There’s so much to cover in a Finite Math course that it often feels like you’d need infinite time to see it all. But if you’re interested in the subject, here’s a brief look at its most common topics.
Logic assesses true and false statements. In a Finite Math course, rather than working with specific statements, you’ll often work with abstract ones represented by letters such as p and q .
Here are a few ways that p and q may appear in compound statements:
These rules can be summarized in a truth table:
p 
q 
~ p 
p ⋀ q 
p ⋁ q 
p → q 
p ↔︎ q 
T 
T 
F 
T 
T 
T 
T 
T 
F 
F 
F 
T 
F 
F 
F 
T 
T 
F 
T 
T 
F 
F 
F 
T 
F 
F 
T 
T 
A set is a list without any repetitions. Much of Set Theory involves how different sets relate to each other. Here are some examples:
These ideas can be demonstrated in the table below:
A = {1, 2, 3} 
B = {3, 4} 
C = {1, 3, 4, 8} 

A ⊆ A? 
A ⊆ B? 
A ⊆ C? 
B ⊆ A? 
B ⊆ B? 
B ⊆ C? 
C ⊆ A? 
C ⊆ B? 
C ⊆ C? 

YES 
NO 
NO 
NO 
YES 
YES 
NO 
NO 
YES 

A ∪ B 
A ∪ C 
B ∪ C 

{1, 2, 3, 4} 
{1, 2, 3, 4, 8} 
{1, 3, 4, 8} 

A ∩ B 
A ∩ C 
B ∩ C 

{3} 
{1, 3} 
{3, 4} 
Combinatorics involves counting the different possible ways to make groups. There are two main ways of forming groups: permutations and combinations.
Use permutations when order matters. For example, if you are choosing class president, vice president, and treasurer from five students, you can find out the number of possible groups with simple multiplication:
5 × 4 × 3 = 60
Use combinations when order doesn’t matter. This time, you are assigning three identical student council positions from five students. You’ll start as if it’s a permutation, figuring out the number of possible groups, but then use some division to eliminate identical groups (like A B C and C B A).
5 x 4 x 33 x 2 x 1 = 10
The basic formula for probability (the likelihood that an event will take place) is:
Probability = number of outcomes fulfilling the requirementstotal number of possibile outcomes
Finite Math will include compound probability, the likelihood of two or more independent events occurring (or of one not occurring):
A vector is a quantity that is assigned a (possibly multidimensional) direction.
A threedimensional array can be represented as < a , b , c >, with a , b , and c each representing the distance travelled in one dimension. For each dimension, one direction is designated as positive with the opposite direction designated as negative. For example, if north, east, and up are positive, then the vector <3, –5, –2> can indicate a distance of 3 units to the north, 5 units to the west, and 2 units downward.
Matrices have a wide variety of applications in fields like computing, chemistry, and quantum mechanics. Despite the complex applications, a matrix is a simple twodimensional table. Here are some examples of what a matrix may look like:
$\left[\begin{array}{ccc}3& 1& 4\\ 0& $ \genfrac{}{}{0.1ex}{}{1}{2}$& \mathrm{\pi}\end{array}\right]$ $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$ $\left[\begin{array}{cc}5& \mathrm{\surd 5}\\ 8& \mathrm{$ {e}^{2}$}\\ 1.2& 2\end{array}\right]$In a Finite Math course, you can expect to learn about some basic operations, such as matrix addition, scalar multiplication, and matrix multiplication.
Statistics is a way to measure lists of numbers in the various ways:
A common thread across all these Finite Math topics is that you have to know how to read what you’re given—whether it’s a set, array, or matrix—and use the right tool for translating it, whether that’s finding an intersection, an if and only if, or a standard deviation. If you feel uneasy with any of these subjects, consider working through some sample problems with a tutor.
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