Peh's Syllabus for Math 3411 MATH 3411. Discrete & Combinatorial Mathematics

MATH 3411. Discrete and Combinatorial Mathematics
Fall Semester 2014

4 semester credit hours.

Course Instructor : Dr. Peh Ng --

Course Time : 10:30-11:35am MWF

Course Venue : Sci 4655

Instructor's OFFICE: Sci 2550 (Science and Math Division Office)

Instructor's OFFICE HOURS: 2:30-3:30 on Mon and Wed; and 9:30am till 10:30am on Thu, or by appointment. (Unless I am on the Twin Cities campus for committee meetings on alternate Wednesdays after 10:30am, I am either in my office, in class or somewhere on campus from 8:30am till about 8:30pm so if you need help, stop by my office or catch me anywhere on campus.)

Instructor's PHONE: 589-6301

Instructor's E-MAIL:

Course Web Page:

Class notes, handouts & textbook: Discrete Source: Prentice Hall Custom Program for Discrete Mathematics from R. Johnsonbaugh's Discrete Math 7th Edition.
To facilitate in-class discussions, it is recommended that you do some reading of the text.

PRE-REQUISITES FOR THIS COURSE: Willingness to work hard, to spend at least 8 hours weekly on this course OUTSIDE of class time, & to think analytically.

COURSE OBJECTIVES/PURPOSES: Students who have successfully completed this course should:

UMM Student Learning Outcomes (SLO) : Students who have successfully completed this course would have achieved UMM's SLO-1b, SLO-2abdefg, SLO-4b as described in UMM's Student Learning Outcomes


1. Logic & Proofs.
Propositions; conditional propositions and logical equivalence; quantifiers; proofs; mathematical induction.

2. Language of Mathematics.
Sets; sequences and strings; functions (plain, one-to-one, onto, generating, special); relations; equivalence relations; matrices of relations.

3. Recurrence Relations.
(The discrete analog of differential equations). Definitions of different types of recurrence relations; solving recurrence relations; numerical approaches to special cases of discrete dynamical systems; applications.

4. Classical Combinatorics
Introduction to combinatorics; basic principles of counting methods; permutations & combinations; inclusion-exclusion principle; generalized permutations and combinations; algorithms for generating permutations & combinations; the Pigeonhole Principle.

5. Applied and Modern Combinatorics

There will be computer and written homework assigned and due on a daily basis during the first portion of the semester and then on a weekly basis after that. Occasionally students will be asked to present their work on the board to the class.

There will be course project that includes a written report and an oral presentation. For more information on topics and expectations, see , handout with a detailed description of the project.

There will be three in-class exams throughout the semester and a comprehensive in-class final exam during finals week. All exams will be closed book/notes; any helpful information, if applicable, will be provided by the instructor.

Discussion of homework or assignments among students aids learning and is encouraged. However, each student is expected to submit his/her own work. No two homeworks should ever be identical on any major part. No cooperation of any kind, or use of unauthorized notes, is allowed during examinations and quizzes.
Cheating, particularly on examinations, hurts students who are honestly earning their grades by devaluing their achievements. It is every student's responsibility to help control academic honesty by reporting it to the professor whenever they see it going on.
Students who violate UMM's academic integrity and honesty code will face consequences according to University Policies which include being expelled.


1. Three exams - 100 points each. 300 points

2. Final exam (Mon, Dec 15 at 8:30am till 10:30am as in the UMM Schedule bulletin) 200 points

3. Course Project (on real-world applications) 100 points
(See Project Handout )

4. Homework - (written and computer). 100 points

Policies on homework, exams, and project.

Course Grades

A 90 ≤ x ≤ 100
A- 88 ≤ x ≤ 89
B+ 86 ≤ x ≤ 87
B 80 ≤ x ≤ 85
B- 78 ≤ x ≤ 79
C+ 76 ≤ x ≤ 77
C 70 ≤ x ≤ 75
C- 68 ≤ x ≤ 69
D+ 66 ≤ x ≤ 67
D 60 ≤ x ≤ 65
F x ≤ 59

All-University Interpretation of Grades

A & A-: achievement that is outstanding relative to the level necessary to meet course requirements.
B, B+ & B-: achievement that is significantly above the level necessary to meet course requirements.
C, C+,C-: achievement that meets the course requirements in every respect.
D, D+: achievement that is worthy of credit even though it fails to meet fully the course requirements.
S : achievement that is satisfactory, which is equivalent to a C- or better (achievement required for an S is at the discretion of the instructor but may be no lower than a C-).
F (or N) : Represents failure (or no credit) and signifies that the work was either (1) completed but at a level of achievement that is not worthy of credit or (2) was not completed and there was no agreement between the instructor and the student that the student would be awarded an I (see also I)
Academic dishonesty: academic dishonesty in any portion of the academic work for a course shall be grounds for awarding a grade of F or N for the entire course.
I (Incomplete) Assigned at the discretion of the instructor when, due to extraordinary circumstances, e.g., hospitalization, a student is prevented from completing the work of the course on time. Requires a written agreement between instructor and student.
For undergraduate courses, one credit is defined as equivalent to an average of three hours of learning effort per week (over a full semester) necessary for an average student to achieve an average grade in the course. For example, a student taking a three credit course that meets for three hours a week should expect to spend an additional six hours a week on coursework outside the classroom.

The University of Minnesota is committed to providing equitable access to learning opportunities for all students. Disability Services (DS) is the campus office that collaborates with students who have disabilities to provide and/or arrange reasonable accommodations. If you have, or think you may have, a disa bility (e.g., mental health, attentional, learning, chronic health, sensory, or physical), please contact DS at 320 - 589 - 6178 to arrange a confidential discussion regarding equitable access and reasonable accommodations. If you are registered with DS and ha ve a current letter requesting reasonable accommodations, please contact your instructor as early in the semester as possible to discuss how the accommodations will be applied in the course. Additional information is available at the DS web site at

As a student you may experience a range of issues that can cause barriers to learning, such as strained relationships, increased anxiety, al cohol/drug problems, feeling down, difficulty concentrating and/or lack of motivation. These mental health concerns or stressful events may lead to diminished academic performance and may reduce your ability to participate in daily activities. University o f Minnesota services are available to assist you. You can learn more about the broad range of confidential mental health services available on campus via the UMM Student Counseling website at : or phone at 320 - 589 - 6060

Here is a link to more policy statements about syllabi:


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Last Modified Tuesday, August 26, 2014
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