Designed for the person who needs to learn Algebra as a prerequisite for further study or for a refresher course before moving on, the book covers all of the basic Algebra concepts such as variables, equations, Quadratic Equations, factoring algebraic Expressions, Exponents, roots, Radicals, and more. It includes numerous step by step examples and practice exercises that help the reader to understand the topics in a "self-study" Format, designed for those who are uncomfortable with Mathematics. With its use of multiple variables, functions, and formulas algebra can be confusing and overwhelming to learn and easy to forget. Perfect for students who need to review or reference critical concepts, Algebra Essentials provides content focused on key topics only, with discrete explanations of critical concepts taught in a typical Algebra course, from functions and FOILs to quadratic and linear equations. This book is also a perfect reference for parents who need to review critical algebra concepts. The book teaches the concepts and techniques of basic algebra with a focus on explaining definitions and theorems, and creating proofs. The theory is supported by numerous examples and plenty of worked-out problems. Its strict logical organization has been designed to help the reader to develop confidence in the subject. By introducing various interesting applications of algebra the book also aims at creating a broad and solid foundation for the study of advanced mathematics. The contents covered in the book are equivalence relations, functions, cardinality, congruence-modulo, mathematical induction and De Moivre's theorem. Further, some basic topics of linear algebra like vectors and matrices, linear equations, Gauss elimination, subspace and its dimension, rank-nullity theorem, linear transformations and their relations to matrices, and eigenvalues and eigenvectors are also covered. Since practice makes the man perfect, there are a good number of problems that stretch the thinking power of the learner. The problems are graded from easy to those involving higher order thinking. By its virtue the book inculcates that mathematical maturity which students need in their current and future courses to grow up into mathematicians of substance.
