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In mathematics, Hodge theory, named after W. V. D. Hodge, is a method for studying the cohomology groups of a smooth manifold M using partial differential equations.The key observation is that, given a Riemannian metric on M, every cohomology class has a canonical representative, a differential form that vanishes under the Laplacian operator of the metric.
Hybrid homeschooling or flex-school [27] is a form of homeschooling in which children split their time between homeschool and a more traditional schooling environment like a school. [61] The number of students who participated in hybrid homeschooling increased during the COVID-19 pandemic .
The curriculum may be of any type of media provided it is in visual form (e.g., textbooks, workbooks, and computer-based including via the Internet), can be obtained from any source desired, and does not have to be provided or approved by the state or the local school district prior to use.
Gordon says that audiation occurs when an individual is "listening to, recalling, performing, interpreting, creating, improvising, reading, or writing music". [10] While listening to music, audiation is analogous to the simultaneous translation of languages, giving meaning to sound and music based on individual knowledge and experience.
Four ordered points on a projective range are called harmonic points when there is a tetrastigm in the plane such that the first and third are codots and the other two points are on the connectors of the third codot. [6] If p is a point not on a straight with harmonic points, the joins of p with the points are harmonic straights.
Gary DeMar is an American writer and lecturer. A former student of Greg Bahnsen, and protégé of Gary North, he has written several books on Christian reconstructionism, apologetics, and eschatology, as well as books targeting the homeschool movement.
According to The Christian Post, Vision Forum, Inc., Phillips' for-profit business, "appeared to have a liquidation sale" in December 2013. [ 15 ] On April 15, 2014, the Phillips family's ex-nanny filed a lawsuit against Phillips and Vision Forum, alleging that she had suffered years of sexual abuse at the hands of Doug Phillips.
Abeka Book, LLC, known as A Beka Book until 2017, is an American publisher affiliated with Pensacola Christian College (PCC) that produces K-12 curriculum materials that are used by Christian schools and homeschooling families around the world. [3] [4] [5] It is named after Rebekah Horton, wife of college president Arlin Horton.