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The software was designed for students outside the classroom to augment their mathematics education and school districts seeking to enhance their mathematics curriculum. [4] [13] In 2012, the firm offered free trial licensing of lessons aligned with the Common Core State Standards Initiative to all schools within the United States.
A complex K3 surface has real dimension 4, and it plays an important role in the study of smooth 4-manifolds. K3 surfaces have been applied to Kac–Moody algebras, mirror symmetry and string theory. It can be useful to think of complex algebraic K3 surfaces as part of the broader family of complex analytic K3 surfaces.
BrainPop (stylized as BrainPOP) is a group of educational websites founded in 1999 by Avraham Kadar, M.D. and Chanan Kadmon, based in New York City. [1] As of 2024, the websites host over 1,000 short animated movies for students in grades K–8 (ages 5 to 14), together with quizzes and related materials, covering the subjects of science, social studies, English, math, engineering and ...
To give some simple examples: the product P 1 × X has Kodaira dimension for any curve X; the product of two curves of genus 1 (an abelian surface) has Kodaira dimension 0; the product of a curve of genus 1 with a curve of genus at least 2 (an elliptic surface) has Kodaira dimension 1; and the product of two curves of genus at least 2 has ...
In particular, Waldhausen showed that there is a map from A(M) to a space Wh(M) which generalizes the map K 1 (Zπ 1 (M)) → Wh(π 1 (M)) and whose homotopy fiber is a homology theory. In order to fully develop A -theory, Waldhausen made significant technical advances in the foundations of K -theory.
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The Principles and Standards for School Mathematics was developed by the NCTM. The NCTM's stated intent was to improve mathematics education. The contents were based on surveys of existing curriculum materials, curricula and policies from many countries, educational research publications, and government agencies such as the U.S. National Science Foundation. [3]
The Fano plane is a Steiner triple system S(2,3,7). The blocks are the 7 lines, each containing 3 points. Every pair of points belongs to a unique line. In combinatorial mathematics, a Steiner system (named after Jakob Steiner) is a type of block design, specifically a t-design with λ = 1 and t = 2 or (recently) t ≥ 2.