The Dance of Number: Dance Moves - Mastering Algebra and Mathematical Reasoning Volume 2

[Overview of the curriculum] Here is a curriculum that: •brings to light the multiplicities of the perichoretic nature of creation and mathematics, •coordinates beauty, truth, and goodness with rigor and heuristics, •teaches mastery of number sense and algebraic syntax, •integrates math themes with history, science, and personalities, •structures mathematics as an interconnected framework, and •explores the dynamic interrelatedness of Arithmetic, Algebra, Geometry, Trigonometry, and Science, plus much, much more. The Dance of Number, ideal for independent study, is a sequenced and tightly integrated curriculum involving four textbooks totaling 1924 pages (Grades 6-10, ages 12-16) consisting of 14 chapters, called the steps of the Dance. The only prerequisite for the first textbook is above average reading comprehension. This curriculum starts from ground zero, teaches the basics of arithmetic from a fresh, vibrant perspective, and then takes the reader on a journey that leads to the borderlands of the mountain range called Calculus. There are plenty of side roads along the way where we stop to gaze at the scenic beauty (i.e., a unified look at principles of Algebra, Geometry, Trigonometry). It is a long trip; its completion is worth the effort. The texts are not named Algebra I or Algebra II, etc., because the four-volume sequence tells an coordinated story engaging the student in the nature of the structure of number, the development of its history, and its interpenetration with science. As the student takes this journey, all the concepts of Arithmetic, high school Algebra, most of Geometry, and a complete study of Trigonometry are unfolded. This is volume 2 of Part 2 of The Dance of Number subtitled Dance Moves ... Mastering Algebra and Mathematical Reasoning (Steps 12 to 14). [General structure and specific features] This volume continues to teach the mastery of algebraic syntax as the following topics are explored: (1) Logarithms, (2) a complete course in Trigonometry, (3) Complex numbers and Fractal Geometry, (4) components of induction and deduction, along with geometric and algebraic demonstrations, (5) the indirect method of proof (reductio ad absurdum), (6) the startling revelations of number systems, (7) Internet security algorithms, (8) arithmetic and geometric sequences, finite and infinite, (9) Mathematical Induction, (10) an introduction to Differential Calculus reasoning along with the use of limits, (11) the world of polynomials, and (12) three-dimensional geometry, including the Platonic solids. More geometric constructions are demonstrated. Pertinent and challenging quotes from mathematicians, scientists, and theologians appear throughout the text. The key proofs from the thirteen books of Euclid’s Elements are described, applied, and seen in their historical context. To complete this thoroughly indexed text, an additional detailed solutions manual is available, a manual that includes the teacher’s guide. A suggested scheduled along with a quiz and exam packet is also available. [Grade level] This text is aimed at grades 10-11 (Algebra II, Trigonometry, Geometry, Mathematical reasoning). [Prerequisite] Successful completion of volume 1 of Part 2 of The Dance of Number (Steps 8-11). [Unique Feature] Here is a unique study of math that is grounded in Trinitarian theology: Discover the beauty of how math principles are interrelated; i.e., how they are interconnected and how they interpenetrate with the physical creation, revealing in a created way the uncreated perichoretic nature of the Triune Creator, Father, Son, and Holy Spirit, who mutually indwell each other in dynamic relationship of loving communion. [Where to go from here] Begin either a full course in Geometry or PreCalculus.