MATH 1100 - Everyday Mathematics

Credit Hours: 4.00

Objectives:

1. Identify and model Euler circuit and Euler path problems.
2. Define basic graph terminology.
3. Use Euler’s Theorem to classify which graphs have Euler circuits and paths.
4. Eulerize graphs when necessary.
5. Identify and model Hamiltonian circuit and Hamiltonian path problems.
6. Recognize complete graphs and state the number of possible Hamiltonian circuits using counting principles.
7. Use brute force, nearest-neighbor, and sorted-edges algorithms to find minimum-cost solutions to traveling salesmen problems.
8. Find minimum-cost spanning trees using Kruskal’s algorithm.
9. Resolve scheduling conflicts using the chromatic number and coloring.

Outcome 2: Upon completion of the course, students will be able collect and organize data into a table and construct appropriate charts and plots to display the data.

Objectives:

1. Identify sampling methods.
2. Identify experimental methods.
3. Create and interpret a histogram.
4. Create and interpret a stemplot.
5. Create and interpret a boxplot.

Outcome 3: Upon completion of the course, students will be able to define, interpret, and calculate measures of central tendency.

Objectives:

1. Find and interpret the shape, center, spread, and outliers of a histogram.
2. Find and interpret the mean and median of a data set.
3. Find and interpret quartiles.
4. Find and interpret the standard deviation and variance from a data set
5. Find and interpret the spread of data of a normal distribution using 68-95-99.7 Rule

Outcome 4: Upon completion of the course, students will be able to display and interpret linear relationships between two variables using regression.

Objectives:

1. Create a scatterplot.
2. Make a prediction using a regression line.
3. Find the equation of the least-squares regression line identifying slope, y-intercept, and correlation with a scientific calculator.
4. Interpret the correlation between two variables.

Outcome 5: Upon completion of the course, students will be able to compute basic probabilities and interpret probability models.

Objectives:

1. Find and interpret the probability of events that are mutually exclusive.
2. Find and interpret the probability of events using complements.
3. Find and interpret the probability of events using counting methods.

Outcome 6: Upon completion of the course, students will be able to demonstrate a working knowledge of various voting systems.

Objectives:

1. Implement the majority rule voting system and identify its advantages in a two-candidate voting system.
2. Implement Condorcet’s Method and know its paradox.
3. Implement the plurality, Borda count, sequential pairwise voting, Hare system, and plurality runoff voting systems for three or more candidates.
4. Manipulate the plurality, Borda count, sequential pairwise voting, Hare system and plurality runoff voting systems.

Outcome 7: Upon completion of the course, students will be able to use methods of division and apportionment to allocate resources fairly.

Objectives:

1. Apply the adjusted winner procedure for two parties.
2. Apply the Knaster inheritance procedure for more than two parties.
3. Explain the basic apportionment problem.
4. Implement the Hamilton Method.

Outcome 8: Upon completion of the course, students will be able to recognize various types of information located in identification numbers

Objectives:

1. Identify the check digit on a traveler’s check, Universal Product Code, bank routing number, and International Standard Book Number and determine if the item is fraudulent.
2. Identify the information contained in a UPC bar code.
3. Identify personal data in a driver’s license number.

Outcome 9: Upon completion of the course, students will be able to decipher encrypted messages.

Objectives:

1. Use Caesar cipher to decipher a message.
2. Use Viegnère cipher to decipher a message.
3. Solve a cryptogram by recognizing frequent letters and words.

Outcome 10: Upon completion of the course, students will be able to classify patterns.

Objectives:

1. Generate the Fibonacci sequence and identify some of its properties.
2. Identify relationships between the Fibonacci sequence and the golden ratio.

Outcome 11: Upon completion of the course, students will be able to use finance and population models.

Objectives:

1. Apply simple interest formula to finance problems.
2. Apply compound interest formula to finance problems.
3. Apply continuous compounding interest formula to finance problems.

1. Graph Theory (8 hours)
   1. Euler paths and circuits
   2. Euler’s Theorem
   3. Eulerize graphs
   4. Hamiltonian paths and circuits
   5. Use various algorithms to find minimum-cost solutions
      1. Brute-force
      2. Nearest-neighbor
      3. Sorted-edges
   6. Kruskal’s algorithm
   7. Use chromatic number to resolve scheduling conflicts
2. Describing and Interpreting Data (8 hours)
   1. Types of sampling methods
   2. Graphs
      1. Histogram
      2. Stemplot
      3. Boxplot
   3. Measures of center
   4. Measures of variance
3. Linear Regression (4 hours)
   1. Scatterplot
   2. Correlation
   3. Predict using regression line
   4. Least-Squares regression line
4. Probability (6 hours)
   1. Basic probability
   2. Counting
   3. Addition Rule
   4. Multiplication Rule
5. Voting Systems (8 hours)
   1. Majority rule
   2. Condorcet’s Method and paradox
   3. Systems for 3 or more candidates
      1. Plurality
      2. Borda count
      3. Sequential pairwise voting
      4. Hare system
      5. Plurality runoff
   4. Manipulation of voting system
6. Division and Apportionment (6 hours)
   1. Adjusted winner procedure
   2. Knaster inheritance procedure
   3. Apportionment
      1. Basic apportionment problem
      2. Hamilton method
7. Identification Numbers (4 hours)
   1. Check digits
   2. UPC bar codes
   3. Driver’s license numbers
8. Encryption (4 hours)
   1. Caesar cipher
   2. Viegnère cipher
   3. Cryptograms
9. Patterns and Symmetries (2 hours)
   1. Fibonacci sequence
   2. Golden ratio
10. Finance and Population Models (2 hours)
    1. Simple interest
    2. Compound interest
    3. Continuous compound interest Total 52 hours with 12 hours available for tests.