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Browse College Definitions
Stars indicate particularly interesting answers or
good places to begin browsing.
 The Fourth Dimension [8/24/1995]

What is the fourth dimension mathematically?
 Fuzzy Logic [04/26/1997]

What is fuzzy logic?
 Galois Theory [06/27/1997]

Does factorization of polynomials have anything in common with Galois
Theory? What are Galois groups?
 General Comments on Standard Deviation [01/15/2004]

Answers to general questions about standard deviation including
vocabulary, interpretation, calculation, and history.
 Identity and Inverse Properties for Zero [01/07/2004]

If we subtract 0 from a number and get the same number, doesn't that
make 0 an identity for subtraction? Also, can't a number be its own
inverse for subtraction?
 Implicit Functions [11/26/1997]

Please give me a definition and several examples of an implicit function.
 Inclusive Definitions: Trapezoids [11/04/2004]

As far as I know, a trapezoid is defined as a quadrilateral with exactly one set of parallel sides. However, a very highly regarded educator and textbook author recently argued that this definition is incorrect. His definition of a trapezoid is that it is a quadrilateral that has at least one pair of parallel sides. A square, therefore, would be considered a trapezoid. Is he correct or are thousands of books going to be published with the wrong definition?
 The Königsberg Bridge [5/20/1996]

Do you have information on Konigsberg's bridge?
 Lagrange Multipliers [01/08/1998]

I have a problem with Lagrange Multipliers  can you help?
 Laplace Transforms [10/15/1997]

Can you explain me the overall concept of changing from TimeDomain to
FrequencyDomain with a Laplace or a Z Transform?
 Limit of x sin(1/x) [04/23/2002]

I assumed from the graph that the function had a limit at x=0 of 0,
but since it involves sin(1/0) I can not prove this using the basic
trigonometric limits (sin x/x and (1cos x)/x), L'Hopital's
rule, or by rearranging the equation. Can you help?
 Linear Algebra  Definition of Orthonormal [10/28/1997]

Show that the transition matrix P from one orthonormal basis to another
is unitary, that is, P*P = I.
 Linear Congruences of Gaussian Integers [04/11/2003]

When does the linear congruence zx congruent to 1 (mod m), for z, x,
and m all Gaussian integers, have a solution? Also, when do we say
that two Gaussian integers are relatively prime?
 Math Symbols [04/07/1997]

What do the common math symbols (backward E, upsidedown A, etc.) mean?
 Matrix Multiplication [09/04/1997]

I am doing a project in Algebra 2 and must research matrix
multiplication.
 The Meaning of 'Or' in Logic Statements [12/19/2003]

If a logic statement says, 'James is taking fencing or algebra,' does
that mean he is taking one class or the other, or could he be taking
both of them?
 Meaning of R++ [9/12/1996]

What do the symbols R_{+} and R_{++} mean?
 A More Formal Definition of the Imaginary Unit i [01/12/2004]

Many students are taught that the imaginary unit i is equal to the
square root of 1. In fact, this informal definition often leads to
confusion. Here's a more formal definition of i which goes a long way
towards clearing up the misconceptions.
 Naming Geometric and Arithmetic Progressions [04/04/2003]

Why is an exponential progression called 'geometric'? Why is a linear
progression called 'arithmetic'?
 Noether Rings [12/01/1997]

What are Noether rings and how do they work?
 Nonagon or Enneagon? [02/06/2003]

Is 'enneagon' really the correct name for a 9sided polygon?
 Pattern or Sequence? [10/02/2003]

What is the difference between a pattern and a sequence?
 Permutations, Combinations, Arrangements, and Strings [10/22/2007]

When a coin is tossed four times, is an outcome of HTTH considered a
permutation, a combination, or something else entirely?
 Pick's Theorem [2/8/1996]

I was wondering what Pick's theorem is.
 Polyhedra: Solids or Surfaces? [06/06/2003]

Is a polyhedron always a solid figure?
 Polynomial Degrees and Definition of a Field [03/02/1998]

The degree of polynomials added together, and definition of a field.
 Profit Margin and Percentage Markup [02/16/2007]

I own a small business and am a little confused about the difference
between a percentage markup and a profit margin. Are they the same
thing? If not, how are they different?
 Proportionality Symbol [05/20/2003]

Do you know the name of the little symbol used in the topic of rates
and variation that means 'in proportion to'?
 Quarternions [2/17/1996]

Can someone tell me what quarternions are?
 Range  Difference or Difference + 1? [08/05/2003]

Is range the same as 'difference' or not?
 Relative and Absolute Extrema of a Function [01/07/2004]

What is the difference between the absolute extrema and the relative
extrema in calculus?
 Rhombus vs. Rhomboid [08/27/2002]

What is the difference between a rhombus and a rhomboid?
 Scientific Notation and Engineering Notation [10/22/2003]

What is the difference between Scientific Notation and Engineering
Notation?
 The Second Octant [04/03/2002]

Where is the second octant? No one seems to know how to count the next
octants after the first.
 The Simplex Method [11/2/1996]

How does the simplex method work and what would I use it for?
 Tensor [10/01/1997]

Is there a layman's definition for a tensor, with an example?
 Tensor Calculus [03/06/1998]

Scalars, vectors, and tensors, and their components.
 Tensors and Spinors Defined [09/30/1999]

What are tensors and spinors? Can you explain giving examples?
 Transfinite Arithmetic [10/28/1997]

What is transfinite arithmetic? I pretty much know what it means, but I
am having trouble applying it to alephnull.
 Transfinite Numbers [11/07/1997]

I know that Georg Cantor discovered transfinite numbers, but what are
they?
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