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Browse College Definitions

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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 Time-Domain to Frequency-Domain 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 (1-cos 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, upside-down 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 9-sided 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 aleph-null.

Transfinite Numbers [11/07/1997]
I know that Georg Cantor discovered transfinite numbers, but what are they?

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