The final category corresponds to work actioned or completed, technology issues, and discussions about publication. A total of 120 comments made reference to one or more of these issues, around a fifth of the total number. While some comments dealt with project coordination, most simply reported that work had been completed, often by stating “done” in response to a previous post prompting revisions. The majority of these comments are of limited interest; nonetheless, a small number refer to journal publication, and provide insight into the puremathematics RA. Surprisingly, the genre is not fixed at the start of the writing process:
for the purpose of testing pure mathematical syllabus content; they must be accessible and comprehensible to candidates; they must strive for realism, albeit sanitised from the complexity of real life; and they must strive for authenticity, where this is possible. The questions analysed in this paper clearly do not give our students the opportunity to engage in genuine mathematical modelling, and it might be unrealistic to expect them to do so. However, longer questions can provide candidates with a ‘flavour’ of how mathematics can be used to model reality. Given the strong backwash of formal assessment on the teaching and learning of students engaged in advanced courses, it would seem to be important to construct examination questions which remind candidates, albeit artificially, of the notion that mathematics, even puremathematics, serves a purpose beyond its own boundaries. Notes
APPLIED AREAS (INCLUDING COMBINATORICS AND NUMERICAL ANALYSIS). The May, 1999, extramural review confirmed the Department’s view that a significantly enhanced pres- ence in applied areas is necessary, both in terms of the graduate curriculum for Master’s students and the offering of a sufficiently broad array of choices for Ph. D. students. To quote the report, There are areas of applied mathematics that might fit well into the program ... We are attracted to the many possibilities in computational mathematics; for example, numerical methods and opti- mization, computational number theory, and computational geometry and topology, to name a few. Combinatorics is another broad area. Of course there are the classical areas of applied mathematics related to partial differential equations, wave mechanics and dynamical systems. The work of W. T. Gowers in combinatorics and combinatorial number theory was noted specifically when he was awarded a Fields Medal in 1998. Professor L. Harper has worked in combinatorics with particular interest in optimization; in recent years he has successfully directed two Ph. D. dissertations. Two specific area in combinatorics that have been mentioned are complexity theory, a relatively new applied topic that is fundamental to computer security, and algebraic combinatorics, which exploits deep relationships between enumeration theory and Lie and commutative algebra. It is expected that at least one of the new appointees will work in some branch of combinatorics. Due to retire- ments this decade there are no longer any faculty members whose primary interests lies in numerical analysis, and it is strongly felt that a presence in this particular specialty needs to be restored. The subject has natural ties to applications of mathematics, advances in computer technology have enabled researchers to handle problems that would have been forbiddingly difficult a few years ago, and students with a good background in numerical mathematics have a wide assortment of attractive career options. As noted before, a critical mass of at least two or three faculty mem- bers will be needed in the long run. It seems premature to be overly specific about other applied areas that might receive priority for hiring, but there is a general agreement that an initiative in at least one more applied area should be launched. Two possibilities that have generated interest are mathematical biology and financial mathematics; the long term plan would include hiring a second or third person in such an area (depending on where the Department actually hires). It is also possible that an applied appointee could work in differential equations, mathematical physics or probability, but a serious involvement with applications would be expected. The demand for graduates with a background in applied mathematics is greater than for puremathematics, and this is an important reason for substantially increasing the Department’s profiles in these areas.
Alireza Khalili Asboei, he has born in the Mazandaran, Babol in 1972. Got B.Sc degree in pure mathe- matics from Teacher Training Uni- versity, M. Sc degree in pure math- ematics, finite group theory field from Tarbiat Modares University, and PHD degree in puremathematics, finite group theory field from Science and Research Branch, Islamic Azad University. Main research interest include finite groups, finite simple groups, permutations groups, and characterization of fi- nite groups.
From this research article it is now crystal clear that the fixed points are very useful in Mathematics. Analysis of mappings and their fixed points enable us to successfully handle many situations in pure and applied Mathematics. Main braches of PureMathematics like Real Analysis, Complex Analysis, Number Theory and branches of Applied Mathematics like Linear Algebra, Numerical Analysis utilise fixed points and related theorems. So it is essential to explore more on fixed points. In the coming research paper we shall further explore the areas like economics, game theory etc.
The real revolution in mathematical physics in the second half of twentieth cen- tury (and in puremathematics itself) was algebraic topology and algebraic geometry . In the nineteenth century, Mathematical physics was essentially the classical theory of ordinary and partial differential equations. The variational calculus, as a basic tool for physicists in theoretical mechanics, was seen with great reservation by mathematicians until Hilbert set up its rigorous foundation by pushing forward functional analysis. This marked the transition into the first half of twentieth cen- tury, where under the influence of quantum mechanics and relativity, mathematical physics turned mainly into functional analysis, complemented by the theory of Lie groups and by tensor analysis. All branches of theoretical physics still can expect the strongest impacts from use of the unprecedented wealth of results of algebraic topology and algebraic geometry of the second half of twentieth century .
ABSTRACT: Automatic segmentation of the blood vessel lumen from ultrasound images is a vital task in clinical identification. Correct measurement and understanding of the puremathematics of the arterial blood vessel (CA) is crucial within the assessment and management. The Proposed work was the thresholding technique as a result of it will notice the arterial blood vessel while not blurring the image. This could stay the ultrasound image resolution. This can be vital particularly in medical image attributable to patient details are going to be lost if low ultrasound image quality occur. Before thresholding, the original B-Mode ultrasound RGB image had to be modified to gray scale and do some image process. After that, the image required to rework into binary image be-fore thresholding. When thresholding, the ultrasound image must be removing some elements that aren't arterial blood vessel and replenish some elements within the middle of the arterial blood vessel. After all these steps, the arterial blood vessel will successfully be detected. Within the planned work, we are going to compare our planned one with the existing technique used for segmentation. additionally, we will use some filters for de-speckling method (i.e., to get rid of the noises present within the image) and finally can notice that filter outperforms best in de-speckling method by measurement the image quality performance and additionally texture analysis.
The authors thank Mustansiriyah University / College of Science / Department of Mathematics and University of Baghdad / College of Education for Pure Science – Ibn Al-Haitham / Department of Mathematics for their supported this work.
also some remarks about the history of these numbers. The Eulerian numbers are taken into account in the article of Bressoud  in the NIST Handbook of Mathematical Functions . In the interesting book of Conway and Guy , the “Eulerian numbers” are also shortly mentioned with one formula but without explicitly giving tables. There exist also an article about the Eulerian numbers in Weisstein’s Encyclopedia of Mathematics .
N. Altshiller-Court, Mathematics in Fun and in Earnest. New American Library, New York, 1961. K. Appel and W. Haken, The solution of the four-color-map problem, Scientific American Vol. 237 No. 4 (October, 1977), 108–121; reprinted with revisions, Mathematics Today: Twelve Informal Essays (ed. by L. A. Steen), 141–180. Vintage Books, New York, 1980.
 T. Allahviraloo, Numerical methods for fuzzy system of linear equations, Applied Mathe- matics and Computation 155 (2004) 493-502.  T. Allahviraloo, Successive over relaxation iteration iterative method for fuzzy system of linear equations, Applied Mathematics and Computation 162 (2005a) 189-196.
KerongoJoash:- Is a lecturer Department of Mathematics, Kisii university. Currently serving as Dean, school of Pure and Applied sciences. He is a holder of B.Ed, MSc applied Mathematics and PhD in Applied Mathematics. OkeloJeconiah:- Is a lecturer Department of Pure and Applied MathematicsJomo Kenyatta University of Agriculture and Technology, Kenya.Currently serving as Director, school of continuing learning. He is a holder of B.Ed, MSc applied Mathematics and PhD in Applied Mathematics.
Computing science has been affecting mathematics in many ways such as computing as the name implies where mathematics is applied when hand computation seems very difficult. Secondly, there are vivid connections between computing science and mathematics in the areas of logic, algorithms, number theories and numerical analysis. Looking at some contemporary computing science area of specialization that is growing on a daily basis: we consider some of these courses and the importance of mathematics in their individual studies: Cryptography (take for instance the RSA algorithm which was developed by Ron Rivest, Adi Shamir, and Leonard Adleman. The algorithm was first publicly described in August 1977 and a patent was filed in December 1977; as the patent was filed after the discovery was made public, the algorithm received a patent in the US only in 1983. The RSA algorithm is the first example of an algorithm for public key cryptography. It also solves the problem of authentication with public key systems. Much like Diffie-Hellman, RSA draws on modular arithmetic. Its security mainly relies upon the difficulty of factorizing a large number which is a product of two large primes. The two primes are part of the private key, whereas the single large number, the product of these two smaller ones is part of the public key. Multiplying two prime numbers together is computationally like a one way process. It is easy to calculate: 757 x 977 = ? But given the product it's comparatively very difficult to factorize it to recover the two primes: 739 589 = ? x ? In practice the primes used by RSA are several hundred digits long, so methods to find such large primes are needed; fortunately such methods exist. Since the security relies on it being difficult to factorize large numbers we are fortunate (or unfortunate) there is no method to quickly factorize numbers). Database engine (the mathematical aspect of the development of the database engine is the understanding of matrices and linear algebra. The transpose, inverse, rows, columns and its manipulation in the design of an algorithm for databases engine).
In Political Science, past election results are analysed using Game Theory to see changes in voting patterns, influence of various factors on voting behaviour. Graph theory, text analysis, multidimensional scaling and cluster analysis, and a variety of special models are some mathematical techniques used in analysing data on a variety of social networks. The market value of Google, Amazon, Facebook and Twitter, all built on intellectual property based on mathematical algorithms, is not much short of half a trillion dollars at current market value. Mathematics is even necessary in psychology and archaeology. Archaeologists use a variety of mathematical and statistical techniques to present the data from archaeological surveys and try to distinguish patterns in their results that shed light on past human behaviour.