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Introduction to Contemporary Mathematics Spring 2012 Course no. Time Location Instructor Office Phone E-Mail Web Fax Office Hours 1332.010 MWF 11:00 MCS 216 Trey Smith MCS 220L (325) 942.2100 ext. 235 [email protected] http://www.angelo.edu/faculty/tsmith/ (325) 942.2503 MWF 10:00-11:00 & 1:00-2:00 TR 11:00-12:00 & 2:00-3:00 Others by Appointment MyMathlab This Course will require registration with MyMathlab. To do this, you will go to the following website: http://pearsonmylabandmastering.com/?cc and click on “Register”. You will need the following information: Course Name: Math 1332, Spring 2012 Course ID: smith46944 Honor Code Angelo State University expects its students to maintain complete honesty and integrity in their academic pursuits. Students are responsible for understanding the Academic Honor Code, which is available on the web at http://www.angelo.edu/forms/pdf/honorcode5.pdf. Accommodation Statement Persons with disabilities which may warrant academic accommodations must contact the Student Life Office, Room 112 University Center, in order to request such accommodations prior to any accommodations being implemented. You are encouraged to make this request early in the semester so that appropriate arrangements can be made. Religious Holidays A student who intends to observe a religious holy day should make that intention known in writing to the instructor prior to the absence. “Religious holy day” means a holy day observed by a religion whose places of worship are exempt from property taxation under Texas Tax Code 11.20. A student absent from classes for the observance of a religious holy day shall be allowed to complete work scheduled for that day within a reasonable amount of time as set out by the instructor. Homework Homework will be done on-line. Since MyMathLab will allow you to redo any assignment, you will easily be able to maintain a homework average of 100. Additionally, there will be a combination of on-line quizzes and in-class quizzes. Attendance Regular class attendance is expected. Quizzes will be given in the beginning of class. If you miss a quiz, you will not be able to make it up. Projects Tests Grading There will be five projects assigned during the semester. You will only need to do three of those projects (for a total of 30 points). No late projects will be accepted. There will be three exams. Each of the exams will be worth 100 of a possible 330 total points. The final exam is not comprehensive; it is simply one of the three regular tests. There will be three tests for this class. During each of the three test periods you will receive a homework/quiz grade worth 0 to 100 points. At the end of a test period you may skip the test and use your homework/quiz grade if you have satisfied the following two conditions: 1) The homework/quiz grade is 70 or better. 2) You have NO absences for that test period. There are absolutely no exceptions to these two conditions. In the event that you do take a test, you will be given the test grade or the average of the homework grade for that period and the test grade…whichever is higher. Additionally, you will have a project grade worth 0 to 30 points. Your grade will be based on a 330 point scale. 297-330 points…A 264-296 points…B 231-263 points…C 198-230 points…D less than 198 points…less than D Calculators Some of the material in this class requires the use of a calculator. You will be allowed to use a calculator on designated exams. Course Topics This is a tentative course schedule. I reserve the right to change the material or test dates. 1. Voting 2. Plurality and Borda 3. Elimination and Pairwise Comparison 4. Weighted Voting 5. Shapley-Shubik 6. Fair-Division 7. Lone-Divider and Lone-Chooser 8. Last Diminisher 9. Sealed Bids 10. Markers 11. Apportionment 12. Hamilton’s Method 13. Jefferson’s Method 14. Test 1 (2.17) 15. Apportionment and Fairness 16. Introduction to Graph Theory 17. Graph Theory 18. Eulerizing Graphs 19. Hamilton Circuits 20. Hamilton Circuits 21. Trees 22. Graph Coloring 23. Fibonacci Numbers 24. Fibonacci Numbers and the Golden Ratio 25. Math of Finance 26. Simple Interest, Compound Interest 27. Annuities 28. Annuities 29. Test 2 (3.30) 30. Rigid Motions 31. Rigid Motions 32. Symmetry 33. Border Patterns 34. Fractals 35. Population Growth 36. Population Growth 37. Probability 38. Probability 39. Probability 40. Odds 41. Statistics 42. Statistics 43. Statistics 44. Test 3 (5.9, 10:30-12:30) Student Learning Outcomes 1. The students will demonstrate factual knowledge including the mathematical notation and terminology used in this course. Students will read, interpret, and use the vocabulary, symbolism, and basic definitions used in a selection from the following topics: voting theory, apportionment, the mathematics of money, probability, statistics, graph theory, and geometry. 2. The students will be able to describe generalizations of mathematics to real- world situations. Students will be able to describe, for example, the role played by mathematics in the theory of voting. The students will be able to describe connections between mathematical concepts and natural and societal phenomena. 3. The students will apply the course material along with techniques and procedures covered in this course to solve various problems and improve decision making. The students will apply such topics related to statistics and probability to improve decision making through a broader understanding of mathematics. They will learn to analyze problems using mathematical ideas and symbolism and learn to obtain the appropriate resources required to better deal with such problems. 4. The students will develop specific skills, competencies, and thought processes sufficient to support further study or work in this field or related fields. Students will develop new approaches and algorithms for solving problems related to networking, scheduling and paths. Relevant Exemplary Educational Objectives (EEOs) (Source: Core Curriculum: Assumptions and Defining Characteristics, Rev. 1999) EEO # 1: To apply arithmetic, algebraic, geometric, higher-order thinking, and statistical methods to modeling and solving real-world situations. EEO # 5: To interpret mathematical models such as formulas, graphs, tables and schematics, and draw inferences from them. EEO # 6: To recognize the limitations of mathematical and statistical models. EEO # 7: To develop the view that mathematics is an evolving discipline, interrelated with human culture, and understand its connections to other disciplines. Course Content Textbook: Excursions in Modern Mathematics 7th ed. by Peter Tannenbaum, Prentice Hall, ISBN 10: 0-321-56803-6, ISBN 13: 978-0-321-56803-8 1. 2. 3. 4. 5. 6. 7. 8. 9. Mathematics of Voting: Preference Ballots, Plurality, Borda, Runoff Voting, Pairwise Comparison, Rankings Weighted Voting: The Banzhaf Power Index, The Shapley-Shubik Power Index Apportionment and Sharing: Fair-Division Games, The Divider-Chooser Method, The Lone-Divider Method, The Lone Chooser Method, The Last Diminisher Method, Sealed Bids, Markers Apportionment: Various methods including Hamilton’s, Jefferson’s, Adam’s, and Webster’s; The Alabama Paradox Euler Paths and Circuits: Euler Circuit Problems, Graphs, Euler’s Theorems, Fleury’s Algorithm, Eulerizing Graphs The Traveling Salesman Problem: Hamilton Paths and Circuits, Complete Graphs, Greedy and Nearest Neighbor Algorithms Networks: Trees, Spanning Trees, Kruskal’s Algorithm, Shortest Networks for Three or more points Scheduling: Directed Graphs, Priority Lists, The Decreasing Time Algorithm, Critical Paths, Independent Tasks Fibonacci Numbers and the Golden Ratio: Fibonacci Numbers, The Golden Ratio, Gnomons, Spiral Growth 10. Math of Finance: Percentages, Simple Interest, Compound Interest, Annuities 11. Mathematics of Symmetry: Rigid Motions, Reflections, Rotations Translations, Glide Reflections, Patterns 12. Fractals: The Koch Snowflake, The Sierpinski Gasket, Chaos, The Mandelbrot Set 13. Collecting Data: Sampling, Random Sampling, The Capture-Recapture Method, Clinical Studies 14. Descriptive Statistics: Graphical Methods, Variables, Data Summaries, Spread 15. Probability: Random Experiments, Sample Spaces, Permutations, Combinations, Equiprobable Spaces, Odds 16. Normal Distributions: Approximately Normal Distributions, Normal Curves, Distributions of Random Events, Statistical Inference.