MATH 145-Finite Mathematics 

Notes on Class Topics

 

Chapter 1:

Linear Equations and Graphs

Chapter 2:

Functions and Graphs

Chapter 3:

Mathematics of Finance
Chapter 1: Power Points Chapter 2: Power Points Chapter 3: Power Points
Linear Equations and Inequalities Functions Simple Interest
Graphs and Lines Elementary Functions:  Graphs and Transformations Compound and Continuous Compound Interest
Linear Regression Quadratic Functions Future Value of an Annuity; Sinking Funds
Chapter 1 Review Exponential Functions Present Value of an Annuity; Amortization
  Logarithmic Functions Chapter 3 Review
  Chapter 2 Review  
     

 

Chapter 4:

Systems of Linear Equations and Matrices

Chapter 5:

Linear Inequalities and Linear Programming

Chapter 6:

Linear Programming: Simplex Method
Introduction to Matrices and Matrix Addition Graphing Linear Inequalities Setting up the initial simplex tableau 
Matrix Multiplication Setting up linear programming problems Solving a standard problem 
Systems of Equations Solving linear programming problems graphically More standard problems
Matrix Inverses Manufacturing checkers and chess sets Nonstandard problems
Summary of Strategy for Row Operations More applications of Linear Programming How the simplex method works for nonstandard problems
Why the method for finding the inverse of a matrix works   A more complex problem
Don't Let the Symbols Throw You for a Loop   Some Final Tips
Modeling Population dynamics with Matrices    
     
Chapter 4: Power Points Chapter 5: Power Points Chapter 6: Power Points
Review: Systems of Linear Equations in Two Variables Inequalities in Two Variables A Geometric Introduction to the Simplex Method
Systems of Linear Equations and Augmented Matrices Systems of Linear Inequalities in Two Variables The Simplex Method: Maximization with Problem Constraints of the Form ≤
Gauss-Jordan Elimination Linear Programming in Two Dimensions:  A Geometric Approach The Dual; Minimization with Problem Constraints of the Form ≥
Matrices: Basic Operations Chapter 5 Review Maximization and Minimization with Mixed Problem Constraints
Inverse of a Square Matrix   Chapter 6 Review
Matrix Equations and Systems of Linear Equations    
Chapter 4 Review    
     

 

Chapter 7:

Logic, Sets and Counting

Chapter 8:

Probability

Chapter 9:

Markov Chains
Introduction to sets Sample space and events What is a Markov Chain
 Set operations and Venn diagrams What is Probability Multi-step transition probabilities
Venn diagrams and data Uniform probability distributions Regular Markov chains
Multiplication principle and tree diagrams Conditional Probability Absorbing Markov chains
Permutations and Combinations Combining conditional probabilities and tree diagrams Markov chain review
Some review problems Independence and independent trials  
 More review problems Expected value  
     
Chapter 7: Power Points Chapter 8: Power Points Chapter 9: Power Points
Logic Sample Spaces, Events, and Probability Properties of Markov Chains
Sets Union, Intersection, and Complement of Events; Odds Regular Markov Chains
Basic Counting Principles Conditional Probability, Intersection, and Independence Absorbing Markov Chains
Permutations and Combinations Bayes' Formula Chapter 9 Review
Chapter 7 Review Random Variable, Probability Distribution, and Expected Value  
  Chapter 8 Review