This course will cover the following topics in eight learning sessions, with one Unit per week. Congruence, units modulo n, lattices and abelian groups, qua¬dratic residues, arithmetic functions, diophantine equations, Farey fractions, continued fractions, partition function, the Sieve method, density of subsets of integers, zeta function, the prime number theorem. Apply the tools and methods of discrete mathematics to real-world problems in computer science, especially in the analysis of recursive algorithms and number theory. MATH Mathematics, M-505-Basic Number Theory I P: M403-M404.Apply logical thinking to write simple proofs of arithmetical statements.Use methods from logics, combinatorics, and graph theory to perform calculations and solve problems involving discrete structures.Identify and define the basic structures of discrete mathematics including sets, combinatorics, logic, graphs, number theory, and functions.Learning Objectives and Outcomes:īy the end of this course students will be able to:
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There are no special requirements that exceed general internet access. There may be additional required/recommended readings, supplemental materials, or other resources and websites necessary for lessons these will be provided for you in the course’s General Information and Forums area, and throughout the term via the weekly course Unit areas and the Learning Guides.
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Numbers and their representation, divisibility and factorization, primes and their distribution, number theoretic functions, congruences, primitive roots, diophantine equations, quadratic residues, sums of squares, number theory and analysis, algebraic numbers, irrational and transcendental numbers. The main required textbooks for this course are listed below and can be readily accessed using the provided links. MATH M405 Number Theory (3 cr.) P: MATH M216. Topics will include sets, logic, induction, elementary counting techniques, functions, graph theory, and number theory. The emphasis will be on the development of technical discrete mathematics skills, rather than rigorous proof. This course is primarily intended for students majoring in Computer Science.
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Faculty Of Health Sciences And Dentistry.Faculty of Tourism and Hotel Management.