A mathematical formula is nothing more than a pattern for solving a specific problem.

The equation is used for the mathematical process of solving the problem.

An approach to problem solving involving collection of data that will support valid, defensible, and supportable conclusions.

As an experimental problem solving platform, the project showcases and collects ideas at scale with local and global impact.

In these cases, statistical mechanics is a more valid method of solving the problem than continuous aerodynamics.

In the field of artificial intelligence, the most difficult problems are informally known as AI-complete or AI-hard, implying that the difficulty of these computational problems is equivalent to solving the central artificial intelligence problem — making computers as intelligent as people, or strong AI.

AI-complete problems are hypothesised to include computer vision, natural language understanding, and dealing with unexpected circumstances while solving any real world problem.

* Dealing with unexpected circumstances while solving any real world problem, whether it's navigation or planning or even the kind of reasoning done by expert systems.

Boulder routes are commonly referred to as problems ( a British appellation ) because the nature of the climb is often short, curious, and much like problem solving.

This field seeks to close the gap between engineering and medicine: It combines the design and problem solving skills of engineering with medical and biological sciences to improve healthcare diagnosis, monitoring and therapy.

The characters ' position in the food chain promotes an emphasis on role-playing and problem solving over combat.

Although player characters are substantially weaker than many of the dangers they face, the game is one of the first to encourage problem solving and outwitting obstacles, rather than out-fighting them.

Brooks stopped teaching recently to " devote 100 % of his time on solving the problem as to why he needed to eat some type of food to keep his physical body alive and allow his light body to manifest completely.

In 1930, Labour MP Oswald Mosley left the party after its rejection of his proposals for solving the unemployment problem.

Because many outstanding problems in number theory, such as Goldbach's conjecture are equivalent to solving the halting problem for special programs ( which would basically search for counter-examples and halt if one is found ), knowing enough bits of Chaitin's constant would also imply knowing the answer to these problems.

On-sighting is a form of adventure climbing emphasizing the skills of route finding, quick thinking and problem solving.

The quantitative answer to this particular problem instance is of little use for solving other instances of the problem, such as asking for a round trip through all sites in Milan whose total length is at most 10 km.

What amounts to an algorithm for solving this problem was described by Aryabhata ( 6th century ; see ).

A method for solving a decision problem given in the form of an algorithm is called a decision procedure for that problem.

A distributed system may have a common goal, such as solving a large computational problem.

A design goal may range from solving the least significant individual problem of the smallest element, to the most holistic influential utopian goals.

This field examines change across a broad range of topics including motor skills and other psycho-physiological processes ; cognitive development involving areas such as problem solving, moral understanding, and conceptual understanding ; language acquisition ; social, personality, and emotional development ; and self-concept and identity formation.

After solving a case Poirot has the habit of collecting all people involved into a single room and explaining them the reasoning that led him to the solution, and revealing that the murderer is one of them.

In solving problems in cylindrical coordinate systems, one obtains Bessel functions of integer order ( α

Therefore, whether solving for one parameter or for both paramters simultaneously, a numerical solution on a computer is typically required.

In popular culture, this puzzle was the Puzzle No. 142 in Professor Layton and Pandora's Box as one of the hardest solving puzzles in the game, which needed to be unlocked by solving other puzzles first.

The most common way to formalize this is by defining a field as a set together with two operations, usually called addition and multiplication, and denoted by + and ·, respectively, such that the following axioms hold ; subtraction and division are defined implicitly in terms of the inverse operations of addition and multiplication :< ref group =" note "> That is, the axiom for addition only assumes a binary operation The axiom of inverse allows one to define a unary operation that sends an element to its negative ( its additive inverse ); this is not taken as given, but is implicitly defined in terms of addition as " is the unique b such that ", " implicitly " because it is defined in terms of solving an equation — and one then defines the binary operation of subtraction, also denoted by "−", as in terms of addition and additive inverse.

The preamble of the charter provides that the members " reaffirm faith in fundamental human rights, in the equal rights of men and women " and Article 1 ( 3 ) of the United Nations charter states that one of the purposes of the UN is: " to achieve international cooperation in solving international problems of an economic, social, cultural, or humanitarian character, and in promoting and encouraging respect for human rights and for fundamental freedoms for all without distinction as to race, sex, language, or religion ".

* Video tutorial on solving one step to multistep equations

“ In one of the most telling complaints, a majority ( 54 %) of Americans believe the news media gets in the way of society solving its problems ,” Pew reported.

The policy towards territorial disputes by the Malaysian government is one of pragmatism, solving disputes in a number of ways, including some resolved in the International Court of Justice.

An alternative method to solving, once finding the first non-trivial solution, one could take the original equation and factor the left hand side as a difference of squares, yielding Once in this form, one can simply raise each side of the equation to the kth power, and recombining the factored form to a single difference statement.

By solving this equation, one arrives at the " equations of motion " of the field.

Considered one of Nintendo's most important franchises, its gameplay consists of a mixture of action, adventure, and puzzle solving.

Each dungeon usually has one major item inside, which is usually essential for solving many of the puzzles in that dungeon and often plays a crucial role in defeating that dungeon's boss as well as progressing through the game.

A new paradigm is chosen because it does a better job of solving scientific problems than the old one.

Because the equation is second order in the time derivative, then by the nature of solving differential equations, one must specify both the initial values of the wave function itself and of its first time derivative, in order to solve definite problems.

Minimal deterrence represents one way of solving the security dilemma and avoiding an arms race.

For example Hermione notes that one obstacle to finding the Philosopher's Stone is a test of logic rather than magical power, and that most wizards have no chance of solving it.

In other words, L can be solved in polynomial time by an oracle machine with an oracle for H. Informally, we can think of an algorithm that can call such an oracle machine as a subroutine for solving H, and solves L in polynomial time, if the subroutine call takes only one step to compute.

There is also a branch of the Russian Academy of Sciences, which contains, among other things, the Institute of Cosmophysical Research, which runs the Yakutsk Extensive Air Shower installation ( one of the largest cosmic-ray detector arrays in the world ), and the Permafrost Research Institute developed with the aim of solving the serious and costly problems associated with construction of buildings on frozen soil.