Posts Tagged ‘combination’
Thursday, December 31st, 2009
How to Write Step Functions
Description
A detailed tutorial on how to write step functions. Step by step tutorial including several examples of how to write step functions for reference.
Overview
A step function, also called a staircase function, is a finite linear combination composed of several different intervals. They are considered to be a piecewise constant function. The graph of a step function is often expressed as steps, or a staircase, which is how it got its name. It simply looks like several disconnected lines, with alternate open and closed ends so that it easily passes the vertical line test for functions.
Tags: closed, combination, constant, diconnected, discrete math, ends, finite, function, graph, intervals, line, linear, lines, open, piecewise, staircase, step, test, vertical
Posted in Discrete Math | No Comments »
Tuesday, December 29th, 2009
How to Use the Product Rule in Algebra
Description
A detailed tutorial on the algebraic product rule. Step by step tutorial including several examples of the algebraic product rule for reference.
Overview
There are many product rules in the world of math. This tutorial focuses on a product rule that is used in algebra and statistics. The product rule states that if two independent tasks T1 and T2 are to be performed, then T1 can be performed m ways and T2 can be performed n ways. Therefore, the number of ways the tasks can be performed together is m * n ways. Remember that this is only the number of possible ways to do something, not how much time it takes to do something. Also, the same method is used no matter how many different tasks you are given.
Tags: algebra, combination, multiplication, multiply, number, permutation, product, rule, statistics, task
Posted in Algebra | No Comments »
Thursday, December 10th, 2009
Overview of Two-Way Counting
Description
A detailed tutorial on two-way counting. Step by step tutorial including several examples of two-way counting for reference.
Overview
Two-way counting is when any expression for a given quantity are determined using two different counting approaches. Many people believe that a quadratic equation is the perfect example of two-way counting, because you find the quantity in more than one way. However, this is incorrect. Two-way counting is actually a backwards method – you have the quantity already, you just need to figure out how you could get it. This is used often in combinations and permutations, where you often already know what quantity you need to have, you just have to figure out how to get there.
Tags: binomial, combination, counting, equation, example, expression, method, permutation, quadratic, quantity, statistics, two, two-way, way
Posted in Statistics | No Comments »
Friday, October 9th, 2009
Introduction to Linear Regression
Description
A detailed tutorial on linear regression. Step by step tutorial including several example problems of linear regression for reference.
Overview
Regression is a type of analysis that is used for analyzing several variables when the focus is on a dependent variable and one or more independent variables. Linear regression is when the dependent variable is a linear combination of the parameters. It can be used for both straight lines and parabolas, and each has a different formula.
Straight Line: 
Parabola: 
Tags: algebra, analyzing, combination, dependent, focus, independent, line, linear, Math, parabola, parameters, regression, straight, variable
Posted in Algebra | No Comments »
Thursday, October 8th, 2009
Subsets in Set Theory
Description
A detailed tutorial on how to identify subsets of a set. Step by step tutorial including several examples of how to find subsets in a set for reference.
Overview
Each set in set theory has a certain amount of subsets. There is an easy way figure out how many subsets a set has. Pretend that every element of a set is 2, and multiply them together. This will be your number of subsets. For example, if you have three elements, you will have 8 subsets, because 2 cubed (which is 2 to the power of 3, or 2 times 2 times 2) is equal to 8. Now that you have determined how many subsets there are, you have to figure out what they are. A subset is defined as any set containing all or part of a set. Two subsets are going to be the set itself, and an empty set. Sometimes they are your only subsets. Now, following the definition, a subset must be all possible sets. This means, sets of one element - one for each element in your set. In addition to that, you may have sets of two elements – one for each possible combination of elements in your set. This should be continued until you have reached the maximum number of elements in the set you atarted out with.
Tags: combination, discrete math, element, empty set, exponent, Math, multiplication, number, set, set theory, subset, to the power, value
Posted in Discrete Math | No Comments »
Tuesday, October 6th, 2009
Logical Equivalence Explained
Description
A detailed tutorial on logical equivalence. Step by step tutorial with several examples of what logical equivalence is and how to identify it for reference.
Overview
In the study of discrete math, it is said that two statements are logically equivalent if and only if their truth tables match. This means that for every possible combination of the antecedent and the consequent, these two statements must have exactly the same answer in order to be logically equivalent. There is only a true or false answer to this question, there is no “possibly” or “maybe”.
Tags: antecedent, combination, consequent, discrete math, equivalence, equivalent, false, logical, logically, match, Math, same, true, truth table
Posted in Discrete Math | No Comments »
Thursday, September 24th, 2009
Set Theory Explained
Description
A detailed tutorial of set theory. Step by step tutorial including several examples of set theory for reference. Knowledge of set theory is required for most upper level math classes.
Overview
Set theory is the practice of sets and subsets. A set is a group of elements – numbers, items, anything. A set is expressed as A = {1, 2, 3, 4}, with A being the set, and anything inside the brackets being part of the set, being elements. A subset is also a set, but one that is the same as or contains part of another set. Each set has at least two subsets, because a subset can also be the exact same set, and an empty set. An empty set is expressed as a O with a line drawn through it, and it is a set that has no elements in it.
Tags: brackets, combination, contains, discrete math, elements, empty sets, Math, numbers, set, set theory, sets, subsets
Posted in Discrete Math | 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 »
