Where probability shows how likely you are to pick an Ace, statistics describes the cards that were actually picked. Statistics is very closely linked to probability. How likely is it that you will pick an Ace? (Answer: 1/13) How likely would it be to pick a Spade? (Answer: 1/4) Now, how likely would it be to pick an Ace of Spades? That only happens once in each deck of cards, so the probability is 1/52. For instance, if you have a complete, shuffled deck of 52 cards and you draw one at random. Probability describes how likely something is to occur. Not only is this my actual bedtime, but it’s a prime example of propositional logic. Simply put, logical statements go, “If this, then that.” For example, consider the logical statement: If the time is 9:00 pm, then I’ll go to sleep. Logic is all about the consequences of actions or arguments. These are some of the types of problems that graph theory looks at. If this graph were on a piece of paper, would you be able to do the following? Traverse each edge in the graph and touch each node: a) without lifting your pencil, and b) without traversing any edge more than once. It’s also made up of lines, called edges, which connect each node and represent the relationship between them. If you look at a graph (example below) you will see that it’s made up of circles, called nodes or vertices, which represent the objects. Thus, Graph Theory is the study of the structures that model relationships between objects. Graphs are another type of data structure. Similar to sets, however, sequences can and often do have repeating values. However, unlike a Set, the data in a sequence must be ordered and only deals with numbers. SequencesĪ Sequence is another collection of data. Sets may have a name or can be contained within another set as seen in our example. Notice that they’re not in increasing order, and that’s okay. In this example, the set is named ‘A’ and the set contains the numbers 3, 3, and 0, followed by the character ‘a’, followed by a set including x, y, and z. Let’s briefly look at an example of a set: Example: A = Sets are one of the many different types of data structures. It’s also okay to have multiples of any given value inside a set. Also, any given set can contain more than one type of object. However, this is the math of Computer Science. These objects aren’t always integers, as you would expect from a math class. A set can contain numbers, characters, strings, or other objects. SetsĪ Set is a collection of data, in no particular order. However, the core topics are sets, sequences, graph theory, logic, probability, and statistics. Discrete math has a diverse range of topics. Most of the math that you actually use in Computer Science is learned in a specific math class called ‘Discrete Mathematics’.
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