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ROCHESTER INSTITUTE OF TECHNOLOGY
COURSE OUTLINE FORM
COLLEGE OF SCIENCE
School of Mathematical Sciences
X New
Revised COURSE: COS-MATH-361 Combinatorics
1.0 Course designations and approvals:
Required Course Approvals:
Academic Unit Curriculum Committee
College Curriculum Committee
Optional Course Designations:
No
Approval
Grant Date
4-15-10
9-20-11
Approval
Request Date
Approval
Grant Date
X
General Education
Writing Intensive
Honors
2.0 Course information:
Course Title:
Credit Hours:
Prerequisite(s):
Co-requisite(s):
Course proposed by:
Effective date:
Yes
Approval
Request Date
4-08-10
11-01-10
X
X
Combinatorics
3
COS-MATH-191 or -200, or permission of instructor
None
School of Mathematical Sciences
Fall 2013
Classroom
Lab
Workshop
Other (specify)
Contact Hours
3
Maximum Students/section
35
2.1 Course conversion designation: (Please check which applies to this course)
X Semester Equivalent (SE) to: 1016-365
Semester Replacement (SR) to:
New
2.2 Semester(s) offered:
Fall
X Spring
Offered every other year only
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Summer
Other
2.3 Student requirements:
Students required to take this course: (by program and year, as appropriate)
None
Students who might elect to take the course:
Students majoring in Applied Mathematics, Computational Mathematics, or Applied
Statistics, Mathematics minors, and students seeking to strengthen their technical
background in mathematics
3.0 Goals of the course: (including rationale for the course, when appropriate)
3.1 To learn the basic techniques of combinatorial mathematics.
3.2 To apply the techniques in particular instances.
3.3 To learn to abstract from particular instances and to handle the resulting abstract structures.
4.0 Course description: (as it will appear in the RIT Catalog, including pre- and co-requisites,
semesters offered)
COS-MATH-361
Combinatorics
This course introduces the mathematical theory of enumeration of discrete structures. Topics
include enumeration, combinatorial proofs, recursion, inclusion-exclusion, and generating
functions. (COS-MATH-191 or -200, or permission of instructor) Class 3, Credit 3 (S)
5.0 Possible resources: (texts, references, computer packages, etc.)
5.1 Kenneth P. Bogart, Combinatorics Through Guided Discovery, (online).
5.2 Richard A. Brualdi, Introductory Combinatorics, Prentice Hall, Upper Saddle River,
NJ.
5.3 Harris, Hirst, Mossinghoff, Combinatorics and Graph Theory, Springer, New York,
NY.
5.4 Miklós Bóna, A Walk Through Combinatorics, World Scientific Publishing, Singapore.
6.0 Topics: (outline) Topics with an asterisk(*) are at the instructor’s discretion, as time permits
6.1 Basic Techniques
6.1.1 Pigeonhole principle
6.1.2 Permutations & combinations of sets and multisets
6.1.3 Bijective proofs
6.2 Binomial Coefficients
6.2.1
6.2.2
6.2.3
6.2.4
The binomial theorem
The multinomial theorem
Binomial identities
Catalan numbers
6.3 Partitions
6.3.1 Compositions
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6.3.2 Set partitions
6.3.3 Integer partitions
6.4 Inclusion-Exclusion
6.4.1 Inclusion-exclusion principle
6.4.2 Derangements
6.4.3 Forbidden positions
6.5 Generating Functions
6.5.1
6.5.2
6.5.3
6.5.4
6.5.5
Generalized binomial coefficient
Ordinary generating functions
Solving recursions
Exponential generating functions
Products of generating functions
6.6 Optional Topics*
6.6.1 Compositions of generating functions
6.6.2 Cycles in permutations
6.6.3 Permutations with restricted cycle structure
7.0 Intended learning outcomes and associated assessment methods of those outcomes:
7.1 Use the basic vocabulary, concepts, rules, and definitions of
enumerative combinatorics
7.2 Apply combinatorial techniques in particular instances
7.3 Generalize from particular instances and use the resulting abstract structures
X
X
X
X
Class Presentation
X
Computer Work
X
Project
Quiz/Exam/Final
Learning Outcomes
Homework
Assessment Methods
8.0 Program goals supported by this course:
8.1 To develop an understanding of the mathematical framework that supports engineering,
science, and mathematics.
8.2 To develop critical and analytical thinking.
8.3 To develop an appropriate level of mathematical literacy and competency.
8.4 To provide an acquaintance with mathematical notation used to express physical and
natural laws.
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9.0 General education learning outcomes and/or goals supported by this course:
9.1
9.2
9.3
9.4
X
X
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Class Presentation
Computer Work
General Education Learning Outcomes
Communication
Express themselves effectively in common college-level
written forms using standard American English
Revise and improve written and visual content
Express themselves effectively in presentations, either in
spoken standard American English or sign language (American Sign Language or English-based Signing)
Comprehend information accessed through reading and discussion
Intellectual Inquiry
Review, assess, and draw conclusions about hypotheses and
theories
Analyze arguments, in relation to their premises, assumptions, contexts, and conclusions
Construct logical and reasonable arguments that include anticipation of counterarguments
Use relevant evidence gathered through accepted scholarly
methods and properly acknowledge sources of information
Ethical, Social and Global Awareness
Analyze similarities and differences in human experiences
and consequent perspectives
Examine connections among the world’s populations
Identify contemporary ethical questions and relevant stakeholder positions
Scientific, Mathematical and Technological Literacy
Explain basic principles and concepts of one of the natural
sciences
Apply methods of scientific inquiry and problem solving to
contemporary issues
Comprehend and evaluate mathematical and statistical in- X X
formation
Perform college-level mathematical operations on quantita- X X
tive data
Describe the potential and the limitations of technology
Use appropriate technology to achieve desired outcomes
Project
Quiz/Exam/Final
Homework
Assessment Methods
9.5
Class Presentation
Computer Work
Project
General Education Learning Outcomes
Creativity, Innovation and Artistic Literacy
Demonstrate creative/innovative approaches to coursebased assignments or projects
Interpret and evaluate artistic expression considering the
cultural context in which it was created
Quiz/Exam/Final
Homework
Assessment Methods
10.0 Other relevant information: (such as special classroom, studio, or lab needs, special
scheduling, media requirements, etc.)
None
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