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Browse College Definitions

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Equivalent Matrices [7/12/1996]
What are equivalent matrices? How do I use them?

Euclidean and Division Algorithms [11/26/1997]
Can you show and explain the proofs of the Euclidean Algorithm and the Division Algorithm?

Exp, Log, and Ln Functions Explained [7/31/1996]
What is the exp function? When is it needed? Also, how do I calculate Log and Ln functions with basic arithmetic and logic?

Galois Theory [11/20/1996]
Please explain Galois Theory.

Information About Topology [11/12/1996]
Where can I learn more about topology?

Modular Forms and Elliptic Curves: Taniyama-Shimura [10/30/1997]
I watched a PBS show on Fermat's last theorem and they kept talking about modular forms and elliptic curves and how they are related. What are they, and how so they relate to one another?

The Number e [6/3/1996]
Is "e" a number like Pi? How does "e" relate to continued fractions?

Set Terminology [07/07/1997]
What does the terminology inf{...} mean?

Use of Tensors [7/23/1996]
What are the uses and properties of tensors?

What is Calculus? [05/06/1997]
What is calculus and how does it work?

0 Raised to a Power [04/25/2002]
What is the limit of 0^n as n approaches infinity? Can you explain why it equals zero or why it can't equal zero, or if it's undefined?

Are Angles Dimensionless? [08/31/2003]
If you look at the dimensions in the equation arc length = r*theta, it appears that angles must be dimensionless. But this can't be right. Or can it?

Bounded Set [06/24/2003]
Let S be a set of real numbers. Prove that the following are equivalent: (a) S is bounded, i.e. there exists a number M greater than 0 such that abs(x) is less than or equal to M for every x in S; (b) S has an upper bound and lower bound.

Ceiling and Floor Function Notation [11/16/2002]
What is the symbol to replace 'integer round-up' ?

Combinatorics: Ramsey Theory [01/12/1998]
Could you help me with a detailed explanation of the theory and a concrete example?

Complete This Square: x^2 + y^2 - 6x + 2 = 0 [03/16/2003]
I thought completing the square only involved quadratic functions, such as f(x) = ax^2 + bx + c = 0. This question relates to the equation of a circle...

Congruence Class of 10^n Modulo 11 [04/14/2003]
What is the congruence class of 10^n modulo 11? Use this to determine the remainder when 654321 is divided by 11.

Congruence Symbol [05/23/2003]
How does congruence (3-lined symbol) relate to equality (=)?

Conjectures vs. Hypotheses [01/12/1999]
What is the difference between the terms 'conjecture' and 'hypothesis'? Should the Riemann hypothesis be the Riemann conjecture?

The Continuum Hypothesis [5/24/1995]
What is it the continuum theory, and has it been resolved?

Contrapositives and Monotonic Functions [03/17/2003]
Defining 'monotonic' (increasing or decreasing functions) and 'contrapositive'.

Covariance [02/05/1997]
What does covariance represent?

Curve Fitting Algorithm [6/20/1996]
Can you explain "least squares approximation"?

Defining Modulus [12/10/2002]
I understand when this term is used to describe the congruent b-c relation as mod (b,m), but why when we apply it to graphs does it translate as 'absoluted/directed value of'?

Defining Multiplication [08/16/2002]
What is the distinction between 3*4 and 4*3?

Defining Positive Zero [03/07/2003]
The definite integral of f(x) from 0 to x has exactly one positive zero at x = a. What's a 'positive zero'?

Definition and Origin of the Word "Radical" [06/22/2005]
I'm curious what the exact definition of "radical" is and also where and when the word originated.

Definition of a Rolling or Moving Average [03/05/2004]
When someone says they have calculated a "rolling average," what exactly does that mean? I cannot find the definition in any math books.

Definitions as a Tool of Mathematics [03/04/2003]
Defining polyhedra: regarding unusual polyhedra, how can we exclude 'doubled' shapes, e.g. two tetrahedra that join at a single vertex (sort of like an hourglass)?

Definitions of Edge and Face in 2D and 3D [10/10/2008]
What is the 'official' definition of 'edge'? Specifically, is an edge restricted to the intersection of two non-coplanar faces or do two- dimensional shapes have edges? I'm also curious about a definition of 'face'. How many faces does a two-dimensional shape have?

Degrees of Freedom [12/17/2002]
What is meant by 'degrees of freedom'?

Determinant of a Matrix [11/05/1997]
Can you give us a definition for the determinant of a matrix?

Difference Between arsinh and arcsinh Functions [05/13/2004]
Why isn't there a "c" in arsinh, arcosh, and artanh? These are the equivalents of arcsin, arccos and arctan but they are hyperbolic.

Eigenvectors [05/13/1997]
What are eigenvectors?

Euclidean Algorithms [3/13/1996]
What is the Euclidean algorithm? What is a "constructible" number? What can you tell me about Diophantine equations?

Explaining the Determinant [11/16/1997]
I am trying to understand what the determinant of a matrix actually is.

Explain Supremum [02/02/1998]
Can you please explain, perhaps with an example, the concept of "supremum"?

Fibonacci sequence [1/28/1996]
What is the explicit formula for the Fibonacci numbers?

Finite Simple Groups [3/15/1996]
What is the Monster - large finite simple group - and why is it interesting?

Flavors of Facts [10/03/2003]
Is 1+1=2 a fact, or is it open to interpretation?

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