| | |INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA | |COURSE OUTLINE | | | | |Kulliyyah / Institute |Information and Communication Technology (KICT) | |Department / Centre |Computer Science (CS) | |Programme |Bachelor of Computer Science (BCS) | |Name of Course / Mode |Discrete Mathematics | |Course Code |CSC 1700 | |Name (s) of Academic staff / |Assoc. Prof. Dr. Azeddine Messikh | |Instructor(s) | | |Rationale for the inclusion of the course|To introduce students Discrete Mathematics and its basic principles. | |/ module in the programme | | |Semester and Year Offered |Semester 1 and 2 | |Status |Kulliyyah Required | |Level |3 | |Proposed Start Date |Semester 1, 2008 | |Batch of Student to be Affected |08xx onwards | |Total Student Learning Time (SLT) |Face to Face | | |Others | | |Total Guided and Independent Learning | | | | | |Lecture | | |Practical | | |Consultation | | | | | | | | |...

...COMBANITARICS
* A branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size (enumerative combinatorics), deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria (as in combinatorial designs andmatroid theory), finding "largest", "smallest", or "optimal" objects (extremal combinatorics and combinatorial optimization), and studying combinatorial structures arising in analgebraic context, or applying algebraic techniques to combinatorial problems (algebraic combinatorics).
* The branch of mathematics studying the enumeration, combination, and permutation of sets of elements and the mathematical relations that characterize their properties.
PROBABILITY OR LIKELIHOOD
* A measure or estimation of how likely it is that something will happen or that a statement is true. Probabilities are given a value between 0 (0% chance or will not happen) and 1 (100% chance or will happen). The higher the degree of probability, the more likely the event is to happen, or, in a longer series of samples, the greater the number of times such event is expected to happen.
GRAPH THEORY
* The study of graphs, which are mathematical structures used to model pair wise relations between objects from a certain collection. A "graph" in this context is a collection of "vertices"...

...introducing this type of teaching strategies, E-Module for Discrete Structures with biometrics is made to enhance the quality of education and instruction inside the classroom.
OVERVIEW OF THE CURRENT STATE OF TECHNOLOGY
In the current system of communication between people and computer, screen and keyboard are the primary channels of information exchange. Advances in technology and the art of computer programming have given rise to a new generation of methods for providing computer access to teachers and students.
Computer laboratory is one of the facilities most needed in universities. Usually, it is being utilized by classes that need the use of computer sucks as ICT and computer programming other classes utilized the used of the traditional “chalk and board”. But due to the fast moving modernization also affects the lifestyle of students, they tend to seek for easier way of studying.
With the use of ““E-Module for Discrete Structures with biometrics”” computer laboratories can be useful not only for computer classes but also to classes that will provide this system.
The term “E-Module for Discrete Structures with biometrics” refers to a software system which, when used in conjunction with a computer, provides system access to teachers and students.
STATEMENT OF THE PROBLEM
General Problem
The study focuses on creating an E-module for Discrete Structure...

...Theory of Knowledge
Éanna OBoyle
ToK Mathematics
“... what the ordinary person in the street regards as mathematics is usually nothing more than the operations of counting with perhaps a little geometry thrown in for good measure. This is why banking or accountancy or architecture is regarded as a suitable profession for someone who is ‘good at figures’. Indeed, this popular view of what mathematics is, and what is required to be good at it, is extremely prevalent; yet it would be laughed at by most professional mathematicians, some of whom rather like to boast of their ineptitude when it comes to totalling a column of numbers....Yet ... it is not the mathematics of the accountant that is of most interest. Rather, it is ... abstract structures and everyday intuition and experience” (p.173, Barrow).
2.1 Mathematical Propositions
2.1.1 Mathematics consist of A Priori Propositions (theorems)
We know mathematical propositions (or theorems) to be true independently of any particular experiences. No one ever checks empirically that, for example, 364.112 + 112.364 = 476.476 by counting objects of those numbers separately, adding them together, and then counting the result. The techical term to describe this independence of experiences is to say that the propositions are a priori. Therefore we say that mathematical propositions are a priori propositions.
2.1.2 Universality
When mathematical propositions...

...Zoltan Dienes’ six-stage theory of learning mathematics
Stage 1.
Most people, when confronted with a situation which they are not sure how to handle, will engage in what is usually described as “trial and error” activity. What they are doing is to freely interact with the situation presented to them. In trying to solve a puzzle, most people will randomly try this and that and the other until some form of regularity in the situation begins to emerge, after which a more systematic problem solving behaviour becomes possible. This stage is the FREE PLAY, which is or should be, the beginning of all learning. This is how the would-be learner becomes familiar with the situation with which he or she is confronted.
Stage 2.
After some free experimenting, it usually happens that regularities appear in the situation, which can be formulated as “rules of a game”. Once it is realized that interesting activities can be brought into play by means of rules, it is a small step towards inventing the rules in order to create a “game”. Every game has some rules, which need to be observed in order to pass from a starting state of things to the end of the game, which is determined by certain conditions being satisfied. It is an extremely useful educational “trick” to invent games with rules which match the rules that are inherent in some piece of mathematics which the educator wishes the learners to learn. This can be or should be the essential aspect of this...

...Chapter 2: THE NATURE OF MATHEMATICSMathematics relies on both logic and creativity, and it is pursued both for a variety of practical purposes and for its intrinsic interest. For some people, and not only professional mathematicians, the essence of mathematics lies in its beauty and its intellectual challenge. For others, including many scientists and engineers, the chief value of mathematics is how it applies to their own work. Because mathematics plays such a central role in modern culture, some basic understanding of the nature of mathematics is requisite for scientific literacy. To achieve this, students need to perceive mathematics as part of the scientific endeavor, comprehend the nature of mathematical thinking, and become familiar with key mathematical ideas and skills.
This chapter focuses on mathematics as part of the scientific endeavor and then on mathematics as a process, or way of thinking. Recommendations related to mathematical ideas are presented in Chapter 9, The Mathematical World, and those on mathematical skills are included in Chapter 12, Habits of Mind.
PATTERNS AND RELATIONSHIPS
Mathematics is the science of patterns and relationships. As a theoretical discipline, mathematics explores the possible relationships among abstractions without concern for whether those abstractions have...

...Biographical Sketch: Thales and Hypatia
Thales
While it is clear that Euclid definitely set a precedent for geometry and mathematics as a whole, he was not alone in his work, his endeavors, or his ideas. He certainly was not the first to come up with these theories or rules for geometry either. Before there was Euclid, there was Thales of Miletus. Thales, along with other mathematicians or “geometers” laid some of the foundation for Euclid to compile in order to write the Elements centuries later. Thales was a “renaissance man” well ahead of his time, dabbling in such subjects as astronomy, engineering, philosophy and of course, mathematics. Exploring his beginnings, and his accomplishments will afford a decent look at his impact on geometry and Euclid.
Thales was born in Miletus in Ionia ca 624 B.C. (O'Grady, n.d.). Often considered the first, or founder of, Ionian natural philosophy it is hard to be certain on many subjects of his beginnings. Thales’ past is checkered with uncertainties, not uncommon for people from this time period. Due to this, Thales’ exact birth year as well as ancestry are not certain as different sources offer conflicting answers. There is a lot of evidence that has survived to attest to the fact that he “was interested in almost everything, investigating almost all areas of knowledge, philosophy, history, science, mathematics, engineering, geography, and politics” (O'Grady, n.d.). Countless records...

...History of mathematics
A proof from Euclid's Elements, widely considered the most influential textbook of all time.[1]
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past.
Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. The most ancient mathematical texts available arePlimpton 322 (Babylonian mathematics c. 1900 BC),[2] the Rhind Mathematical Papyrus (Egyptian mathematics c. 2000-1800 BC)[3] and the Moscow Mathematical Papyrus (Egyptian mathematics c. 1890 BC). All of these texts concern the so-calledPythagorean theorem, which seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry.
The study of mathematics as a subject in its own right begins in the 6th century BC with the Pythagoreans, who coined the term "mathematics" from the ancient Greekμάθημα (mathema), meaning "subject of instruction".[4]Greek mathematics greatly refined the methods (especially through the introduction of deductive reasoning andmathematical rigor in proofs) and expanded the subject matter of mathematics.[5] Chinese...

...A mathematician is a person whose primary area study is the field of mathematics. Mathematicians are concerned with logic, space, transformations, numbers and more general ideas which encompass these concepts. Some notable mathematicians include Archimedes of Syracuse, Leonhard Paul Euler, Johann Carl Friedrich Gauss, Johann Bernoulli, Jacob Bernoulli, Muhammad ibn Mūsā al-Khwārizmī, Georg Friedrich Bernhard Riemann, Gottfried Leibniz, Euclid of Alexandria, Jules Henri Poincaré, Srinivasa Ramanujan, Alexander Grothendieck, David Hilbert, Joseph-Louis Lagrange, Georg Cantor, Évariste Galois, and Pierre de Fermat.
Some scientists who research other fields are also considered mathematicians if their research provides insights into mathematics—one notable example is Isaac Newton. Conversely, some mathematicians may provide insights into other fields of research—these people are known as applied mathematicians.
Education
Mathematicians usually cover a breadth of topics within mathematics in their undergraduate education, and then proceed to specialize in topics of their own choice at the graduate level. In some universities, a qualifying exam serves to test both the breadth and depth of a student's understanding of mathematics; the students who pass are permitted to work on a doctoral dissertation. There are notable cases where mathematicians have failed to reflect their ability in their university education, but...