MATH 104 – Finite Mathematics

 

Objective 1: Identify and apply mathematical formulas to solve specific problems.

 

Algebraic formulas are used in:

·         solving story problems,

·         deductive reasoning,

·         compound interest,

·         standard deviation,

·         z-scores,

·         deriving Fahrenheit from Celsius,

·         deriving present value from compound interest, and

·         deriving x-scores from z-scores.

 

      Algebraic thinking is required to do:

·         dimensional analysis,

·         scientific notation,

·         order of operations,

·         similar triangles,  and

·         square units.

     

 

Objective 2: Identify sound and unsound reasoning.

 

·         Deductive reasoning creates valid arguments.  Often, we use algebra here.

·         Inductive reasoning can also suggest a conjecture that may be sound.  However, it becomes important to rule out the possibility of counterexamples.  Many and varied examples need to be considered to avoid invalid arguments. 

 

Objective 3: Identify relevant information and then develop a plan to solve a problem using an appropriate technique, such as: drawing pictures, considering simplified versions of the problem, organizing the given information into a table, writing down all known relevant formulas or relationships among the given information.

 

·         In Finite Math, we spend a few days discussing problem solving in general.  In this unit, we suggest all of the above techniques. 

·         Then we continue this theme of problem solving as we delve into content areas such as: geometry, math of finance, probability, and statistics.

 

Objective 4: Perform previously developed, multiple step procedures to solve a given problem.

 

Multiple step procedures we study include:

·         Solving geometry problems which require different units (inches, square inches, feet, square feet,...)

·         Compound interest problems

·         Given the interest rate and length of the loan, calculate the total cost of a home

·         Calculating compound probabilities

·         Finding the raw scores that would correlate with the middle 50% of test takers on a standardized test

 

Objective 5: Build a mathematical vocabulary in several content areas.

 

In Finite, we stress the following content areas and learn the following terms (among others):

·         Problem Solving (inductive reasoning, deductive reasoning)

·         Math of Finance (simple interest, compound interest, amount financed, installment price, total cost of home, total interest paid)

·         Probability (sample space, empirical probability, theoretical probability, factorial, multiplication rule, permutation, combination, complementary events, compound probability)

·         Statistics (mean, median, mode, midrange, range, variation, standard deviation, z-score, normal curve, skewed distributions)