MTH 151 - Mathematics of Our World

• 1. Numbers in Our Lives 
• 1.1 Give examples of identification numbers such as Social Security Numbers, Vehicle Identification Numbers, International Standard Book Numbers, and Universal Product Codes.
• 1.2 Determine the length of an identification number and if the number is numeric or alphanumeric.
• 1.3 Explain transmission errors and ways to avoid or minimize such errors.
• 1.4 Use the UPC check-digit scheme to determine the check digit, find a missing digit, and check the validity of a number.
• 1.5 Apply the division algorithm for whole numbers and integers to find the quotient and remainder of a given dividend.  Use the appropriate notation to express the dividend in terms of its quotient and remainder. 
• 1.6 Use the definition of congruence modulo m to verify congruences. 
• 1.7 Illustrate and apply the arithmetic properties of congruence modulo m.
• 1.8 Use the mod 9 check-digit scheme to determine the check digit, find a missing digit, and check the validity of a number.
1.9 Identify a data coding system as a binary code.
• 1.10 Translate messages from English to Morse code and from Morse code to English.
• 1.11 Given a UPC bar code, determine the Universal Product Code.

• 2. Voting and Elections 
• 2.1 Build a preference table given voters’ ballots. 
• 2.2 Given a preference table, find the majority winner (if one exists), the plurality winner, the Borda Count winner, the plurality with elimination winner, and the pairwise comparison winner.
• 2.3 Discuss the advantages and disadvantages of the majority method, the plurality method, the Borda Count method, the plurality with elimination method, and the pairwise comparison method.
• 2.4 Define the fairness criteria: the Majority criterion, the Head-to-head criterion, the Monotonicity criterion, and the Irrelevant-Alternatives criterion.
• 2.5 Given a preference table, determine if a fairness criterion has been violated.
• 2.6 Explain the implication of Arrow’s impossibility theorem.

• 3. Routes and Networks 
• 3.1 Identify any vertices, edges, loops, adjacent vertices, weights, paths, and circuits in a given graph.
• 3.2 Determine if a graph is connected.
• 3.3 Compute the degree of a vertex.
• 3.4 Sketch a graph from a map (road maps, neighborhoods, floor plans, etc.).
• 3.5 Explain the difference between a path and a circuit.  Be able to give examples of a path and a circuit from a given graph.
• 3.6 Define and identify an Euler path and Euler circuit.  Give a real-life illustration that requires the use of an Euler circuit.
• 3.7 Use Euler’s Theorem to state if a graph has an Euler path, Euler circuit, or neither.
• 3.8 Use Fleury’s algorithm to find an Euler path/Euler circuit for a given graph.
• 3.9 Sketch a weighted graph given any of the following: a map, table, or word problem. 
• 3.10 Identify a subgraph, tree, and spanning tree.
• 3.11 Use Kruskal’s algorithm to find the minimal spanning tree in a weighted graph.
• 3.12 Define and identify a Hamilton path and Hamilton circuit.  Give a real-life illustration that requires the use of a Hamilton circuit.
• 3.13 Determine if a graph is complete.  Compute the number of edges in a complete graph.
• 3.14 Compute the number of Hamilton paths in a complete graph.
• 3.15 Sketch a complete weighted graph given any of the following: a map, table, or word problem. 
• 3.16 Solve a traveling salesperson problem by computing the cost of all possible Hamilton circuits.
• 3.17 Find an approximate solution to a traveling salesperson problem using the Nearest-Neighbor algorithm and the Cheapest-Link Algorithm.

• 4. Statistical Research Design and Display
• 4.1 Define and identify the elements, population, sample, qualitative (nominal and ordinal) variables, and quantitative variables in a given statistical study.
• 4.2 Explain the use of and need for a sample for statistical inference.
• 4.3 Define and be able to choose a simple random sample using a random number table or a random number generator.
• 4.4 Give reasons for using random sampling in statistical research.
• 4.5 Define bias and identify common sources of bias such as sampling errors, processing errors, and effects of question wording and survey format.
• 4.6 Discuss methods used to avoid or minimize bias.
• 4.7 Critically evaluate a media account or summary of a statistical study
• 4.8 Discuss the advantages and disadvantages of various types of graphs relative to a given data set.
• 4.9 Give examples of graphs which illustrate how choices of categories, scale, and visual design clarify or distort the data.

 

Revised: 02/07