Heartland Community College
Course Prefix and Number: MATH 131
Course Title: Explorations in Mathematics
Days and Time the course meets: Monday & Wednesday 7:00 – 8:15
Credit Hours: 3
Instructor’s Name:
Phone Numbers:
E-mail Address:
Office:
Office Hours:
Bruce Lininger
309-268-8640
bruce.lininger@heartland.edu
2402 ICB
Monday & Wednesday 6:30 – 7:00 p.m. & after class by appointment
Student Communication
Just a reminder that to access WebCT, IRIS, and your Heartland Student Email, you will need to log
into myHeartland, at https://my.heartland.edu
Catalog Description:
Prerequisite: MATH 096 or MATH 099 (or assessment) and MATH 098 (or at least one year of
high school geometry) with a grade C or higher.
This course focuses on mathematical reasoning and the solving of real-life problems, rather than on
routine skills. Three or four topics are studied in depth, with at least three chosen from the
following list: counting and probability, geometry, graph theory, logic and set theory, mathematical
modeling, mathematics of finance, game theory, linear programming, and statistics.
Textbook:
Excursions in Modern Mathematics, Seventh Edition, Peter Tannenbaum and Robert Arnold,
Prentice Hall, 2004.
Required Supplies:
A scientific calculator that uses algebraic logic or a graphing calculator is required for this course.
Relationship to Academic Development Programs and Transfer:
This course satisfies the general education mathematics requirement for the A.A. degree and counts
as part of the general education mathematics requirement for the A.S. degree.
Important Dates
Classes Begins
Drop course with refund
Spring Break!!
Last day to withdraw and receive a “W”
Class ends
Final Exam
January 10, 2011
January 24, 2011
March 7 - 12, 2011
April 7, 2011
May 4, 2011
May 9, 2011
Course Topics:
This course will cover at least 3 of the following topics:
1.
2.
3.
4.
5.
6.
7.
8.
9.
Mathematical Modeling
Geometry
Graph Theory
Game Theory
Linear Programming
Logic and Set Theory
Counting Techniques and Probability
Statistics
Mathematics of Finance
Course Objectives (Learning Outcomes)
After completing this course, the student should be able to:
1.
2.
3.
4.
5.
Interpret mathematical models such as formulas, graphs, tables, and schematics, and draw
logical and reasonable inferences from them.
Represent mathematical information symbolically, visually, numerically, and verbally.
Apply concepts and various methods to solve mathematical models using specific parameters.
Estimate and check answers to mathematical problems in order to determine reasonableness,
identify alternatives, and select optimal results.
Recognize the limitations of mathematical models.
Methods of Instruction:
Instructional methods will include lectures, discussions, and group work that will emphasize
applying problem solving strategies to discover and reinforce concepts. Attendance is required to be
successful. You can not get it all out of the textbook.
Syllabus Disclaimer: This syllabus is subject to change. Any changes will be announced in class.
Course Policies:
Method of Evaluation (Tests/Exams, Grading System):
Student grades are based on successful completion of homework, quizzes, tests and other
assignments as the instructor feels are necessary. You will likely have 4 exams and a final exam.
There will also be assignments that will require you to work problems, do research, and write your
findings. Your final exam will be worth approximately 20% of your final grade in this course.
Grade Scale:
100 - 90%
89 - 80
79 - 70
69 - 60
59 -0
A
B
C
D
F
Make-up of tests and assignments: Requesting make-up exams or quizzes is strongly discouraged.
You’ll get behind. If a make-up is unavoidable, please notify me prior to the exam date.
Required Writing and Reading:
Required writing will be part of most assignments and tests. Students will be expected to explain
how they found the solution, describe the solution process, and interpret the answer in the context of
the problem. Students are expected to read the material in the textbook for each section studied.
Student Evaluations
In the last 3 – 4 weeks of class, all students are expected to complete a course evaluation form
online, at www.studentevals.com/heartland. More information about evaluations will be provided
in class.
Participation (or Attendance)
Regular class attendance is an important part of educational success and is expected of all students.
Students who miss class are responsible for the material covered that day, including obtaining the
homework assignments and lecture notes. Attendance will be a calculated part of your grade. I also
reserve the right to give unannounced quizzes.
Student Conduct, Academic Integrity, Plagiarism, Incompletes
Please refer to the Student Conduct Policy in the Heartland Community College CATALOG for
specific policies concerning discipline, academic integrity, plagiarism and incompletes.
http://www.heartland.edu/catalog/index.jsp
Heartland Library Information http://www.heartland.edu/library
The Library, located in the Students Commons Buildings at the Raab Road campus, provides
Heartland students with a full range of resources including books, online journal databases, videos,
newspapers, periodicals, reserves, and interlibrary loan. Librarians are available to assist in locating
information.
Tutoring Center:
http://www.heartland.edu/asc/tutor.html
(309) 268-8231
Testing Center:
http://www.heartland.edu/asc/testing.html
(309) 268-8231
Academic Disabilities
If you have a documented disability and wish to discuss academic accommodations, please contact
Anita Moore at 268-8249 or anita.moore@heartland.edu.
Notice of Cancelled Class Sessions
Cancelled class sessions, for all HCC classes, will be listed under Cancelled Class Meetings in the
A-Z Index and under Academic Information in the Current Students page on the HCC Web site. Go
to http://www.heartland.edu/classCancellations/ to learn what classes have been cancelled for that
day and the upcoming week. Be sure to check the last column, which might contain a message from
the instructor.
Tentative Schedule
Math 131 Explorations in Mathematics
Spring 2011
Jan 10th
Jan 12th
Jan 17th
Jan 19th
Jan 24th
Jan 26th
Jan 31st
Feb 2nd
Feb 7th
Feb 9th
Feb 14th
Feb 16th
Feb 21st
Feb 23th
Feb 28th
Mar 2nd
Mar 14th
Mar 16th
Mar 21st
Mar 23rd
Mar 28th
Mar 30th
Go over syllabus and make introductory remarks.
5.1 – 5.3 Introduction to Graphs, Graph Concepts and Terminology
5.4 – 5.5 Graph Models & Euler’s Theorem
No Class – MLK Holiday
5.6 & 5.7 Fleury’s Algorithm and Eulerizing Graphs
6.1 – 6.2 Hamilton Circuits and Paths, complete graphs, factorial notation.
6.3 – 6.5 Traveling Salesman Problems (TSPs) - weighted graphs, the bruteforce and nearest-neighbor algorithms, efficient and inefficient algorithms
6.6 – 6.8 approximate and optimal algorithms, the repetitive nearest-neighbor
algorithm, and the cheapest-link algorithm
Review for Exam I
Exam I, Chapters 5 & 6
7.1 – 7.3 Minimum network problems, subgraphs, spanning sub graphs, trees,
and spanning trees, and Kruskal’s Algorithm
8.1 – 8.2 Processors, tasks, task states, processing time, precedence relations,
independent tasks, critical time, directed graphs, arcs, incident to and from,
indegree, outdegree, path and cycle, project digraph
8.3 - 8.4 Scheduling with priority lists, decreasing-time list, decreasing-time
algorithm
8.5 – 8.6 Critical time for a vertex, critical path, backflow algorithm, critical
path list, critical-path algorithm
8.7 Drawing a project digraph from information in a table and calculating
maximum error for independent tasks using the critical-path algorithm.
Review Chapter 7 & 8 exercises and Review for Exam II
Exam II, Chapters 7 & 8
10.1 – 10.2 Population Growth: The Linear Growth Model, Recursive and
Explicit Descriptions, finding the sum of N consecutive terms of an
Arithmetic Sequence and using percentages to calculate increases and
decreases.
10.3 Exponential Growth, Recursive and Explicit Descriptions, finding the
sum of N consecutive terms of a Geometric Sequence
15.1 – 15.2 Sample Spaces and the Multiplication Rule
15.3 Permutations and Combinations
15.4 – 15.6 Probability & Odds
Review for Exam III
Apr 4th
Exam III, Chapters 10 & 15
Apr 6th
Apr 18th
Apr 20th
Apr 25th
Apr 27th
May 2nd
14.1 Descriptive statistics, frequency tables, bar graphs, relative frequency
bar graphs, pictograms, pie charts, and variables
14.2 Class intervals, frequency histograms, and relative frequency histograms
14.3 Numerical Summaries of Data, mean, median, quartiles, five-number
summaries, and box plots
14.4 Measures of Spread, range, interquartile range, standard deviation, and
variance
16.1-16.2 Normal distributions, normal curves, symmetry, standard deviation,
and
quartiles
16.3-16.5
Normal distributions cont.
16.6-16.7 Normal distributions cont.
Review for Exam 4 on Chapters 14 & 16
EXAM IV, Chapters 14 & 16
May 4th
May 9th
Review for the Final Exam
FINAL EXAM: 7:00 – 8:15 p.m.
Apr 11th
Apr 13th
Schedule is TENTATIVE and will change. You are responsible for knowing these changes