keep the carry) _ _ X - Multiply the second digit by 2 and
add the carry (keep the carry) _ X _ - The first digit is one
(plus the carry) X _ _
Example:
- If the number is 16, square the second digit:
6 × 6 = 36 _ _ 6 - Multiply the second digit by 2 and
add the carry: 2 × 6 + 3 = 15 _ 5 _ - The first digit is one plus the carry:
1 + 1 = 2 2 _ _ - So 16 × 16 = 256.
See the pattern?
- For 19 × 19, square the second digit:
9 × 9 = 81 _ _ 1 - Multiply the second digit by 2 and
add the carry: 2 × 9 + 8 = 26 _ 6 _ - The first digit is one plus the carry:
1 + 2 = 3 3 _ _ - So 19 × 19 = 361.
Saturday, September 5, 2009
Murderous Maths London Covent Garden
The author of the Murderous Maths books demonstrates a few odd tricks filmed in London's Covent Garden
Wednesday, August 26, 2009
Mathematics
Donate Now
A vertical jet is deflected into a horizontal sheet by a horizontal impactor.
Surprising geometry emerges in the study of fluid jets. In this image, a vertical jet is deflected into a horizontal sheet by a horizontal impactor. At the sheet's edge, fluid flows outward along bounding rims that collide to create fluid chains. (Photo courtesty A.E. Hasha and J.W.M. Bush.)
An undergraduate degree in mathematics provides an excellent basis for graduate work in mathematics or computer science, or for employment in such mathematics-related fields as systems analysis, operations research, or actuarial science.
Because the career objectives of undergraduate mathematics majors are so diverse, each undergraduate's program is individually arranged through collaboration between the student and his or her faculty advisor. In general, students are encouraged to explore the various branches of mathematics, both pure and applied.
Undergraduates seriously interested in mathematics are encouraged to elect an upper-level mathematics seminar. This is normally done during the junior year or the first semester of the senior year. The experience gained from active participation in a seminar conducted by a research mathematician is particularly valuable for a student planning to pursue graduate work.
There are three undergraduate programs that lead to the degree Bachelor's of Science in Mathematics: a General Mathematics Option, an Applied Mathematics Option for those who wish to specialize in that aspect of mathematics, and a Theoretical Mathematics Option for those who expect to pursue graduate work in pure mathematics. A fourth undergraduate program leads to the degree Bachelor's of Science in Mathematics with Computer Science; it is intended for students seriously interested in theoretical computer science.
Department of Mathematics links
Visit the MIT Department of Mathematics home page at:
http://www-math.mit.edu/
Review the MIT Department of Mathematics curriculum at:
http://ocw.mit.edu/OcwWeb/web/resources/curriculum/index.htm#18
In addition to courses, supplementary mathematics resources are also available. Various MIT faculty are openly sharing these resources as a service to MIT OCW users. The resources include calculus textbooks by Professors Gilbert Strang and Daniel Kleitman.
http://ocw.mit.edu/OcwWeb/web/resources/supplemental/index.htm
A vertical jet is deflected into a horizontal sheet by a horizontal impactor.
Surprising geometry emerges in the study of fluid jets. In this image, a vertical jet is deflected into a horizontal sheet by a horizontal impactor. At the sheet's edge, fluid flows outward along bounding rims that collide to create fluid chains. (Photo courtesty A.E. Hasha and J.W.M. Bush.)
An undergraduate degree in mathematics provides an excellent basis for graduate work in mathematics or computer science, or for employment in such mathematics-related fields as systems analysis, operations research, or actuarial science.
Because the career objectives of undergraduate mathematics majors are so diverse, each undergraduate's program is individually arranged through collaboration between the student and his or her faculty advisor. In general, students are encouraged to explore the various branches of mathematics, both pure and applied.
Undergraduates seriously interested in mathematics are encouraged to elect an upper-level mathematics seminar. This is normally done during the junior year or the first semester of the senior year. The experience gained from active participation in a seminar conducted by a research mathematician is particularly valuable for a student planning to pursue graduate work.
There are three undergraduate programs that lead to the degree Bachelor's of Science in Mathematics: a General Mathematics Option, an Applied Mathematics Option for those who wish to specialize in that aspect of mathematics, and a Theoretical Mathematics Option for those who expect to pursue graduate work in pure mathematics. A fourth undergraduate program leads to the degree Bachelor's of Science in Mathematics with Computer Science; it is intended for students seriously interested in theoretical computer science.
Department of Mathematics links
Visit the MIT Department of Mathematics home page at:
http://www-math.mit.edu/
Review the MIT Department of Mathematics curriculum at:
http://ocw.mit.edu/OcwWeb/web/resources/curriculum/index.htm#18
In addition to courses, supplementary mathematics resources are also available. Various MIT faculty are openly sharing these resources as a service to MIT OCW users. The resources include calculus textbooks by Professors Gilbert Strang and Daniel Kleitman.
http://ocw.mit.edu/OcwWeb/web/resources/supplemental/index.htm
Notation, language, and rigor
Leonhard Euler
Main article: Mathematical notation
Most of the mathematical notation in use today was not invented until the 16th century.[21] Before that, mathematics was written out in words, a painstaking process that limited mathematical discovery.[22] In the 18th century, Euler was responsible for many of the notations in use today. Modern notation makes mathematics much easier for the professional, but beginners often find it daunting. It is extremely compressed: a few symbols contain a great deal of information. Like musical notation, modern mathematical notation has a strict syntax and encodes information that would be difficult to write in any other way.
Mathematical language can also be hard for beginners. Words such as or and only have more precise meanings than in everyday speech. Additionally, words such as open and field have been given specialized mathematical meanings. Mathematical jargon includes technical terms such as homeomorphism and integrable. But there is a reason for special notation and technical jargon: mathematics requires more precision than everyday speech. Mathematicians refer to this precision of language and logic as "rigor".
The infinity symbol ∞ in several typefaces.
Mathematical proof is fundamentally a matter of rigor. Mathematicians want their theorems to follow from axioms by means of systematic reasoning. This is to avoid mistaken "theorems", based on fallible intuitions, of which many instances have occurred in the history of the subject.[23] The level of rigor expected in mathematics has varied over time: the Greeks expected detailed arguments, but at the time of Isaac Newton the methods employed were less rigorous. Problems inherent in the definitions used by Newton would lead to a resurgence of careful analysis and formal proof in the 19th century. Today, mathematicians continue to argue among themselves about computer-assisted proofs. Since large computations are hard to verify, such proofs may not be sufficiently rigorous.[24]
Axioms in traditional thought were "self-evident truths", but that conception is problematic. At a formal level, an axiom is just a string of symbols, which has an intrinsic meaning only in the context of all derivable formulas of an axiomatic system. It was the goal of Hilbert's program to put all of mathematics on a firm axiomatic basis, but according to Gödel's incompleteness theorem every (sufficiently powerful) axiomatic system has undecidable formulas; and so a final axiomatization of mathematics is impossible. Nonetheless mathematics is often imagined to be (as far as its formal content) nothing but set theory in some axiomatization, in the sense that every mathematical statement or proof could be cast into formulas within set theory.[25]
Main article: Mathematical notation
Most of the mathematical notation in use today was not invented until the 16th century.[21] Before that, mathematics was written out in words, a painstaking process that limited mathematical discovery.[22] In the 18th century, Euler was responsible for many of the notations in use today. Modern notation makes mathematics much easier for the professional, but beginners often find it daunting. It is extremely compressed: a few symbols contain a great deal of information. Like musical notation, modern mathematical notation has a strict syntax and encodes information that would be difficult to write in any other way.
Mathematical language can also be hard for beginners. Words such as or and only have more precise meanings than in everyday speech. Additionally, words such as open and field have been given specialized mathematical meanings. Mathematical jargon includes technical terms such as homeomorphism and integrable. But there is a reason for special notation and technical jargon: mathematics requires more precision than everyday speech. Mathematicians refer to this precision of language and logic as "rigor".
The infinity symbol ∞ in several typefaces.
Mathematical proof is fundamentally a matter of rigor. Mathematicians want their theorems to follow from axioms by means of systematic reasoning. This is to avoid mistaken "theorems", based on fallible intuitions, of which many instances have occurred in the history of the subject.[23] The level of rigor expected in mathematics has varied over time: the Greeks expected detailed arguments, but at the time of Isaac Newton the methods employed were less rigorous. Problems inherent in the definitions used by Newton would lead to a resurgence of careful analysis and formal proof in the 19th century. Today, mathematicians continue to argue among themselves about computer-assisted proofs. Since large computations are hard to verify, such proofs may not be sufficiently rigorous.[24]
Axioms in traditional thought were "self-evident truths", but that conception is problematic. At a formal level, an axiom is just a string of symbols, which has an intrinsic meaning only in the context of all derivable formulas of an axiomatic system. It was the goal of Hilbert's program to put all of mathematics on a firm axiomatic basis, but according to Gödel's incompleteness theorem every (sufficiently powerful) axiomatic system has undecidable formulas; and so a final axiomatization of mathematics is impossible. Nonetheless mathematics is often imagined to be (as far as its formal content) nothing but set theory in some axiomatization, in the sense that every mathematical statement or proof could be cast into formulas within set theory.[25]
Fields of mathematics
An abacus, a simple calculating tool used since ancient times.
Mathematics can, broadly speaking, be subdivided into the study of quantity, structure, space, and change (i.e. arithmetic, algebra, geometry, and analysis). In addition to these main concerns, there are also subdivisions dedicated to exploring links from the heart of mathematics to other fields: to logic, to set theory (foundations), to the empirical mathematics of the various sciences (applied mathematics), and more recently to the rigorous study of uncertainty.
Quantity
The study of quantity starts with numbers, first the familiar natural numbers and integers ("whole numbers") and arithmetical operations on them, which are characterized in arithmetic. The deeper properties of integers are studied in number theory, from which come such popular results as Fermat's Last Theorem. Number theory also holds two widely-considered unsolved problems: the twin prime conjecture and Goldbach's conjecture.
As the number system is further developed, the integers are recognized as a subset of the rational numbers ("fractions"). These, in turn, are contained within the real numbers, which are used to represent continuous quantities. Real numbers are generalized to complex numbers. These are the first steps of a hierarchy of numbers that goes on to include quarternions and octonions. Consideration of the natural numbers also leads to the transfinite numbers, which formalize the concept of counting to infinity. Another area of study is size, which leads to the cardinal numbers and then to another conception of infinity: the aleph numbers, which allow meaningful comparison of the size of infinitely large sets.
Mathematics can, broadly speaking, be subdivided into the study of quantity, structure, space, and change (i.e. arithmetic, algebra, geometry, and analysis). In addition to these main concerns, there are also subdivisions dedicated to exploring links from the heart of mathematics to other fields: to logic, to set theory (foundations), to the empirical mathematics of the various sciences (applied mathematics), and more recently to the rigorous study of uncertainty.
Quantity
The study of quantity starts with numbers, first the familiar natural numbers and integers ("whole numbers") and arithmetical operations on them, which are characterized in arithmetic. The deeper properties of integers are studied in number theory, from which come such popular results as Fermat's Last Theorem. Number theory also holds two widely-considered unsolved problems: the twin prime conjecture and Goldbach's conjecture.
As the number system is further developed, the integers are recognized as a subset of the rational numbers ("fractions"). These, in turn, are contained within the real numbers, which are used to represent continuous quantities. Real numbers are generalized to complex numbers. These are the first steps of a hierarchy of numbers that goes on to include quarternions and octonions. Consideration of the natural numbers also leads to the transfinite numbers, which formalize the concept of counting to infinity. Another area of study is size, which leads to the cardinal numbers and then to another conception of infinity: the aleph numbers, which allow meaningful comparison of the size of infinitely large sets.
Mathematics as science
Carl Friedrich Gauss, himself known as the "prince of mathematicians",[26] referred to mathematics as "the Queen of the Sciences".
Carl Friedrich Gauss referred to mathematics as "the Queen of the Sciences".[27] In the original Latin Regina Scientiarum, as well as in German Königin der Wissenschaften, the word corresponding to science means (field of) knowledge. Indeed, this is also the original meaning in English, and there is no doubt that mathematics is in this sense a science. The specialization restricting the meaning to natural science is of later date. If one considers science to be strictly about the physical world, then mathematics, or at least pure mathematics, is not a science. Albert Einstein stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."[6]
Many philosophers believe that mathematics is not experimentally falsifiable, and thus not a science according to the definition of Karl Popper.[28] However, in the 1930s important work in mathematical logic showed that mathematics cannot be reduced to logic, and Karl Popper concluded that "most mathematical theories are, like those of physics and biology, hypothetico-deductive: pure mathematics therefore turns out to be much closer to the natural sciences whose hypotheses are conjectures, than it seemed even recently."[29] Other thinkers, notably Imre Lakatos, have applied a version of falsificationism to mathematics itself.
An alternative view is that certain scientific fields (such as theoretical physics) are mathematics with axioms that are intended to correspond to reality. In fact, the theoretical physicist, J. M. Ziman, proposed that science is public knowledge and thus includes mathematics.[30] In any case, mathematics shares much in common with many fields in the physical sciences, notably the exploration of the logical consequences of assumptions. Intuition and experimentation also play a role in the formulation of conjectures in both mathematics and the (other) sciences. Experimental mathematics continues to grow in importance within mathematics, and computation and simulation are playing an increasing role in both the sciences and mathematics, weakening the objection that mathematics does not use the scientific method.[citation needed] In his 2002 book A New Kind of Science, Stephen Wolfram argues that computational mathematics deserves to be explored empirically as a scientific field in its own right
The opinions of mathematicians on this matter are varied. Many mathematicians[who?] feel that to call their area a science is to downplay the importance of its aesthetic side, and its history in the traditional seven liberal arts; others[who?] feel that to ignore its connection to the sciences is to turn a blind eye to the fact that the interface between mathematics and its applications in science and enineering has driven much development in mathematics. One way this difference of viewpoint plays out is in the philosophical debate as to whether mathematics is created (as in art) or discovered (as in science). It is common to see universities divided into sections that include a division of Science and Mathematics, indicating that the fields are seen as being allied but that they do not coincide. In practice, mathematicians are typically grouped with scientists at the gross level but separated at finer levels. This is one of many issues considered in the philosophy of mathematics.[citation needed]
Mathematical awards are generally kept separate from their equivalents in science. The most prestigious award in mathematics is the Fields Medal,[31][32] established in 1936 and now awarded every 4 years. It is often considered the equivalent of science's Nobel Prizes. The Wolf Prize in Mathematics, instituted in 1978, recognizes lifetime achievement, and another major international award, the Abel Prize, was introduced in 2003. These are awarded for a particular body of work, which may be innovation, or resolution of an outstanding problem in an established field. A famous list of 23 such open problems, called "Hilbert's problems", was compiled in 1900 by German mathematician David Hilbert. This list achieved great celebrity among mathematicians, and at least nine of the problems have now been solved. A new list of seven important problems, titled the "Millennium Prize Problems", was published in 2000. Solution of each of these problems carries a $1 million reward, and only one (the Riemann hypothesis) is duplicated in Hilbert's problems.
Carl Friedrich Gauss referred to mathematics as "the Queen of the Sciences".[27] In the original Latin Regina Scientiarum, as well as in German Königin der Wissenschaften, the word corresponding to science means (field of) knowledge. Indeed, this is also the original meaning in English, and there is no doubt that mathematics is in this sense a science. The specialization restricting the meaning to natural science is of later date. If one considers science to be strictly about the physical world, then mathematics, or at least pure mathematics, is not a science. Albert Einstein stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."[6]
Many philosophers believe that mathematics is not experimentally falsifiable, and thus not a science according to the definition of Karl Popper.[28] However, in the 1930s important work in mathematical logic showed that mathematics cannot be reduced to logic, and Karl Popper concluded that "most mathematical theories are, like those of physics and biology, hypothetico-deductive: pure mathematics therefore turns out to be much closer to the natural sciences whose hypotheses are conjectures, than it seemed even recently."[29] Other thinkers, notably Imre Lakatos, have applied a version of falsificationism to mathematics itself.
An alternative view is that certain scientific fields (such as theoretical physics) are mathematics with axioms that are intended to correspond to reality. In fact, the theoretical physicist, J. M. Ziman, proposed that science is public knowledge and thus includes mathematics.[30] In any case, mathematics shares much in common with many fields in the physical sciences, notably the exploration of the logical consequences of assumptions. Intuition and experimentation also play a role in the formulation of conjectures in both mathematics and the (other) sciences. Experimental mathematics continues to grow in importance within mathematics, and computation and simulation are playing an increasing role in both the sciences and mathematics, weakening the objection that mathematics does not use the scientific method.[citation needed] In his 2002 book A New Kind of Science, Stephen Wolfram argues that computational mathematics deserves to be explored empirically as a scientific field in its own right
The opinions of mathematicians on this matter are varied. Many mathematicians[who?] feel that to call their area a science is to downplay the importance of its aesthetic side, and its history in the traditional seven liberal arts; others[who?] feel that to ignore its connection to the sciences is to turn a blind eye to the fact that the interface between mathematics and its applications in science and enineering has driven much development in mathematics. One way this difference of viewpoint plays out is in the philosophical debate as to whether mathematics is created (as in art) or discovered (as in science). It is common to see universities divided into sections that include a division of Science and Mathematics, indicating that the fields are seen as being allied but that they do not coincide. In practice, mathematicians are typically grouped with scientists at the gross level but separated at finer levels. This is one of many issues considered in the philosophy of mathematics.[citation needed]
Mathematical awards are generally kept separate from their equivalents in science. The most prestigious award in mathematics is the Fields Medal,[31][32] established in 1936 and now awarded every 4 years. It is often considered the equivalent of science's Nobel Prizes. The Wolf Prize in Mathematics, instituted in 1978, recognizes lifetime achievement, and another major international award, the Abel Prize, was introduced in 2003. These are awarded for a particular body of work, which may be innovation, or resolution of an outstanding problem in an established field. A famous list of 23 such open problems, called "Hilbert's problems", was compiled in 1900 by German mathematician David Hilbert. This list achieved great celebrity among mathematicians, and at least nine of the problems have now been solved. A new list of seven important problems, titled the "Millennium Prize Problems", was published in 2000. Solution of each of these problems carries a $1 million reward, and only one (the Riemann hypothesis) is duplicated in Hilbert's problems.
Monday, August 24, 2009
Applied mathematics
Applied mathematics considers the use of abstract mathematical tools in solving concrete problems in the sciences, business, and other areas.
Applied mathematics has significant overlap with the discipline of statistics, whose theory is formulated mathematically, especially with probability theory. Statisticians (working as part of a research project) "create data that makes sense" with random sampling and with randomized experiments; the design of a statistical sample or experiment specifies the analysis of the data (before the data be available). When reconsidering data from experiments and samples or when analyzing data from observational studies, statisticians "make sense of the data" using the art of modelling and the theory of inference – with model selection and estimation; the estimated models and consequential predictions should be tested on new data.[35]
Computational mathematics proposes and studies methods for solving mathematical problems that are typically too large for human numerical capacity. Numerical analysis studies methods for problems in analysis using ideas of functional analysis and techniques of approximation theory; numerical analysis includes the study of approximation and discretization broadly with special concern for rounding errors. Other areas of computational mathematics include computer algebra and symbolic computation.
Applied mathematics has significant overlap with the discipline of statistics, whose theory is formulated mathematically, especially with probability theory. Statisticians (working as part of a research project) "create data that makes sense" with random sampling and with randomized experiments; the design of a statistical sample or experiment specifies the analysis of the data (before the data be available). When reconsidering data from experiments and samples or when analyzing data from observational studies, statisticians "make sense of the data" using the art of modelling and the theory of inference – with model selection and estimation; the estimated models and consequential predictions should be tested on new data.[35]
Computational mathematics proposes and studies methods for solving mathematical problems that are typically too large for human numerical capacity. Numerical analysis studies methods for problems in analysis using ideas of functional analysis and techniques of approximation theory; numerical analysis includes the study of approximation and discretization broadly with special concern for rounding errors. Other areas of computational mathematics include computer algebra and symbolic computation.
Applied mathematics
Applied mathematics considers the use of abstract mathematical tools in solving concrete problems in the sciences, business, and other areas.
Applied mathematics has significant overlap with the discipline of statistics, whose theory is formulated mathematically, especially with probability theory. Statisticians (working as part of a research project) "create data that makes sense" with random sampling and with randomized experiments; the design of a statistical sample or experiment specifies the analysis of the data (before the data be available). When reconsidering data from experiments and samples or when analyzing data from observational studies, statisticians "make sense of the data" using the art of modelling and the theory of inference – with model selection and estimation; the estimated models and consequential predictions should be tested on new data.[35]
Computational mathematics proposes and studies methods for solving mathematical problems that are typically too large for human numerical capacity. Numerical analysis studies methods for problems in analysis using ideas of functional analysis and techniques of approximation theory; numerical analysis includes the study of approximation and discretization broadly with special concern for rounding errors. Other areas of computational mathematics include computer algebra and symbolic computation.
Applied mathematics has significant overlap with the discipline of statistics, whose theory is formulated mathematically, especially with probability theory. Statisticians (working as part of a research project) "create data that makes sense" with random sampling and with randomized experiments; the design of a statistical sample or experiment specifies the analysis of the data (before the data be available). When reconsidering data from experiments and samples or when analyzing data from observational studies, statisticians "make sense of the data" using the art of modelling and the theory of inference – with model selection and estimation; the estimated models and consequential predictions should be tested on new data.[35]
Computational mathematics proposes and studies methods for solving mathematical problems that are typically too large for human numerical capacity. Numerical analysis studies methods for problems in analysis using ideas of functional analysis and techniques of approximation theory; numerical analysis includes the study of approximation and discretization broadly with special concern for rounding errors. Other areas of computational mathematics include computer algebra and symbolic computation.
nspiration, pure and applied mathematics, and aesthetics
nspiration, pure and applied mathematics, and aesthetics
Main article: Mathematical beauty
Sir Isaac Newton (1643-1727), an inventor of infinitesimal calculus.
Mathematics arises from many different kinds of problems. At first these were found in commerce, land measurement and later astronomy; nowadays, all sciences suggest problems studied by mathematicians, and many problems arise within mathematics itself. For example, the physicist Richard Feynman invented the path integral formulation of quantum mechanics using a combination of mathematical reasoning and physical insight, and today's string theory, a still-developing scientific theory which attempts to unify the four fundamental forces of nature, continues to inspire new mathematics.[15] Some mathematics is only relevant in the area that inspired it, and is applied to solve further problems in that area. But often mathematics inspired by one area proves useful in many areas, and joins the general stock of mathematical concepts. A distinction is often made between pure mathematics and applied mathematics however pure mathematics topics often turn out to have applications e.g. number theory in cryptography. This remarkable fact that even the "purest" mathematics often turns out to have practical applications is what Eugene Wigner has called "the unreasonable effectiveness of mathematics."[16] As in most areas of study, the explosion of knowledge in the scientific age has led to specialization: there are now hundreds of specialized areas in mathematics and the latest Mathematics Subject Classification runs to 46 pages[17]. Several areas of applied mathematics have merged with related traditions outside of mathematics and become disciplines in their own right, including statistics, operations research, and computer science.
For those who are mathematically inclined, there is often a definite aesthetic aspect to much of mathematics. Many mathematicians talk about the elegance of mathematics, its intrinsic aesthetics and inner beauty. Simplicity and generality are valued. There is beauty in a simple and elegant proof, such as Euclid's proof that there are infinitely many prime numbers, and in an elegant numerical method that speeds calculation, such as the fast Fourier transform. G. H. Hardy in A Mathematician's Apology expressed the belief that these aesthetic considerations are, in themselves, sufficient to justify the study of pure mathematics.[18] Mathematicians often strive to find proofs of theorems that are particularly elegant, a quest Paul Erdős often referred to as finding proofs from "The Book" in which God had written down his favorite proofs.[19][20] The popularity of recreational mathematics is another sign of the pleasure many find in solving mathematical questions.
Main article: Mathematical beauty
Sir Isaac Newton (1643-1727), an inventor of infinitesimal calculus.
Mathematics arises from many different kinds of problems. At first these were found in commerce, land measurement and later astronomy; nowadays, all sciences suggest problems studied by mathematicians, and many problems arise within mathematics itself. For example, the physicist Richard Feynman invented the path integral formulation of quantum mechanics using a combination of mathematical reasoning and physical insight, and today's string theory, a still-developing scientific theory which attempts to unify the four fundamental forces of nature, continues to inspire new mathematics.[15] Some mathematics is only relevant in the area that inspired it, and is applied to solve further problems in that area. But often mathematics inspired by one area proves useful in many areas, and joins the general stock of mathematical concepts. A distinction is often made between pure mathematics and applied mathematics however pure mathematics topics often turn out to have applications e.g. number theory in cryptography. This remarkable fact that even the "purest" mathematics often turns out to have practical applications is what Eugene Wigner has called "the unreasonable effectiveness of mathematics."[16] As in most areas of study, the explosion of knowledge in the scientific age has led to specialization: there are now hundreds of specialized areas in mathematics and the latest Mathematics Subject Classification runs to 46 pages[17]. Several areas of applied mathematics have merged with related traditions outside of mathematics and become disciplines in their own right, including statistics, operations research, and computer science.
For those who are mathematically inclined, there is often a definite aesthetic aspect to much of mathematics. Many mathematicians talk about the elegance of mathematics, its intrinsic aesthetics and inner beauty. Simplicity and generality are valued. There is beauty in a simple and elegant proof, such as Euclid's proof that there are infinitely many prime numbers, and in an elegant numerical method that speeds calculation, such as the fast Fourier transform. G. H. Hardy in A Mathematician's Apology expressed the belief that these aesthetic considerations are, in themselves, sufficient to justify the study of pure mathematics.[18] Mathematicians often strive to find proofs of theorems that are particularly elegant, a quest Paul Erdős often referred to as finding proofs from "The Book" in which God had written down his favorite proofs.[19][20] The popularity of recreational mathematics is another sign of the pleasure many find in solving mathematical questions.
Mathematics
From Wikipedia, the free encyclopedia
Jump to: navigation, search
"Maths" and "Math" redirect here. For other uses of "Mathematics" or "Math", see Mathematics (disambiguation) and Math (disambiguation).
This article is semi-protected.
Euclid, Greek mathematician, 3rd century BC, as imagined by Raphael in this detail from The School of Athens.[1]
Mathematics is the science and study of quantity, structure, space, and change. Mathematicians seek out patterns,[2][3] formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions.[4]
There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions".[5] Albert Einstein, on the other hand, stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."[6]
Through the use of abstraction and logical reasoning, mathematics evolved from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records go (see: History of Mathematics). Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Mathematics continued to develop, in fitful bursts, until the Renaissance, when mathematical innovations interacted with new scientific discoveries, leading to an acceleration in research that continues to the present day.[7]
Today, mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new disciplines. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind, although practical applications for what began as pure mathematics are often discovered later.[8]
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"Maths" and "Math" redirect here. For other uses of "Mathematics" or "Math", see Mathematics (disambiguation) and Math (disambiguation).
This article is semi-protected.
Euclid, Greek mathematician, 3rd century BC, as imagined by Raphael in this detail from The School of Athens.[1]
Mathematics is the science and study of quantity, structure, space, and change. Mathematicians seek out patterns,[2][3] formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions.[4]
There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions".[5] Albert Einstein, on the other hand, stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."[6]
Through the use of abstraction and logical reasoning, mathematics evolved from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records go (see: History of Mathematics). Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Mathematics continued to develop, in fitful bursts, until the Renaissance, when mathematical innovations interacted with new scientific discoveries, leading to an acceleration in research that continues to the present day.[7]
Today, mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new disciplines. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind, although practical applications for what began as pure mathematics are often discovered later.[8]
Sunday, August 23, 2009
Maths, Magic & Mystery with Dr Burkard Polster
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Poppy Masselos
Monday, October 13, 2008 at 08:22pm
Don’t miss the following professional development.
If there is a school subject that is universally hated then it has to be maths. No other subject conjures up such strong emotions when adults reminisce about their school days and with no other subject are people so willing to admit that they just don’t get it.
Corinda State High School staff and students will be dared to look at maths differently when Dr Burkard Polster — Monash University maths lecturer - visits the school to present Maths, Magic and Mystery.
Described as Monash University’s resident Mathemagician, mathematical juggler, origami expert, bubble-master, shoelace charmer, and Count von Count impersonator, Dr Polster has a growing reputation as a mathematics communicator. In addition to public lectures on mathematics at Melbourne Museum, he has also appeared on TV discussing such burning issues as how to balance wobbly tables, and how to lace your shoes.
Dr Polster will do a number of presentations to both mathematics staff and students during his 2 day visit to Brisbane. He will use his unique presentation style to challenge mathematics teachers to find ways to explain and explore mathematical issues in an accessible and entertaining way.
Dr Polster is the author of numerous research articles and books including “The Mathematics of Juggling”, “QED: Beauty in Mathematical Proof”, and “Eye Twisters: Ambigrams and Other Visual Puzzles to Amaze and Entertain”.
WHAT: Maths, Magic & Mystery with Dr Burkard Polster
WHEN: Wednesday 15th October 1:40 — 5:30pm
Thursday 16th October 9:15 — 2:50pm
WHERE: Corinda State High School
Pratten Road, Corinda.
Check out Maths Masters
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Poppy Masselos
Poppy Masselos
Poppy is a registered teacher with decades of experience in the classroom. A large part of her career in the past has been to help teachers to make sense of new and emerging technologies and to help infuse these in all curriculum areas in all grade levels.
She is an advocate for creating exciting curricula for all students and uses the education section of The Courier-Mail to inform, celebrate, spotlight and direct teacher and student attention to the latest happenings in the world of education. Poppy believes that newspapers are the best solution to data smog or "information overload" that we are all experiencing in the 21st century.
Poppy began her journalism career writing about the Net for Ipswich's Queensland Times. She started at The Courier-Mail with a column called Cyber-Ed in the mid 90's and edited the popular Internet Sites for the Classroom books published by the paper.
In her spare time, Poppy is an avid news and media junkie sourcing magazines and newspapers from all over the world. Her favourite topics are the new sciences such as genetics, robotics and nanotechnologies, travel, art, literature, cinema and online innovations. She loves new foods, food blogs, movies, world music, writer's festivals, biographies, new trends, innovative fashion and design, sunsets and Radio National. One day she hopes that technology will be created to convert dream images into video footage!
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Poppy Masselos
Monday, October 13, 2008 at 08:22pm
Don’t miss the following professional development.
If there is a school subject that is universally hated then it has to be maths. No other subject conjures up such strong emotions when adults reminisce about their school days and with no other subject are people so willing to admit that they just don’t get it.
Corinda State High School staff and students will be dared to look at maths differently when Dr Burkard Polster — Monash University maths lecturer - visits the school to present Maths, Magic and Mystery.
Described as Monash University’s resident Mathemagician, mathematical juggler, origami expert, bubble-master, shoelace charmer, and Count von Count impersonator, Dr Polster has a growing reputation as a mathematics communicator. In addition to public lectures on mathematics at Melbourne Museum, he has also appeared on TV discussing such burning issues as how to balance wobbly tables, and how to lace your shoes.
Dr Polster will do a number of presentations to both mathematics staff and students during his 2 day visit to Brisbane. He will use his unique presentation style to challenge mathematics teachers to find ways to explain and explore mathematical issues in an accessible and entertaining way.
Dr Polster is the author of numerous research articles and books including “The Mathematics of Juggling”, “QED: Beauty in Mathematical Proof”, and “Eye Twisters: Ambigrams and Other Visual Puzzles to Amaze and Entertain”.
WHAT: Maths, Magic & Mystery with Dr Burkard Polster
WHEN: Wednesday 15th October 1:40 — 5:30pm
Thursday 16th October 9:15 — 2:50pm
WHERE: Corinda State High School
Pratten Road, Corinda.
Check out Maths Masters
Share |
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*
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Profile
Poppy Masselos
Poppy Masselos
Poppy is a registered teacher with decades of experience in the classroom. A large part of her career in the past has been to help teachers to make sense of new and emerging technologies and to help infuse these in all curriculum areas in all grade levels.
She is an advocate for creating exciting curricula for all students and uses the education section of The Courier-Mail to inform, celebrate, spotlight and direct teacher and student attention to the latest happenings in the world of education. Poppy believes that newspapers are the best solution to data smog or "information overload" that we are all experiencing in the 21st century.
Poppy began her journalism career writing about the Net for Ipswich's Queensland Times. She started at The Courier-Mail with a column called Cyber-Ed in the mid 90's and edited the popular Internet Sites for the Classroom books published by the paper.
In her spare time, Poppy is an avid news and media junkie sourcing magazines and newspapers from all over the world. Her favourite topics are the new sciences such as genetics, robotics and nanotechnologies, travel, art, literature, cinema and online innovations. She loves new foods, food blogs, movies, world music, writer's festivals, biographies, new trends, innovative fashion and design, sunsets and Radio National. One day she hopes that technology will be created to convert dream images into video footage!
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Get Schooled
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Crochet and hyperbolic geometry 0
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Are teachers scared of teaching numeracy?
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* Ambo quits after address mix-up
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* Stud workers await release
* Footbrawl at girls' carnival
* Ill-equipped to save girl
Courier Mail Entertainment News
* Queenslanders chase Idol glory
* Fatherly flick for Hoges, 'Kenny'
* Best children's books judged
* Liberating role for shy Romeo
* Welcome to Lily Allen's world
* Liberating role for shy Romeo
Courier Mail Sports News
* Flintoff halts Ponting stand
* Farina banished as Roar draw
* Cartwright's referee worry
* Izzy's back for Broncos
* Mic Mac faces stern test
* Lions eye home final
Article: Is maths magic?
Article from: Mathematics Teaching
Article date:
July 1, 2008
Author:
Askew, Mike CopyrightCopyright The Association of Teachers of Mathematics Jul 2008. Provided by ProQuest LLC. (Hide copyright information)
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It was an honour to be invited to give the afterdinner talk at this year's joint conference. But how to write up what was mainly a performance of magic? Writing about conjuring is a bit like ventriloquism on the radio: it loses something in translation. But here's a few loosely-connected thoughts.
For those of you who don't know me, I work in primary mathematics education and, in my spare time, enjoy close-up magic. For me, these are two distinct aspects of my life, not least because they involve different relationships widi the 'authence'. In my work as a maths educator, I want to be as transparent as possible. I want the people I am working with to know exactly what is going on and I try ...
Article date:
July 1, 2008
Author:
Askew, Mike CopyrightCopyright The Association of Teachers of Mathematics Jul 2008. Provided by ProQuest LLC. (Hide copyright information)
Ads by Google
Infinity Headlight System
Brilliant, portable, & shadow-free for dental and surgical use.
www.SheerVision.com
Truth About Scientology
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Scientology.org
It was an honour to be invited to give the afterdinner talk at this year's joint conference. But how to write up what was mainly a performance of magic? Writing about conjuring is a bit like ventriloquism on the radio: it loses something in translation. But here's a few loosely-connected thoughts.
For those of you who don't know me, I work in primary mathematics education and, in my spare time, enjoy close-up magic. For me, these are two distinct aspects of my life, not least because they involve different relationships widi the 'authence'. In my work as a maths educator, I want to be as transparent as possible. I want the people I am working with to know exactly what is going on and I try ...
Maths Magic
The application of mathematical abilities in modern work, and the importance of strongly grounding students in the principles of the subject, will be the focus of a Mathematics Awareness Campaign this month. Science, as a related subject, will also be a part of the programme of activities. All government schools will be involved, and private schools have also been invited to participate.
The events will begin next week with a fun and educational two-part Maths Competition. Maths Part One will begin at 9:00am on Tuesday, 7 February, for junior students; and on Wednesday the 8th at 11:00am for senior students. Both of these events will be held at the John Gray High School's Library, and will entail individual and group computation and problem solving tasks. The Cayman Brac competition on the same days will be held at the Teachers' Centre.
Part Two of the Maths Competition will be held on February 21 & 22, in the form of an oral maths competition. The Fidelity Group of Companies is again sponsoring this year's Students Maths Competitions.
Dr. Desiree Charles, government's Education Officer - Mathematics, is spearheading the project. She said that this special effort to increase interest and involvement of students, parents and teachers in mathematics activities is an annual part of the Education Department's curriculum.
School teachers and students are also now enjoying lessons and fun learning activities as they work on their mathematics and science projects. These will be displayed at the mathematics and science exhibitions. The first of these exhibitions will be held on Friday and Saturday (February 9 & 10), from 9am to 4pm at the Aston Rutty Centre, Cayman Brac.
Grand Cayman's Maths and Science Exhibition will take place during February 20-24.
These activities will culminate with the National Mathematics Day observance on Grand Cayman and Cayman Brac on Friday, 24 February.
Plans are also underway for Grand Cayman's Mathematics Fair the following day, Saturday, 25 February, at the Mary Miller Hall, adjacent to the Lighthouse School in Red Bay. Activities during these days will include free maths t-shirts for all students, refreshments, maths quizzes, learning experiences prizes, supermarket give-a-ways and airline tickets.
During classroom lessons, students are being encouraged to explore a range of activities: from designing clothes and art projects, to maths competitions and exploring the application of work in various areas of life and work.
Whle much of the focus is on children, adult involvement in the effort to instil quantifying skills is also a priority. Two special maths conferences will also take place earlier in the month for the benefit of teachers and parents, featuring talks by a visiting expert mathematician. A teachers' lecture will be held on Monday, 13 February, at Prospect Primary School's Hall at 4:40pm. There is a fee of $25.
Parents will benefit from a second stimulating conference which takes place the following day, Tuesday, 14 February, at the George Hicks High School, starting at 6:00pm. There is a $10 admission cost for attendees.
For more information on this Mathematics Awareness Campaign, or any maths-related issue, please contact Dr. Charles at the Education Department, 945-1199.
For further information contact
The events will begin next week with a fun and educational two-part Maths Competition. Maths Part One will begin at 9:00am on Tuesday, 7 February, for junior students; and on Wednesday the 8th at 11:00am for senior students. Both of these events will be held at the John Gray High School's Library, and will entail individual and group computation and problem solving tasks. The Cayman Brac competition on the same days will be held at the Teachers' Centre.
Part Two of the Maths Competition will be held on February 21 & 22, in the form of an oral maths competition. The Fidelity Group of Companies is again sponsoring this year's Students Maths Competitions.
Dr. Desiree Charles, government's Education Officer - Mathematics, is spearheading the project. She said that this special effort to increase interest and involvement of students, parents and teachers in mathematics activities is an annual part of the Education Department's curriculum.
School teachers and students are also now enjoying lessons and fun learning activities as they work on their mathematics and science projects. These will be displayed at the mathematics and science exhibitions. The first of these exhibitions will be held on Friday and Saturday (February 9 & 10), from 9am to 4pm at the Aston Rutty Centre, Cayman Brac.
Grand Cayman's Maths and Science Exhibition will take place during February 20-24.
These activities will culminate with the National Mathematics Day observance on Grand Cayman and Cayman Brac on Friday, 24 February.
Plans are also underway for Grand Cayman's Mathematics Fair the following day, Saturday, 25 February, at the Mary Miller Hall, adjacent to the Lighthouse School in Red Bay. Activities during these days will include free maths t-shirts for all students, refreshments, maths quizzes, learning experiences prizes, supermarket give-a-ways and airline tickets.
During classroom lessons, students are being encouraged to explore a range of activities: from designing clothes and art projects, to maths competitions and exploring the application of work in various areas of life and work.
Whle much of the focus is on children, adult involvement in the effort to instil quantifying skills is also a priority. Two special maths conferences will also take place earlier in the month for the benefit of teachers and parents, featuring talks by a visiting expert mathematician. A teachers' lecture will be held on Monday, 13 February, at Prospect Primary School's Hall at 4:40pm. There is a fee of $25.
Parents will benefit from a second stimulating conference which takes place the following day, Tuesday, 14 February, at the George Hicks High School, starting at 6:00pm. There is a $10 admission cost for attendees.
For more information on this Mathematics Awareness Campaign, or any maths-related issue, please contact Dr. Charles at the Education Department, 945-1199.
For further information contact
Maths magic in a suitcase
Article | Published in TES Magazine on 27 September, 2002 | By: Chris Olley Section: Article
Chris Olley finds that the right resources are all it takes to get students excited about numbers
It is Friday afternoon at St Paul's Catholic College in Sunbury-on-Thames and Year 7 are in animated activity. Although they are discussing the upcoming weekend, the pupils are not having a "lazy" afternoon; they are taking part in a hands-on maths lesson using materials from Fresco Interactives.
The students circulate freely among a range of engaging tasks on beautifully produced, colourful display panels with dry wipe pens attached. Some are working alone, others congregate in small groups. They stop when their interest has been captured and get stuck in.
One panel shows the Fibonnaci sequence, tempting students to look for patterns. The girl working here is investigating odd and even numbers and is tempted to explore the prime numbers in the sequence. She had earlier worked on a drum-shaped display looking at the patterns in Pascal's triangle, which she said was quite easy. Fibonnaci proves to be a bigger challenge and she is completely absorbed.
From the other side of the room her friend calls her over to try out "Tables against time", the most popular activity with the group. The referee rolls a 12-sided die to choose a table and two players compete to place the solutions printed on the faces of a set of cubes on to the answer grid. There are some nice heavy strips for playing Nim, which is another favourite.
A group of boys I talk to had engaged with issues of strategy, knew how the game was going to end and were clear on the best number to choose given your opponent's move.
There is a clever activity using Pentominos, which involves placing the shapes on a 100 square and investigating the numbers covered by the shape. GCSE coursework fans will recognise T-totals as a special case of this.
Gillian Lomas is the inspiration behind this innovative collection of maths resources. Her background is in interactive practical science exhibitions but a combination of factors led to the creation of Fresco Interactives. She was influenced by Paul Stephens, whose Magical Mathsworks Circus tours the country engaging young people in interactive, hands-on mathematical activities. And the idea of MathFests - bringing maths puzzles and games into shopping centres and school festivals - was beginning to take hold during Maths Year 2000. Putting these sources together, Gillian developed the idea for an interactive maths system in a box.
The final kit was produced when she joined forces with Fresco, a company which manufactures display systems. The kit itself actually comes in four large boxes, but it's nothing that a few strong students and a class full of willing helpers cannot handle. The whole kit can be set out and put away in little more than the time needed for a modest practical lesson. The materials are hard-wearing and the displays are printed on the inside of plastic laminates, so they will not rub off. Everything has its own holder and the complete kit fits neatly into a set of suitcases. At the very least the Fresco Interactives kit provides a range of engaging maths activities that are bright and lively. Students leave a maths lesson interested and contented and say good things about their maths experience.
Simon Winchcombe, head of maths at St Paul's, says that maths should be "seen, discovered and connected". He sees the Fresco materials as an excellent source for discovery. A number of the activities engage students with abstract ideas and provide a springboard into successfully developing mathematical thinking.
The experienced maths teacher will be able to extend the activities that have engaged students the most. Simon, though, is not sure whether he could use the kit in an ordinary classroom setting with 30 mixed ability students. It would need a large room and probably another adult, he says.
A prime reason for getting the kit was to involve the school's feeder primaries. Headteachers and maths co-ordinators met to see the kit and were delighted. It will tour the primaries giving each school a fortnight for pupils to get a really positive experience of maths with equipment that has come from their prospective secondary. Equally, it would be ideal for use in numeracy summer schools providing activities that everyone can engage in, as well as extending higher achievers.
Fresco Interactives has brought together a set of tried and tested activities in a highly useable format. In an age when the focus is so heavily on exam preparation it is an uplifting experience to be among students keen to explore mathematical ideas just because they are interested.
The Numeracy Strategy Kit costs £2,250 (excluding VATand delivery). Parts of the kit can be bought separately.A free video is available for schools considering purchasing the Numeracy Strategy Kit by contacting Fresco Interactives, Unit C6, Tenterfields Business Park, Luddenfoot, West Yorkshire HX2 6EQ.
Tel: 01422 886883
Email: interactives@fresco.co.uk.
www.frescointeractives.co.uk
Chris Olley is a maths education consultant
Chris Olley finds that the right resources are all it takes to get students excited about numbers
It is Friday afternoon at St Paul's Catholic College in Sunbury-on-Thames and Year 7 are in animated activity. Although they are discussing the upcoming weekend, the pupils are not having a "lazy" afternoon; they are taking part in a hands-on maths lesson using materials from Fresco Interactives.
The students circulate freely among a range of engaging tasks on beautifully produced, colourful display panels with dry wipe pens attached. Some are working alone, others congregate in small groups. They stop when their interest has been captured and get stuck in.
One panel shows the Fibonnaci sequence, tempting students to look for patterns. The girl working here is investigating odd and even numbers and is tempted to explore the prime numbers in the sequence. She had earlier worked on a drum-shaped display looking at the patterns in Pascal's triangle, which she said was quite easy. Fibonnaci proves to be a bigger challenge and she is completely absorbed.
From the other side of the room her friend calls her over to try out "Tables against time", the most popular activity with the group. The referee rolls a 12-sided die to choose a table and two players compete to place the solutions printed on the faces of a set of cubes on to the answer grid. There are some nice heavy strips for playing Nim, which is another favourite.
A group of boys I talk to had engaged with issues of strategy, knew how the game was going to end and were clear on the best number to choose given your opponent's move.
There is a clever activity using Pentominos, which involves placing the shapes on a 100 square and investigating the numbers covered by the shape. GCSE coursework fans will recognise T-totals as a special case of this.
Gillian Lomas is the inspiration behind this innovative collection of maths resources. Her background is in interactive practical science exhibitions but a combination of factors led to the creation of Fresco Interactives. She was influenced by Paul Stephens, whose Magical Mathsworks Circus tours the country engaging young people in interactive, hands-on mathematical activities. And the idea of MathFests - bringing maths puzzles and games into shopping centres and school festivals - was beginning to take hold during Maths Year 2000. Putting these sources together, Gillian developed the idea for an interactive maths system in a box.
The final kit was produced when she joined forces with Fresco, a company which manufactures display systems. The kit itself actually comes in four large boxes, but it's nothing that a few strong students and a class full of willing helpers cannot handle. The whole kit can be set out and put away in little more than the time needed for a modest practical lesson. The materials are hard-wearing and the displays are printed on the inside of plastic laminates, so they will not rub off. Everything has its own holder and the complete kit fits neatly into a set of suitcases. At the very least the Fresco Interactives kit provides a range of engaging maths activities that are bright and lively. Students leave a maths lesson interested and contented and say good things about their maths experience.
Simon Winchcombe, head of maths at St Paul's, says that maths should be "seen, discovered and connected". He sees the Fresco materials as an excellent source for discovery. A number of the activities engage students with abstract ideas and provide a springboard into successfully developing mathematical thinking.
The experienced maths teacher will be able to extend the activities that have engaged students the most. Simon, though, is not sure whether he could use the kit in an ordinary classroom setting with 30 mixed ability students. It would need a large room and probably another adult, he says.
A prime reason for getting the kit was to involve the school's feeder primaries. Headteachers and maths co-ordinators met to see the kit and were delighted. It will tour the primaries giving each school a fortnight for pupils to get a really positive experience of maths with equipment that has come from their prospective secondary. Equally, it would be ideal for use in numeracy summer schools providing activities that everyone can engage in, as well as extending higher achievers.
Fresco Interactives has brought together a set of tried and tested activities in a highly useable format. In an age when the focus is so heavily on exam preparation it is an uplifting experience to be among students keen to explore mathematical ideas just because they are interested.
The Numeracy Strategy Kit costs £2,250 (excluding VATand delivery). Parts of the kit can be bought separately.A free video is available for schools considering purchasing the Numeracy Strategy Kit by contacting Fresco Interactives, Unit C6, Tenterfields Business Park, Luddenfoot, West Yorkshire HX2 6EQ.
Tel: 01422 886883
Email: interactives@fresco.co.uk.
www.frescointeractives.co.uk
Chris Olley is a maths education consultant
All About MathMagic:
MathMagic was a K-12 telecommunications project developed in El Paso, Texas by Alan A. Hodson. The intent of the project was to provide motivation for students to use computer technology while increasing problem-solving strategies and communications skills. MathMagic posted challenges in each of four categories (k-3, 4-6, 7-9 and 10-12) which are now archived and available to view in plain text or download in MS Word file format.
Archived Challenges:
Each grade band directory has links to plain text files that can be viewed online (or downloaded) and to MS Word documents that can be downloaded.
* K-3
Archived Challenges:
Each grade band directory has links to plain text files that can be viewed online (or downloaded) and to MS Word documents that can be downloaded.
* K-3
MathMagic was a K-12 telecommunications project developed in El Paso, Texas by Alan A. Hodson. The intent of the project was to provide motivation for students to use computer technology while increasing problem-solving strategies and communications skills. MathMagic posted challenges in each of four categories (k-3, 4-6, 7-9 and 10-12) which are now archived and available to view in plain text or download in MS Word file format.
Archived Challenges:
Each grade band directory has links to plain text files that can be viewed online (or downloaded) and to MS Word documents th
Archived Challenges:
Each grade band directory has links to plain text files that can be viewed online (or downloaded) and to MS Word documents th
All About MathMagic:
MathMagic was a K-12 telecommunications project developed in El Paso, Texas by Alan A. Hodson. The intent of the project was to provide motivation for students to use computer technology while increasing problem-solving strategies and communications skills. MathMagic posted challenges in each of four categories (k-3, 4-6, 7-9 and 10-12) which are now archived and available to view in plain text or download in MS Word file format.
Archived Challenges:
Each grade band directory has links to plain text files that can be viewed online (or downloaded) and to MS Word documents th
Archived Challenges:
Each grade band directory has links to plain text files that can be viewed online (or downloaded) and to MS Word documents th
Math Magic - Tricks and Methods
Home
How do people do it? How can you multiply by 25 or multiply by 3367 in your head? Here is the answer!!!!
Below you will find a list of PDF files that can help you with all of your mental math needs. Refer to this site regularly for updates and additional files!!! If you want to search the files through html, click on the corresponding link!
Note: If the files are taking too long to view or you would like to download them for future reference, right-click on a link and choose the "Save Target As..." option.
(*Currently 192 PDF Files*)
Basic Memorization....For ALL
Cubes and Higher Powers (html) Fractions, Decimals, and Percents (html)
Square Numbers (html) Order Of Operations (html)
Prime Numbers (html) Roman Numerals (html)
Divisibility Rules (html) Basic Conversions (html)
For The Elementary Level Students
FOIL Method (html) Double And Half Method (html)
Squaring A 2-Digit Number (html) Squaring A Number Ending In 5 (html)
Squaring A Number From 40-49 (html) Squaring A Number From 50-59 (html)
Squaring A Number From 90-99 (html) Multiplying 2 Numbers Whose 1's Digits Add To 10 (html)
Multiply Numbers Less Than 100 (html) Multiply Numbers Greater Than 100 (html)
Multiplying Numbers In The Form: ab + bc (html) Multiplying By 5 (html)
Multiplying By 11 (html) Multiplying By 25 (html)
Multiplying By 50 (html) Multiplying By 101 (html)
Adding And Subtracting Fractions (html) Comparing Fractions (html)
Multiplying Mixed Numbers (#1) (html) Adding Sequences In The Form: 1+2+...+n (html)
Adding Sequences In The Form: 1+3+...+2n-1 (html) Percents (html)
GCD (html) LCM (html)
Definitions (html) Ratios (html)
Square Roots (html) Subtracting Reverses (html)
Approximating Series (html)
For The Junior High Or Middle School Student
Squaring A Number Ending In 6 (html) Squaring A Number Ending In 7 (html)
Squaring A Number Ending In 8 (html) Squaring A Number Ending In 9 (html)
Difference Of 2 Squares (html) Multiplying 2 Numbers Ending In 5 (html)
Multiplying 2 Numbers Whose 10's Digits Add To 10 (html) Adding Squared Numbers In The Form: a2+(2a)2 (html)
Adding Squared Numbers In The Form: a2+(3a)2 (html) Adding Squared Numbers In The Form: a2+(7a)2 (html)
Adding Squared Numbers In The Form: a2+(10a)2 (html) Multiplying Numbers Less Than 1000 (html)
Multiplying Numbers Greater Than 1000 (html) Multiplying 4 Consecutive Integers (html)
Multiplying By 12-19 (html) Multiplying By 15 (html)
Multiplying By 75 (html) Multiplying By 111 (html)
Multiplying By 125 (html) Multiplying By 143 (html)
Multiplying By 167 (html) Multiplying By 375 (html)
Multiplying By 625 (html) Multiplying By 875 (html)
Multiplying By 1001 (html) Multiplying By 1111 (html)
Adding a/b + b/a (html) Multiplying a x a/b (html)
Multiplying Mixed Numbers (#2) (html) Adding 3 Fractions (#1) (html)
Adding 3 Fractions (#2) (html) Subtracting 3 Fractions (html)
Calculating Fractions (#1) (html) Calculating Fractions (#2) (html)
Repeating Decimals (#1) (html) Repeating Decimals (#2) (html)
Adding Finite Geometric Sequence (html) Changing Base b to Base 10 (html)
Changing Base 10 to Base b (html) Changing Base 2 to Base 4 (html)
Changing Base 2 to Base 8 (html) Changing Base 3 to Base 9 (html)
Adding 2 Bases Together (html) Finding The Next Term Of A Sequence (html)
Cube Roots (html) Multiplying By 9 (#1) (html)
Multiplying By 9 (#2) (html) Multiplying By 8 (html)
Polynomials (html) Positive Integral Divisors (html)
Sum Of Positive Integral Divisors (html) Relatively Prime (html)
Triangular Numbers (html) Finding Remainders (html)
Dividing By 40 (html) Dividing By 25 (html)
Dividing By 9 (html) Approximating Square Roots (html)
Approximating Cube Roots (html) Approximating Multiplying 2 Numbers (html)
Approximating Dividing By Specific Numbers (html) Approximating Multiplying 3 Numbers (html)
Approximating Multiplying By Specific Numbers (html) Approximating Higher Powers (html)
Factorials (html) Squares/Rectangles (html)
Circles (html) Triangles (html)
Parallelograms (html) Trapezoids (html)
Cubes (html) Spheres (html)
Rectangular Solids (html) Cylinders (html)
Multiply 2 Nums One's Add To 5 (html) Multiply 2 Nums With Same Ten's (html)
Multiply 1 Num Above And Below 100 (html)
For The High School Aged Students (Advanced Level)
Adding 2 Squared Numbers (html) Multiplying By 286 (html)
Multiplying By 429 (html) Multiplying By 572 (html)
Multiplying By 715 (html) Multiplying By 858 (html)
Multiplying By 3367 (html) Multiplying By 14443 (html)
Multiplying By 101101 (html) Multiplying By 142857 (html)
Changing Base b to Base 10 Fraction/Decimal (html) Changing Base 10 to Base b Fraction/Decimal (html)
Multiplying 2 Bases (html) Adding Sequences In The Form: 12+22+...+n2 (html)
Adding Sequences In The Form: 13+23+...+n3 (html) Adding A Sequence In The Form: 1/a+1/a2+...+1/an (html)
Adding Sequences In The Form: a + a/b + a/b2 + ... (html) Finding The nth Term Of A Sequence (html)
Pentagonal Numbers (html) Hexagonal Numbers (html)
Heptagonal Numbers (html) Octagonal Numbers (html)
Manipulating Polygonal Numbers (html) Approximating en (html)
Approximating pn (html) Changing Probability To Odds (html)
Permutations (html) Combinations (html)
Probability With Coins (html) Probability With Dice (html)
Probability With Cards (html) Probability With Balls (html)
Arranging Committees (html) Arranging Objects (html)
Words/Numbers (html) Binomial Expansions (html)
Basic Trig Memorizations (html) Trig Definitions (html)
Convert Radians -> Degrees (html) Pythagorean Triples (html)
Inscribed Circles (html) Circumscribed Circles (html)
Ellipses (html) Determining Regions In A Plane (html)
Distinct Diagonals Of A Polygon (html) Interior/Exterior Angles Of A Polygon (html)
Determining Values For Triangles (html) Polyhedrons (html)
Distance Between 2 Points (html) Slope Of A Line Through 2 Points (html)
Solving For 2 Variables (html) Imaginary Numbers (html)
Matrices (html) Compound Functions (html)
Inverse Functions (html) Parabolas (html)
Modular Math (html) Vectors (html)
Polar And Rectangular Coordinates (html) Asymptotes (html)
Limits (html) Logs (html)
Derivatives (html) Integrals (html)
Maximum/Minimum Values (html) Repeating Decimals #3 (html)
Add 3 Fractions #3 (html) Adding Consecutive Squares (html)
Squaring 101a, 102a, 103a (html) Adding: a2 + b2 - (a-b)2 (html)
Finding Remainder In Bases (html) Adding: 13 - 23 + 33 - ...+ n3 (html)
Adding A Sequence In The Form: 1/a-1/a2-...-1/an (html) Adding: n(n!) + (n-1)(n-1)! +...+ 1(1!) (html)
Dividing Factorial #1 (html) Dividing Factorial #2 (html)
Solving: a2 - b2 = a3 (html)
How do people do it? How can you multiply by 25 or multiply by 3367 in your head? Here is the answer!!!!
Below you will find a list of PDF files that can help you with all of your mental math needs. Refer to this site regularly for updates and additional files!!! If you want to search the files through html, click on the corresponding link!
Note: If the files are taking too long to view or you would like to download them for future reference, right-click on a link and choose the "Save Target As..." option.
(*Currently 192 PDF Files*)
Basic Memorization....For ALL
Cubes and Higher Powers (html) Fractions, Decimals, and Percents (html)
Square Numbers (html) Order Of Operations (html)
Prime Numbers (html) Roman Numerals (html)
Divisibility Rules (html) Basic Conversions (html)
For The Elementary Level Students
FOIL Method (html) Double And Half Method (html)
Squaring A 2-Digit Number (html) Squaring A Number Ending In 5 (html)
Squaring A Number From 40-49 (html) Squaring A Number From 50-59 (html)
Squaring A Number From 90-99 (html) Multiplying 2 Numbers Whose 1's Digits Add To 10 (html)
Multiply Numbers Less Than 100 (html) Multiply Numbers Greater Than 100 (html)
Multiplying Numbers In The Form: ab + bc (html) Multiplying By 5 (html)
Multiplying By 11 (html) Multiplying By 25 (html)
Multiplying By 50 (html) Multiplying By 101 (html)
Adding And Subtracting Fractions (html) Comparing Fractions (html)
Multiplying Mixed Numbers (#1) (html) Adding Sequences In The Form: 1+2+...+n (html)
Adding Sequences In The Form: 1+3+...+2n-1 (html) Percents (html)
GCD (html) LCM (html)
Definitions (html) Ratios (html)
Square Roots (html) Subtracting Reverses (html)
Approximating Series (html)
For The Junior High Or Middle School Student
Squaring A Number Ending In 6 (html) Squaring A Number Ending In 7 (html)
Squaring A Number Ending In 8 (html) Squaring A Number Ending In 9 (html)
Difference Of 2 Squares (html) Multiplying 2 Numbers Ending In 5 (html)
Multiplying 2 Numbers Whose 10's Digits Add To 10 (html) Adding Squared Numbers In The Form: a2+(2a)2 (html)
Adding Squared Numbers In The Form: a2+(3a)2 (html) Adding Squared Numbers In The Form: a2+(7a)2 (html)
Adding Squared Numbers In The Form: a2+(10a)2 (html) Multiplying Numbers Less Than 1000 (html)
Multiplying Numbers Greater Than 1000 (html) Multiplying 4 Consecutive Integers (html)
Multiplying By 12-19 (html) Multiplying By 15 (html)
Multiplying By 75 (html) Multiplying By 111 (html)
Multiplying By 125 (html) Multiplying By 143 (html)
Multiplying By 167 (html) Multiplying By 375 (html)
Multiplying By 625 (html) Multiplying By 875 (html)
Multiplying By 1001 (html) Multiplying By 1111 (html)
Adding a/b + b/a (html) Multiplying a x a/b (html)
Multiplying Mixed Numbers (#2) (html) Adding 3 Fractions (#1) (html)
Adding 3 Fractions (#2) (html) Subtracting 3 Fractions (html)
Calculating Fractions (#1) (html) Calculating Fractions (#2) (html)
Repeating Decimals (#1) (html) Repeating Decimals (#2) (html)
Adding Finite Geometric Sequence (html) Changing Base b to Base 10 (html)
Changing Base 10 to Base b (html) Changing Base 2 to Base 4 (html)
Changing Base 2 to Base 8 (html) Changing Base 3 to Base 9 (html)
Adding 2 Bases Together (html) Finding The Next Term Of A Sequence (html)
Cube Roots (html) Multiplying By 9 (#1) (html)
Multiplying By 9 (#2) (html) Multiplying By 8 (html)
Polynomials (html) Positive Integral Divisors (html)
Sum Of Positive Integral Divisors (html) Relatively Prime (html)
Triangular Numbers (html) Finding Remainders (html)
Dividing By 40 (html) Dividing By 25 (html)
Dividing By 9 (html) Approximating Square Roots (html)
Approximating Cube Roots (html) Approximating Multiplying 2 Numbers (html)
Approximating Dividing By Specific Numbers (html) Approximating Multiplying 3 Numbers (html)
Approximating Multiplying By Specific Numbers (html) Approximating Higher Powers (html)
Factorials (html) Squares/Rectangles (html)
Circles (html) Triangles (html)
Parallelograms (html) Trapezoids (html)
Cubes (html) Spheres (html)
Rectangular Solids (html) Cylinders (html)
Multiply 2 Nums One's Add To 5 (html) Multiply 2 Nums With Same Ten's (html)
Multiply 1 Num Above And Below 100 (html)
For The High School Aged Students (Advanced Level)
Adding 2 Squared Numbers (html) Multiplying By 286 (html)
Multiplying By 429 (html) Multiplying By 572 (html)
Multiplying By 715 (html) Multiplying By 858 (html)
Multiplying By 3367 (html) Multiplying By 14443 (html)
Multiplying By 101101 (html) Multiplying By 142857 (html)
Changing Base b to Base 10 Fraction/Decimal (html) Changing Base 10 to Base b Fraction/Decimal (html)
Multiplying 2 Bases (html) Adding Sequences In The Form: 12+22+...+n2 (html)
Adding Sequences In The Form: 13+23+...+n3 (html) Adding A Sequence In The Form: 1/a+1/a2+...+1/an (html)
Adding Sequences In The Form: a + a/b + a/b2 + ... (html) Finding The nth Term Of A Sequence (html)
Pentagonal Numbers (html) Hexagonal Numbers (html)
Heptagonal Numbers (html) Octagonal Numbers (html)
Manipulating Polygonal Numbers (html) Approximating en (html)
Approximating pn (html) Changing Probability To Odds (html)
Permutations (html) Combinations (html)
Probability With Coins (html) Probability With Dice (html)
Probability With Cards (html) Probability With Balls (html)
Arranging Committees (html) Arranging Objects (html)
Words/Numbers (html) Binomial Expansions (html)
Basic Trig Memorizations (html) Trig Definitions (html)
Convert Radians -> Degrees (html) Pythagorean Triples (html)
Inscribed Circles (html) Circumscribed Circles (html)
Ellipses (html) Determining Regions In A Plane (html)
Distinct Diagonals Of A Polygon (html) Interior/Exterior Angles Of A Polygon (html)
Determining Values For Triangles (html) Polyhedrons (html)
Distance Between 2 Points (html) Slope Of A Line Through 2 Points (html)
Solving For 2 Variables (html) Imaginary Numbers (html)
Matrices (html) Compound Functions (html)
Inverse Functions (html) Parabolas (html)
Modular Math (html) Vectors (html)
Polar And Rectangular Coordinates (html) Asymptotes (html)
Limits (html) Logs (html)
Derivatives (html) Integrals (html)
Maximum/Minimum Values (html) Repeating Decimals #3 (html)
Add 3 Fractions #3 (html) Adding Consecutive Squares (html)
Squaring 101a, 102a, 103a (html) Adding: a2 + b2 - (a-b)2 (html)
Finding Remainder In Bases (html) Adding: 13 - 23 + 33 - ...+ n3 (html)
Adding A Sequence In The Form: 1/a-1/a2-...-1/an (html) Adding: n(n!) + (n-1)(n-1)! +...+ 1(1!) (html)
Dividing Factorial #1 (html) Dividing Factorial #2 (html)
Solving: a2 - b2 = a3 (html)
MathMagic
From Wikipedia, the free encyclopedia
(Redirected from Mathmagic)
Jump to: navigation, search
MathMagic Developer(s) InfoLogic, Inc.
Stable release 6.4 for Mac, 4.2 for Windows / July 2009
Operating system Mac OS X, Microsoft Windows
Type Desktop publishing, Technical writing
License Proprietary
Website MathMagic.com
MathMagic, with its text form logotype [Math+Magic], is an equation editor for Windows and Mac OS including Mac OS X. MathMagic is a bit similar with MathType in terms of user interface but it seems to focus more on high quality printing - targeting publishing market, and higher productivity with easier interface and various faster input methods via keyboard shortcuts, palettes, macros, and clips.
MathMagic Pro Edition for InDesign, MathMagic Pro Edition for QuarkXPress, MathMagic Personal Edition for many other word processors such as Microsoft Word, Pages, Nisus Writer, Mellel, and presentation software such as PowerPoint and Keynote are available.
They come with many free mathematical symbol fonts in TrueType and OpenType format.
MathMagic was first released in 1998 at Seybold Expo San Francisco for Macintosh Desktop Publishing market, as an XTension for QuarkXPress 3.3x.
Later, InfoLogic introduced its stand-alone application version of MathMagic Personal Edition, MathMagic Pro Editions, and MathMagic Prime Editions, for various markets.
MathMagic supports MathML and TeX including Plain TeX, LaTeX, AMS LaTeX, MediaWIKI TeXvc, via copy and paste, import and export, or just dragging the files onto MathMagic application. So, MathMagic is widely used as a front-end WYSIWYG equation editor for MathML users and LaTeX users.
TeX expressions can also be typed directly in MathMagic editor window and equations can be copied out to clipboard in various TeX format. This helps TeX novice learn and practice his or her TeX skill.
Equation from Wiki pages can be drag and dropped, or copied and pasted into MathMagic window via right-button click and Copy Image command from the web page.
(Redirected from Mathmagic)
Jump to: navigation, search
MathMagic Developer(s) InfoLogic, Inc.
Stable release 6.4 for Mac, 4.2 for Windows / July 2009
Operating system Mac OS X, Microsoft Windows
Type Desktop publishing, Technical writing
License Proprietary
Website MathMagic.com
MathMagic, with its text form logotype [Math+Magic], is an equation editor for Windows and Mac OS including Mac OS X. MathMagic is a bit similar with MathType in terms of user interface but it seems to focus more on high quality printing - targeting publishing market, and higher productivity with easier interface and various faster input methods via keyboard shortcuts, palettes, macros, and clips.
MathMagic Pro Edition for InDesign, MathMagic Pro Edition for QuarkXPress, MathMagic Personal Edition for many other word processors such as Microsoft Word, Pages, Nisus Writer, Mellel, and presentation software such as PowerPoint and Keynote are available.
They come with many free mathematical symbol fonts in TrueType and OpenType format.
MathMagic was first released in 1998 at Seybold Expo San Francisco for Macintosh Desktop Publishing market, as an XTension for QuarkXPress 3.3x.
Later, InfoLogic introduced its stand-alone application version of MathMagic Personal Edition, MathMagic Pro Editions, and MathMagic Prime Editions, for various markets.
MathMagic supports MathML and TeX including Plain TeX, LaTeX, AMS LaTeX, MediaWIKI TeXvc, via copy and paste, import and export, or just dragging the files onto MathMagic application. So, MathMagic is widely used as a front-end WYSIWYG equation editor for MathML users and LaTeX users.
TeX expressions can also be typed directly in MathMagic editor window and equations can be copied out to clipboard in various TeX format. This helps TeX novice learn and practice his or her TeX skill.
Equation from Wiki pages can be drag and dropped, or copied and pasted into MathMagic window via right-button click and Copy Image command from the web page.
Problem of the Month (August 2009)
This month we investigate three problems involving products.
1. Consider rectangular grids of digits where the product of the numbers in the rows is equal to the product of the numbers in the columns. Since leading 0's should not exist and trailing 0's are less interesting, we only allow positive digits. We also have excluded grids that contain multiple copies of the same factor. We call these multiplicative grids. For example, the 3×2 rectangular grids are shown below.
135 156 194 567 576
154 295 276 432 444
Can you find some multiplicative grids? What about other bases? What about non-rectangular grids? What if each entry in the grid is k digits?
2. Suppose k, m, and n are positive integers. If we group the integers 1 through mn into m groups of n and multiply the numbers in each group, how close can the sum of k of these products be to the sum of the other m-k products? For example,
7⋅8⋅11 = 1⋅3⋅12 + 2⋅4⋅5 + 6⋅9⋅10
2⋅5⋅6 + 8⋅9⋅11 = 1⋅3⋅4 + 7⋅10⋅12
Unfortunately, sometimes we can only get close. This left-hand side and right-hand side differ by 2:
4⋅5⋅8⋅12 ≈ 1⋅2⋅7⋅10 + 3⋅6⋅9⋅11
What are the best we can do for various values of m, n, and k?
3. For which integers n > 1 and m does the expression P = xn + xn-1 + . . . + x2 + x + m factor over the integers? What infinite families are there? Can you find any other polynomials of this form that factor over the integers without a linear factor, other than the ones below?
x7 + x6 + x5 + x4 + x3 + x2 + x – 2 = (x3 + x – 1)(x4 + x3 + x + 2)
x13 + x12 + x11 + . . . + x3 + x2 + x – 3 = (x3 + x2 – 1)(x10 + x8 + x7 + 2x5 + x3 + 2x2 – x + 3)
x4 + x3 + x2 + x + 12 = (x2 + 3x + 4)(x2 – 2x + 3)
x8 + x7 + x6 + x5 + x4 + x3 + x2 + x + 20 = (x4 – x3 + x2 – 3x + 4)(x4 + 2x3 + 2x2 + 4x + 5)
x10 + x9 + x8 + . . . + x3 + x2 + x – 22 = (x2 + x + 2)(x8 – x6 + 2x5 + x4 – 4x3 + 3x2 + 6x – 11)
x5 + x4 + x3 + x2 + x – 55 = (x2 – x + 5)(x3 + 2x3 – 2x – 11)
1. Consider rectangular grids of digits where the product of the numbers in the rows is equal to the product of the numbers in the columns. Since leading 0's should not exist and trailing 0's are less interesting, we only allow positive digits. We also have excluded grids that contain multiple copies of the same factor. We call these multiplicative grids. For example, the 3×2 rectangular grids are shown below.
135 156 194 567 576
154 295 276 432 444
Can you find some multiplicative grids? What about other bases? What about non-rectangular grids? What if each entry in the grid is k digits?
2. Suppose k, m, and n are positive integers. If we group the integers 1 through mn into m groups of n and multiply the numbers in each group, how close can the sum of k of these products be to the sum of the other m-k products? For example,
7⋅8⋅11 = 1⋅3⋅12 + 2⋅4⋅5 + 6⋅9⋅10
2⋅5⋅6 + 8⋅9⋅11 = 1⋅3⋅4 + 7⋅10⋅12
Unfortunately, sometimes we can only get close. This left-hand side and right-hand side differ by 2:
4⋅5⋅8⋅12 ≈ 1⋅2⋅7⋅10 + 3⋅6⋅9⋅11
What are the best we can do for various values of m, n, and k?
3. For which integers n > 1 and m does the expression P = xn + xn-1 + . . . + x2 + x + m factor over the integers? What infinite families are there? Can you find any other polynomials of this form that factor over the integers without a linear factor, other than the ones below?
x7 + x6 + x5 + x4 + x3 + x2 + x – 2 = (x3 + x – 1)(x4 + x3 + x + 2)
x13 + x12 + x11 + . . . + x3 + x2 + x – 3 = (x3 + x2 – 1)(x10 + x8 + x7 + 2x5 + x3 + 2x2 – x + 3)
x4 + x3 + x2 + x + 12 = (x2 + 3x + 4)(x2 – 2x + 3)
x8 + x7 + x6 + x5 + x4 + x3 + x2 + x + 20 = (x4 – x3 + x2 – 3x + 4)(x4 + 2x3 + 2x2 + 4x + 5)
x10 + x9 + x8 + . . . + x3 + x2 + x – 22 = (x2 + x + 2)(x8 – x6 + 2x5 + x4 – 4x3 + 3x2 + 6x – 11)
x5 + x4 + x3 + x2 + x – 55 = (x2 – x + 5)(x3 + 2x3 – 2x – 11)
Problem of the Month (August 2009)
This month we investigate three problems involving products.
1. Consider rectangular grids of digits where the product of the numbers in the rows is equal to the product of the numbers in the columns. Since leading 0's should not exist and trailing 0's are less interesting, we only allow positive digits. We also have excluded grids that contain multiple copies of the same factor. We call these multiplicative grids. For example, the 3×2 rectangular grids are shown below.
135 156 194 567 576
154 295 276 432 444
Can you find some multiplicative grids? What about other bases? What about non-rectangular grids? What if each entry in the grid is k digits?
2. Suppose k, m, and n are positive integers. If we group the integers 1 through mn into m groups of n and multiply the numbers in each group, how close can the sum of k of these products be to the sum of the other m-k products? For example,
7⋅8⋅11 = 1⋅3⋅12 + 2⋅4⋅5 + 6⋅9⋅10
2⋅5⋅6 + 8⋅9⋅11 = 1⋅3⋅4 + 7⋅10⋅12
Unfortunately, sometimes we can only get close. This left-hand side and right-hand side differ by 2:
4⋅5⋅8⋅12 ≈ 1⋅2⋅7⋅10 + 3⋅6⋅9⋅11
What are the best we can do for various values of m, n, and k?
3. For which integers n > 1 and m does the expression P = xn + xn-1 + . . . + x2 + x + m factor over the integers? What infinite families are there? Can you find any other polynomials of this form that factor over the integers without a linear factor, other than the ones below?
x7 + x6 + x5 + x4 + x3 + x2 + x – 2 = (x3 + x – 1)(x4 + x3 + x + 2)
x13 + x12 + x11 + . . . + x3 + x2 + x – 3 = (x3 + x2 – 1)(x10 + x8 + x7 + 2x5 + x3 + 2x2 – x + 3)
x4 + x3 + x2 + x + 12 = (x2 + 3x + 4)(x2 – 2x + 3)
x8 + x7 + x6 + x5 + x4 + x3 + x2 + x + 20 = (x4 – x3 + x2 – 3x + 4)(x4 + 2x3 + 2x2 + 4x + 5)
x10 + x9 + x8 + . . . + x3 + x2 + x – 22 = (x2 + x + 2)(x8 – x6 + 2x5 + x4 – 4x3 + 3x2 + 6x – 11)
x5 + x4 + x3 + x2 + x – 55 = (x2 – x + 5)(x3 + 2x3 – 2x – 11)
1. Consider rectangular grids of digits where the product of the numbers in the rows is equal to the product of the numbers in the columns. Since leading 0's should not exist and trailing 0's are less interesting, we only allow positive digits. We also have excluded grids that contain multiple copies of the same factor. We call these multiplicative grids. For example, the 3×2 rectangular grids are shown below.
135 156 194 567 576
154 295 276 432 444
Can you find some multiplicative grids? What about other bases? What about non-rectangular grids? What if each entry in the grid is k digits?
2. Suppose k, m, and n are positive integers. If we group the integers 1 through mn into m groups of n and multiply the numbers in each group, how close can the sum of k of these products be to the sum of the other m-k products? For example,
7⋅8⋅11 = 1⋅3⋅12 + 2⋅4⋅5 + 6⋅9⋅10
2⋅5⋅6 + 8⋅9⋅11 = 1⋅3⋅4 + 7⋅10⋅12
Unfortunately, sometimes we can only get close. This left-hand side and right-hand side differ by 2:
4⋅5⋅8⋅12 ≈ 1⋅2⋅7⋅10 + 3⋅6⋅9⋅11
What are the best we can do for various values of m, n, and k?
3. For which integers n > 1 and m does the expression P = xn + xn-1 + . . . + x2 + x + m factor over the integers? What infinite families are there? Can you find any other polynomials of this form that factor over the integers without a linear factor, other than the ones below?
x7 + x6 + x5 + x4 + x3 + x2 + x – 2 = (x3 + x – 1)(x4 + x3 + x + 2)
x13 + x12 + x11 + . . . + x3 + x2 + x – 3 = (x3 + x2 – 1)(x10 + x8 + x7 + 2x5 + x3 + 2x2 – x + 3)
x4 + x3 + x2 + x + 12 = (x2 + 3x + 4)(x2 – 2x + 3)
x8 + x7 + x6 + x5 + x4 + x3 + x2 + x + 20 = (x4 – x3 + x2 – 3x + 4)(x4 + 2x3 + 2x2 + 4x + 5)
x10 + x9 + x8 + . . . + x3 + x2 + x – 22 = (x2 + x + 2)(x8 – x6 + 2x5 + x4 – 4x3 + 3x2 + 6x – 11)
x5 + x4 + x3 + x2 + x – 55 = (x2 – x + 5)(x3 + 2x3 – 2x – 11)
Thursday, August 20, 2009
How do I put AdSense on my blog (using Layouts)?
Print
First of all, choose the blog that you want to put AdSense on, and go to the Layout | Monetize tab. You can get there by clicking the Layout link on the dashboard, or clicking the Template tab from the posting or settings page of the blog.
Once you're there, choose one of the three options to display your ads: in your sidebar and posts, just in your sidebar, or just below your posts.
The next page asks you to either sign up for a new AdSense account or use an existing one. Once you've signed in or created or account, you'll get a confirmation screen. If for any reason you need to switch to using a different AdSense account, click the switch AdSense accounts
Print
First of all, choose the blog that you want to put AdSense on, and go to the Layout | Monetize tab. You can get there by clicking the Layout link on the dashboard, or clicking the Template tab from the posting or settings page of the blog.
Once you're there, choose one of the three options to display your ads: in your sidebar and posts, just in your sidebar, or just below your posts.
The next page asks you to either sign up for a new AdSense account or use an existing one. Once you've signed in or created or account, you'll get a confirmation screen. If for any reason you need to switch to using a different AdSense account, click the switch AdSense accounts
First of all, choose the blog that you want to put AdSense on, and go to the Layout | Monetize tab. You can get there by clicking the Layout link on the dashboard, or clicking the Template tab from the posting or settings page of the blog.
Once you're there, choose one of the three options to display your ads: in your sidebar and posts, just in your sidebar, or just below your posts.
The next page asks you to either sign up for a new AdSense account or use an existing one. Once you've signed in or created or account, you'll get a confirmation screen. If for any reason you need to switch to using a different AdSense account, click the switch AdSense accounts
First of all, choose the blog that you want to put AdSense on, and go to the Layout | Monetize tab. You can get there by clicking the Layout link on the dashboard, or clicking the Template tab from the posting or settings page of the blog.
Once you're there, choose one of the three options to display your ads: in your sidebar and posts, just in your sidebar, or just below your posts.
The next page asks you to either sign up for a new AdSense account or use an existing one. Once you've signed in or created or account, you'll get a confirmation screen. If for any reason you need to switch to using a different AdSense account, click the switch AdSense accounts
How do I put AdSense on my blog (using Layouts)?
Print
First of all, choose the blog that you want to put AdSense on, and go to the Layout | Monetize tab. You can get there by clicking the Layout link on the dashboard, or clicking the Template tab from the posting or settings page of the blog.
Once you're there, choose one of the three options to display your ads: in your sidebar and posts, just in your sidebar, or just below your posts.
The next page asks you to either sign up for a new AdSense account or use an existing one. Once you've signed in or created or account, you'll get a confirmation screen. If for any reason you need to switch to using a different AdSense account, click the switch AdSense accounts
Print
First of all, choose the blog that you want to put AdSense on, and go to the Layout | Monetize tab. You can get there by clicking the Layout link on the dashboard, or clicking the Template tab from the posting or settings page of the blog.
Once you're there, choose one of the three options to display your ads: in your sidebar and posts, just in your sidebar, or just below your posts.
The next page asks you to either sign up for a new AdSense account or use an existing one. Once you've signed in or created or account, you'll get a confirmation screen. If for any reason you need to switch to using a different AdSense account, click the switch AdSense accounts
First of all, choose the blog that you want to put AdSense on, and go to the Layout | Monetize tab. You can get there by clicking the Layout link on the dashboard, or clicking the Template tab from the posting or settings page of the blog.
Once you're there, choose one of the three options to display your ads: in your sidebar and posts, just in your sidebar, or just below your posts.
The next page asks you to either sign up for a new AdSense account or use an existing one. Once you've signed in or created or account, you'll get a confirmation screen. If for any reason you need to switch to using a different AdSense account, click the switch AdSense accounts
First of all, choose the blog that you want to put AdSense on, and go to the Layout | Monetize tab. You can get there by clicking the Layout link on the dashboard, or clicking the Template tab from the posting or settings page of the blog.
Once you're there, choose one of the three options to display your ads: in your sidebar and posts, just in your sidebar, or just below your posts.
The next page asks you to either sign up for a new AdSense account or use an existing one. Once you've signed in or created or account, you'll get a confirmation screen. If for any reason you need to switch to using a different AdSense account, click the switch AdSense accounts
Getting started with Google Reader
from Welcome to Google Reader! by the Google Reader team
Google Reader lets you subscribe to your favorite websites so new content comes to you when it's posted.
Reader keeps track of which things you've read so that when you only see unread items when you come back. If there's a dark blue border around an item, Reader is marking that item as read.
Give it a try by scrolling down to the next item!
Google Reader lets you subscribe to your favorite websites so new content comes to you when it's posted.
Reader keeps track of which things you've read so that when you only see unread items when you come back. If there's a dark blue border around an item, Reader is marking that item as read.
Give it a try by scrolling down to the next item!
Getting started with Google Reader
from Welcome to Google Reader! by the Google Reader team
Google Reader lets you subscribe to your favorite websites so new content comes to you when it's posted.
Reader keeps track of which things you've read so that when you only see unread items when you come back. If there's a dark blue border around an item, Reader is marking that item as read.
Give it a try by scrolling down to the next item!
Google Reader lets you subscribe to your favorite websites so new content comes to you when it's posted.
Reader keeps track of which things you've read so that when you only see unread items when you come back. If there's a dark blue border around an item, Reader is marking that item as read.
Give it a try by scrolling down to the next item!
Wednesday, August 19, 2009
Math or Magic
As someone once said: 'There's an easy way to do something, and an unlimited number of difficult ways'.
Take simple division, for example:
Suppose you need to divide 43 by 9.
The answer is 4 (the first figure of 43) and the remainder is 7 (4 + 3).
Similarly 35 divided by 9 is 3 remainder 8.
In the Vedic system we use the natural properties of numbers.
The number 9 has the property that it is 1 below 10. So every 10 contains one 9 and one remainder.
Therefore, in 40, there will be 4 nines and 4 remainder. and so in 43 there must be 4 nines and 7 remainder.
This can be developed in many ways. For example to divide 123 by 9 the answer is 13 remainder 6.
The first figure of the answer (1 in the 13) is the first figure of 123.
The second figure of the answer (3 in the 13) is 1+2 (add the first two figures of 123).
The remainder is 6 is 1+2+3 (add all three figures of 123).
As B. K. Tirthaji (the man who reconstructed the Vedic system) said: 'its magic until you understand it, and its mathematics thereafter'
Take simple division, for example:
Suppose you need to divide 43 by 9.
The answer is 4 (the first figure of 43) and the remainder is 7 (4 + 3).
Similarly 35 divided by 9 is 3 remainder 8.
In the Vedic system we use the natural properties of numbers.
The number 9 has the property that it is 1 below 10. So every 10 contains one 9 and one remainder.
Therefore, in 40, there will be 4 nines and 4 remainder. and so in 43 there must be 4 nines and 7 remainder.
This can be developed in many ways. For example to divide 123 by 9 the answer is 13 remainder 6.
The first figure of the answer (1 in the 13) is the first figure of 123.
The second figure of the answer (3 in the 13) is 1+2 (add the first two figures of 123).
The remainder is 6 is 1+2+3 (add all three figures of 123).
As B. K. Tirthaji (the man who reconstructed the Vedic system) said: 'its magic until you understand it, and its mathematics thereafter'
Fantastic Math Trick
Multiply Up to 20X20 In Your Head
In just FIVE minutes you should learn to quickly multiply up to 20x20 in your head. With this trick, you will be able to multiply any two numbers from 11 to 19 in your head quickly, without the use of a calculator.
I will assume that you know your multiplication table reasonably well up to 10x10.
Try this:
Take 15 x 13 for an example.
Always place the larger number of the two on top in your mind.
Then draw the shape of Africa mentally so it covers the 15 and the 3 from the 13 below. Those covered numbers are all you need.
First add 15 + 3 = 18
Add a zero behind it (multiply by 10) to get 180.
Multiply the covered lower 3 x the single digit above it the "5" (3x5= 15)
Add 180 + 15 = 195.
In just FIVE minutes you should learn to quickly multiply up to 20x20 in your head. With this trick, you will be able to multiply any two numbers from 11 to 19 in your head quickly, without the use of a calculator.
I will assume that you know your multiplication table reasonably well up to 10x10.
Try this:
Take 15 x 13 for an example.
Always place the larger number of the two on top in your mind.
Then draw the shape of Africa mentally so it covers the 15 and the 3 from the 13 below. Those covered numbers are all you need.
First add 15 + 3 = 18
Add a zero behind it (multiply by 10) to get 180.
Multiply the covered lower 3 x the single digit above it the "5" (3x5= 15)
Add 180 + 15 = 195.
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