re applied to derive the following results for the observed association between prime number distribution and quantum-like chaos. (i) Number theoretical concepts are intrinsically related to the quantitative description of dynamical systems. (ii) Continuous periodogram analyses of different sets of adjacent prime number spacing intervals show that the power spectra follow the model predicted universal inverse power-law form of the statistical normal distribution. The prime number distribution therefore exhibits self-organized criticality, which is a signature of quantum-like chaos. (iii) The continuum real number field contains unique structures, namely, prime numbers, which are analogous to the dominant eddies in the eddy continuum in turbulent fluid flows. Keywords: quantum-like chaos in prime numbers, fractal structure of primes, quantification of prime number distribution, prime numbers and fluid flows 1. Introduction he continuum real number field (infinite numbe

Mathematics is our “invisible culture ” (Hammond 1978). Few people have any idea how much mathematics lies behind the artifacts and accoutrements of modern life. Nothing we use on a daily basis—houses, automobiles, bicycles, furniture, not to mention cell phones, computers, and Palm Pilots—would be possible without mathematics. Neither would our economy nor our democracy: national defense, Social Security, disaster relief, as well as political campaigns and voting, all depend on mathematical models and quantitative habits of mind. Mathematics is certainly not invisible in education, however. Ten years of mathematics is required in every school and is part of every state graduation test. In the late 1980s, mathematics teachers led the national campaign for high, publicly visible standards in K-12 education. Nonetheless, mathematics is the subject that parents most often recall with anxiety and frustration from their own school experiences. Indeed, mathematics is the subject most often responsible for students ’ failure to attain their educational goals. Recently, mathematics curricula have become the subject of ferocious debates in school districts across the country. My intention in writing this essay is to make visible to curious and uncommitted outsiders some of the forces that are currently shaping (and distorting) mathematics education. My focus is on the

researchers with a novel, and perhaps startling perspective on mathematical thinking. However, as evidenced by reviewers ’ criticisms (Gold, 2001; Goldin, 2001; Madden, 2001), their perspective – though liberating for many, with its humanistic emphases – remains controversial. Nonetheless, we believe this perspective deserves further constructive response. In this paper, we propose that several of the book’s flaws can be addressed through a more rigorous establishment of conceptual distinctions as well as a more appropriate set of methodological approaches. In the past decade, several mathematics education researchers have emphasised the embodied nature of mathematical understanding, working toward displacing the more prevalent, conventional views found in both psychology and philosophy and studying implications for mathematics learning. These researchers have argued that sensory-motor action plays a crucial role in mathematical activity. A major struggle has been to explain how abstract, formal mathematical ideas can emerge from concrete sensory-motor experiences. This struggle has more recently found promising

Introduction DNA topology is of fundamental importance for a wide range of biological processes [1]. Since the topological state of genomic DNA is of importance for its replication, recombination and transcription, there is an immediate interest to obtain information about the supercoiled state from sequence periodicities [2,3]. Identification of dominant periodicities in DNA sequence will help understand the important role of coherent structures in genome sequence organization [4,5]. Li [6] has discussed meaningful applications of spectral analyses in DNA sequence studies. Recent studies indicate that the DNA sequence of letters A, C, G and T exhibit the inverse power law form 1/f frequency spectrum where f is the frequency and a the exponent. It is possible, therefore, that the sequences have longrange order [7-14]. Inverse power-law form for power spectra of fractal space-time fluctuations is generic to dynamical systems in nature and is identified as self-organized criticality

this paper shows (Section 2) that Fibonacci series underlies fractal fluctuations on all space-time scales

Abstract. The goal of this essay is a description of modern mathematical practice, with emphasis on differences between this and practices in the nineteenth century. I explain how and why these differences greatly increased the effectiveness of mathematical methods and enabled sweeping developments in the twentieth century. A particular concern is the significance for mathematics education: elementary education remains modeled on the mathematics of the nineteenth century and before, and use of modern methodologies might give advantages similar to those seen in mathematics. This draft is about 90 % complete, and comments are welcome. 1.

functions to model and solve problems. With this learning goal in mind, Minnesota students will have the opportunity to pursue the following instructional components: • Recognize, describe, and generalize patterns and build mathematical models to make predictions. • Analyze the interaction between quantities and/or variables to model patterns of change. • Use algebraic concepts and processes to represent and solve problems that involve variable quantities. As biology is the science of life and physics the science of energy and matter, so mathematics is