Fall 2005 Math 105: Introduction to Mathematical
Ideas
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Class Hours: |
MWF
1:10p.m.-2p.m. |
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Instructor: |
Dr. Ling Long |
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Course website: |
http://orion.math.iastate.edu/linglong/F05M105.htm |
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Office: |
452 Carver Hall |
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Phone: |
515-294-8150
(O) |
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E-mail: |
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Office Hours: |
Please click
here for homework assignments, thanks.
The Math Help Room (385 Carver) offers help
to math105. The hours are:
Monday-Thursday 9:00am-4:00pm
and Friday 9:00am-2:00pm
The
following math graduate students offer be tutors of this course, please contact
them by their emails Theodore Rice [tarice@iastate.edu],
Course prerequisites: Satisfactory performance on placement exam, 2 years of high school algebra, 1 year of high school geometry.
Course description: Topics from mathematics and mathematical applications with emphasis on their non-technical content.
Textbook: Excursions in Modern Mathematics, 5th edition, by Peter Tannenbaum.
Calculator: Calculator is not required for this course, but if you need one, TI-83 to TI-89 will work.
Exams: There are 2 class exams (Sep. 28th Wed. and Nov. 2nd Wed.) and 1 final exam (to be announced later).
Homework: Homework will be assigned regularly and collected weekly and will be graded. Late homework is not accepted.
Quizzes: will be given about regularly and the lowest two quiz scores will be dropped in the end. No makeup quizzes will be given.
Attendance: will be taken once
every week.
Grading: Two midterms, each contributes 20%, quizzes (around 10) contribute 20%, homework assignments (around 10) contribute 10%, and finial contributes 30% to the final grade.
Course syllabus: This course will cover selected topics from Ch.5, 6, 7, 9, 10, 11, 12, 15 and 3
(Subject to modification!)
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Chapter |
Topics |
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5.1 to 5.3 5.4 to 5.5 5.6 to 5.7 |
Routing problems;
Graphs; Graph concepts and terminology Graph models;
Eulerˇ¦s theorem Fleuryˇ¦s algorithm; Eulerizing graphs |
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6.1 to 6.2 6.3 to 6.4 6.5 to 6.6 6.7 to 6.8 |
Traveling-salesman
problems; Simple strategies for solving TSPs The brute-force
and nearest-neighbor algorithms; Approximate algorithms The repetitive
nearest-neighbor algorithm; The cheapest-link algorithm |
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7.1 to 7.3 |
Trees; Minimum
spanning trees; Kruskalˇ¦s
algorithm |
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9.1 to 9.2 9.3 to 9.4 |
Fibonacci
numbers; The golden ratio Gnomons; Gnomonic
growth
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10.1 to 10.2 10.3 to 10.4 |
The dynamics of
population growth; The linear growth model
The exponential growth
model; The logistic growth model |
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11.1 to 11.3 11.4 to 11.6 11.7 to 11.8 |
Geometric
symmetry; Rigid motions; Reflections Rotations;
Translations; Glide reflections Symmetry
revisited; Patterns |
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12.1 to 12.4 |
Fractal Geometry (Will
not be covered in the final exam) |
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15.1 15.2 15.3 to 15.4 15.5 to 15.7 |
Random
experiments and sample spaces Counting: The
multiplication rule Permutations and
combinations; What is a probability? Probability spaces;
Probability spaces with equally likely outcomes; Odds |
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3.1 3.2 3.3 |
Fair-Division
games Two players: the
Divider-Chooser method The Lone-Divider
method |
Students
are encouraged to study and work together but copying each other's
work is not acceptable. Any cheating or dishonesty will be treated seriously,
especially in an examination, and a grade of zero will usually be given. Final course grade will
solely base on the performance on exams, quizzes and homework.
If you
have a disability and require accommodations, please contact the instructor
early in the semester so that your learning needs may be appropriately met. You
will need to provide documentation of your disability to the Disability
Resources (DR) office, located on the main floor of the