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Course Outline
MATH
Discrete Mathematics
Study Program
Mathematics
Effective Date 01 September 2017 Revision 2
1. Course Description
This course provides basic concepts of logic and discrete mathematics. Topics included are the logic of compound and quantified statements, some methods of proof, counting including permutations and combinations, number theory. Besides that, this courses studying about set theory, number theory function, recursion, fuzzy set, relations, graphs and finite automata. This course supports the other courses related with mathematical problem solving, computer science, and programming logic. On the other side, by this course students wil develop the reasoning power to analyze discrete problems
2. Graduate Competency
Each course in the study program contributes to the graduate competencies that are divided into employability and entrepreneurial skills and study program specific outcomes, in which students need to have demonstrated by the time they complete their course.
BINUS University employability and entrepreneurial skills consist of planning and organizing, problem solving and decision making, self management, team work, communication, and initiative and enterprise.
2.1. Employability and Entrepreneurial Skills
Aspect Key Behaviour
2.2. Study Program Specific Outcomes
Study Program Specific Outcomes (SO-1) - Able to create software application design with the implementation of database system principal design to solve structured and semi-structured data
3. Topics - The logic of compound statements part 1 - The logic of compound statements part 2 - The logic of quantified statements - Methods of proof - Counting - Set Theory - Number Theory - Function, recursion, and fuzzy set - Relations - Graph Theory - Trees - Graph Applications - Finite Automata
Course Outline MATH6025 - Discrete Mathematics | 2
4. Learning Outcomes On successful completion of this course, student will be able to: - LO 1: Evaluate the logic of compound and quantified statements and how do to proof - LO 2: Explain Set Theory, Counting method and Number Theory - LO 3: Explain Function, recursion, fuzzy set, Relations and Graph Theory - LO 4: Explain Trees & Graph theory and its application - LO 5: Explain Automata and graph its application in computer science 5. Teaching And Learning Strategies In this course, the lecturers might deploy several teaching learning strategies, including Discussion, Lecture, Individual and Team Assignment, Demonstrate problem-solving through case studies, and Problem Solving. 6. Textbooks and Other Resources 6.1 Textbooks 1. Susanna S. Epp. (2011). Discrete mathematics with applications. 04. Brooks/Cole Publising. Boston. ISBN: 9780495391326.
The book in the first list is a must to have for each student.
6.2 Other Resources
- http://www.cs.nthu.edu.tw/~cchen/CS4351/ch3.ppt
- http://www.cs.kent.edu/~jbaker/Discrete-Sp11/../Inroduction.ppt
- http://www.cs.cmu.edu/afs/cs.cmu.edu/academic/class/15251- f08/Site/Materials/Lectures/Lecture20/lecture20-handout.pdf
- Discrete Mathematics
- http://www.maths.manchester.ac.uk/~mdc/old/1K1/notes07.pdf
- http://www.personal.kent.edu/~rmuhamma/GraphTheory/MyGraphTheory/trees.htm
- http://www.utm.edu/departments/math/graph/
- http://www.mathsisfun.com/combinatorics/combinations-permutations.html
- http://www.math.hmc.edu/funfacts/ffiles/20009.5.shtml
- http://www.efunda.com/math/settheory/settheory.cfm
- http://www.sparknotes.com/math/algebra2/functions/section1.html
- http://www.mathwarehouse.com/algebra/relation/math-function.php
- http://www.ee.surrey.ac.uk/Projects/Labview/boolalgebra/index.html
- http://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/sbaa/report.fuzzysets.html
- http://www.mathsisfun.com/algebra/binomial-theorem.html
- http://www.tutors4you.com/permutationcombinationtutorial.htm
- http://mathworld.wolfram.com/DirectedGraph.html
- http://www.purplemath.com/modules/binomial.htm
- http://www.sjsu.edu/faculty/watkins/fuzzysets.htm
- http://www.austinlinks.com/Fuzzy/overview.html
- http://www.facstaff.bucknell.edu/mastascu/eLessonsHTML/Logic/Logic3.html
- http://www.ijest.info/docs/IJEST10- 02 - 09 - 124.pdf
- http://www.csee.umbc.edu/~artola/fall02/Number theory.ppt
- http://www.richardclegg.org/networks2/Lecture11_06.pdf 7. Schedule
Theory
Session/ Mode
Related LO Topics References
1 F2F
LO 1 The logic of compound statements part 1
- Logical form and logical equivalence
- Conditional statements
- Valid and invalid arguments
- Fuzzy logic
- The logic of compound statements
- Discrete mathematics with applications, Chapter 1
- Boolean Algebra, http://www.ee.surrey.ac.uk/P rojects/Labview/boolalgebra/i ndex.html
- Fuzzy Logic: The Logic of Fuzzy Sets,
Course Outline MATH6025 - Discrete Mathematics | 4
- The Binomial Theorem http://www.mathsisfun.com/c ombinatorics/combinations- permutations.html
- Binomial Theorem, http://www.mathsisfun.com/a lgebra/binomial-theorem.html
- Permutation and Combination, http://www.tutors4you.com/p ermutationcombinationtutoria l.htm
- The Binomial Theorem: Formulas, http://www.purplemath.com/ modules/binomial.htm 9 F2F
LO 2 Counting
- Introduction
- Multiplication Rule and Addition Rule
- Permutation and Combinations
- The Binomial Theorem
- Counting
- Discrete mathematics with applications, Chapter 6
- Combination-Permutation, http://www.mathsisfun.com/c ombinatorics/combinations- permutations.html
- Binomial Theorem, http://www.mathsisfun.com/a lgebra/binomial-theorem.html
- Permutation and Combination, http://www.tutors4you.com/p ermutationcombinationtutoria l.htm
- The Binomial Theorem: Formulas, http://www.purplemath.com/ modules/binomial.htm 10 F2F
LO 2 Set Theory
- Properties of set
- Boolean algebra
- Set Theory
- Discrete mathematics with applications, chapter 5
- Set Theory, http://www.efunda.com/math/ settheory/settheory.cfm 11 F2F
LO 2 Number Theory
- Divisors
- Primer Factorization
- Congruence
- Quadratic Residues
- Number Theory
- Discrete mathematics with applications, Chapter 4
- Number Theory, http://www.cs.nthu.edu.tw/~c chen/CS4351/ch3.ppt
- Introduction to Number Theory, http://www.csee.umbc.edu/~ artola/fall02/Number theory.ppt 12 F2F
LO 2 Number Theory
- Divisors
- Primer Factorization
- Congruence
- Quadratic Residues
- Number Theory
- Discrete mathematics with applications, Chapter 4
- Number Theory, http://www.cs.nthu.edu.tw/~c chen/CS4351/ch3.ppt
- Introduction to Number Theory, http://www.csee.umbc.edu/~
Course Outline MATH6025 - Discrete Mathematics | 5
artola/fall02/Number theory.ppt 13 F2F
LO 3 Function, recursion, and fuzzy set
- Definition of function
- Inverse function
- Recursion
- Definition of fuzzy set
- Properties of fuzzy set
- Function, recursion, and fuzzy set
- Discrete mathematics with applications, Chapter 7- 8
- Function, http://www.mathwarehouse.c om/algebra/relation/math- function.php
- Fuzzy set and Operations, http://www.doc.ic.ac.uk/~nd/s urprise_96/journal/vol4/sbaa/ report.fuzzysets.html
- Fuzzy Logic Overview, http://www.austinlinks.com/F uzzy/overview.html 14 F2F
LO 3 Function, recursion, and fuzzy set
- Definition of function
- Inverse function
- Recursion
- Definition of fuzzy set
- Properties of fuzzy set
- Function, recursion, and fuzzy set
- Discrete mathematics with applications, Chapter 7- 8
- Function, http://www.mathwarehouse.c om/algebra/relation/math- function.php
- Fuzzy set and Operations, http://www.doc.ic.ac.uk/~nd/s urprise_96/journal/vol4/sbaa/ report.fuzzysets.html
- Fuzzy Logic Overview, http://www.austinlinks.com/F uzzy/overview.html 15 GSLC
LO 3 Relations
- Reflexivity, Symmetry and Transitivity
- Equivalence Relations
- Partial Order Relations
- Relations
- Discrete mathematics with applications, Chapter 10
- Relations and Function, http://www.sparknotes.com/ math/algebra2/functions/sect ion1.html 16 GSLC
LO 3 Relations
- Reflexivity, Symmetry and Transitivity
- Equivalence Relations
- Partial Order Relations
- Relations
- Discrete mathematics with applications, Chapter 10
- Relations and Function, http://www.sparknotes.com/ math/algebra2/functions/sect ion1.html 17 F2F
LO 4 Graph Theory
- Introduction
- Paths and Circuits
- Matrix Representations of Graphs
- Isomorphism of Graphs
- Graphs Coloring
- Graph Theory
- Discrete mathematics with applications, Chapter 11
- Graph Theory Tutorial, http://www.utm.edu/departm ents/math/graph/
- Discrete Mathematics
- Directed Graph, http://mathworld.wolfram.co m/DirectedGraph.html
- Basic Graph Theory, http://www.richardclegg.org/n etworks2/Lecture11_06.pdf
Course Outline MATH6025 - Discrete Mathematics | 7
Sp11/../Inroduction.ppt
- Application of Graph theory in Computer Science an overview, http://www.ijest.info/docs/IJE ST10- 02 - 09 - 124.pdf 24 F2F
LO 5 Graph Applications
- Shortest path problem
- Travelling saleman problem
- Assigment problem
- Application in Computer Science
- Graph Applications
- Discrete mathematics with applications, Chapter 12
- Application in computer science, http://www.cs.kent.edu/~jbak er/Discrete- Sp11/../Inroduction.ppt
- Application of Graph theory in Computer Science an overview, http://www.ijest.info/docs/IJE ST10- 02 - 09 - 124.pdf 25 F2F
LO 5 Finite Automata
- Introduction
- Deterministic Finite Automata
- Non deterministic Finite Automata
- Finite Automata
- Discrete mathematics with applications, Chapter 13
- Deterministic Finite Automata, http://www.cs.cmu.edu/afs/cs .cmu.edu/academic/class/ 251 - f08/Site/Materials/Lectures/L ecture20/lecture20- handout.pdf 26 F2F
LO 5 Finite Automata
- Introduction
- Deterministic Finite Automata
- Non deterministic Finite Automata
- Finite Automata
- Discrete mathematics with applications, Chapter 13
- Deterministic Finite Automata, http://www.cs.cmu.edu/afs/cs .cmu.edu/academic/class/ 251 - f08/Site/Materials/Lectures/L ecture20/lecture20- handout.pdf 8. Evaluation
Theory
Assessment Activity Weight
Learning Outcomes (^1 2 3 4 ) Assignment 25% √ √ √ √ √ Mid Exam 35% √ √ √ Final Exam 40% √ √ √
Practicum
- Final Evaluation Score
Aspects Weight
Theory 100% Practicum 0%
Course Outline MATH6025 - Discrete Mathematics | 8
9. A. Assessment Rubric (Study Program Specific Outcomes)
LO Indicators
Proficiency Level Excellent (85 – 100)
Good (75 – 84)
Average (65 – 74)
Poor (<= 64)
LO 1
1.1. Student's is able to explain the logic of compound statements
Student’s explanation is fully correct and the interpretatio n are clearly stated
Student’s explanation is mostly correct with minor error and the interpretatio n are wel stated
Student’s explanation is fairly correct with some errors and the interpretatio n are less appropriate
Student’s explanation is incorrect and the interpretatio n are in appropriate
1.2. Student's is able to explain the logic of quantified statements
Student’s explanation is fuly correct and the interpretatio n are clearly stated
Student’s explanation is mostly correct with minor error and the interpretatio n are wel stated
Student’s explanation is fairly correct with some errors and the interpretatio n are less appropriate
Student’s explanation is incorrect and the interpretatio n are inappropriat e
LO 2
2.1. Student's is able to explain the counting method and number theory and set theory
Student’s explanation is fuly correct and the interpretatio n are clearly stated
Student’s explanation is mostly correct with minor error and the interpretatio n are wel
Student’s explanation is fairly correct with some errors and the interpretatio n are less appropriate
Student’s explanation is incorrect and the interpretatio n are inappropriat e
2.2. Student's is able to explain application of counting method number theory and set theory
Application is fuly correct and the interpretatio n are clearly stated
Application is mostly correct with minor error and the interpretatio n
Application is fairly correct with some errors and the interpretatio n are less
Application is incorrect and the interpretatio n are inappropriat e
LO 3
3.1. Student's is able to explain the function, relation and fuzzy set.
Student’s explanation is ful y correct and the interpretatio n are clearly stated
Student’s explanation is mostly correct with minor error and the interpretatio n are wel stated
Student’s explanation is fairly correct with some errors and the interpretatio n are less appropriate
Student’s explanation is incorrect and the interpretatio n are inappropriat e
3.2. Student's is able to explain application of function, relation and fuzzy set.
Application is fuly correct and the interpretatio n are clearly stated
Application is mostly correct with minor error and the interpretatio n are wel stated
Application is fairly correct with some errors and the interpretatio n are less appropriate
Application is incorrect and the interpretatio n are inappropriat e
LO 4
4.1. Student's is able to explain the Graph theory and Trees
Student’s explanation is ful y correct and
Student’s explanation is mostly correct with
Student’s explanation is fairly correct with
Student’s explanation is incorrect and the
