Finite Mathematics

Introduction

Finite math is a little bit different from Algebra Geometry and Calculus The objective of finite math is to develop analitical skills and problem solving skills. The problem solving questions consist of real life applications. It is useful in science, and technology, but it is especially useful in business.

This page will provide students with a better understanding of MFN.OA1 before they actually take the course. It will contain a brief overview of each unit and will provide links to tutors, extra finite problems and other finite math sites.

Specific Units Breakdown







Units Covered


        Unit 1: Combinatorics

There are several interesting topics covered in this unit. The first topic covered is set theory. It will be a review for people who have taken grade 11 math. It involves union, intersections and the idea of the universe. The rest of the topics covered play a very important role in this course. They are used for the next chapter and other chapters to follow. There is a common theme for these topics: the possibility of an event occurring. The topics include:

The Fundamental Counting Principle
A method of counting the possibility of combining events.
Factoral/Permutation
Methods dealing with arrangements of elements. E.g. How many ways can you rearrange 20 people?
Combinations
Methods dealing with arrangements where order is not important. 


  Unit 2: Probability

People often find this unit difficult. Its main focus is the probability of events occurring. The first section covered involve probability of a single event, e.g. what is the probability of rolling six on a die? There is a general formula introduced here called The Uniform Probability Model.

Other topics :

Combinatorics in Probability
Using the skills from the last unit to find the possibility of events and its sample space.
Independent/dependent Events
Finding the probability of two events. These events may or may not have any connections.
Conditional Prbability
Finding the probability of events with a condition. 


  Unit 3: Matrices

This unit is very similar to the Matrices studied in Algebra-Geometry. The first section is devoted to basic skills. It introduces matrices and shows students how perform calculations.

Other topics :

Coding Messages
Involve the inverse matrices. Each letter in the alphabet is assigned a number. Using this concept, a secret code is formed and solved using matrices.
Networking
Application of Matrices. This is used for networks of systems, e.g. a travel route involving a couple of cities. A matrix is used to find possible routes through any number of cities.
Markov Chain
This unit introduces the transition matrix and looks at its affect of a set of numbers over a period of time. 


  Unit 4: Solving Systems Equations

This involves solving two or three equations that have a common answer for their variable.

3 Equations, 3 Unknowns
Solving for the three unknown variables using elimination. The equations must be homogeneous where each term is of the same degree in the variable.
Solving Using Matrices
The above topic is solved easily using a matrix.
Linear Programming
Problems consisting of optimizing: maximizing or minimizing some function subject according to various constraints. It requires some Algebra skills.


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  Unit 5: Binomial Theorem

In this section you are exposed to neat little theorems that could be helpful for many years to come. This unit would require some Algebra skills. Don't worry, however, the algebra you know from grade 12 is more than enough to cover it.

Binomial Theorem is used to expand equations like (a+x)n where n is a real number. There are formulas that help students to expand equations where n = more than 3.

Pascal's Triangle is also introduced to give the coefficients in the binomial expansion.


  Unit 6: Sequences and Series

This unit revisits the sequences and series topics covered in Grade 11. It is intended to expand on your previous knowledge. It covers the following:

Mathematical Induction
A thinking method for solving or proving problems. It is similar to the one learned in Algebra-Geometry. 


  Unit 7: Applications of Probability

The knowledge of probability from the previous unit resurfaces. It is used as an aid to understanding certain types of probability application problems.

The topics covered include:



  Unit 8: Statistics

A very useful section of math, especially in business. This unit will have an overview of the nature of statistics and some of its use in probability.


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Finite Links

The following will contain a list of resources available on the net about Finite math. We will give you a brief description of each site, rate, and potenital benefits to different groups of people.

Topics


Pascal's Triangle

This site gives you an indepth explanation of Pascal's Triangle. The topic most useful to you under the heading Probability/Combinatorics. On the bottom of this page are two topics that is will be of interest to you. They are the following:

  Binomial Expansion and Pascal's Triangle
This site explains to readers where, how, and why Pascal's Triangle is used. It is rather lengthy. 
  Binomial Theorem
This is a question asked by a person regarding the Binomial Theorem. The problem is: What is the fourth term of (2a-6b)11?


Pascal's Triangle

This is another explanation of Pascal's Triangle. This was originally a question asked by someone. It might be a little easier to understand.




Probability

This site contains all questions asked by others to Dr. Math regarding the subject of Probability. It might be helpful to look around for topics that may help you with Finite Math.

Some intersting questions that may relate to your homework are:




Sequences and Series

This site contains all questions asked by others to Dr. Math regarding Sequences and Series. You should look carefully for related topics.




Statistics

This site will be the same as above. However, the topic covered is Statistics




Linear Equations

This site will help you to solve three equations with three unknowns.




Combinatorics

This site contains various combinatorics topics. Browse carefully for related topics that would benefit you.



What's Combinatorics? What's Optimization?

This site contain an explaination of Combinatorcis along with its relationship with optimization




General Browsing

List of Math Topics

This site gives you a list of Math Topics on the net. When you click on a topic, different sites relating to it will come up.


Math Search Engines

This site allows you to search for math related topics, similar to a search engine.




Math Tutorials

Dr. Math

This site allows you to ask questions. Before you ask questions you may want to search through their posted questions mentioned in the specific topics section on this web page.

If you don't like forms you can also send E-mail. If you want a different tutor, please try the Algebra-Geometry page and the Calculus page.


dr.math@forum.swarthmore.edu
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