Download Introduction to Contemporary Mathematics

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
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2.
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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.