|[pic] |Syllabus |
| |College of Information Systems & Technology |
| |MTH/221 Version 1 |
| |Discrete Math for Information Technology |
Copyright © 2010 by University of Phoenix. All rights reserved.
Course Description
Discrete (as opposed to continuous) mathematics is of direct importance to the fields of Computer Science and Information Technology. This branch of mathematics includes studying areas such as set theory, logic, relations, graph theory, and analysis of algorithms. This course is intended to provide students with an understanding of these areas and their use in the field of Information Technology.
Policies
Faculty and students/learners will be held responsible for understanding and adhering to all policies contained within the following two documents:
• University policies: You must be logged into the student website to view this document. • Instructor policies: This document is posted in the Course Materials forum.
University policies are subject to change. Be sure to read the policies at the beginning of each class. Policies may be slightly different depending on the modality in which you attend class. If you have recently changed modalities, read the policies governing your current class modality.
Course Materials
Grimaldi, R. P. (2004). Discrete and combinatorial mathematics: An applied introduction. (5th ed.). Boston, MA: Pearson Addison Wesley.
Article References
Albert, I. Thakar, J., Li, S., Zhang, R., & Albert, R. (2008). Boolean network simulations for life scientists. Source Code for Biology and Medicine, 14(3), 16.
Alikhani, S., & Peng, Y-H. (2009). Chromatic zeros and the golden ratio. Applicable Analysis & Discrete Mathematics, 3(1), 120–22.
Arvind, V., Cheng, C. T., & Devanur, N. R. (2008). On computing the distinguishing numbers of planar graphs and beyond: A counting approach. SIAM Journal on Discrete Mathematics, 22(4), 1297–1324.
Banning, J., Eversole, B., Most, D., & Kuk, L. (2008). Crisp sets and Boolean algebra: A research strategy for student affairs. College Student Journal, 42(3), 847–52.
Benedikt, M. & Koch, C. (2009). From XQuery to relational logics. ACM Transactions on Database Systems, 34(4).
Cusi, A. & Malara, N. (2010). Improving awareness about the meaning of the principle of mathematical induction. PNA: Revista de Investigación en Didáctica de la Matemática, 4(1), 15–22.
Drumheller, R. (2010). Streaming media market trends. Faulkner Information Services.
Liu, P-F., Cai, Y-D., Qian, Z-L., Ni, S-Y., Dong, L-H., Lu, C-H., …Lu, W-C. (2009). FastCluster: A graph theory based algorithm for removing redundant sequences. Journal of Biomedical Science & Engineering, 2, 621–625.
Nybolm, M. A. (2008). Counting the perfect powers. Mathematical Spectrum, 41(1), 27–31.
Spielman, D. A. & Teng, S-H. (2009). Smoothed analysis: An attempt to explain the behavior of algorithms in practice. Communications of the ACM, 52(10), 76–84.
Yaacov, I. B. (2008). Continuous first order logic for unbound metric structures. Journal of Mathematical Logic, 8(2), 197–223.
All electronic materials are available on the student website.
|Week One: Basic Enumeration and Logic & Set Theory |
| |Details |Due |Points |
|Objectives |Apply basic enumeration techniques. | | |
| |Simplify assertions and compound statements in first-order logic. | | |
| |Apply basic set-theoretic concepts. | | |
|Readings |Read Ch. 1, sections 1.1–1.4, of Discrete and Combinatorial Mathematics. | | |
| |Read Ch. 2, “Fundamentals of Logic,” of Discrete and Combinatorial Mathematics. | | |
| |Read Ch. 3, sections 3.1–3.3, of Discrete and Combinatorial Mathematics. | | |
| |Read the Week One Read Me First. | | |
| |Read this week’s Electronic Reserve Readings. | | |
|Participation & Discussion |Participate in class discussion. Respond to weekly discussion questions. |Wed 9/18 & Fri |4 |
|Questions | |9/20 | |
|Nongraded Activities and |Select a method for turning in textbook exercises. Due to the nature of this course, symbols | | |
|Preparation |are actively used in individual assignments. You may choose one of the following methods to | | |
| |complete the assignments: | | |
| | | | |
| |Write out the names of symbols rather than using the symbols. | | |
| |Download Microsoft® Equation Editor. There is a tutorial available on your student website if| | |
| |you choose this method. | | |
| |Handwrite your assignments and scan them if you have access to a scanner. | | |
|Team |Prepare your team charter. Submit it to your Learning Team forum title it "Final Team |Mon 9/23 |NA |
|Charter |Charter" | | |
|Learning Team Instructions |Resources: The Association of Computing Machinery (ACM) website, the Society of Individual | | |
| |and Applied Mathematics (SCIAM) website, and the University Library | | |
| | | | |
| |Begin working on the Research Presentation, due in Week Five. | | |
| | | | |
| |Prepare a 15- to 20-slide Microsoft® PowerPoint® presentation describing existing research | | |
| |efforts in ONE of the following areas: | | |
| | | | |
| |Computer vision, such as automatic recognition of objects, boundaries, and so on | | |
| |Computational linguistics, such as information extraction, corpus analysis, and so on | | |
| |Automatic proof programs | | |
| |Automated routing programs, such as shipping, circuitry, electric power, and so on | | |
| |Ultra-high-speed or high-precision computation | | |
| | | | |
| |Note. You may select other topic areas with facilitator approval. | | |
| | | | |
| |Review the rubric posted in the course materials forum for the grading standards on this | | |
| |assignment. | | |
| | | | |
| |Include in your presentation how ONE or more (not all) of the course topics (see below) | | |
| |related to your chosen research area. | | |
| | | | |
| |Logic and set theory | | |
| |Enumeration | | |
| |Algorithmic concepts | | |
| |Relations and functions | | |
| |Graph theory | | |
| |Trees | | |
| |Boolean algebra | | |
|Individual |Complete 10 questions below. Please review the rubric posted in week 1 for math problems. |Mon 9/23 |10 |
|Selected Textbook Exercises |Submit to your assignment tab. Submit a certificate of originality for this assignment. | | |
| | | | |
| |Ch. 1 of Discrete and Combinatorial Mathematics | | |
| | | | |
| |Exercises 1.1/1.2 problem 1a | | |
| |Exercises 1.4, problem 1a | | |
| | | | |
| |Ch. 2 of Discrete and Combinatorial Mathematics | | |
| | | | |
| |Exercise 2.1, problem 2 | | |
| |Exercise 2.2, problem 2 | | |
| |Exercise 2.3, problem 2b | | |
| |Exercise 2.4, problem 1 | | |
| |Exercise 2.5, problem 1 | | |
| | | | |
| |Ch. 3 of Discrete and Combinatorial Mathematics | | |
| | | | |
| |Exercise 3.1, problem 1 | | |
| |Exercise 3.2, problem 3a | | |
| |Exercise 3.3, problem 1 | | |
| |
|Week Two: Algorithmic Concepts and Relations & Functions, Part 1 |
| |Details |Due |Points |
|Objectives | | | |
| |Apply the principles of mathematical induction and recursion. | | |
| |Solve problems of iteration. | | |
| |Manipulate relations and simple functions, and their inverses. | | |
| |Apply the basic concepts of computational complexity and algorithmic analysis. | | |
|Readings |Read Ch. 4, “Properties of the Integer: Mathematical Induction,” of Discrete and | | |
| |Combinatorial Mathematics. | | |
| |Read Ch. 5, “Relations and Functions,” of Discrete and Combinatorial Mathematics. | | |
| |Read the Week Two Read Me First. | | |
| |Read this week’s Electronic Reserve Readings. | | |
|Participation & Discussion |Participate in class discussion. Respond to weekly discussion questions. |Wed 9/25 & Fri |4 |
|Questions | |9/27 | |
|Individual |Complete 10 questions below. Please review the rubric posted in week 1 for math problems. |Mon 9/30 |10 |
|Selected Textbook Exercises |Submit to your assignment tab. Submit a certificate of originality for this assignment. | | |
| | | | |
| |Ch. 4 of Discrete and Combinatorial Mathematics | | |
| | | | |
| |Exercise 4.1, problem 5a | | |
| |Exercise 4.2, problem 18a | | |
| | | | |
| |Ch. 4 of Discrete and Combinatorial Mathematics | | |
| | | | |
| |Exercise 4.3, problem 22a | | |
| |Exercise 4.4, problem 1a | | |
| | | | |
| |Ch. 5 of Discrete and Combinatorial Mathematics | | |
| | | | |
| |Exercise 5.1, problem 4 | | |
| |Exercise 5.2, problem 4 | | |
| |Exercise 5.3, problem 1a | | |
| |Exercise 5.4, problem 13a | | |
| | | | |
| |Ch. 5 of Discrete and Combinatorial Mathematics | | |
| | | | |
| |Exercise 5.7, problem 1a | | |
| |Exercise 5.8, problem 5a | | |
|Team |Complete 3 questions below. Please review the rubric posted in week 1 for math problems. |Mon 9/30 |3 |
|Selected Textbook Exercises |Have one team member submit to their assignment tab. Submit a certificate of originality for| | |
| |this assignment. | | |
| | | | |
| |Ch. 4 of Discrete and Combinatorial Mathematics | | |
| | | | |
| |Exercise 4.3, problems 12a, & 15 | | |
| | | | |
| |Ch. 5 of Discrete and Combinatorial Mathematics | | |
| | | | |
| |Exercise 5.1, problem 8 | | |
| | | | |
|Week Three: Relations & Functions, Part 2, and More Enumeration |
| |Details |Due |Points |
|Objectives | | | |
| |Use the properties of relations. | | |
| |Apply the properties of equivalence relations and partitions. | | |
| |Use the principle of inclusion and exclusion. | | |
|Readings |Read Ch. 7, sections 7.1–7.4, of Discrete and Combinatorial Mathematics. | | |
| |Read Ch. 8, sections 8.1–8.2, of Discrete and Combinatorial Mathematics. | | |
| |Review Ch. 5, “Relations and Functions,” of Discrete and Combinatorial Mathematics. | | |
| |Read the Week Three Read Me First. | | |
| |Read this week’s Electronic Reserve Readings. | | |
|Participation & Discussion |Participate in class discussion. Respond to weekly discussion questions. |Wed 10/2 & Fri |4 |
|Questions | |10/4 | |
|Individual |Complete 10 questions below. Please review the rubric posted in week 1 for math problems. |Mon 10/7 |10 |
|Selected Textbook Exercises |Submit to your assignment tab. Submit a certificate of originality for this assignment. | | |
| | | | |
| |Ch. 7 | | |
| | | | |
| |Exercise 7.1, problems 10a, 10b | | |
| |Exercise 7.2, problem 15a | | |
| |Exercise 7.3, problems 1, 6a | | |
| | | | |
| |Ch. 7 | | |
| | | | |
| |Exercise 7.4, problems 1a, 2a | | |
| | | | |
| |Ch. 8 | | |
| | | | |
| |Exercise 8.1, problems 4, 12 | | |
| |Exercise 8.2, problem 4 | | |
|Team |Complete 3 questions below. Please review the rubric posted in week 1 for math problems. |Mon 10/7 |3 |
|Selected Textbook Exercises |Have one team member submit to their assignment tab. Submit a certificate of originality for| | |
| |this assignment. | | |
| | | | |
| |Ch. 7 | | |
| | | | |
| |Exercise 7.4, problems 12a, & 13 | | |
| | | | |
| |Ch. 8 | | |
| | | | |
| |Exercise 8.1, problem 20 | | |
|Week Four: Graph Theory and Trees |
| |Details |Due |Points |
|Objectives | | | |
| |Apply properties of general graphs. | | |
| |Identify graph isomorphisms, planarities, connected components, and chromatic numbers. | | |
| |Identify properties of a tree. | | |
|Readings |Read Ch. 11, “An Introduction to Graph Theory,” of Discrete and Combinatorial Mathematics. | | |
| |Read Ch. 12, sections 12.1–12.3 & 12.5, of Discrete and Combinatorial Mathematics. | | |
| |Read the Week Four Read Me First. | | |
| |Read this week’s Electronic Reserve Readings. | | |
|Participation & Discussion |Participate in class discussion. Respond to weekly discussion questions. |Wed 10/9 & Fri |4 |
|Questions | |10/11 | |
|Individual |Complete 10 questions below. Please review the rubric posted in week 1 for math problems. |Mon 10/14 |10 |
|Selected Textbook Exercises |Submit to your assignment tab. Submit a certificate of originality for this assignment. | | |
| | | | |
| |Ch. 11 of Discrete and Combinatorial Mathematics | | |
| | | | |
| |Exercise 11.1, problems 3, 11 | | |
| | | | |
| |Ch. 11 of Discrete and Combinatorial Mathematics | | |
| | | | |
| |Exercise 11.2, problem 4 | | |
| |Exercise 11.3, problem 5a | | |
| |Exercise 11.4, problem 3a | | |
| |Exercise 11.5, problem 2 | | |
| | | | |
| |Ch. 12 of Discrete and Combinatorial Mathematics | | |
| | | | |
| |Exercise 12.1, problem 2 | | |
| |Exercise 12.2, problem 6 | | |
| |Exercise 12.3, problem 2a | | |
| |Exercise 12.5, problem 1 | | |
|Team |Complete 4 questions below. Please review the rubric posted in week 1 for math problems. |Mon 10/14 |4 |
|Selected Textbook Exercises |Have one team member submit to their assignment tab. Submit a certificate of originality for| | |
| |this assignment. | | |
| | | | |
| |Ch. 11 of Discrete and Combinatorial Mathematics | | |
| | | | |
| |Exercise 11.1, problems 6, & 16a | | |
| | | | |
| |Ch. 12 of Discrete and Combinatorial Mathematics | | |
| | | | |
| |Exercise 12.1, problems, 7, & 11 | | |
|Week Five: Boolean Logic and Algebra |
| |Details |Due |Points |
|Objectives | | | |
| |Apply the basic concepts of Boolean algebra. | | |
| |Use the basic laws of Boolean algebra. | | |
| |Convert Boolean expressions into a disjunctive or conjunctive normal form. | | |
|Readings |Read Ch. 15, section 15.1, of Discrete and Combinatorial Mathematics. | | |
| |Read the Week Five Read Me First. | | |
| |Read this week’s Electronic Reserve Readings. | | |
|Participation & Discussion |Participate in class discussion. Respond to weekly discussion questions. |Wed 10/16 & Fri|4 |
|Questions | |10/18 | |
|Individual |Complete 5 questions below. Please review the rubric posted in week 1 for math problems. |Mon 10/21 |10 |
|Selected Textbook Exercises |Submit to your assignment tab. Submit a certificate of originality for this assignment. | | |
| | | | |
| | | | |
| |Ch. 15 of Discrete and Combinatorial Mathematics | | |
| | | | |
| |Exercise 15.1, problems 1a, 2a, 4a, 9, & 12 | | |
|Learning Team |Submit the final Research Presentation. |Mon 10/21 |20 |
|Research Presentation | | | |
| |Please review the rubric posted in week 1 for the team project | | |
| |Have one team member submit to their assignment tab | | |
| |Submit a certificate of originality for this assignment | | | 