RMU – Spring Semester 2015 – Resources for…
·
INFS3450A,
Instructor: Powell
Please use the RMU Help Desk if
you have technical problems (in the lab or with remote access):
call 412-397-2211 or e-mail help@rmu.edu - web www.rmu.edu/help
Tutoring: for
Passouts:
o
passout files for
F Ethics in Information Technology - Links to ACM (Codes of Ethics) and other sources, discussion topics.
ü Links and Resources: Applications of Formal Structures and Other Relevant Links (according to course topics; £ = required)
ü Topic Pages [DMAFISP4: References to Powell/Acharya/Holdan/Maxwell/Wood/Wu]
1. Introduction
1.1. Links and Resources: Formal Structures and Other Relevant Links (according to course topics; £ = required)
1.2. Algebraic Notation and Order of Precedence
1.3. Symbols, Signs, and Operators
2. Logic
2.1. Truth Tables
2.2. DeMorgan’s Laws and Equivalent Statements
2.3. Evaluating a Logic Expression
2.4. Equivalence, Contradiction, Tautology
2.5. Consulting a Prolog file.
2.6. Prolog Lists.
2.7. Building a Circuit Model.
2.8. Arity (
2.9. Tarski's World and Logic Resources, please see:
2.9.1. https://faculty.washington.edu/smcohen/120/Chapter9.pdf
2.9.2. http://people.cis.ksu.edu/~tamtoft/CIS301/Fall04/Slides/03.pdf
2.9.3. http://ada.evergreen.edu/dandi/logic/tests/sherriAnswers.pdf
2.9.4. http://www.logicinaction.org/docs/ch4.pdf
2.10. See also Netmasks/Genmasks and Wildcard Marks (
3.
Sets
3.1.
Set Notation and
Specifying the Members of a Set.
3.2. Subsets and Proper Subsets.
3.3. Sets and Set Operations.
3.4. Venn Diagrams.
3.5. Set Operations Using Prolog
3.6. Venn Diagrams and Categorical Logic
3.8. Partitions and their Applications
4. Number
Systems and Representation
4.1. Decimal, Binary, Hex
4.2. Number Systems: Arabic, Roman, Base 2, Base 10, Base 16, Base 20.
4.3. Mesoamerican Base 20 and Modified Base 20 Number Systems
4.4. The Bit Budget Concept, see Bit Budget page
4.5.
Computer
Operations Using Binary and Hex
4.5.1.
Number
System Conversions.
4.5.2.
Logical
Operations.
4.5.3.
Shift
Operations.
4.5.4.
Binary
Addition with and without overflow
4.5.5.
Two’s Complement Operations
4.6.
Scientific Notation and Floating Point.
4.7.
Interpreting Binary Flags in Hexadecimal
4.7.1.
Interpreting Binary
Flags 1 in Hexadecimal: Internet Examples (IP)
4.7.2.
Interpreting Binary
Flags 2 in Hexadecimal: Internet Examples (
4.7.3.
Interpreting Binary
Flags 3 in Hexadecimal: Internet Examples (BPDU)
4.7.4.
Interpreting Binary
Flags 4 in Hexadecimal: Internet Examples (OSPF)
4.7.5.
Interpreting Binary
Flags 5 in Hexadecimal: Internet Examples (CDP)
4.7.6.
Interpreting Binary
Flags 6 in Hexadecimal: Internet Examples (BGP)
4.8.
Internet Addresses and Masks
4.8.1.
Anatomy of an
IPv4 Address
4.8.2.
IPv4 Netmasks/Genmasks
(expressed in dotted-decimal mode and CIDR notation)
4.8.3.
IPv4 Wildcard Masks (used in OSPF, EIGRP routing
and ACLs)
4.8.4.
IPv4 Address Ranges
4.8.5.
IPv4 Address Types
4.8.6.
IPv4 Address Practice Using CIDR Notation
(rather than classes A, B, C)
4.8.7.
Dotted Decimal in IPv4 (base 2) and in Mayan
Long Count dates (modified base 20 in Archaeology)
4.8.8.
IPv6: Examples of IPv4-mapped IPv6 Addresses
4.8.9.
IPv6: IPv6 Addresses
4.8.10.
IPv6: EUI-64
4.8.11.
Color Vectors (
4.8.12.
“Binary Clock” (BCD = Binary Coded Decimal Model)
4.8.13.
Calculator: Using Windows 7® Calculator.
5. Relations,
Functions, Operators
5.1. Properties of Binary Relations.
5.2. Equivalence Relations.
5.4. Reflexive and Strict Partial Orders.
5.5. Prefix Notation Practice Using Prolog
5.6. Modulus (Mod) Function and Non-decimal Arithmetic.
6. Counting,
Randomization, Permutations, Combinations
6.1. Randomization Examples.
6.2. Randomization and Permutation Applications.
7. Relational
Database Concepts
7.1. Relational Database Concepts and Examples
7.2. Aggregates in Database Functions; Equivalence Relations.
7.3. Exclusionary Queries; see Harvey/Baugh/Johnston/Ruzich/Grant, “The Challenge of Negation in Searches and Queries.”
8. Algorithms
and Recursion
8.1. Recursion in Prolog.
8.2. Lindenmayer Systems 1: Recursion and Applications - Logo
9. Codes,
Encryption, Compression
9.1. Characters and Codes 1 – ASCII
9.2. Characters and Codes 2 – ASCII Extended, ASCII Control Characters
9.3. Characters and Codes 3 – Unicode, ISO 10646 (Universal Character Set)
9.4. Parity Bits (Odd and Even) using ASCII Characters and Parity Checking
9.5. Cryptographic Computations
9.6. Summary of Codes
9.7. Codes 6: Compression
9.8. Codes 7: Radix 64.
9.9. Codes 8: CDMA.
9.10. Sorting and Collating Sequences
10. Graphs,
Trees, and Networks
10.1. Graphs 1 – Introduction to Graphs and Subgraphs; Communication of Adjacency
10.1.1. Graphs 1 – Vertex, Edge, Adjacency, Incident On, Degree, Components, Connected
10.1.2. Graphs 1 – Parallel Edges, Loops, Reflexive, Simple Graph
10.1.3. Graphs 1 – Loops, Subgraph, Reflexive Graph
10.1.4. Graphs 1 – Neighbor, Neighborhood, Distinguished Vertex
10.2. Graphs 2 – Paths and Cycles in Graphs.
10.3. Graphs 3 – Planarity in Graphs.
10.4. Ordered Graphs
10.4.1. Graphs 4.1– Directed Graphs
10.4.2. Graphs 4.2 – Ordered Graphs: Summary (Directed Graphs, Hasse Diagrams, Rooted Trees)
10.5. Graphs 5 – Graph Representation
10.6. Graphs 6 – Graph Reduction and Applications
10.7. Graphs 7 – Cyclic and Acyclic Graphs
10.8. Graphs 8 – Graph Coloring (Graph Vertex Coloring)
10.9. Trees 1 – Introduction to Trees.
10.10. Trees 2 – Spanning Trees and Applications
10.11. Trees 3 – Spanning Trees in Cisco Switching (CCNA)
10.12. Trees 4 – Applications of Tree Structures (Decision Trees); see $ORDER applications in associative arrays in InterSystems Caché ObjectScript, FIS Global GT.M and ISO M
10.13. Networks 1 – Introduction.
10.14. Networks 2 – Transport Networks
10.15. Networks 3 – Matching Networks
10.16. Isomorphism of Graphs and Trees
10.17. Graph Databases (Videos and Links, including regarding Neo technology's Neo4j)
11. State
Transitions, Automata and Pattern Matching
11.1.
Comparison and State
Tables: Finite-State Machines,
11.2.
Building and Testing
11.3. Building and Testing Finite-State Automata.
11.4. Building and Testing Mealy Finite-State Machines with Output
11.5. Lindenmayer Systems 2: Grammars, Recursion, Applications of L-Systems
11.6. Pattern Matching (UNIX, ISO SQL, Microsoft Access, Caché ObjectScript and ISO M) and Regular Expressions
12. Documentation
of Computer Languages
12.1. Languages and Grammars
13. Specification,
Verification, and Validation
13.1. Specification, Verification, and Validation
14. Summary
14.1.
Specialized Terminology and
Concepts for this Course:
Strict Partial Order,
Strongly Connected Digraphs
Source and Target Sets in Relations
14.2. Practical Applications of Formal Structures – Examples
Topics pages
developed/maintained by
Valerie J. H. Powell, RT(R ), PhD, RMU C&IS Department, Peter Y. Wu, PhD,
RMU C&IS Department, and
E. Gregory Holdan, PhD, RMU Mathematics Education
Program, Mathematics Department
Current
Information, Announcements, and Reminders
þ Please inform yourself regarding information technology issues.
& Required textbook:
1. Valerie J. H. Powell, Sushil Acharya, E. Gregory Holdan, Mark M. Maxwell, Sushma Mishra, David F. Wood, Peter Y. Wu, eds., Discrete Mathematics Applications for Information Systems Professionals 4th ed. (distributed in class)
& Recommended book resources:
1. Stan Gibilisco, Math Proofs Demystified: A Self-Teaching Guide (McGraw-Hill, 2005).
2. Myke Predko, Digital Electronics Demystified: A Self-Teaching Guide (McGraw-Hill, 2005).
3.
Neville Dean, The Essence of Discrete
Mathematics (Prentice Hall – Pearson Education, 1997).
Updated: 2015-04-16
RMU C&IS
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