The modulus of elasticity (= Young’s modulus) E is a material property, that describes its stiffness and is therefore one of the most important properties of solid materials.

For example, if we want the product of two numbers modulo n, then we multiply them normally and the answer is the remainder when the normal product is divided by n. The value n is sometimes called …

Let m > 0 be a positive integer called the modulus. We say that two integers a and b. are congruent m. dulo m if b − a is divisible by m. In other words, �. dm) ⇐⇒ a − b = m · k for some integerk. Note: …

The modulus of rigidity, also called shear modulus, indi-cates the resistance to deflection of a member caused by shear stresses. The three moduli of rigidity denoted by GLR, GLT, and GRT are the …

The modulus of a number is denoted by writing vertical lines around the number. Note also that the modulus of a negative number can be found by multiplying it by −1 since, for example, −(−8) = 8.

We define the real and imaginary parts of z by Re z = x and Im z = y. The modulus of z, denoted by |z|, is a nonnegative real number given by. |z| = px2 + y2 . The modulus of z is often called the absolute …

Modular arithmetic motivates many questions that don’t arise when study-ing classic arithmetic. For example, in classic arithmetic, adding a positive number a to another number b always produces a …