Math.3336: Discrete Mathematics Primes and Greatest Common Divisors Instructor: Dr. Blerina Xhabli. Discrete Mathematics Primes and Greatest Common Divisors 12/26. STANDARD 14 — DISCRETE MATHEMATICS K-12 Overview All students will apply the concepts and methods of discrete mathematics. Yet it poses challenges to all students. It is fun to do, is often geometry based, and can stimulate an interest in mathematics on the part of students at all levels and of all abilities. K-12 Development and Emphases.

This two-volume set collects and presents many fundamentals of mathematics in an enjoyable and elaborating fashion. The idea behind the two books is to provide substantials for assessing more modern developments in mathematics and to present impressions which indicate that mathematics is a fascinating subject with many ties between the diverse mathematical disciplines. Slavkin sneg noti restaurant. The present volume examines many of the most important basic results in geometry and discrete mathematics, along with their proofs, and also their history.

Contents Geometry and geometric ideas Isometries in Euclidean vector spaces and their classification in ℝ n The conic sections in the Euclidean plane Special groups of planar isometries Graph theory and platonic solids Linear fractional transformation and planar hyperbolic geometry Combinatorics and combinatorial problems Finite probability theory and Bayesian analysis Boolean lattices, Boolean algebras and Stone’s theorem Details.

Most middle and high school math curricula follow a well-defined path: Pre-algebra → Algebra 1 → Geometry → Algebra 2 → Trig / Precalculus → Calculus Other middle and high schools prefer an “integrated” curriculum, wherein elements of algebra, geometry, and trigonometry are mixed together over a three- or four-year sequence. However, both of these approaches generally lack a great deal of emphasis on discrete math: topics such as combinatorics, probability, number theory, set theory, logic, algorithms, and graph theory. Because discrete math does not figure prominently in most states’ middle or high school “high-stakes” progress exams, and because it also does not figure prominently on college-admissions exams such as the SAT, it is often overlooked. However, discrete math has become increasingly important in recent years, for a number of reasons: Discrete math is essential to college-level mathematics and beyond. Discrete math—together with calculus and abstract algebra—is one of the core components of mathematics at the undergraduate level. Students who learn a significant quantity of discrete math before entering college will be at a significant advantage when taking undergraduate-level math courses.

Discrete math is the mathematics of computing. The mathematics of modern computer science is built almost entirely on discrete math, in particular combinatorics and graph theory. This means that in order to learn the fundamental algorithms used by computer programmers, students will need a solid background in these subjects. Indeed, at most universities, a undergraduate-level course in discrete mathematics is a required part of pursuing a computer science degree. Discrete math is very much “real world” mathematics.

Many students’ complaint about traditional high school math—algebra, geometry, trigonometry, and the like—is What is this good for? The somewhat abstract nature of these subjects often turns off students. By contrast, discrete math, in particular counting and probability, allows students—even at the middle-school level—to very quickly explore non-trivial “real world” problems that are challenging and interesting. Discrete math shows up on most middle and high school math contests. Prominent math competitions such as MATHCOUNTS (at the middle school level) and the American Mathematics Competitions (at the high school level) feature discrete math questions as a significant portion of their contests. On harder high school contests, such as the AIME, the quantity of discrete math is even larger. Students that do not have a discrete math background will be at a significant disadvantage in these contests.