ROCHESTER INSTITUTE OF TECHNOLOGY COURSE OUTLINE FORM COLLEGE OF SCIENCE. School of Mathematical Sciences

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! ROCHESTER INSTITUTE OF TECHNOLOGY COURSE OUTLINE FORM COLLEGE OF SCIENCE School of Mathematical Sciences New Revised COURSE: COS-MATH-131 Discrete Mathematics 1.

11-17-10 Optional Course Designations: Yes No General Education Writing Intensive Honors Approval Request Date Approval Grant Date 2.

1 ! ROCHESTER INSTITUTE OF TECHNOLOGY COURSE OUTLINE FORM COLLEGE OF SCIENCE School of Mathematical Sciences New Revised COURSE: COS-MATH-131 Discrete Mathematics 1.0 Course designations and approvals: Required Course Approvals: Approval Approval Request Date Grant Date Academic Unit Curriculum Committee College Curriculum Committee Optional Course Designations: Yes No General Education Writing Intensive Honors Approval Request Date Approval Grant Date 2.0 Course information: Course Title: Discrete Mathematics Credit Hours: 4 Prerequisite(s): COS-MATH-101 or equivalent Co-requisite(s): None Course proposed by: School of Mathematical Sciences Effective date: Fall 2013 Contact Hours Maximum Students/section Classroom 4 35 Lab Workshop Other (specify) 2.1 Course conversion designation: (Please check which applies to this course) Semester Equivalent (SE) to: Semester Replacement (SR) to: , New 2.2 Semester(s) offered: Fall Spring Summer Offered every other year only Other Page 1 of??

2 2.3 Student requirements: Students required to take this course: (by program and year, as appropriate) First-year Game Design and Development, and Information Technology majors Students who might elect to take the course: 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 provide knowledge of the mathematical concepts needed for computer technology. 3.2 To discuss the many applications of discrete mathematics to computer science and computer information systems. 3.3 To stress the applications of theorem results in information technology and game design and development. 4.0 Course description: (as it will appear in the RIT Catalog, including pre- and co-requisites, semesters offered) COS-MATH-131 Discrete Mathematics This course in an introduction to the topics of discrete mathematics, including number systems, sets and logic, relations, combinatorial methods, graph theory, regular sets, vectors, and matrices. (COS-MATH-101 or equivalent) Class 4, Credit 4 (F, S) 5.0 Possible resources: (texts, references, computer packages, etc.) 5.1 Molluzzo and Buckley, A First Course in Discrete Mathematics, Waveland Press, Long Grove, IL. 5.2 Siegel, Schaum s Outline of Discrete Mathematics, McGraw-Hill, Columbus, OH. 5.3 Wallis, W.D., A Beginner s Guide to Discrete Mathematics, Birkhauser, New York, NY. 6.0 Topics: (outline) Topics with an asterisk(*) are at the instructor s discretion, as time permits 6.1 Number Systems The binary, octal, and hexadecimal systems The integers Modular arithmetic 6.2 Sets Sets, subsets, power sets, and Venn diagrams Set representations Intersections, unions, and complement 6.3 Logic Conjunction, disjunction, and negation Tautologies and contradictions Logical implication and decision tables First order quantifiers Page 2 of??

3 6.3.5 Proof techniques 6.4 Functions Introduction to relations through the Cartesian product of sets Partial orders and equivalence relations Operations on functions; one-to-one, onto, and inverse functions Recursively defined functions Mathematical induction 6.5 Counting Permutations and combinations Binomial coefficients Pigeonhole principle 6.6 Graph Theory Examples of graphs, including K n, C n, trees, directed graphs, and weighted graphs Isomorphic graphs Graph traversal problems, including the traveling salesman problem Shortest paths and Dijkstra s algorithm 6.7 Arrays Vectors and matrices Matrices associated with graphs Matrix operations Bit clearing, bit masking 6.8 Regular Sets Regular expressions Linear grammars Finite state automata Equivalence of regular expressions, linear grammars, and finite state automata 7.0 Intended learning outcomes and associated assessment methods of those outcomes: Assessment Methods Learning Outcomes 7.1 Use binary, octal, and hexidecimal representations of natural numbers 7.2 Use notation of set theory and logic and elementary proof techniques in written communication Page 3 of??

4 Assessment Methods Learning Outcomes 7.3 Use language of set theory to analyze functions, relations, graphs, and inverse functions 7.4 Write proofs using mathematical induction 7.5 Solve elementary combinatorial problems using the rules of product and sum, the binomial theorem, and binomial coefficients 7.6 Multiply matrices, and perform Boolean operations on matrices 7.7 Identify classes of graphs and describe their properties 7.8 Apply basic algorithms of graph theory 7.9 Examine operation of finite state automata and regular expressions 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. 9.0 General education learning outcomes and/or goals supported by this course: Assessment Methods General Education Learning Outcomes 9.1 Communication Express themselves effectively in common college-level written forms using standard American English Revise and improve written and visual content Page 4 of??

5 Assessment Methods General Education Learning Outcomes 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 9.2 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 9.3 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 9.4 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 information Perform college-level mathematical operations on quantitative data Describe the potential and the limitations of technology Use appropriate technology to achieve desired outcomes 9.5 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 Page 5 of??

6 10.0 Other relevant information: (such as special classroom, studio, or lab needs, special scheduling, media requirements, etc.) None Page 6 of??

Probability and Game Theory Course Syllabus

Probability and Game Theory Course Syllabus DATE ACTIVITY CONCEPT Sunday Learn names; introduction to course, introduce the Battle of the Bismarck Sea as a 2-person zero-sum game. Monday Day 1 Pre-test