W
_________________________________________________________________________________________________
- walk
. - May be
read at http://www.harcourt.com/dictionary /browse/19/
.
- Wallis formulas
. - May be
read at http://www.harcourt.com/dictionary /browse/19/
.
- wallpaper patterns
.
- Waring problem
. - In his Meditationes
algebraicae, Edward Waring (1734-1793) proposed a generalization of Lagrange's four-square
theorem (PL), stating that every rational integer is the sum
of a fixed number g(n) of >nth
powers of integers, where n is any given positive integer and
g(n) depends only on n. Waring
originally speculated that g(2) = 4, g(3) = 9,
and g(4) = 19. This problem has occupied mathematicians down to the
present day.
- Watson-Sommerfeld transformation
.
- May be read at http://www.harcourt.com/dictionary /browse/19/
.
- weak convergence
. - May be
read at http://www.harcourt.com/dictionary /browse/19/
.
- weak direct product
. - May be
read at http://www.harcourt.com/dictionary /browse/19/
.
- weaker topology
. - May be
read at http://www.harcourt.com/dictionary /browse/19/
.
- weak topology
. - May be
read at http://www.harcourt.com/dictionary /browse/19/
.
- weak* topology
. - May be
read at http://www.harcourt.com/dictionary /browse/19/
.
- Weber differential equation
.
- May be read at http://www.harcourt.com/dictionary /browse/19/
.
- Wedderburn theorems
. - May be
read at http://www.harcourt.com/dictionary /browse/19/
.
- weirdness in arithmetic theory
. - In the
traditional (quasi-axiomatic) teaching of arithmetic, students are "programmed" in "the
rule of signs" by such cant as "positive times positive equals positive, positive times negative
equals negative, negative times negative equals positive". Huh? "negative times negative equals
positive" -- "that's weird!" Similarly, "to divide one fraction by another fraction, invert the
divisor fraction and multiply". Weird! Actually, in constructing integers as vectors of naturals
and rationals as vectors of integers, the student can see that these rules follow from
perhaps the most "holy" of all rules in mathematics: closure ("all-in-the-family"),
which banishes "the weirdness".
- Weierstrass approximation theorem
.
- May be read at http://www.harcourt.com/dictionary /browse/19/
.
- Weierstrass elliptic function
.
- May be read at http://www.harcourt.com/dictionary /browse/19/
.
- Weierstrass functions
. - May be
read at http://www.harcourt.com/dictionary /browse/19/
.
- weight function
. - May be
read at http://www.harcourt.com/dictionary /browse/19/
.
- Weingarten formulas
. - May be
read at http://www.harcourt.com/dictionary /browse/19/
.
- well-defined, left ("left cancellative"
.
- An operation o is left well-defined (left cancellative) iff
a o b = a o c implies that b = c. The
operations of addition and multiplication are left well-defined ("left
cancellative") in all of the standard number systems of arithmetic. PL well-defined, right
and well-defined.
.
- well-defined, right ("right cancellative"
.
- An operation o is right well-defined (right cancellative) iff
a o b = c o b implies that a = c. The
operations of addition and multiplication are right well-defined ("right
cancellative") in all of the standard number systems of arithmetic. PL well-defined, left and well-defined.
- well-defined ("cancellative")
. - An
operation o is well-defined (cancellative) iff it is both both
left well-defined and right well-defined. The operations of addition and multiplication
are well-defined ("cancellative") in all of the standard number systems of arithmetic. PL
well-defined, right and well-defined, left. An operation o
has an partial or total inverse (PL) iff it is well-defined. It is noted elsewhere
that (1)defining inverses and (2)rendering them total induces all of the number systems
(PL) besides the natural numbers (PL). Hence, the well-defined property relates
critically to the development of arithmetic.
- well-formed formula
. - May be
read at http://www.harcourt.com/dictionary /browse/19/
.
- well-ordering
. - May be
read at http://www.harcourt.com/dictionary /browse/19/
.
- well-ordering principle
. - May be
read at http://www.harcourt.com/dictionary /browse/19/
.
- well-posed problem
. - May be
read at http://www.harcourt.com/dictionary /browse/19/
.
- Weyl group
. - May be
read at http://www.harcourt.com/dictionary /browse/19/
.
- wheel
. - May be
read at http://www.harcourt.com/dictionary /browse/19/
.
- Whewell equation
. - May be
read at http://www.harcourt.com/dictionary /browse/19/
.
- white stochastic process
. - May be
read at http://www.harcourt.com/dictionary /browse/19/
.
- Whittaker differential equation
.
- May be read at http://www.harcourt.com/dictionary /browse/19/
.
- whole numbers
. - Slang for integers
or "integral fractions".
- Wiener-Hopf method
. - May be
read at http://www.harcourt.com/dictionary /browse/19/
.
- Wiener-Khintchine theorem
. - May be
read at http://www.harcourt.com/dictionary /browse/19/
.
- Wiener process
. - May be
read at http://www.harcourt.com/dictionary /browse/19/
.
- Wilson's theorem
. - May be
read at http://www.harcourt.com/dictionary /browse/19/
.
- winding number
. - May be
read at http://www.harcourt.com/dictionary /browse/19/
.
- witch of Agnesi
. - May be
read at http://www.harcourt.com/dictionary /browse/19/
.
- word
. - May be
read at http://www.harcourt.com/dictionary /browse/19/
.
- Wronskian
. - May be
read at http://www.harcourt.com/dictionary /browse/19/
.