* 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" or "nodes" and a collection of edges that connect pairs of vertices. A graph may be undirected, meaning that there is no distinction between the two vertices associated with each edge, or its edges may be directed from one vertex to another; see graph (mathematics) for more detailed definitions and for other variations in the types of graph that are commonly considered. Graphs are one of the prime objects of study in discrete mathematics.

* A branch of mathematics concerned about how networks can be encoded and their properties...

...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...

...DISCRETE MATHEMATICS
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects can often be enumerated by integers. More formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets (sets that have the same cardinality as subsets of the integers, including rational numbers but not real numbers). However, there is no exact, universally agreed, definition of the term "discrete mathematics." Indeed, discrete mathematics is described less by what is included than by what is excluded: continuously varying quantities and related notions.
The set of objects studied in discrete mathematics can be finite or infinite. The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deals with finite sets, particularly those areas relevant to business.
Research in discrete mathematics increased in the latter half of...

...SIAM REVIEW Vol. 41, No. 1, pp. 135–147
c 1999 Society for Industrial and Applied Mathematics
The Discrete Cosine Transform∗
Gilbert Strang†
Abstract. Each discrete cosine transform (DCT) uses N real basis vectors whose components are π cosines. In the DCT-4, for example, the jth component of vk is cos(j + 1 )(k + 1 ) N . These 2 2 basis vectors are orthogonal and the transform is extremely useful in image processing. If the vector x gives the intensities along a row of pixels, its cosine series ck vk has the coeﬃcients ck = (x, vk )/N . They are quickly computed from a Fast Fourier Transform. But a direct proof of orthogonality, by calculating inner products, does not reveal how natural these cosine vectors are. We prove orthogonality in a diﬀerent way. Each DCT basis contains the eigenvectors of a symmetric “second diﬀerence” matrix. By varying the boundary conditions we get the established transforms DCT-1 through DCT-4. Other combinations lead to four additional cosine transforms. The type of boundary condition (Dirichlet or Neumann, centered at a meshpoint or a midpoint) determines the applications that are appropriate for each transform. The centering also determines the period: N − 1 or N in the established transforms, N − 1 or N + 1 in the other four. The key point is that all these “eigenvectors 2 2 of cosines” come from simple and familiar matrices. Key words. cosine transform, orthogonality, signal processing AMS subject...

...2015
Math Curse By: Jon Scieszka and Lane Smith
Math Curse, written by Jon Scieszka and Lane Smith, takes us on a journey with a small child who is cursed by math. His teacher’s name is Mrs. Fibonacci, who was a well know mathematician who connected a mathematical sequence found in nature. Of course Mrs. Fibonacci told her class and this child how easily math can be seen in the outside world. Our main character goes on amath rampage that drives him crazy. Scieszka and Smith do a great job a combining mathematical concepts as well as rhymes and brain games. The book is continuously rhyming accompanied by humorous art work that gives the story a kind of flow. Want a little bit of a challenge? Try answering a number of math questions asked throughout the book. The math used consisted mainly of patterns if not basic math of a 3rd grader. Fractions were mentioned but as any 3rd grader would be our main character was terrified of them. So much so that he may have considered answering the question in French instead of math.
Overall the book seemed good for the target audience. There was appealing art work on each page, as well as rhymes. The Rhyming scheme made a big difference because it made the story have a sense of flow. Our authors also made the story interesting for an older more sophisticated audience with the introduction of Ms. Fibonacci who...

...Article Review 1
DeGeorge, B., Santoro, A. (2004). “Manipulatives: A Hands-On Approach to Math.” Principal, 84 (2), (28-28).
This article speaks about the importance and significance of the use of manipulatives in the classroom, specifically in the subject of math. Manipulatives have proven to be valuable when used in a math class and are even more valuable to the children when they are young, and are learning new math concepts. Students are able to physically visualize the math concepts and gain knowledge because they understand what they’re learning a whole lot better and they also are able to gain insights on those concepts. Different examples of manipulatives may include counting with beans or M&M’s, using pattern blocks, puzzles, tangrams, and flash cards, just to name a few.
Using manipulatives in a math class are beneficial to both the student and the teacher because the teacher is able to explain the concepts to the students in a much easier manner using the hands-on technique, rather than explaining it verbally. It’s especially beneficial to the student because by incorporating these manipulatives into their learning process, they are able to pick up the concepts much quicker and in a way that they better understand, yet are having fun while doing it. When they have the concepts down, the students’ self-esteem goes up and they feel encouraged to keep on going.
After...

...The Discrete Cosine Transform
(DCT):
Theory and Application
1
Syed Ali Khayam
Department of Electrical & Computer Engineering
Michigan State University
March 10th 2003
1
This document is intended to be tutorial in nature. No prior knowledge of image processing concepts is
assumed. Interested readers should follow the references for advanced material on DCT.
ECE 802 – 602: Information Theory and Coding
Seminar 1 – The Discrete Cosine Transform: Theory and Application
1. Introduction
Transform coding constitutes an integral component of contemporary image/video processing
applications. Transform coding relies on the premise that pixels in an image exhibit a certain
level of correlation with their neighboring pixels. Similarly in a video transmission system,
adjacent pixels in consecutive frames2 show very high correlation. Consequently, these
correlations can be exploited to predict the value of a pixel from its respective neighbors. A
transformation is, therefore, defined to map this spatial (correlated) data into transformed
(uncorrelated) coefficients. Clearly, the transformation should utilize the fact that the information
content of an individual pixel is relatively small i.e., to a large extent visual contribution of a
pixel can be predicted using its neighbors.
A typical image/video transmission system is outlined in Figure 1. The objective of the source
encoder is to exploit the redundancies in image...

...Classification of simulation models
1. Monte carlo simulation – describe system w/c are both stochastic and static
2. Continuous simulation – the system modeled are dynamic but may be deterministic and stochastic
3. Discrete event simulation – used to model systems which are assumed to change only at discrete set point of time
4. Combined/Discrete/Continuous simulation – combination of discrete and continuous
Steps in building a model and simulation
1. Define an achievable goal
2. Put together a complete mix of skills on the team
3. Involve the end-user
4. Choose the appropriate simulation tools
5. Model the appropriate level of detail
6. Start early to collect the necessary input data
7. Provide adequate and on-going documentation
8. Develop a plan for adequate model verification
9. Develop a plan for model validation
10. Develop a plan for statistical output analysis
Model levels
1. Conceptual – very high level
* What are the state variable w/c are dynamic
* How concept should the model be
2. Specification – on paper
* May involve pseudocode or equation
* How will the model receive input
3. Computational – a computer program
Discrete event system – it is one way of building up models to observe the time based behavior of the system
Queuing characteristic
1....

...Discrete wavelet transform 2
Others
Other forms of discrete wavelet transform include the non- or undecimated wavelet transform (where downsampling
is omitted), the Newland transform (where an orthonormal basis of wavelets is formed from appropriately
constructed top-hat filters in frequency space). Wavelet packet transforms are also related to the discrete wavelet
transform. Complex wavelet transform is another form.
Properties
The Haar DWT illustrates the desirable properties of wavelets in general. First, it can be performed in
operations; second, it captures not only a notion of the frequency content of the input, by examining it at different
scales, but also temporal content, i.e. the times at which these frequencies occur. Combined, these two properties
make the Fast wavelet transform (FWT) an alternative to the conventional Fast Fourier Transform (FFT).
Time Issues
Due to the rate-change operators in the filter bank, the discrete WT is not time-invariant but actually very sensitive to
the alignment of the signal in time. To address the time-varying problem of wavelet transforms, Mallat and Zhong
proposed a new algorithm for wavelet representation of a signal, which is invariant to time shifts.[3] According to this
algorithm, which is called a TI-DWT, only the scale parameter is sampled along the dyadic sequence 2^j (j∈Z) and
the wavelet transform is calculated for each point in time.[4][5]...