Arithmetic-Logic-Polynomials-Set of Real Numbers-Volume 1

Hello there! Thank you for taking the time to explore this book.

This mathematics book is in PDF format. It contains four chapters. I will show you the table of contents to give you an idea of its content:

Chapter 1: Arithmetic.

 Natural Numbers-Euclidean division- Even numbers-Odd numbers-Divisors of an integer-The Sieve of Eratosthenes-

 Prime Factorization-Multiples of an integer-Greatest common divisor-Lowest common multiple-Euclidean Algorithm-

GCD and LCM using prime factorization-The congruence relation- Bezout Theorem-Exercises.

Chapter 2: Introduction to Logic.

Logic and Set Theory-Proposition- Logical negation-Conjunction of two propositions-Disjunction of two propositions-

 Logical implication- Logical equivalence-Logical quantifiers-De Morgan's laws-Strategies for Proofs-

 Direct Proof-Proof by contraposition-Proof by Contradiction-Reasoning by induction- Proof by cases-

 Factorial of a natural number-Exercises.

Chapter 3:  Polynomials.

What is a polynomial ?-Value of a polynomial at a point-Addition and multiplication of polynomials-

Roots of a polynomial-Factoring polynomials-Quadratic equations-Sign of a quadratic expression-

Cubic equations-Depressed form of a cubic polynomial-Equality of polynomials-Exercises.

Chapter 4:  The set of real numbers.

Set operations-Sets of numbers in the real number system-Intervals in the set of real numbers-

Cardinality of a set-Functions- Injective function-Surjective function- Bijective function-

The absolute value of a real number-Exponents and powers-Powers of 10 and scientic notation-

Square root of a positive real number- Remarkable identities-Comparing very large and very small numbers-

Exercises.

I hope  this book brings you inspiration, knowledge, and joy.

Happy reading.

A.  Ahmed, Teacher of Mathematics.

Thank you very much.