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 TOPICS This page:   definitions    Search   Dr. Math See also the Internet Library:   dictionaries COLLEGE Algorithms Analysis Algebra    linear algebra    modern algebra Calculus Definitions Discrete Math Exponents Geometry    Euclidean/plane      conic sections/        circles      constructions      coordinate plane      triangles/polygons    higher-dimensional      polyhedra    non-Euclidean Imaginary/Complex   Numbers Logic/Set Theory Number Theory Physics Probability Statistics Trigonometry 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 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? Properties? Axioms? What to Call Characteristics of Field, and When [07/14/2014] An adult finds inconsistent labels for the characteristics of fields and rings. Doctor Peterson explains how different levels of abstraction warrant different vocabulary. 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. Page: []

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