IN BRIEF Transcendental numbers: Numbers that are not the root of any non-zero polynomial. Irrational numbers: Numbers that cannot be expressed as a fraction. Property of being transcendental: Corresponds to the absence of a polynomial with integer coefficients that cancels it. Notable examples: π and e are common examples of transcendental numbers. Algebraic numbers: Contrast … Read more
IN BRIEF Complex analysis: field of study of complex numbers. Definition of a complex number: z = a + bi with a and b real, i imaginary unit. Visualization of complex numbers in the plane with coordinates. Operations on complex numbers: addition, subtraction, multiplication, etc. Basic concepts related to imaginary numbers and their importance in … Read more
IN BRIEF Prime number: a natural integer that is divided only by 1 and itself. Examples of prime numbers: 2, 3, 5, 7, 11, 13. Importance in arithmetic: every number is uniquely decomposed into products of prime numbers. Cryptography: prime numbers ensure the security of online data. Historical developments, notably by Eratosthenes and his sieve. … Read more
IN BRIEF Even numbers: integers that are multiples of 2. Odd numbers: integers that are not multiples of 2. A number is even if it ends with 0, 2, 4, 6, or 8. A number is odd if it cannot be divided by 2 without a remainder. The sum of several odd integers: even if … Read more