Fall 2005 Math 105: Introduction to Mathematical Ideas

 

Class Hours:

MWF 1:10p.m.-2p.m.

Instructor:

Dr. Ling Long

Course website:

http://orion.math.iastate.edu/linglong/F05M105.htm

Office: 

452 Carver Hall

Phone:

515-294-8150 (O)

E-mail: 

linglong@iastate.edu

Office Hours:

MWF 12:10p.m.-1:00p.m. &W 4:10p.m.-5p.m. & F 10-10:50a.m.


 

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], Jun-Koo Park [jkpark@iastate.edu] Elynn Cheng [elynn@iastate.edu], Adil Kaymaz [kaymaz@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!)         

Chapter

Topics

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

6.1 to 6.2

6.3 to 6.4

6.5 to 6.6

6.7 to 6.8

Hamilton circuits and Hamilton paths; Complete graphs

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

7.1 to 7.3

Trees; Minimum spanning  trees; Kruskalˇ¦s algorithm

9.1 to 9.2

9.3 to 9.4

Fibonacci numbers; The golden ratio

Gnomons; Gnomonic growth                                                                                  

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

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

12.1 to 12.4

Fractal Geometry (Will not be covered in the final exam)

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

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 Student Services Building, Room 1076, 515-294-6624.