Math/Chaos Theory
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Introduction to Group Theory
Groups are an interesting area of study in algebra, and find applications in other areas of mathematics, computer science, and other fields.
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Relations, Functions and Operations
The concepts of relations, functions and operations are a starting point in the understanding of various concepts in algebra, analysis and other areas of mathematics.
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Metric Spaces
A metric space is a set, together with a distance function defined on it, satisfying certain properties.
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Transcendental Numbers
Transcendental numbers are numbers, possibly complex, that cannot be expressed as the roots of polynomial equations with integer coefficients.
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The Evolution and Completeness of Number Systems
Number systems have been developed and extended over a long period of time, with the gaps in each system paving the path to a new one.
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Introduction to Series
A series, in mathematics, is the sum of the terms of an underlying sequence.
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Fermat's Little Theorem and RSA Cryptography
Pierre de Fermat's "Little Theorem" lies at the base of the RSA cryptographic algorithm.
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Countable Sets and Uncountable Sets
A set is said to be countable if all its elements can be listed in the form of a sequence.
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Srinivasa Ramanujan - A Biography
Born in a poor family in a south Indian village, Ramanujan greatly influenced the world of mathematics, in spite of his lack of formal education.
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Introduction to Sequences
A sequence is a function from the set of natural numbers to any given set.
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Michael Green and the Lucasian Chair
Michael Green, theoretical physicist, succeeds the likes of Sir Isaac Newton, Charles Babbage and Paul Dirac to become the next Lucasian Professor at Cambridge.
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Women in Mathematics
Until not too long ago, women were discouraged from studying science and mathematics. Even so, there were a select few who held their own and made their mark.
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The Beal Conjecture
The Beal Conjecture is an interesting number theoretic problem that came about as a by-product of Andrew Beal's work on Fermat's Last Theorem.
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Russell's Paradox
Mathematical statements are either true or false. When they are neither, they remind mathematicians to formulate their theories more accurately.
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Did Derren Brown Predict the Lottery Results?
Is there a pattern to the random winning numbers of lottery? Did Derren Brown predicted the British Lotto numbers by analysis of past draws or he create an illusion?
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Pythagoras' Theorem
Pythagoras' Theorem is a profound result that has allowed mathematicians to cut corners for centuries, and is surely among the greatest in all mathematics.
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A Brief Overview of Pi
Both a mathematical constant and an irrational value, the quest to find pi has absorbed mathematicians' minds for millennia.
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Binary, Octal, and Hexadecimal Number Systems
Computers store data using binary numbers. Binary numbers take up space to write down, so the octal and hexadecimal number systems are used to abbreviate them.
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Prime Factorization
Prime factors help when determining least common denominators and multiples. Prime factorization finds all the numbers (factors) which make up a larger number.
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How to Prove Pythagoras Theorem
Pythagoras Theorem is one of the best known formulae in mathematics, and one simple proof is demonstrated, along with some background about Pythagoras himself.
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What Does FOIL Mean in Mathematics?
Just like PEMDAS, FOIL is another acronym or mnemonic seen often in math classes. What does it mean though and how do students use "foiling" in their homework?
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Order of Operations in Mathematics
Many learned the Great Lakes as HOMES, but who knew such great mnemonics are now used in math classes? One prime example is PEMDAS in teaching the order of operations.
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The Game of Life
In 1970, British mathematician John Conway invented "The Game of Life," which became increasingly popular throughout the nineteen seventies among math enthusiasts.
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The Sieve of Eratosthenes
Throughout mathematical history, thinkers have attempted to come up with a great many methods by which to discover prime numbers. Eratosthenes' was perhaps the simplest.
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Rubik's Cube Evolves
Erno Rubik, inventor of the original Rubik's Cube, has invented the Rubik's 360 puzzle, unveiled on February 5, 2009 at the German toy industry fair.
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Using Roman Numerals
How long until Superbowl CII? What is LXIV + DCM? These are questions that most modern individuals could not reasonably know how to answer.
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Who Was Archimedes?
Archimedes is highly regarded in many circles. It was his remarkable mind - unrivaled but for a few individuals in history - which led to his legendary historical status.
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Commutativity in Mathematics and Nature
In mathematics, commutativity is a long word describing a very simple concept. A commutative process is one which can be reversed with no change in result.
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Ludwig Boltzmann's Statistics
When Atomic Theory began to grow in popularity during the nineteenth century, it did so in part thanks to the mathematical work of Austrian Physicist Ludwig Boltzmann.
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Multi-Variable Systems
Solving multi-variable systems is easy. All it takes is patience through a few easy steps.
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Chaos Theory and Water Droplets
Researchers at MIT have been working to explore the always-difficult world of chaos theory by way of a rather simple experiment involving bouncing water droplets.
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The Mathematics of the Beatles
In October of 2008, a math professor at Dalhousie University in Nova Scotia revealed an astonishing discovery: He had used math to understand the music of the Beatles!
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New Findings in Beauty and Mathematics
Mathematicians - like all scientists - are often on the lookout for a certain element of "beauty" in their formulas. But what does this beauty actually look like? And sh
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The Math and Physics of Golf Balls
New methods of computation are allowing mathematicians and physicists to finally begin to truly understand the physics of airflow around golf balls in flight.
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Complex Numbers
Complex numbers are numbers which are combinations of any real number plus the imaginary number. While difficult to comprehend, imaginary numbers are quite real.
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Computer-Assisted Proofs
Much of mathematics, both theoretical and practical, has been built up throughout the centuries in the language of proofs - formal statements of mathematical reasoning.
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What are Irrational Numbers?
Irrational numbers, though of great importance in many branches of mathematics, are difficult concepts for the human mind to grasp, for they are real, yet infinite.
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The Bernoulli Family Tree
The Bernoulli family, through four generations in the 16th and 17th centuries, was one of the most prominent and important mathematical and scientific families.
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Difference Equations and Modern Physics
Whereas in much of physics scientists tend to rely on differential equations to describe phenomena, certain physical theories find success by denying continuity.
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UCLA Find New Prime Number
Mathematicians at the University of California in Los Angeles (UCLA) were celebrating last night after discovering a new 13 million digit Mersenne Prime Number.
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The Rhind Papyrus
The Rhind Papyrus is perhaps the best known demonstration of the mathematics of ancient Egypt during the Second Intermediate Period.
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What is Differential Geometry?
Differential Geometry is a form of advanced mathematics which deals with the properties of continuous manifolds in multiple dimensions, using basic tools of calculus.
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The Poincare Conjecture
Discovered by French mathematician Henri Poincare in the first decade of the 20th century, the Poincare Conjecture is used to define spherical topology.
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Squaring the Circle
The problem of finding a square which has the exact same area as a given circle is a problem which for centuries eluded some of history's greatest mathematicians.
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Spherical Geometry
While most people are familiar with foundational geometrical principles which are essentially "flat," non-Euclidean geometry plays an important role in many cases.
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Hyperbolic Geometry
One of the most common families of non-Euclidean geometry is hyperbolic geometry - a self-consistent geometry of "obtuse" curvature.
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Lie Groups
The term "lie group" (pronounced "lee") refers to certain classifications of manifolds - a highly technical, difficult form of mathematics, but one with great pragmatic
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Numerical Integration
Numerical integration is a form of calculus which seeks to find the area under either a simple or a complex curve - more difficult than it sounds.
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Mathematical Identities
Over the course of one's mathematical education, they inevitably are forced to memorize a great many mathematical identities, maybe without even realizing it.
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The Prisoner's Dilemma
Developed by Merrill Flood and Melvin Dresher at RAND in 1950, the case of the "Prisoner's Dilemma" has become a classic example of a game theory conundrum.
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