Discrete Mathematics
MATH 339
Spring 2007
Meets: 11:00-11:50 MWF Room: Madeleva231W
Instructor: Charles Peltier
Office: Mad 214
Phone 4498(H:232-4951)
email cpeltier
Office Hrs: M 1-2 T10-11 W 10-11, Th 1-2, F 10-11 or see/call me to make an appointment
Text: Rosen, Discrete Mathematics and its Applications, 6th Ed, Custom Edition (chapters 5,7, 9, 10 of full edition) McGraw-Hill,
2006.
References:(available in library-call number noted)
Brualdi, Introductory Combinatorics QA164 B88 - Good development of combinatorial material
Busacker and Saaty, Finite Graphs and Networks QA166 B97 - Lots of applications
Knuth, The Art of Computer Programming (3 volumes) QA76.5 K74 - Lots of combinatorial problems
Liu, Introduction to Combinatorial Mathematics QA164 L78 - Easy to read- comprehensive
Lucas, Roberts, Thrall, Discrete and Systems Models QA37 M69 vol.3 - Good model descriptions
Riordan, Introduction to Combinatorial Analysis QA165 R58 - Good proofs, complete description of theory
Roberts, Discrete Mathematical Models QH323.5 - Many graph-theoretic models
Ryser, Combinatoric Mathematics QA165 R99 - Classic book on combinatorics
Blackboard site: Documents (assignments, problem solutions, test solutions, etc) for this course will be available at the Blackboard
site for Math339. The site also provides communication tools (email addresses for all class members, a discussion area, etc.)
Course Goals: The major goals for this course are
1. learning of the content,
2. development of problem-solving skills (using available tools – usually in new ways – to solve non-routine problems),
3. development of communication skills in mathematics (writing problem solutions, discussing solutions and approaches, orally
presenting solutions, longer expository writing).
Content: The course emphasizes discrete methods [distinguished from the "continuous" methods involved in calculus and
computational algebra] used for formulating mathematical models; all the topics are in the area of mathematics called
"combinatorics" which deals with arrangements of objects from a finite set into patterns. Brualdi (see references) identifies the
four types of problems:
1. Is a specified arrangement possible (if not always, then when is it possible)?
2. How many ways are there to achieve a specified arrangement, and how can we classify them (to facilitate counting)?
3. What different properties can we identify in specific arrangements?
4. What is the "best" way to arrange the objects, how can we "best" achieve the arrangement?
Problem-solving through use of general theory and special cases will be an essential part of the course. Based on [Tucker,
Applied Combinatorics, Wiley]. I would suggest you consider the following four aspect of combinatorial problem-solving:
1. systematic analysis of different possibilities
2. exploration of the logical structure of a problem
3. ingenuity to combine known tools to solve new problems
4. persistence (including starting early so there is time to go away and come back).
Topics: (See Rosen
A: Numerical combinatorics: general counting methods, combinatorial proofs of numerical relationships. generating functions,
recurrence relations, inclusion and exclusion.
B: Graph Theory: basic graph concepts, covering circuits, trees, network algorithms.
Procedures: The course will proceed section-by section through the text, beginning with chapter 9; the material is divided into 3-day,
2-section “blocks” of material [with a few exceptions -see schedule below] The regular class lectures on the first two days will
assume that the reading has been done and that you have looked at the exercises; I will not attempt to give a complete and
seamless presentation of the text material, but will expect questions and discussion. On the last day of each block, students will be
called on to present solutions (or approaches, if you do not have a full solution) to the assigned problems, and everyone will be
expected to participate in discussion of these solutions (correct, complete, or otherwise). Participation in these discussions is
required and will be graded.
Each student is to hand in her own solutions at the end of this meeting; a selection of the problems not presented will be
graded. In general, full sentences (symbolic or English) are required, with an explanation of each step in the solution. [The
"solutions" in the text would not be acceptable as solutions - they should properly be labeled "hints"] There is not much numerical
work involved in this material, but there is a lot of logic and analysis of steps [that is, a lot of "mathematics" as opposed to
"arithmetic"], and it is essential these be shown.
Writing: There will be several short writing assignments during the semester, including some opportunity for revision. The
assignments will provide an opportunity to work toward the Sophomore and Junior level writing requirements.
Grading: Total points on
1.) 4 Tests: Dates 2/5, 2/28, 4/4, 5/8(exam week- 8am) 100 points each;
2.) Discussions and exercises 150 points
3.) Writing assignments 50 points:
Total of 600 points possible.
Grading scale
- from top & bottom 2% of each
Academic Honesty Policy: See statement in Student Handbook on Academic Honesty (accessible online via the Blackboard site for
this course) In this course academic dishonesty will result in a grade of 0 for the work involved, and notification of the Office of
Academic Affairs. A second occurrence will result in failure for the course, with notice to Academic Affairs.
You should work together and/or seek help from the instructor on regular assignments, but each student must hand in her own
work and is responsible for her own understanding. For help in thinking about the distinction see the Mathematics Department
Honesty Guide (also available through the Blackboard site)
The best way to combine working together with doing your own work is to be sure you bring your own ideas to any consultation
or group effort and destroy (or store out of reach) any written notes from consultations or group work before writing your own
solutions. On tests, no assistance (including other people, books, notes, etc.) is permitted without explicit permission from the
instructor.
Schedule for Math 339 Spring 07
In each block of material, the sections listed are to be read before class on the first date listed. “Exercise” reference indicates text
pages with exercises for the block.
Block/Dates
Material
Exercises
Comments
I: 1/15 - 1/19 (M-F)
Section 5.1, 5.2
p.24, p.33
II: 1/22 - 1/26
Sections 5.3, 5.4
p.40, p.49
III: 1/29 –2/2
Section 5.5
p. 59, p.68
Test I Monday 2/5
IV: 2/7 - 2/12 (W-M)
Sections 7.1, 7.2
p.84, p.99
V: 2/14 - 2/19
Sections 7.3, 7.4
p.110, p.124
VI: 2/21 - 2/26
Sections 7.5, 7.6
p.132, p.142
Test 2 Wednesday 2/28
VII: 3/2 – 3/7 (F-W)
Sections 9.1, 9.2
p.158, p.171
VIII: 3/9 – 3/21
Sections 9.3, 9.4
p. 181, p.192
IX: 3/23 - 3/28
Sections 9.5, 9.6
p.206, p.218
X: 3/30 - 4/2
Section 9.7
p. 228
Test 3 Wed 4/4
XI: 4/11- 4/16 (W-M)
Sections 9.8, 10.1
p.235, p.267
XII: 4/18 – 4/23
Sections10.2, 10.3
p.282, p.296
XIII 4/25-5/2
Sections 10.4, 10.5
p. 308, 316
Tuesday 5/8
Test 4 Tuesday 5/8 8am