Math Concepts Flashcards
(279 cards)
1
Q
Systems are generally tested for this property by calculating the largest Lyapunov exponent and seeing if it is positive.
A
Chaos Theory
2
Q
De Morgan’s laws state that this operation performed on the union of two sets is equal to the intersection of this operation performed on each of the sets.
A
Complementary
3
Q
Basic arithmetic operation of combining two or more numbers to obtain their sum.
A
Addition
4
Q
Its equation is x squared plus y squared equals r squared.
A
Circle
5
Q
For a Cartesian space it is the number of coordinates needed to specify a point.
A
Dimension
6
Q
This quantity for a smooth manifold is the number of independent variables needed to parametrize it, and for a vector space this quantity is the cardinality of the largest linearly independent subset.
A
Dimension
7
Q
If a function whose values are numbers of this type is differentiable at every point of its domain, then it is known as a holomorphic function.
A
Complex Numbers
8
Q
This operation can be performed on a complex function if both its real and imaginary parts are harmonic, or equivalently =, that it satisfies the Cauchy-Riemann equations, a condition called holomorphicity.
A
Derivative
9
Q
A geometric problem that involves dividing an angle into three equal parts using only a compass and straightedge.
A
Angle Trisection
10
Q
Written as A given B equals probability of B given A times probability of B given A times probability of A over probability of B.
A
Bayes’ Theorem
11
Q
Characterized by the famous “butterfly effect”, where small changes in initial conditions can lead to significant differences in outcomes.
A
Chaos Theory
12
Q
The Scharz-Christoffel mapping is applied on sets of these numbers, as are all conformal mappings.
A
Complex Numbers
13
Q
The study of random variables that do not have this property is called free probability.
A
Commutative/Commutative Property
14
Q
For an orthogonal projection, the kernel and image have this relationship.
A
Complementary
15
Q
In the calculus of variations, the smallest value of this quantity for distinct objects is the geodesic.
A
Distance
16
Q
Contrasted with concave.
A
Convexity
17
Q
This function is on the main diagonal of a two-dimensional rotation matrix.
A
Cosine function/Cosine
18
Q
Has a volume equal to one-third pi time r squared times h.
A
Cone
19
Q
Applying this operation to a constant give zero since it gives the instantaneous rate of change.
A
Derivative
20
Q
It is the base for solutions to the differential equation y-prime equals y, and the derivative of this number to the power x is equal to itself.
A
e/Euler’s Number
21
Q
According to the inverse function theorem, a function which has continuity and this property is homeomorphic.
A
Differentiable
22
Q
This value gives the ratio of the area of a shape after a linear transformation to the original area.
A
Determinant
23
Q
Its namesake law is a generalization of the Pythagorean Theorem.
A
Cosine function/Cosine
24
Q
This number is equal to approximately 2.718.
A
e/Euler’s Number
25
Both communitive and associative
Addition and Multiplication
26
This line segment is the longest possible chord of a circle, since it passes through the center.
Diameter
27
This value equals zero when a homogeneous equation has a nontrivial solution.
Determinant
28
Name this operation taken on matrices and symbolized by straight lines.
Determinant
29
The difference between them and their totient is at least two.
Composite Number
30
This type of equation relates a function to its rate of change.
Differential Equations
31
A double angle identity for this function is that with an input of two theta, it equals the quantity on minus the tangent squared of theta over the quantity one plus the tangent squared of theta.
Cosine function/Cosine
32
Arbitrarily long sequences of these numbers can be found by starting at n-factorial plus n, and there is no jump in the function pi of x at each of them.
Composite Number
33
Solutions from Cramer’s rule can be found by taking the quotient of two values for this quantity that can be found by expanding along a row.
Determinant
34
Although every differentiable function has this property, the opposite does not hold- as exemplified by the Weirestrass function being not differentiable, despite having this property.
Continuity
35
The impossibility of trisecting an arbitrary angle using only those two tools.
Angle Trisection
36
The covering variety of this property is always less than or equal to the large inductive variety.
Dimension
37
An algorithm named for Euclid can be used to find the GCD, or to perform this operation on integers. (The Euclidean Algorithm)
Division
38
Can be used to solve the Monty Hall problem.
Bayes' Theorem
39
Identify this property that applies to addition and multiplication in which x plus y equals y plus x.
Commutative/Commutative Property
40
Used to calculate the posterior probability and relates the actual probability of an event to the measured probability in a test.
Bayes' Theorem
41
Refers to the measurement of the extent or size of a two-dimensional space or shape.
Area
42
Matrices with the property described by this term are both upper triangular and lower triangular, and their only nonzero elements form a line between the upper left and lower right corners.
Diagonal
43
Give this term for lines which are neither horizontal nor vertical.
Diagonal
44
An interval with this property contains its limit points, which means that it includes both of its endpoints.
Closed
45
The nth Catalan number can be found using one over n plus one times one of these numbers.
Binomial Coefficients
46
Integrating functions of this type gives a quartic equation, while differentiating them gives a quadratic.
Cubic
47
The process of finding a derivative is called what?
Differentiation
48
This term refers to angles whose values sum to 90.
Complementary
49
These numbers are crossed out in the Sieve of Eratosthenes, because they are divisible by a lower, circled number.
Composite Number
50
Prince Rupert’s problem deals with two of these and it is an equilateral zonohedron.
Cube
51
The tesseract is a higher-dimensional analogue of this shape.
Cube
52
What measurement is equal to twice the circle’s radius.
Diameter
53
One type of this operation occurs when there are multiple variables, and it is called partial.
Derivative
54
One of these is named after Dijkstra
Algorithm
55
In the standard normal density function, this number is raised to the minus x squared over two power.
e/Euler's Number
56
Big-O used to express the amount of time and space these procedures use.
Algorithm
57
Can be calculated using Brettschneider’s formula.
Area of a Quadrilateral
58
This is an even trigonometric function which is the reciprocal of secant and the cofunction of sine.
Cosine function/Cosine
59
This is evaluated to find a characteristic equation, which is solved to find eigenvalues.
Determinant
60
The midpoint of each side of a triangle, the foot of each altitude, and the midpoint of each line segment stretching from the vertex of the orthocenter are the nine points used to define one of these shapes (This type would be called the nine-point one).
Circle
61
Families of these geometric shapes orthogonal to one another are named for Apollonius of Perga.
Circle
62
Edward Larenz pioneered this field of math by concluding that weather is nearly impossible to predict accurately due to its sensitivity to initial conditions.
Chaos Theory
63
This quantity raised to the power of i pi is equal to negative one.
e/Euler's Number
64
Groups with this property have only normal subgroups and are called abelian.
Commutative/Commutative Property
65
A “synthetic” version of this operation can be used on polynomials.
Division
66
Real functions have this property is for all x in the domain, the limit of the function as it approaches x equals the function’s value at that point.
Continuity
67
For a group of sets of this type in the plane, if any three of the sets intersect, then they all intersect by Helly’s Theorem.
Convexity
68
The classic problem of “squaring” this shape was shown to be impossible when pi was proven to be transcendental.
Circle
69
It has thirteen axes of symmetry and eleven different nets.
Cube
70
One theorem named for Thales concerns right angles formed by three points on this shape.
Circle
71
This mathematical operation is the inverse of the integral.
Derivative
72
One method of calculating this operation involves expansion by minors, which takes into account that this function is alternation multilinear.
Determinant
73
DeMoivre’s theorem (calculating roots of this number) can be used when raising this type of number to a power.
Complex Numbers
74
The hyperbolic version of this function defines a catenary, and equals half the quantity e to the x plus e to the negative x.
Cosine function/Cosine
75
Surface area is twenty-four times its radius squared and its volume is eight times its radius cubed.
Cube
76
A well-known Axiom A diffeomorphism in this field of study is the Smale horseshoe.
Chaos Theory
77
The primary difference between a group and a quasi-group is that a quasi-group lacks this property.
Associative Property
78
Pressure is defined as force per units of this quantity.
Area
79
One of these things is classified as homogeneous if it does not contain any functions in terms of x that are not multiplied by other functions, which means that it has no constant terms.
Differential Equations
80
Name these “coefficients” that describe the number of ways to choose k things from n possibilities, or n choose k.
Binomial Coefficients
81
Finite intervals that include both endpoints are known by this term and denoted with square brackets.
Closed
82
ABC conjecture considers A+B=C (the largest of these numbers is this function of the other two)
Addition
83
This theory features fractal entities called strange attractors, such as one named after Edward Larenz.
Chaos Theory
84
Can be found “under a curve” via integration.
Area
85
CLRS textbook is an introduction to these things
Algorithm
86
It’s the inverse of multiplication
Division
87
Three-dimensional analogue of a square.
Cube
88
Unit one of these is described by x squared plus y squared equals 1. (and has an area of pi)
Circle
89
The generalized Poincare conjecture sorts of manifolds into top, piecewise linear, or having this property.
Differentiable
90
If f has this property, then f of a is always equal to the limit of f of x as x approaches a.
Continuity
91
The Euclidean Algorithm gives the largest integer that can be used for this action on two different integers.
Division
92
Functions with the complex version of this property have du dx equal dv dy and du dy equal negative dv dx, which are known as the Cauchy-Riemann equations.
Differentiable
93
This operation produces fractions.
Division
94
Subtraction possesses the “anti” form of this property.
Commutative/Commutative Property
95
This transcendental irrational is the base of the natural logarithm.
e/Euler's Number
96
Two disjoint open sets of this type can always be separated by a hyperplane.
Convexity
97
Its result is called a quotient.
Division
98
Gauss was the first person to illustrate this theorem, which requires that its inputs be relatively prime, using a system of modular congruences.
Chinese Remainder Theorem
99
Several theorems about these numbers can be proven using the maximum modulus principle.
Complex Numbers
100
Carmichael numbers are numbers of this type that satisfy Fermat’s Little Theorem.
Composite Number
101
Repetition of this function is denoted by a capital sigma.
Addition
102
Positive in the first and fourth quadrants, in a right triangle it is the adjacent leg over the hypotenuse.
Cosine function/Cosine
103
This operation applied to a composition of two functions is this operation applied to the second according to the chain rule.
Differentiation
104
Name this shape whose slices are used to generate ellipses, parabolas, and hyperbolas.
Cone
105
The sign of this operation tells whether a linear transformation preserves orientation.
Determinant
106
This measure is 2 for polygons and 3 for solids.
Dimension
107
The shoestring methos for finding the area of a polygon is based on a formula that uses this operation.
Determinant
108
This value can be used to determine the nature roots of a function.
Discriminant
109
The incomplete beta function can compute the cumulative density function for this object’s namesake probability distribution.
Binomial
110
Given three points on a circle, Thales’ Theorem says that is two of the points can form this, then the three points can form a right angle.
Diameter
111
When this operation can be repeated infinitely, the input function is called smooth.
Differentiation
112
This function is squared in Malus’s law and appears in a law relating the radiant intensity of Lambertian surfaces.
Cosine function/Cosine
113
The general ability to do this action separates fields from commutative rings. The ability to always do this action also separates the mathematical set “Q” from “Z”.
Division
114
On a closed interval, a function of this type will assume all intermediate value.
Continuity
115
This operation finds a function’s instantaneous rate of change, the inverse of integration.
Differentiation
116
Tartaglia taught Cardano a method for solving equations of this type, and eliminating one of their terms is called “depressing” them.
Cubic
117
Taking this operation on a set produces a set which is disjoint from it.
Complementary
118
Reciprocal of a number (x)
1/x
119
A line segment connecting two points on this shape is known as a chord.
Circle
120
Two methods for calculating this value are Dodgson condensation and cofactor expansion.
Determinant
121
Not defined if the second operand is zero.
Division
122
Mathematical operations have this property when the result is always the same set as the operands.
Closed
123
Minkowski’s taxicab geometry created a version of this quantity named for Manhattan.
Distance
124
A metric space is a set in which this notion can be quantified, and on those spaces, this notion must satisfy non-negativity, symmetry, and the triangle inequality.
Distance
125
The law of this function states that, for a triangle ABC, c squared equals a squared plus b squared minus 2 a b times this function of x is the secant of x.
Cosine function/Cosine
126
This word describes a six-faced Platonic solid, or a polynomial of degree three.
Cubic
127
Each ratio in the law of sines is equal to this measurement for the circle circumscribed about the triangle.
Diameter
128
One of these structures is named for Peter Shor
Algorithm
129
The smallest set of this type that encloses a given set is known as that set’s “hull” of this type.
Convexity
130
The fundamental theorem of algebra states that any polynomial has at least one root in this set.
Complex Numbers
131
Refer to step-by-step procedures or sets of rules used to perform tasks.
Algorithm
132
This quantity is the separation between two points in space.
Distance
133
This action either produces rationals from the integers or yields a remainder, and you can’t do it with zero.
Division
134
A function with this property within a closed and bounded interval will attain a minimum and maximum at least once by the extreme value theorem.
Continuity
135
This word describes a method of proof that attempts to write every number in binary, then constructs a number that cannot have been represented in that list; that argument shows that the real numbers are uncountable and was advanced by Cantor.
Diagonal
136
This word denotes polygons whose internal angles are all less than 180 degrees because it lacks an internal reflex angle.
Convexity
137
Like its dual, for whom its symmetries are named, this shape has 24 rotational symmetries.
Cube
138
For the boundary of the Mandelbrot Set, the “fractal” version of this quantity is two, while for a tesseract this quantity is equal to four.
Dimension
139
An ancient problem asks if it is possible to construct a square with area equal to a given one of these shapes using a compass and straightedge (known as “squaring” this shape).
Circle
140
The arc length of a function f from a to b is the integral of square root quantity one plus this operation of f squared.
Differentiation
141
Four x cubed minus three x equals a constant used to determine if the classical version of this task can be done.
Angle Trisection
142
This system is seen in dynamical systems like the logistical map and double pendulum.
Chaos Theory
143
Christoffel symbols are used to calculate the “covariant” form of this operation.
Derivative
144
This property works for multiplication or addition, but not for division or subtraction.
Associative Property
145
This adjective describes the distribution modeling the number of successes in a sample of size n drawn with replacement.
Binomial
146
For a system of linear equations, doping this on collections of coefficients is used to find solutions according to Cramer’s rule.
Determinant
147
This word describes the lowest-degree equation that is guaranteed to have both a finite relative minimum as well as a real root.
Cubic
148
Can be drawn without lifting the pencil.
Continuity
149
A mathematical concept that deals with modular arithmetic and finding solutions to systems of modular equations. Named after mathematician Sun Tzu (Sunzi).
Chinese Remainder Theorem
150
This operation finds the slope of a line tangent to a curve.
Differentiation
151
In conics, if this value is less than 0, a circle or ellipse forms.
Discriminant
152
This number is the limit, as n goes to infinity, of the quantity “1 plus 1-over-n” to the n, which you might run into while calculating compound interest.
e/Euler's Number
153
It equals zero at critical points, and applying this operation on velocity with respect to time gives acceleration.
Derivative
154
Result of this operation on two vectors can be found with the “parallelogram rule”.
Addition
155
Its derivative can be found via Jacobi’s formula or by summing the values obtained by differentiating one input at a time.
Determinant
156
Any function from a set with the discrete topology will have this property, as the discrete topology includes all elements and thus all subsets are open.
Continuity
157
These objects give the number of ways to select r objects from a group of n.
Binomial Coefficients
158
This property generally does not hold for matrix multiplication, division, or subtraction, while it does hold for the dot product, and holds along with the associative property for addition and multiplication.
Commutative/Commutative Property
159
Unlike quaternions, octonions lack this property for multiplication.
Associative Property
160
The derivative of “this number to the x” is just “this number to the x”.
e/Euler's Number
161
Those with modulus one can be generated by the function “cis x”, which appears in de Moivre’s formula, and can also be expressed as the rotation matrix.
Complex Numbers
162
This number used as x gives the largest output of the function x raised to the reciprocal of x power.
e/Euler's Number
163
This term describes curves in the plane with no endpoints that completely surround an area.
Closed
164
Raising one of these to the nth power yield an expansion with n+1 terms, whose coefficients can be found on the rows of Pascal’s Triangle using this algebraic expression’s namesake theorem.
Binomial
165
The Jacobian is the determinant of a matrix whose entries come from performing this operation.
Differentiation
166
Truncating this shape gives a frustum.
Cone
167
This word refers to line segments that connect non-adjacent vertices of a polygon.
Diagonal
168
Found by adding a set of numbers and dividing by the number of values in the set.
Arithmetic Mean
169
e/Euler's Number
170
In cylindrical coordinates, the equation z equals r gives one of these shapes.
Cone
171
This set of numbers expressed in the form “a plus b i” where I squared is negative one.
Complex Numbers
172
These numbers are solutions to quadratics with negative discriminant.
Complex Numbers
173
This word also refers to square matrices whose only nonzero elements have a row number equal to their column number.
Diagonal
174
Invertible entities have nonzero value for this operation, which for a two-by-two input is equal to ad minus bc.
Determinant
175
This quantity appears in the denominator of Stirling’s formula for the asymptotics of the factorial function.
e/Euler's Number
176
The field of analysis named for this often studies holomorphic functions.
Complex Numbers
177
This shape consists of all the points in spherical coordinates for which rho goes from zero to a constant times cosine phi, and phi goes from zero to a constant less than pi over two.
Cone
178
The “directional” form of this operation can be found using the gradient.
Derivative
179
The limit as x approaches 0, of this function minus 1, all over x, equals 0.
Cosine function/Cosine
180
For a function, this value can be calculated by dividing its integral by the width of the interval of the integral.
Arithmetic Mean
181
For a composition of functions, the chain rule can be used to find it.
Derivative
182
If two angles have this property, the sine of one is equal to the cosine of the other.
Complementary
183
In quantum mechanics, certain pairs of linear operators that lack this property, such as position and momentum, are said to be complementary.
Commutative/Commutative Property
184
The quaternions are a generalization of them, and multiplying one by its namesake conjugate yields a real number.
Complex Numbers
185
This term can describe something with a barrier, such as a locked door.
Closed
186
In category theory, a diagram has this property if composing different paths gives the same result.
Commutative/Commutative Property
187
Apollunius’ Problem is the construction of one of these shapes tangent to three others.
Circle
188
This function has a universal attracting fixed point at the Dottie number.
Cosine function/Cosine
189
Used to find the credibility interval.
Bayes' Theorem
190
The coefficient of the nth term in a Taylor series is the nth order of this operation over n factorial.
Derivative
191
Its hyperbolic analogue describes the shape of a catenary.
Cosine function/Cosine
192
A problem involving this shape’s difficulty arises from the fact that the Delian constant is not Euclidean.
Cube
193
A surface is a manifold with two for this value.
Dimension
194
A measure of central tendency that represents the average value of a set of numbers.
Arithmetic Mean
195
A function has this property if its second derivative is positive on that interval.
Convexity
196
This property states that the order in which consecutive occurrences of certain binary operations are carried out will not affect the result of an expression.
Associative Property
197
One of the problems of antiquity was to double this figure.
Cube
198
Functions that possess the complex version of this property in a disk are called holomorphic.
Differentiable
199
Spheres tangent to one of these and a plane are called Dandelin spheres.
Cone
200
The ordinary types of these use only one independent variable, and some ordinary types are initial value problems.
Differential Equations
201
Proving that a space is a vector subspace requires proving that it has this property.
Closed
202
Has a constant finite curvature.
Circle
203
The Jacobian matrix consists of functions on which one type of this operation has been performed, and it can be used to define a gradient.
Derivative
204
This theorem is often illustrated using groups of soldiers.
Chinese Remainder Theorem
205
On any interval, there is at least one point where this operation is equal to the average slope of a function over that interval, according to the mean-value theorem.
Differentiation
206
Solutions to common types of these are exponential or logistic functions, and the simplest examples can be solved using the separation of variables.
Differential Equations
207
Can be approximated by infinitely altering sides with a process that involves drawing three arcs.
Angle Trisection
208
The entries of Pascal’s triangles are these, which arise when multiplying a two-term polynomial with itself.
Binomial Coefficients
209
Faa di Bruno’s formula can be used to find higher order examples of these operations.
Derivative
210
Multilinear and alternating functions can be written as a constant times this value.
Determinant
211
The absolute value of these numbers is called the modulus.
Complex Numbers
212
A set of points equidistant from a center.
Circle
213
Equal to the length of the adjacent side over the hypotenuse.
Cosine function/Cosine
214
If this value is positive in a quadratic equation, then there are two real solutions, and the formula for finding this value in a quadratic equation is b squared minus four a c.
Discriminant
215
A function that lacks this property everywhere but is continuous is named for Weierstrass.
Differentiable
216
Applying this operation to two functions multiplied together requires using the product rule.
Derivative
217
This property does not hold for subtraction of positive numbers because the difference of two positive numbers can be negative.
Closed
218
If this value is 0 in cubic functions, there is one root of multiplicity 2.
Discriminant
219
Numerator = 1
Denominator = x
1/x
220
A type of polynomial that contains two terms.
Binomial
221
A set is compact if and only if the set is bounded and has this property, according to the Heine-Borel Theorem.
Closed
222
Lucas’s theorem reduces one of these numbers to a product of them modulo p.
Binomial Coefficients
223
This property states that each point in a function’s domain has a derivative.
Differentiable
224
A square has two of these things, and their length is equal to the side length times root 2.
Diagonal
225
Donald Knuth designed one of these for matrices named X.
Algorithm
226
Cromwell’s rule limits the cases where this theorem can be applied.
Bayes' Theorem
227
In Euclidian geometry, this quantity for points x and y can be represented as the norm of x minus y, which can otherwise be written as the square root of the sum squared differences between each component of two vectors a and b.
Distance
228
This theorem allows probability to change upon the acquisition of new evidence.
Bayes' Theorem
229
For a cube of side length s, the structure by this name has a length of s root 3.
Diagonal
230
Heron’s formula can be used to find this for triangles using a semi perimeter.
Area
231
Identify these numbers which have a factor besides one and themselves and are therefore not prime.
Composite Number
232
Taking this operation on a set can be denoted with a bar over the set’s name.
Complementary
233
Inverse of subtraction
Addition
234
The LRL vector is usually scaled by the namesake vector of this quantity.
Eccentricity
235
This quantity equals the square root of 1 plus two times the energy times angular momentum squared over the mass times Big G squared.
Eccentricity
236
This quantity multiplies the sine of its namesake anomaly, then is subtracted from that anomaly, in order to calculate the mean anomaly.
Eccentricity
237
For Earth, this quantity is approximately 0.016.
Eccentricity
238
This quantity multiplies the cosine of the angle to the point of closest approach in the denominator of a mathematical description of Kepler’s First Law.
Eccentricity
239
The nonzero value for this quantity explains why the time between equinoxes is not equal.
Eccentricity
240
Name this quantity which represents the ratio of focal length and semimajor axis length for an elliptical orbit, symbolized epsilon.
Eccentricity
241
Curves named after this shape have equation y-squared equals x-cubed plus a times x plus b and were used to help prove Fermat’s Last Theorem.
Ellipses
242
If points A, B, and C are marked on a trammel, and B and C are allowed to move freely on two perpendicular lines, then A will trace out one of these figures.
Ellipses
243
These simplest Lissajous figures are the shapes of the paths of objects trapped in orbit by inverse-square forces like gravity.
Ellipses
244
This figure with positive eccentricity less than one has area equal to pi times the product of its semi-axes, and this figure is the set of all points the sum of whose distances to two foci are constant.
Ellipses
245
Identify this oval-shaped conic section.
Ellipses
246
The volume of a unit sphere in a dimension that is one of these numbers can be written as pi to the k over k factorial.
Even Numbers
247
The function 2x over the quantity x minus 1 squared generates these numbers, which are an ideal in the natural numbers.
Even Numbers
248
The word describing these numbers also names permutations with positive signature.
Even Numbers
249
An unproven statement regarding them is that all but one of them can be written as the sum of two primes.
Even Numbers
250
That statement is Goldbach’s conjecture.
Even Numbers
251
They share their name with functions for which f of negative x equals f of x, and when written in binary this kind of number ends in a 0.
Even Numbers
252
Identify this set of numbers including 0, 2 ,4, 6, and 32, the opposite of odd numbers.
Even Numbers
253
F. Scott Fitzgerald hated this thing because he said it “is like laughing at you own joke.”
Exclamation Mark
254
When this thing follows an integer n, it is asymptotically equal to the square root of two pi n times the quantity n over e to the n, according to an approximation named for James Stirling.
Exclamation Mark
255
In chess two of these things denote an excellent move.
Exclamation Mark
256
Name this symbol which mathematically denotes a factorial.
Exclamation Mark
257
This word preceded by “hyper” describes a function of a equal to the K-function of a+1.
Factorial
258
The formula for the kth Catalan number is this function of 2k divided by this function of k times this function of k+1.
Factorial
259
This function of successive natural numbers forms the denominators of the terms in a Taylor series.
Factorial
260
For zero, this function can be shown to equal one, by equating this function of n to the number of permutations of n objects.
Factorial
261
Name this function which gives the product of all positive integers equal to or less than a specified integer, symbolized by an exclamation point.
Factorial
262
According to a Donald Knuth conjecture, this function along with the square root and floor functions and the number 3 can generate any natural number.
Factorial
263
The Pochhammer Symbol is used to represent its rising and falling types.
Factorial
264
Stirling’s approximation is used to calculate very large terms of this operation.
Factorial
265
The solution to this problem was originally approached using horizontal Iwasawa theory, and a weaker version of this result is derived from Falting’s theorem.
Fermat’s Last Theorem
266
The proof of this theorem relied on Ribet’s work on the epsilon conjecture.
Fermat’s Last Theorem
267
It was proven for all primes less than 100 using Sophie Germain’s theorem.
Fermat’s Last Theorem
268
Its proof relied on a result that states that any elliptic curveover the rationals can be obtained from a rational map, known as the Taniyama-Shimura conjecture.
Fermat’s Last Theorem
269
The originator of this result claimed to have miraculous proof of it that the margin couldn’t contain.
Fermat’s Last Theorem
270
Name this result proven by Andrew Wiles, which states that for n greater than 2, there are no integers x, y, and z such that x to the n plus y to the n equals z to the n.
Fermat’s Last Theorem
271
This statement holds for exponent p in an irregular pair if the pair satisfies Vandiver’s Criteria.
Fermat’s Last Theorem
272
One method of testing whether a number n is one of these involves asking whether 5n squared minus 4 or 5 n squared plus 4 is a perfect square.
Fibonacci Numbers/Sequence
273
One method of generating these numbers is to repeatedly take powers of the two-by-two matrix one-one-one-zero, and the Wall-Sun-Sun primes are defined using these numbers.
Fibonacci Numbers/Sequence
274
The generating function x divided by the quantity 1 minus x minus x squared creates these numbers.
Fibonacci Numbers/Sequence
275
The ratio between successive members of these numbers approaches 1 plus the square root of 5 all over 2, which is known as the golden ratio.
Fibonacci Numbers/Sequence
276
Name this sequence of numbers, a given member of which is a sum of the previous two entries.
Fibonacci Numbers/Sequence
277
This set of numbers begins [1,1,2,3,5,8…]
Fibonacci Numbers/Sequence
278
Three of these numbers cannot form a Pythagorean triplet, and neither can the similar Lucas numbers.
Fibonacci Numbers/Sequence
279
The shallow diagonals in Pascal’s triangle sum to these numbers, which were used by their namesake to describe the population of a group of rabbits.
Fibonacci Numbers/Sequence
