2 Please refer to the learning outcomes for each of the topic covered At the end of this course, students should be able to use all basic concepts of mathematical structures to solve problems in information system.Please refer to the learning outcomes for each of the topic covered
3 Credit and assessment6 hours per week – please refer to the time tableAssessmentWhenWhatHow much?Week 3 (final session)Quiz 15%Week 4 (Friday)Test35%Week 6 (final session)Quiz 2Week 7 (final session)Quiz 3Week 8 (Exam Week)Final Exam50%
4 What is Discrete Structure What is Discrete Mathematics ?Discrete mathematics is mathematics that deals with discrete objects.Discrete objects are those which are not connected from each other.Integers (whole numbers), automobiles, houses, people etc. are all discrete objects.On the other hand real numbers which include irrational as well as rational numbers are not discrete. (A number which has a decimal portion, even if that decimal portion is zero. Real numbers are also called floating point numbers. The following are real numbers: 2.25, 41.00, -4.5, , and )Discrete mathematics is the study of mathematical relationships between distinct or individual parts.The concepts from discrete math are directly applicable to computing concepts.
5 Why discrete structure? Computers are based in binary. Their mechanical function depends on two things; the electrical current is there or it is not. Therefore, everything a computer can do, from turning on through complex calculations, stems from those electrical inputs. As that simple input is combined with others to form more complex pieces it still relies upon base two for its computations. Since it cannot have a fractional input of there or not, it is ideal for discrete mathematical concepts.
6 How do we apply it?Algorithmic –how to create a list of generic instructions that is non-specific enough to be used in many situations.Boolean Algebra – how to calculate expressions given. Also includes electronics concepts such as logic gates.Combinatorics – the overall concept of problem solving. It is related to common math concepts such as algebra and probability and is seen in computing through concepts such as iterations and recursion.Counting ranges from simple finger counting to enumerations and counting in different number systems.Graph Theory – the use of mathematical structures to create a model of information in order to discover relationships among information in a set.Information Theory – applying mathematics to communication. It relies heavily on probability and statistics and is applied in areas such as data analysis, networking and other electronic communications, quantum computing and neurobiology.Logic – once considered a branch of philosophy, it now is heavily used to understand reasoning through electronic logic gates. It is closely related to proofs.Mathematical Relations – related to set theory, relations are properties that assign a value for truth such as found when evaluating inequalities.Proofs – logical demonstration that a mathematical expression is true. Set Theory – the study of a collection of objects.Trees – a division of graph theory, trees are specifically applied in computer science through the study of data structures.Discrete Mathematics: The Study of Math Based on Making Decisions
8 Teaching Plan When Topics to be covered Week 1 – 2 Introduction Part 1 : Basic Knowledge / Digging the old knowledgeSet: terms used, its operations, Venn Diagram.Sequence and String: its characteristics, concatenation, subsequence.Matrix: Operations on matrix, Boolean matrix.Logic: compound statement, Truth Table, logically equivalent, QuantifierWeek 3 – 4Part 2: Intermediate / Using basic knowledge to explore new topics or enhance topics already known.Induction: types of induction, example for each type.Counting techniques: Permutation, Combination & Pigeon Hole.Relation: Definition, set, matrix and digraph representation, relation’s properties, equal relation, relation’s manipulation, closure, Poset, Hasse diagram, topological sorting.AssessmentWeek 3 : Quiz 1 – Covering week 1 & 2Week 4 : Test - Covering Set, Sequence and String, Matrix, Logic, Induction & Counting Technique
9 Teaching Plan When Topics to be covered Week 5 - 6 Part 3: Reuse / Using previous chapters and implement it to solve problems.Function: characteristics, cyclic function, permutation functionGraph: characteristics, path and cycle, Euler and HamiltonTree: Characteristics, labelled tree, minimal spanning tree, Prim and KruskalAssessmentWeek 6 – Quiz 2 – On Relation and FunctionWeek 7Language: grammar, language representationRevisionWeek 7 – Quiz 3 – On Graph and Tree
10 References Primary Secondary Kolman B., Busby R.C. and Ross S.: Discrete Mathematical Structures, 5th Edition, Prentice Hall, 2005.SecondaryKenneth H. Rosen: Discrete Mathematics and Its Application, 5th Edition, McGraw-Hill, 2005.Johnsonbaugh R.: Discrete Mathematics, 5th Edition, Prentice Hall, 2001.H. F. Mattson, Jr.: Discrete Mathematics with applications, John Wiley, 2004
11 Tips Do all tutorial / homework given Redo all problems discussed Rewrite your class note with important point and added pointDiscuss with friends in small groupReady for all test / quiz