Math for beginners

Math for beginners is a book in which I have tried to make the general concepts about basic math skills, algebra, and geometry and trigonometry easy to understand for students who have to study those subjects for the first time, and also to refresh the memory of many persons about the said subjects which they have probably studied some years earlier.

I have tried to include in this book most of the topics the vast majority of students have to deal with in their math courses in basic math skills, algebra, and geometry and trigonometry.

In the first two chapters I have explained what sort of numbers we use in math, I have explained the concept of the bases of numeration, and how to deal with normal and with scientific notation, and I have insisted on the order of operations rules. I have explained how to operate with fractions. I have explained the rules to find the sign of the result of an operation, how raising to an exponent n is the inverse operation of taking the n-th root. I have analyzed prime numbers, and the prime factorization of a natural number, how to simplify fractions, and to find the l.c.d. This book includes a lot of examples.

At chapter III I have explained the concept of variable that is so difficult to grasp for many students, I have analyzed the definitions of the various types of functions and equations, including their domain, range and codomain. I have explained how to deal with linear and quadratic equation, how linear functions can be written either in 3 forms and how to write the equations of vertical and horizontal lines, and how to graph them. I have shown the ideas on which solving linear and quadratic equations are based.

At chapter IV I have analyzed the different kinds of functions we normally use, and included many examples about their applications in practical problems. I have included formulas as well as many drawings and graphs in the Definitions and Formulas chapter.

I have shown why different ways to write functions are equivalent to each other.

I have analyzed the main topics about polynomials, like how to factor them using the fundamental theorem of polynomials and the rational root theorem, and how to do synthetic and long divisions of polynomials, as well as the general behavior of polynomials to be able to graph them.

At chapter V I have also analyzed exponential and logarithmic functions.

At chapter VI I have explained where the number pi comes from.

I have explained what the Pythagorean Theorem means regarding right triangles.

I have also shown how to evaluate the perimeters and areas of several figures. I have shown what the different relationships between angles are.

Regarding trigonometry I have explained what the six basic trigonometric functions are, and how they are related to right triangles and how to use the Pythagorean Theorem to find the relationships between them using right triangles. I have also included a list of several trigonometric identities.

I have included equations of parabolas, and equations of circles, ellipses and hyperbolas in several forms. Also in the Definitions and Formulas Chapter I have included examples of applications of such equations. Besides I have included how to work with composite functions and how to work with variations.

I do believe that the information in this book will be enough to ensure that students will find most of the information on such topics they need to understand and learn on the aforementioned topics.