1/14 SYLLABUS Page 1 of 6 Code: MATH 146 Title: ADVANCED TOPICS IN MATHEMATICS FOR THE LIBERAL ARTS Division: MATHEMATICS Department: MATHEMATICS Course Description: This is a survey course with topics chosen from the mathematics of voting, fair division, apportionment, Euler circuits, the Traveling Salesman Problem, networks, scheduling, finance, and fractal geometry. Prerequisites: A grade of C or higher in MATH 145 (Algebraic Modeling) or MATH 025 (Elementary Algebra) or satisfactory completion of the college’s basic skills requirement in algebra. Credits: 4 Lecture Hours: 4 Lab/Studio Hours: 0 REQUIRED TEXTBOOK/MATERIALS: 1. Computer Software: A MyMathLab (MML) access code will be required for online assignments in all sections. MML also provides access to the e-book: Peter Tannenbaum, Excursions in Modern Mathematics, 7th edition, Pearson, Prentice Hall, 2010. 2. Calculator: You will need a scientific calculator for this course, such as the TI-30 XIIS. OTHER TIME COMMITMENTS: • In addition to the regular class hours, you will need to set aside time each week for homework. The weekly time will vary by topic and level of difficulty, but as an estimate, you should expect two homework hours for each class hour per week. For example, if your class meets for four hours per week, you should expect to spend about eight hours per week on homework. • If you are having any difficulty with the course material, you may need to allow time to see your instructor during office hours or to get help in the Math Lab. COURSE LEARNING OUTCOMES: Upon completion of this course, students will be able to: • Demonstrate the mathematical skills appropriate to this course. (M) • Analyze and solve application problems. (M) • Explain how mathematical knowledge can be used in an applied situation and interpret solutions in the context of the situation. (M) Learning Outcome(s) support the following General Education Knowledge Area:  (M) Mathematics1/14 SYLLABUS Page 2 of 6 GRADING STANDARD: In this course, you will be evaluated by means of tests, labs and quizzes (and possibly homework). A. TESTS There will be three tests, one after each unit. All supporting work must be shown on tests in order for your instructor to properly assess your understanding of the material. The tests will be given in class and it is expected that you will be in class to take the test on the day it is given. If you are very ill (verifiable with a doctor’s note) or you have some other emergency, you must contact your instructor immediately. B. LABS/QUIZZES/HOMEWORK There are daily labs in this course. They are done in groups but handed in individually. The labs contain problems that reinforce the concepts and skills learned in class. There are also periodic quizzes and your instructor may also choose to use certain homework assignments for evaluation. GRADING Each test is graded on the basis of 100 points. The labs are averaged to form your “lab grade”, and the quizzes are averaged to form your “quiz grade.” Your final course average is determined by a weighted average as follows: Test 1 25% Test 2 25% Test 3 25% Quizzes/labs/homework/other assignments 25% FINAL GRADE Your final grade is determined as follows: If your final course average is Your final grade is 90 – 100 A 88 – 89 A- 86 – 87 B+ 80 – 85 B 78 – 79 B- 76 – 77 C+ 70 – 75 C 60 – 69 D** Below 60 F Incomplete INC is only given at the discretion of your instructor. This may occur in documented cases of hardship or emergency. In this case, you must meet with the instructor to discuss the work that must be completed to earn a grade in the course. All work must be completed within 21 days after the end of the term, exclusive of official college closings.1/14 SYLLABUS Page 3 of 6 Withdrawal You may withdraw from the course, without penalty, up to a date set by the College. If you do not withdraw from the course but stop attending, your grade at the end of the semester will be F. COURSE CONTENT: (TEXT SECTION) Unit 1: The Mathematics of Social Choices. In this unit, you will study mathematical applications from social science, such as the mathematics of voting, weighted voting systems, fair division and the mathematics of apportionment. Unit 1 Outcomes: You will: o Use preference ballots and preference schedules to summarize the voting in an election (1.1) o Use the plurality method and the Borda count method to find a winner (1.2, 1.3) o Use the plurality-with-elimination method and the pairwise comparisons method to find a winner (1.4, 1.5) o Determine a weighted voting system and how to find the Banzhaf power index (2.1, 2.2) o Use Banzhaf Power and Shapley-Shubik Power Index to find the power distribution of the weighted voting system (2.3, 2.4) o Explain and apply the basic concepts of fair division (3.1, 3.2) o Define and apply the lone-divider method for three or more players (3.3) o Use the discrete fair-division method, the method of sealed bids, and method of Markers to demonstrate fair division (3.6, 3.7) o Interpret the basic concepts of the mathematics of apportionment (4.1) o Solve apportionment problems using Hamilton’s method, Jefferson’s method, Adams’s method and Webster’s method. (4.2, 4.4, 4.5, 4.6) o Compare and contrast the fairness and the paradoxes of different methods of apportionment (4.3) Unit 2: Management Science. In this unit, you will use various methods for solving problems involving the organization and management of activities with a large number of steps or variables. Unit 2 Outcomes: You will: o Use graphs to model real-world problems (5.1, 5.2, 5.3, 5.4) o Use Euler’s theorems to eulerize a graph (5.5, 5.7) o Explain the difference between a Hamilton circuit, Hamilton path, Euler circuit and Euler path (6.1, 6.2) o Find an optimal solution for a traveling-salesman problem (6.3, 6.4) o Use the brute-force algorithm, the nearest neighbor algorithm, the repetitive nearest- neighbor algorithm, and the cheapest-link algorithm to find an optimal or approximate optimal solution (6.5, 6.6, 6.7, 6.8) o Interpret an optimal solution in the context of a traveling-salesman problem (6.5, 6.6, 6.7, 6.8) o Define a tree and use the properties of a tree (7.1, 7.2) o Use Kruskal’s algorithm to find an optimal (minimum expense or shortest distance) solution of a minimum spanning tree (7.3) o Find and interpret the shortest distance between three points