Posts Tagged ‘possibilities’
Tuesday, October 20th, 2009
How to Write Proofs by Exhaustion
Description
A detailed tutorial on writing proofs by exhaustion. Step by step tutorial including several examples of how to write proofs by exhaustion for reference.
Overview
A proof by exhaustion is one of the easier types of proofs to write. All this proof involves is testing cases – every case possible for what you are trying to prove. This can be made easier by using variables instead of numbers, or by testing for an even number and odd number, positive and negative number, etc. That way you do not have to test many numbers in order to prove. If even one of the cases does not work out, then whatever you are testing for has been disproven.
Tags: cases, discrete math, disproven, even, exhaustion, Math, method, negative, odd, positive, possibilities, proof, proofs, proven, variable, write
Posted in Discrete Math | No Comments »
Tuesday, October 6th, 2009
Introduction to Tree Diagrams
Description
A detailed tutorial on how to make tree diagrams. Step by step tutorial including several examples of how to make tree diagrams for reference.
Overview
A tree diagram is a specific type of diagram that is often used to organize items and possibilities. It has a unique network topology. It can be seen as a type of network diagram, which can in turn be seen as a cluster diagram. Tree diagrams are very useful when trying to figure out probabilities and statistics.
Tags: algebra, cluster, diagram, Math, network, organize, possibilities, probabilities, statistics, topology, tree, unique
Posted in Algebra | No Comments »
Thursday, September 17th, 2009
Law of Large Numbers Explained
Description
A detailed tutorial on the Law of Large Numbers. Step by step tutorial including several examples of the Law of Large Numbers for reference.
Overview
The Law of Large Numbers, or the LLN, is a theorem in probability and statistics that refers to how long the mean of the possible choices for a random variable will remain the same. It is called the “stability” of the mean. Rolling a die is the best example of the Law of Large Numbers; although the numbers on the die are not large, no matter what the outcome is the mean is always the same. Anything with a set amount of possibilities like that, such as flipping a coin, would have the same result with the stability of the mean.
Tags: average, expected, expected value, law of large numbers, Math, mean, possibilities, probability, random, statistics, value, variable
Posted in Statistics | No Comments »
Thursday, September 17th, 2009
Introduction to Combinations
Description
A detailed tutorial on the solving of combinations. Step by step tutorial including several examples of how to solve combinations for reference.
Overview
Combinations are often used with permutations. A combination is actually just the written representation of the permutation – with the permutation, you figure out how many different combinations there are, but with combinations you actually write down what those combinations are, not just how many there is. Many people prefer permutations because permutations are a lot less work. However, combinations do come up frequently, most notably in logic courses like discrete math.
Tags: combination, combinations, discrete math, items, Math, multiplication, numbers, possibilities, precalculus, sets, statistics, variables
Posted in Algebra | No Comments »
Thursday, September 17th, 2009
Introduction to Permutations
Description
A detailed tutorial on the solving of permutations. Step by step tutorial including several examples of how to solve permutations for reference.
Overview
A permutation is an ordered sequence of elements, also known as a set. Basically, a permutation is when you have a set amount of possibilities to be one thing (typically a variable), and then you have one less than that number of possibilities for your next variable, etc. Often you can use this to figure out exactly how many possible combinations in a set there are. Permutations are used very often in math, all done slightly different depending on the branch of mathematics, but it is first introduced in precalculus.
Tags: items, Math, multiplication, numbers, permutation, permutations, possibilities, precalculus, sets, statistics, variables
Posted in Algebra | No Comments »
