Math Challenge Ii B Number Theory
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Math Challenge II-B Number Theory
The math challenge curriculum textbook series is designed to help students learn the fundamental mathematical concepts and practice their in-depth problem solving skills with selected exercise problems. Ideally, these textbooks are used together with Areteem Institute's corresponding courses, either taken as live classes or as self-paced classes. According to the experience levels of the students in mathematics, the following courses are offered: Fun Math Problem Solving for Elementary School (grades 3-5) Algebra Readiness (grade 5; preparing for middle school) Math Challenge I-A Series (grades 6-8; intro to problem solving) Math Challenge I-B Series (grades 6-8; intro to math contests e.g. AMC 8, ZIML Div M) Math Challenge I-C Series (grades 6-8; topics bridging middle and high schools) Math Challenge II-A Series (grades 9+ or younger students preparing for AMC 10) Math Challenge II-B Series (grades 9+ or younger students preparing for AMC 12) Math Challenge III Series (preparing for AIME, ZIML Varsity, or equivalent contests) Math Challenge IV Series (Math Olympiad level problem solving) These courses are designed and developed by educational experts and industry professionals to bring real world applications into the STEM education. These programs are ideal for students who wish to win in Math Competitions (AMC, AIME, USAMO, IMO, ARML, MathCounts, Math League, Math Olympiad, ZIML, etc.), Science Fairs (County Science Fairs, State Science Fairs, national programs like Intel Science and Engineering Fair, etc.) and Science Olympiad, or purely want to enrich their academic lives by taking more challenges and developing outstanding analytical, logical thinking and creative problem solving skills. In Math Challenge II-B, students learn and practice in areas such as algebra and geometry at the high school level, as well as advanced number theory and combinatorics. Topics include polynomials, inequalities, special algebraic techniques, trigonometry, triangles and polygons, collinearity and concurrency, vectors and coordinates, numbers and divisibility, modular arithmetic, residue classes, advanced counting strategies, binomial coefficients, and various other topics and problem solving techniques involved in math contests such as the American Mathematics Competition (AMC) 10 and 12, ARML, beginning AIME, and Zoom International Math League (ZIML) Junior Varsity and Varsity Divisions. The course is divided into four terms: Summer, covering Algebra Fall, covering Geometry Winter, covering Combinatorics Spring, covering Number Theory The book contains course materials for Math Challenge II-B: Number Theory. We recommend that students take all four terms. Each of the individual terms is self-contained and does not depend on other terms, so they do not need to be taken in order, and students can take single terms if they want to focus on specific topics. Students can sign up for the online live or self-paced course at https: //classes.areteem.org
Frontiers in Number Theory, Physics, and Geometry II
Author: Pierre E. Cartier
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-07-18
Ten years after a 1989 meeting of number theorists and physicists at the Centre de Physique des Houches, a second event focused on the broader interface of number theory, geometry, and physics. This book is the first of two volumes resulting from that meeting. Broken into three parts, it covers Conformal Field Theories, Discrete Groups, and Renormalization, offering extended versions of the lecture courses and shorter texts on special topics.
Noncommutative Geometry and Number Theory
Author: Caterina Consani
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-12-18
In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new connections between the fields of number theory, algebraic geometry and noncommutative geometry. The articles collected in this volume present new noncommutative geometry perspectives on classical topics of number theory and arithmetic such as modular forms, class field theory, the theory of reductive p-adic groups, Shimura varieties, the local L-factors of arithmetic varieties. They also show how arithmetic appears naturally in noncommutative geometry and in physics, in the residues of Feynman graphs, in the properties of noncommutative tori, and in the quantum Hall effect.