Algebra (selected topics)

The contents are divided into ten chapters. It deals with Mathematical Induction, Partial Fractions, Finite Series, Binomial Theorems, Matrices and their applications, Determinants in a brief manner, eigenvalues and eigenvectors, settles the digitalization problem for symmetric matrices, theory of equations, (specially Horner¿s Method), Bi-quadratic equations, Cubic Equations (Cardan's method), Quartic Equations, Ferrari's Solution and Reciprocal Equations, Linear programming, fundamentals of sets, the fundamentals of logic. We will discuss "deductive logic" or deductive reasoning. We will show how sets and logic are so interrelated that the techniques of one can be used to solve problems in the other. Through these techniques, we will discuss and solve many classical word problems and puzzles. In chapter 10, we show that the Boolean algebra of sets and logic can also be applied to a third system, namely, the electrical system called "switching theory".