# Bloomington Tutors | Blog Finite math, K201, calculus, and statistics explained

Finite M118
Oct 30, 2013

## A linear programming word problem - with a surprise twist!

Today, I thought I'd tackle a problem from one of the most "popular" courses (read "required for almost all majors") at this school - finite math. For those of you who haven't heard of this course before, finite math is actually an amalgam of miscellaneous topics from probability theory, linear algebra, and stats, created by math departments at various universities as a way to introduce college freshmen to rigorous, analytical thinking. It's not a real field of mathematics, in the sense that you won't find any professional mathematicians who specialize in "finite mathematics." However, there are mathematicians who specialize in the topics introduced in this course, such as combinatorics and probability.

One of the topics covered in finite math ("finite", by those in the know) is linear programming. This is basically a fancy term for a constrained optimization problem consisting of linear constraints and a linear objective function. In this blog post, I will tackle the followin...

Finite M118
Sep 05, 2017

## Finite Math - Probability with Combinations

This video covers one of the more challenging types of combination and probability problems that are commonly seen on finite exams. We'll need to split the event space into two cases, and compute the number of combinations for each case. Finally, we'll add our two cases together and divide by the total number of combinations in our sample space.

This content was developed with the help of our tutors Grace and Alex, and our design intern Patrick. Thanks everyone!

Finite M118
Aug 30, 2017

## Finite Math - Set Theory

Welcome to to the very first video in our finite math series! In this video, we'll talk about the basic concept of sets. Then, we'll use these concepts to frame a simple problem that involves determining how many elements are in a set.

This content was developed with the help of our tutors Grace and Alex, and our design intern Patrick. Thanks everyone!

Finite M118
Apr 27, 2015

## Going steady (state) with Markov processes

After the finite midterm, you may have been confused and annoyed when the class seemed to abruptly shift from probabilities and permutations to matrices and systems of equations. They seem to have nothing to do with each other!

Well, today is your lucky day. Probability theory and matrices have finally met, fallen in love, and had a beautiful baby named Markov.

Let me explain. Markov processes are widely used in economics, chemistry, biology and just about every other field to model systems that can be in one or more states with certain probabilities. These probabilities change over time.

For example, we might want model the probability of whether or not Amazon.com turns a profit each quarter. So, Amazon.com (the system) can be in two possible states at the end of each quarter: either they turn a profit, or they don't. Their chance of turning a profit this quarter depends on whether or not they turned a profit last quarter. For example, if they profited last quarte...

Finite M118
Apr 19, 2015

## How to understand and solve Leontief input-output model (technology matrix) problems

Today, let's take a look at everyone's favorite matrix application problem, Leontief input-output models. You might know them simply as "technology matrix" problems, but actually the technology matrix is only one part of the problem. The really interesting part is in the derivation of the matrix equation - something that most finite math courses seem to gloss over in the end-of-semester frenzy.

So, let's take a look at a typical "technology matrix" problem, and see if we can't understand how the problem actually works. Hopefully, it will make it easier to remember than an arbitrary formula.

Example: An economy consists of two codependent industries - steel and lumber. It takes 0.1 units of steel and 0.5 units of lumber to make each unit of steel. It takes 0.2 units of steel and 0.0 units of lumber to make each unit of lumber. The economy will export 16 units of steel and 8 units of lumber next month. How many units of steel and lumber will they need to product...