Abstract Mathematics?
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Abstract mathematics is a huge field, with many parts. I would say, the simplest way to think about is that it is not focused on applications, like problems from engineering, or physics, or chemistry or economics. The problems in pure math, or abstract math, come from the field itself. \n\nIn real math, there is very little done with arithmetic. It all is about constructing rules for systems, called axioms, and then finding out what the implications of those axioms are. The main activity is doing proofs, which can be very challenging. \n\nIt includes things like set theory, and number theory. \n\nAnd for 2+2=5: if you set up your axioms the right way, you can prove anything. For example, what do the symbols 2, +, = and 5 mean anyway?
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There used to be a lot of them, but with computers these days they are being solved by brute force. Examples include Fermat's Last Theorem and the Four Color problem in topology. You can look those up to see what they are, and you will probably find sites listing other unsolved mathematical puzzles.
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Check out http://math.mit.edu/research/index.html
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Some form of math has been around as long as people have.  "The evolution of mathematics might be seen to be an ever-increasing series of abstractions, or alternatively an expansion of subject matter. The first abstraction was probably that of numbers. The realization that two apples and two oranges do have something in common, namely that they fill the hands of exactly one person, was a breakthrough in human thought. In addition to recognizing how to count concrete objects, prehistoric peoples also recognized how to count abstract quantities, like time -- days, seasons, years. Arithmetic (e.g. addition, subtraction, multiplication and division), naturally followed. Monolithic monuments testify to a knowledge of geometry."
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http://aleph0.clarku.edu/~djoyce/mathhist/mathhist.html
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There are two seminar papers by Magnus Hestenes that should give you a good start:\n\n"A  Ternary Algebra with Applications to Matrices and Linear Transformation"\n\n"On a Ternary Algebra"
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mathematics\n\nScience of structure, order, and relation that has evolved from counting, measuring, and describing the shapes of objects. It deals with logical reasoning and quantitative calculation. Since the 17th century it has been an indispensable adjunct to the physical sciences and technology, to the extent that it is considered the underlying language of science. \n\nAmong the principal branches of mathematics are algebra, analysis, arithmetic, combinatorics, Euclidean and non-Euclidean geometries, game theory, number theory, numerical analysis, optimization, probability, set theory, statistics, topology, and trigonometry.
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Abstract algebra is the field of mathematics concerned with the study of algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras.\nLinear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (also called linear spaces), linear transformations, and systems of linear equations in finite dimensions.\nIn abstract algebra, a Boolean algebra is an algebraic structure (a collection of elements and operations on them obeying defining axioms) that captures essential properties of both set operations and logic operations. Specifically, it deals with the set operations of intersection, union, complement; and the logic operations of AND, OR, NOT.\n\nCollege algebra covers Algebraic operations, Equations and inequalities, Functions and their properties, Number systems and operations.\nThe easiest one is College Algebra
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What you want is a math forum...\n\nNot a how hot is my avatar forum... Good luck with that!
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Ask Dr. Math is my favorite.  You can also try Mathworld, though I usually find that I leave it more confused than when I entered.
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Have fun:\nhttp://www.math.nyu.edu/~griffith/teaching/06numanalysis/labs/bisection/
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Try searching for "Mathematics site:ph"\nYou can replace Mathematics by more specific areas of interest.
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Here are some topics you could try:\nVedic Mathematics\nPolynomials\nLinear Equations\nNumber Systems\nLines and Angles\nQuadrilaterals\nAreas\nTriangles\nSurface Areas\nVolumes
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You might try asking this question under "Mathematics."
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I did a paper on the History of 0,1, and infinity for a grad school paper.  It worked out really well.  There is a lot of history of how different societies developed mathematics and accepted fractions, algebra.  Good luck!
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I am a math major so I have taken every math class. Start with Elementary Statristics...it is not that bad mostly pie and bar graphs for the first half of the semester.
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Here's a nice site:\n\nhttp://www.mathematische-basteleien.de/tangrams.htm