Consider first-order linear ODEs of the general form:

Consider the general definition of the Cartesian product:

Consider in a vector space V, the general linear group GL ( V ).

Consider a bounded linear transformation T defined everywhere over a general Banach space.

Consider region D in the plane: a unit circle or general polygon — the asymptotics of the problem, which are the interesting aspect, aren't dependent on the exact shape.

Consider a general decision situation having n decisions ( d < sub > 1 </ sub >, d < sub > 2 </ sub >, d < sub > 3 </ sub >, ..., d < sub > n </ sub >) and m uncertainties ( u < sub > 1 </ sub >, u < sub > 2 </ sub >, u < sub > 3 </ sub >, ..., u < sub > m </ sub >).

Consider the following situation, which is a general setting of many supervised learning problems.

Consider the general inseparable equation

Consider the subset sum problem, an example of a problem that is easy to verify, but whose answer may be difficult to compute.

Consider a problem that has these four properties:

Consider the problem of determining the index of the database entry which satisfies some search criterion.

Consider the two-dimensional problem introduced above:

Consider, for example, the Closest pair problem:

:: • Consider whether a proposed improvement will solve the problem, or cause " crash migration.

Consider the problem of finding solutions of the form ƒ ( r, θ, φ ) = R ( r ) Y ( θ, φ ).

Consider the problem of factoring the polynomial

Consider the following problem.

Consider a simple 1D advection problem defined by the following partial differential equation

Consider the problem of a mine owner who must decide at what rate to extract ore from his mine.

Use your experience: Consider the problem and try to make sense of it.

Consider the following stochastic programming problem

Consider a problem that can be solved using a recursive algorithm such as the following:

Consider a complex, real-world problem, like those of marketing or making policies for a nation, where there are many governing factors, and most of them cannot be expressed as numerical time series data, as one would like to have for building mathematical models.

Consider the initial value problem

Consider the following problem in deterministic optimal control over the time period:

Consider the unconstrained optimization problem.

Consider the circuit minimization problem: given a circuit A computing a Boolean function f and a number n, determine if there is a circuit with at most n gates that computes the same function f. An alternating Turing machine, with one alternation, starting in an existential state, can solve this problem in polynomial time ( by guessing a circuit B with at most n gates, then switching to a universal state, guessing an input, and checking that the output of B on that input matches the output of A on that input ).

Consider the problem of estimating the probability that a test point in N-dimensional Euclidean space belongs to a set, where we are given sample points that definitely belong to that set.

Consider the problem of distributing objects given by a generating function into a set of n slots, where a permutation group G of degree n acts on the slots to create an equivalence relation of filled slot configurations, and asking about the generating function of the configurations by weight of the configurations with respect to this equivalence relation, where the weight of a configuration is the sum of the weights of the objects in the slots.

Consider the distribution on the figure.

Consider the behaviour of a belief distribution as it is updated a large number of times with independent and identically distributed trials.

Consider a uniform plasma, with thermal electrons ( distributed according to the Maxwell – Boltzmann distribution with the temperature ).

Consider a random variable X whose probability distribution belongs to a parametric family of probability distributions P < sub > θ </ sub > parametrized by θ.

Consider the variance formula: e = PQ, wherein P is equal to the proportion of " 1's " or " cases " and Q is equal to ( 1-P ), the proportion of " 0's " or " noncases " in the distribution.

A particular setting of n and p characterizes a particular probability distribution over a discrete random variable, with possible outcomes ( the support of the distribution ) ranging between 0 and n. Consider the following cases:

Consider a discrete charge distribution consisting of N point charges q < sub > i </ sub > with position vectors r < sub > i </ sub >.

Consider the data to be a single observation from an absolutely continuous distribution on

Consider it as a standby setup, at negligible cost, for those emergencies when the furnace quits, a blizzard holds up fuel delivery, or for cool summer mornings or evenings when you don't want to start up your whole heating plant.

Consider the features of Utopian communism: generous public provision for the infirm ; ;

Consider, for instance, the following equations:

Consider, for instance, particles suspended in a viscous fluid in a gravitational field.

Consider a complete orthonormal system ( basis ),, for a Hilbert space H, with respect to the norm from an inner product.

Consider for example the compound ( 3Z, 6E )- 3, 5, 7-trimethylnona-3, 6-diene.

* Consider the set of all functions from the real number line to the closed unit interval, and define a topology on so that a sequence in converges towards if and only if converges towards for all.

* Consider the set K of all functions ƒ: → satisfying the Lipschitz condition | ƒ ( x ) − ƒ ( y )| ≤ | x − y | for all x, y ∈.

* Consider the importance of genetic resources for food and agriculture for food security

Consider for instance the sequence defined by and.

Consider the unitary form defined above for the DFT of length N, where

Consider the following simple grammar for arithmetic expressions :< syntaxhighlight lang =" bnf ">

Consider a project that has been planned in detail, including a time-phased spend plan for all elements of work.

Consider, for example,

Geometric arrangement for Fresnel's calculation Consider the case of a point source located at a point P < sub > 0 </ sub >, vibrating at a frequency f. The disturbance may be described by a complex variable U < sub > 0 </ sub > known as the complex amplitude.

Consider Japan, for instance, which used to have optional jury trials for capital or other serious crimes between 1928 and 1943.

Consider for example determining which of the following are to be considered diseases ( i. e., abnormal states requiring cure ): alcoholism, homosexuality, and chronic fatigue syndrome.

Consider for example workers who take coffee beans, use a roaster to roast them, and then use a brewer to brew and dispense a fresh cup of coffee.

Consider the context of evaluating each one of a class of events A < sub > 1 </ sub >, A < sub > 2 </ sub >, A < sub > 3 </ sub >,..., A < sub > n </ sub > ( for example, is the occurrence of the event harmful or not ?).

Consider the closed intervals for all integers k ; there are countably many such intervals, each has measure 1, and their union is the entire real line.

Consider, for example, a reference frame moving relative to another at velocity in the direction.

Consider, for example, what happens when an object in the periphery of the visual field moves, and a person looks toward it.