# Mathematics for Technology I (Math 1131)

Durham College, Mathematics
Free
• 0 lessons
• 0 quizzes
• 10 week duration
• ##### Numerical Computation

Here you'll be introduced to the bare basics of mathematics. Topics include commonly used words and phrases, symbols, and how to follow the order of operations.

• ##### Measurements

An introduction to numerical computation. Emphasis is placed on scientific and engineering notation, the rule of significant figures, and converting between SI and Imperial units.

• ##### Trigonometry with Right Triangles

Here we focus on right angle triangles within quadrant I of an x-y plane. None of the angles we evaluate here are greater than 90°. A unit on trigonometry with oblique triangles is covered later.

• ##### Trigonometry with Oblique Triangles

This unit is a continuation of trigonometry with right triangles except we'll extend our understanding to deal with angles *greater* than 90°. Resolving and combining vectors will be covered at the end of this unit.

• ##### Geometry

This unit focuses on analyzing and understand the characteristics of various shapes, both 2D and 3D.

## Mathematics for Technology I (Math 1131)

### Number Types and Symbols

In mathematics, you will have trouble understanding the material unless you clearly understand the language of the words that are being used. Here are some commonly used words and phrases that you need to know, and that will be repeated throughout the duration of this course.

## Integers

The values:

… −4,   −3,   −2,   −1,   0,   1,   2,   3,   4 …

are called integers because integers are positive or negative whole numbers, including zero. The three dots on the ends indicate that the sequence of numbers continues indefinitely in both directions.

## Rational Numbers

The rational numbers include the integers and all other numbers that can be expressed as the quotient (the result of division) of two integers. In other words, a rational number is any number that can be expressed as a fraction. Some rational numbers are:

7 is a rational number because all whole numbers can be expressed as the number over 1:

$\frac{7}{1}$

## Irrational Numbers

These are numbers that cannot be expressed as a quotient. For example:

All of these equations can never be the quotient of a fraction because they’re never ending numbers. Evaluating the √2 gives you 1.414213562 …

## Symbols of Equality and Inequality

Several symbols are used to show the relative positions of two quantities on the number line.

x = y   means that x equals y, and that x and y occupy the same position on the number line.

x ≠ y   means that x and y are not equal and have different locations on the number line.

x > y   means that x is greater than y, and x lies to the right of y on the number line.

x < y   means that x is less than y, and x lies to the left of y on the number line.

x ≈ y   means that x is approximately equal to y, and that x and y are near each other on the number line. Other symbols sometimes used for approximately equal to are ≅ and ≃.

## Reciprocal

The reciprocal is a function that takes any number and flips it (reciprocates). For example, the reciprocal of 5 is 1/5. Generally, this is summarized as:

More examples:

## Exponents

Given the mathematical expression:

52

This statement is the same as taking the base (positive 5) and multiply it in itself 2 times (exponent of 2). This can be read as 5 raised to the power of 2 or 5-squared.

More examples:

Notice the significance of the brackets in #2: by not enclosing the base in brackets, the sign of the answer is changes from being positive in #1 to negative in #2.

## Absolute Value

The absolute value of a number is its magnitude regardless of its sign. It is written |n|, where n is any number. It is the distance between n and zero on the number line, without regard to direction. For example:

Note: you must treat the absolute a symbol of grouping, much like parentheses.