8.2 Systems of Equations and Matrices: Terminology in Context

In the previous section, you encountered mathematical terms in isolation. Now, you will focus on how mathematical terminology and STEM expressions are used in context, that is, within sentences and text (recall, 'STEM' stands for Science, Technology, Engineering and Mathematics).

Mathematical terms rarely appear alone, they occur in text alongside other words. For example, the word mathematics rarely appears on its own. It of course occurs in sentences and in texts, for example as a sentence in a book on the philosophy of mathematics: Debates about whether mathematics is discovered or invented raise deep questions about the nature of mathematical objects and truth.

By studying terminology and expressions in context, you will become more familiar with how they are used, helping you recognise and apply them more confidently in your own work.

 

In this activity, complete multiple texts on the topic of systems of equations and matrices by filling in the missing mathematical terms.

Most of the missing terms are words you learned in the previous section, or are listed in the Glossary, Section 8.7. However, there may also be a few new terms. If you encounter any unfamiliar words (either as missing words or in the surrounding text), look them up and note them in your vocabulary book.

Note that after each mathematical notation, its pronunciation is given in brackets in italics. Furthermore, the stressed syllables are in bold.

This activity continues from the previous one. You will again work with words and phrases in a text, but this time, the focus is on STEM expressions, not just mathematical terms.

Your task is to drag and drop the correct phrase from the list into each gap in the text.

An example of a STEM expression is: the distance between successive crests or troughs in a wave, which determine many of its properties. This is an example of a string of words which is used in mathematics and beyond.

Note that after each mathematical notation, its pronunciation is given in brackets in italics.

Language Focus

The prefix non- is used extensively in this chapter to form the opposite of mathematical properties. You have already encountered non-commutative, non-singular, and non-zero in the notation above. In each case, non- simply negates the base term, that is, it means not having this property.

The prefix anti- is different from non-: it does not simply negate a property but instead indicates opposition or reversal, often in a directional or structural sense. For example, anticlockwise means in the direction opposite to clockwise. The distinction between non- and anti- is explored in more detail in the Mathematics Focus in Section 8.5.

The prefix non- is regularly used in mathematics. Further examples from this and other chapters include:

Base term non- form Meaning of non- form
commutative non-commutative the order of inputs affects the result
singular non-singular a square matrix that has an inverse
zero non-zero not equal to [latex]0[/latex]
linear non-linear does not satisfy the conditions of linearity
negative non-negative greater than or equal to [latex]0[/latex] (note this is not the same as positive)

You may wish to add further examples to your notes as you encounter them in your studies.

 

In the next section, you will learn how to read out individual mathematical symbols. While the current and previous sections focused on mathematical terminology, the next section will help you communicate using mathematical symbols.

 

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