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TINFO 240 – DISCRETE MATH FOR INFORMATION TECHNOLOGY
Spring 2016
Today's fast moving information technology field requires professionals with discrete math skills that will
require them to manipulate mathematical concepts and interpret statistical data. Networking and database
technologies require knowledge in probability, sets, graphs, and trees and this course will give the student
a good working knowledge of these areas.
Course Description: Examines selected topics of discrete mathematics and statistics as applicable to
students of information technology and systems. Topics covered include basic logic, discrete probability,
functions, relations, and sets, graphs and trees, regular expressions, and application of mathematics to IT.
Student Learning Goals: Upon successful completion of the course, students should be able to:
• Apply formal methods of propositional and predicate logic.
• Render a well-formed formula in predicate logic in English.
• Understand the basics of matrix math.
• Determine how to map algorithm speeds to Big – O notation.
• Understand the complexity of algorithms.
• Explain the importance and limitations of predicate logic.
• Calculate probabilities of events and expectations for random variables.
• Differentiate between dependent and independent events.
• Apply the binomial theorem to independent events and Bayes’ theorem to dependent events.
• Apply the tools of probability to create simple discrete event simulations.
• Explain, with examples, the basic terminology of functions, relations, and sets.
• Perform the standard operations associated with sets, functions, and relations.
• Relate practical examples to the appropriate set, functions, or relation model, and interpret the
associated operations and terminology in context.
This course supports the achievement of the following program outcomes:
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An ability to apply knowledge of computing and mathematics appropriate to the discipline
An ability to analyze a problem, and identify and define the computing requirements appropriate to its
solution
An ability to use current techniques, skills, and tools necessary for computing practice
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In addition, the course covers a majority of the Math and Statistics for IT (MS) from the Information
Technology Body of Knowledge, including but not limited to:
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Basic Logic
Discrete Probability
Functions, Relations, and Sets
Graphs and Trees
UWT Student Learning Goals that this course contributes to
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Inquiry and Critical Thinking: Students will acquire skills and familiarity with modes of inquiry
and examination from diverse disciplinary perspectives, enabling them to access, interpret,
analyze, quantitatively reason, and synthesize information critically.
Required Materials:
The course textbook is Discrete Mathematics and its Applications, Seventh Edition, Kenneth H. Rosen,
2012, ISBN 978-0-07-338309-5. The textbook is essential; mandatory readings will be assigned, and
most homework problems will come directly from the textbook. You may also be interested in obtaining
the Student's Solutions Guide, ISBN 978-0-07-735350-6, which contains solutions to most of the oddnumbered problems related to the homework assignments.
Canvas:
Students will be enrolled on the course website on Canvas. The Canvas site for the course
includes several required readings for class as well as information about the experiential
exercises (e.g., your role assignments, confidential role materials), lecture notes and other
class information.
Evaluation and Grading:
Assignment
Percentage
Homework
20%
Exams (2 @ 25% each)
50%
Final Exam
50%
Total
100%
Homework: Your homework will consist of 5 assignments that will be turned on online on Canvas.
Doing well on the homework will prepare you for the course exams. The answers for the odd number
problems are located in the back of text.
Exams: There will be two exams and a final exam. All exams are open book, open note.
Class Participation: All class sessions involve active discussion based on the readings and homework
problems. Your contribution to the course not only reflects what you do in the class, but also the work
you do outside of the class preparing for problem solving exercises. You should come to class prepared
to summarize key points from the day’s readings.
Late Assignments: An assignment submitted late, but before the beginning of the lecture following the
due date, will receive a late penalty of 50%. Assignments submitted after the beginning of the lecture
following the due date will receive no credit. The score on a late assignment is computed by taking 50%
of the number of points earned on the assignment and rounding up. For example, assume that a student
submits an assignment one lecture late, and would have gotten 15 points on the assignment if it had been
submitted on time.
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No assignment will receive credit for being submitted more than one lecture late. However, all
assignments (whether they will receive credit or not) must be submitted in order to pass the class.
Overall course grades (decimal) will be calculated from the weighted average of assignments and exams
using the UW grading system.
Grade equivalence: The UW grading
system, http://www.tacoma.washington.edu/enrollmentservices/grading.cfm, will be used. The following
table shows the minimum decimal grades for the specified percentage scores. Decimal grades may be
adjusted upward.
Grade
4.0
3.9
3.8
3.7
3.6
3.5
Score
98-100
95-97
93-94
92
91
90
Grade
3.4
3.3
3.2
3.1
3.0
2.9
2.8
2.7
2.6
2.5
Score
89
88
87
86
85
84
83
82
81
80
Grade
2.4
2.3
2.2
2.1
2.0
1.9
1.8
1.7
1.6
1.5
Score
79
78
77
76
75
74
73
72
71
70
Grade
1.4
1.3
1.2
1.1
1.0
0.9
0.8
0.7
0.0
Score
69
68
67
66
65
64
62-63
61
0-60
Academic integrity and collaboration policy: All assignments and the programming project must be
completed individually. However, limited collaboration is permitted as follows.
These actions are acceptable:
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Contacting the instructor for help with, or clarification on, an assignment.
Posting messages to the class discussion board about parts of an assignment, without posting
solutions.
Discussing an assignment in general terms with other students, without sharing solutions or
algorithmic details.
These actions are not acceptable:
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Sharing your assignment solution with another student.
Sitting with another student and "walking them through" the solution by telling them how to solve the
problem in detail.
Discussing the algorithm(s) for completing an entire assignment or large portions of an assignment in
detail with another student.
Receiving solutions from other students, the Internet, or other sources and submitting it as your own
work.
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Students found to violate the academic integrity policy will receive zero credit for the assignment and
may be reported to the University.
Campus Support: There are several campus resources that you can use to get additional help, either for
counseling or for specific kinds of help (for example, reading, writing, math, study skills, etc.). Contact
them for further information.
Counseling Center (Student Health and Wellness – SHAW): The Counseling Center offers short-term,
problem-focused counseling to UW Tacoma students who may feel overwhelmed by the responsibilities
of college, work, family, and relationships. Counselors are available to help students cope with stresses
and personal issues that may interfere with their ability to perform in school. The service is provided
confidentially and without additional charge to currently enrolled undergraduate and graduate students.
To schedule an appointment, please call 692-4522 or stop by the Student Counseling Center (SCC),
located in MAT 253. Additional information can also be found by
visiting http://www.tacoma.washington.edu/studentaffairs/SHW/scc_about.cfm/
Disability Support Services (Student Health and Wellness – SHAW): The University of Washington
Tacoma is committed to making physical facilities and instructional programs accessible to students with
disabilities. Disability Support Services (DSS) functions as the focal point for coordination of services for
students with disabilities. In compliance with Title II of the Americans with Disabilities Act, any enrolled
student at UW Tacoma who has an appropriately documented physical, emotional, or mental disability
that "substantially limits one or more major life activities [including walking, seeing, hearing, speaking,
breathing, learning and working]," is eligible for services from DSS. If you are wondering if you may be
eligible for accommodations on our campus, please contact the DSS reception desk at 692-4522, or
visit http://www.tacoma.washington.edu/studentaffairs/SHW/dss_about.cfm/
Inclement Weather Updates: As the winter storm season approaches, make sure you’re signed up
for UW Alert to learn about campus closures and other emergency information via text message. The UW
Alert system will be used to notify the campus community if UW Tacoma operations are delayed or
suspended due to inclement weather. In addition, a message will be left on the Inclement Weather Hotline
at 253-383-INFO and sent to local radio and television stations. Campus closure information will also be
sent via e-mail and an update will be posted on the UW Tacoma Web page. Read the inclement weather
Q&A
The Teaching and Learning Center (TLC): The Teaching and Learning Center offers academic support
for students at all levels. More information is available at http://www.tacoma.washington.edu/tlc/
In the Interest of Public Health: If you have a flu-like illness please remain home until 24 hours after
resolution of your fever without the use of fever-reducing medications. To encourage this, lecture slides
will be posted on the course web site, your lowest quiz grade and lowest lab grade will be dropped, and
all homework assignments allow for late turn in.
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TINFO 240 Discrete Math for IT
Spring 2016
WEEK 1
Topic 1: Sets, Set Operations, and Functions
• Read Chapter 2.1 -2.3
Roster Method
Set Builder Notation
Venn Diagrams
Subsets
Cartesian Products
Set Identities
Function Mapping and Composite Functions
Topic 2: Sequences and Summations, Cardinality of Sets, Matrices
• Read Chapter 2.4-2.6
Closed Formula Sequences
Summations
Countable and Uncountable Sets
Matrix Math
Transpose Matrix
Zero – One Matrices
WEEK 2
Topic 1: Algorithms
• Read Chapter 3.1
Properties of Algorithms
Searching, Sorting, Greedy Algorithms
Halting Problem
Topic 2: Growth of Functions
• Read Chapter 3.2
Big O Notation
Estimating Functions
Topic 3: Complexity of Functions
• Read Chapter 3.3
Time Complexity
Understanding Complexity
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WEEK 3
Topic 1: Divisibility and Modular Arithmetic
• Read Chapter 4.1
The Division Algorithm, Modular Arithmetic, Modulo m
Topic 2: Integer Representations and Algorithms
• Read Chapter 4.2
Representations of Integers
Number Conversions, Algorithms for Integer Operations
Topic 3: Primes and Greatest Common Divisors
• Read Chapter 4.3
Fundamental Theorem of Arithmetic
The Prime Number Theorem
Greatest Common Divisors and Least Common Multiples
The Euclidean Algorithm
Due: Homework 1
WEEK 4
Topic 1: Solving Congruences
• Read Chapter 4.4
Linear Congruences
Chinese Remainder Theorem
Computer Arithmetic With Large Integers
Fermat’s Little Theorem
Topic 2: Applications of Congruences
• Read Chapter 4.5
Hashing Functions
Parity Check Bits
Topic 3: Cryptography
• Read Chapter 4.6
Classic Cryptography – Caesar Cipher
Public Key Encryption
Protocols
Topic 4: Exam Review
Topic 5: Exam 1
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DUE: Homework 2
WEEK 5
Topic 1: The Basics of Counting
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Read Chapter 6.1
The Product Rule
Complex Counting Problems
The Division Rule
Topic 2: The Pigeonhole Principle
• Read Chapter 6.2
The Pigeonhole Principle
Applications
WEEK 6
Topic 1: Permutations and Combinations
• Read Chapter 6.3
Permutations and Combinations
Applications
Topic 2: Binomial Coefficients and Identities
• Read Chapter 6.4
The Binomial Theorem
Pascal’s Identity and Triangle
Vandermonde’s Identity
Topic 3: Generalized Permutations and Combinations
• Read Chapter 6.5
Permutations and Combinations with Repetition
Permutations with Indistinguishable Objects
WEEK 7
Topic 1: An Introduction to Discrete Probability
• Read Chapter 7.1
Finite Probability
Probabilities of Complements and Union of Events
Probabilistic Reasoning
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Topic 2: Probability Theory
• Read Chapter 7.2
Assigning Probabilities
Probabilities of Complements and Union of Events
Conditional Probability
Interdependence
Bernoulli Trials and Binomial Distribution
Random Variables and the Birthday Problem
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Due: Homework 3
WEEK 8
Topic 1: Bayes’ Theorem
• Read Chapter 7.3
Bayes’ Theorem
Topic 2: Expected Value and Variance
• Read Chapter 7.4
Expected Value
Linearity of Expectations
Average Case Computational Complexity
Geometric Distribution
Topic 3: Exam 2 Review
Due: Homework 4
WEEK 9
Topic 1: Exam 2
Topic 2: Graphs and Graph Models
• Read Chapter 10.1
Various Graph Models
Topic 3: Graph Terminology and Special Types of Graphs
• Read Chapter 10.2
Simple and Bipartite Graphs
Applications of Graphs
Topic 4: Representing Graphs and Graph Isomorphism
• Read Chapter 10.3
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Adjacency Matrices
Determining Isomorphic Graphs
Due: Homework 4
WEEK 10
Topic 1: Introduction to Trees
• Read Chapter 11.1
Rooted Trees
Properties of Trees
Topic 2: Applications of Trees
• Read Chapter 11.2
Binary Search Trees
Decision Trees
Game Trees
Topic 3: Tree Traversal
• Read Chapter 11.3
Traversal Algorithms – Pre, In, Post Order
Topic 4: Spanning Trees
• Read Chapter 11.4
Depth First Search
Breadth First Search
Backtracking
Topic 5: Final Review
Due: Homework 5
Final Exam