Posts Tagged ‘diagram’
Thursday, December 10th, 2009
Inverse Image of Sets
Description
A detailed tutorial on the inverse image of sets. Step by step tutorial on the inverse image of sets for reference. Knowledge of the inverse image of sets is important in advanced discrete mathematics courses.
Overview
Say that you have a function f: A –> B. Then, X is a subset of A and Y is a subset of B. The image of X or the image set of X is f(X) = {y belongs to B: y = f(x) for some x belonging to X}. The inverse image of Y is defined as f^-1(Y) = {x belongs to A: f(x) belongs to Y}. The inverse image is simply a reversed form of the image. Often when asked to find the inverse image, it will help to set up a drawing of the image of the function, connecting everything where it needs to go. Then to find the inverse you simply reverse your work.
Tags: a, b, connect, diagram, discrete math, form, function, image, image set, inverse, mapping, picture, reverse, set, subset, x, y
Posted in Discrete Math | No Comments »
Tuesday, November 10th, 2009
How to Make Factor Trees
Description
A detailed tutorial on how to make factor trees. Step by step tutorial including several examples on how to make factor trees for reference.
Overview
A factor tree is a type of tree diagram that splits numbers into their factors. It is a very useful method of simplification. First, start with a number and draw two lines from it. Two numbers that when multiplied equal your first number need to go there. A great number to start with is 2, if your number is an even number. you can start with any two numbers you like, provided they fit the guidelines, excluding anything paired with the number one – because then you won’t get anywhere. Then for each of your two numbers, if they are not simplified, you do the same process with them. Keep it up until you are down to simplified, or prime, numbers. You will know you have reached one when the only multiples are one and itself.
Tags: algebra, diagram, even, factor, itself, multiple, number, odd, one, prime, simplification, simplified, simplify, tree, two
Posted in Algebra | No Comments »
Tuesday, November 10th, 2009
How to Make a Box-and-Whisker Plot
Description
A detailed tutorial on how to make a box-and-whisker plot. Step by step tutorial including several examples of how to make a box-and-whisker plot for reference.
Overview
A box-and-whisker plot is named for it’s resemblance to a cat’s face – the box is the face of the cat, and the lines extending out from either side are known as whiskers. Sometimes box-and-whisker plots are simply called box plots. They are used to graph sets of numbers according to five values: the highest value, known as the maximum, the second highest value, known as the upper quartile, the median, or the middle, the second lowest value, known as the lower quartile, and the lowest value, known as the minimum. The box centers around the median and the whiskers extend out to the other numbers.
Tags: algebra, box, box-and-whisker, boxplot, diagram, graph, highest, line, lower, lowest, maximum, median, middle, minimum, plot, quartile, upper, value, whisker
Posted in Algebra | 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 »
Tuesday, September 29th, 2009
The Use of Venn Diagrams in Set Theory
Description
A detailed tutorial on using Venn diagrams in set theory. Step by step tutorial including several examples of how to use a Venn diagram in set theory for reference.
Overview
A Venn diagram is something we’ve all heard about before – probably in an english class. Venn diagrams are used as a visual representation for sets of different items, called elements. But it stands to reason that if you can use a venn diagram for sets, you can use them for set theory – a branch of mathematics that uses different sets of numbers. For set theory, they are used to display intersection and unions, and you can fill them out just like you would with a normal Venn diagram.
Tags: algebra, De Morgan's Rules, De Morgan's Theorem, diagram, elements, intersection, set theory, sets, union, Venn
Posted in Algebra | No Comments »
