#PERMUTATION COMBINATIONS P UPLET SOFTWARE#
The labs were designed to help students explore modern, sophisticated techniques in several areas of computer science: computer-system analysis and design, programming in C/C++ and Java, software quality assurance, data communication in networking systems, computer security, system simulation and modeling, numerical analysis, image processing, multimedia applications, Web development, and database design and management.
The author shares his experiences teaching various online computer-science courses (via the Canvas™ and synchronous web conferencing tools) using state-of-the-art free-license software tools for conducting online virtual labs and numerous students' projects. The “extra mile” opportunities and examples of students’ outstanding capstone projects are considered in details. Extracurricular activities (Math Clubs, Summer Bootcamps, Field Trips, National Math and Robotics Contests, etc.) helped students reveal curiosity and the power of innovations.
The results of this project became a rich foundation for revision of STEM curricula. The enrichment of these concepts with data, knowledge, and methods from other disciplines (mathematics, linguistics, psychology, physiology, etc.) is also analyzed.
#PERMUTATION COMBINATIONS P UPLET CODE#
Steganography with digital images), strategies of testing computer programs, implementation of encryption algorithms, computer-generated image visualization, studies of code complexity with predictions of potential programming errors, and search for large prime numbers. In this article, the focus is made on analyses of several modern advanced mathematical and computational methods and numerical algorithms (e.g., modular arithmetic, the graph theory, computer graphics, and The recent revision of STEM Higher Education requires the identification in the Rivier University curricula of math and computer science methods that can be effectively studied and benefit students in exploring various practical applications, including cybersecurity, data analytics, biotechnology, robotics, space exploration, geophysics, system simulation and modeling, etc. Source: Data Calculated with Applets Described in Riabov and Higgs 2011 Java applets Higgs 2010, 2011) created using the ideas from (Ferguson and Schneier 2002 Bishop 2002) were used effectively by students in explorations of the number theory (e.g., prime numbers and Euler's totient function) and modular arithmetic (e.g., co-primes, multiplicative inverses, and Galois fields). These and many other related topics (e.g., numerical systems, the Fundamental Theorem of Arithmetic, primes, etc.) are covered in the "traditional" Discrete Mathematics introductory-level course, and the more advanced topics (modular arithmetic, abstract groups, Abelian groups, rings, commutative rings, integer domains, and fields) (Graham, Knuth, and Patashnik 1994) are reviewed in the advanced elective courses, such as Computer Security (Riabov and Higgs 2011). Since the 1970s, many cryptographic methodologies (Rivest, Shamir, and Adleman 1978 Graham, Knuth, and Patashnik 1994) utilize major discoveries of the theory of numbers, including the modular arithmetic, co-primes, multiplicative inverses, and Galois field properties framed with the Fermat's Little Theorem and fundamental properties of Euler's totient function (Ferguson and Schneier 2002 Kaufman, Perlman, and Speciner 2002). of way’s of choosing r objects out ot these objects (i.e. If there are l objects of one kind, m objects of another kind and so on then the no.If there are l objects of one kind, m objects of another kind, n objects of another kind, then the number of ways of choosing r objects out of these objects i.e.
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