Number Theory Modular Arithmetic Pdf Download

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This course will cover a variety of topics, including: arithmetic functions, arithmetic functions defined over the complex numbers and prime numbers, the Riemann zeta function, the arithmetic properties of the square root of two and the golden ratio, prime number theory, factorization, quadratic forms, arithmetic progressions, Gauss's first inequality, the CramÃ©r conjecture, the CramÃ©r-Rao inequality, applications of number theory to cryptography, and number theory in physics.

Number theory is a broad area of mathematics which concerns the study of natural numbers, positive integers, rational numbers, integers modulo a given number, and the rational numbers modulo a given prime number. It is also a branch of algebra which emphasizes the applications of number theory to other disciplines such as geometry, graph theory, and other mathematical areas. The course is intended for students who are enrolled in an undergraduate mathematics course and are interested in a more applied mathematics approach to number theory. It is for students who are ready to begin to take a course in advanced graduate mathematics in number theory, and a course in algebra. This course is equivalent to undergraduate courses at the advanced undergraduate level (or more).

Number theory is an introduction to the study of the number system, primarily the positive integers. It builds the system of numbers from basic axioms and definitions and explores the ramifications and interactions of these basic building blocks. The course is rigorous and proof based. Number theory is a broad area of mathematics which concerns the study of the natural numbers, positive integers, rational numbers, integers modulo a given number, and the rational numbers modulo a given prime number.

There is an emphasis on number theory, but the course is also acceptable to mathematics majors who are interested in number theory. We will cover basic number theory and some applications in mathematics and other areas of science. We will sometimes delve deeply into the subject in order to emphasize the basic ideas and concepts. This should be useful to advanced students and may have some applications in other areas of mathematics.

Almost all undergraduate mathematics classes start with some form of number theory. See, for example, Etingof's Classical Number Theory and Fermat's Last Theorem or Chapter 3 of Serre's Numbers: A very short introduction to arithmetic . Number theory is also the basis of cryptography, and the course is intended to introduce and consolidate students' mathematical maturity for these applications. High-level number theory and the tools of the algebraic number field are also useful for problems in number theory and algebraic geometry. 827ec27edc