8.6 Systems of Equations and Matrices: Exploring Mathematics Through Text
In the previous section, you practised reading and performing mathematical dialogues. This is spoken communication. In this section, you will focus on written mathematical communication. This book uses several different types of text across the chapters. This gives you exposure to a variety of mathematical writing.
The text below is a fictional announcement for an end-of-term celebration event organised by the Mathematics Student Society at the fictional Westmere University. It takes the form of an informal but structured event invitation, addressed directly to mathematics students. Imagine that this announcement has been sent by email to all students enrolled on mathematics programmes at Westmere University, or that it appears on the society's noticeboard and social media channels.
Your task is to read the text and work through the activities. The activities have a logical structure: they begin with more global or whole-text activities, that examine the purpose and audience of the text, and they gradually narrow to a focus on individual language items. In mathematical writing, there is an inherent connection between ‘macro’ text-external elements (such as audience and purpose) and ‘micro’ text-internal aspects (such as individual words and phrases).
By working through the various activities below, you will be able to:
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Work with extended mathematical prose texts to enhance your understanding of both mathematical concepts and the structure of mathematical writing.
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Identify and develop your command of useful academic phrases and sentence structures within text.
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Apply this language in your own writing and mathematical discussions.
Activity 1: Overall purpose and audience of the text
The purpose of this activity is to help you think about three features of a text: its audience (who reads it), its purpose (why it was written), and its structure (how it is organised). Academic writing takes many different forms. Each form has its own conventions, purposes, and ways of organising information. Noticing these differences will help you become a stronger academic reader and writer.
Question 1: the audience of this text
All texts have an audience, that is, a person or a group of people for whom the text is written. Look over the text and select the most likely audience of the four possibilities listed below. Next, select the ‘Answer’ button below the options.
Possible audience 1: Students who are attending an open day in the mathematics department at Westmere University.
Possible audience 2: Students who are preparing for exams on matrices and want to take a break from revision.
Possible audience 3: Students who want to celebrate the end of the term.
Possible audience 4: Students who are members of the Mathematics Student Society.
Answer
Possible audience 3 is the correct answer. The text is an invitation to an end-of-term social event for mathematics students, especially those finishing the term and looking to celebrate after a demanding assessment period. The informal, celebratory tone and the references to prizes and refreshments confirm that the intended audience is students who have completed their assessments and are no longer in an examination period.
Note that Possible audience 4 may seem plausible, since the event involves mathematics. However, the text is addressed to all mathematics students, not only to those who belong to a specific student organisation.
Question 2: The overall structure of this text
An invitation can contain various components and can be structured in various ways. Consider the list below of possible components of the invitation. Re-read the text and re-order the listed components to match the order in which they appear in the text. Note that some of the listed components are not present in the text, so you will not use all of the items listed.
You may not need to read the text in detail for this activity. The purpose is simply to identify what sections the text consists of and in what order they appear.
For any that are present, note any language or structural features of the item that indicates what it is. For example, b) below, is the first item to appear in the text. This is indicated by the use of bullet points and the phrase at a glance in the heading. Next, select the ‘Answer’ button below.
- A comment from a member of the committee about the nature of the event.
- A list of the most important information about the event. (This is the first item chronologically as detailed above.)
- When next year's event will be.
- An announcement of marks for any module related to the mathematics of the event.
- What to do to take part.
- Which members of staff will be present.
- The structure of the event.
- Feedback from last year's event.
- What it is possible to win at the event.
Answer
First b) A list of the most important information about the event.
This appears immediately after the introductory paragraph in the form of a bulleted list of key details. We would expect this information to come early in the text, since potential attendees will want to know the essential facts quickly. This is signalled by the heading The event at a glance. Note the phrase at a glance: a glance is a quick, brief look, so the phrase means a short overview of the most important information. This phrase can be used with other nouns, for example, the module at a glance or the history of mathematics at a glance.
Second g) The structure of the event.
This is indicated by the sentence The quiz is divided into four rounds, after which each of the four rounds is described in turn. Note the verb phrase is divided into, which is commonly used in mathematical and academic writing to describe how something is broken down into parts, for example, the proof is divided into three steps or the chapter is divided into two sections.
Third e) What to do to take part.
This is signalled by the heading How to register, the phrase Getting involved, and a numbered list of three steps. Note that numbered lists in English-language texts typically indicate a sequence, that is, the steps should be followed in order.
Fourth i) What it is possible to win at the event.
This is indicated by the heading Prizes, followed by a listing of first, second, and third prizes. Note that in English, prizes are conventionally listed in descending order, from first to last.
Fifth a) A comment from a member of the committee about the nature of the event.
This is indicated by the heading A Word from Sophie. Note that a word here is used non-literally: it does not refer to a single word but to a short personal statement or message. This non-literal use also appears in the phrase have a word with someone, which means to speak to someone, often to address a concern or problem.
The following items do not appear in the text:
- c) When next year's event will be.
- d) An announcement of marks for any module related to the mathematics of the event.
- f) Which members of staff will be present.
- h) Feedback from last year's event.
Question 3: Creative thinking
You are now familiar with both the audience of this text and its overall structure. Before moving on, take a moment to think about what other components could reasonably appear in a text of this type. There are no right or wrong answers here, the purpose of this question is to encourage you to think creatively about the conventions of this kind of text.
Select the ‘Answer’ button below for some possible answers.
Answer
Additional items that could be present include:
- Some feedback from last year's event, noting how successful it was and encouraging students to attend again.
- A request for individuals to volunteer to assist with the running of the event on the night.
- A short section on the history of the event, explaining when it was first organised and how it has developed over the years.
- A frequently asked questions (FAQ) section addressing common queries such as whether students can attend alone or whether prior knowledge of a particular area of mathematics is required.
THE MATHEMATICS STUDENT SOCIETY
🎉 END OF TERM CELEBRATION & MATRIX MASTERS QUIZ 🎉
Friday, 20th December | 6:00 pm – late
The Alderton Building, Lecture Hall LH2
Dear Fellow Mathematicians,
You made it! The end of term is finally here, and the Mathematics Student Society (MSS) wants to celebrate with you in style.
We are absolutely delighted to invite you to our End of Term Celebration, this year featuring the very first Matrix Masters Quiz, a fun, team-based evening dedicated to the topic that has kept us all busy this term: systems of equations and matrices. Whether row reduction has become your best friend or Gaussian elimination is still giving you nightmares, this is the perfect occasion to laugh about it with your fellow students over hot drinks and snacks.
Bring your friends, form a team, and get ready for a brilliant evening!
The Event at a Glance
Date: Friday, 20th December 2030
Time: 6:00 pm (doors open 5:45 pm) - until late
Venue: The Alderton Building, Lecture Hall LH2
Format: Team quiz (teams of 3–5) + social evening
Entry: Free for MSS members / £2 for non-members
RSVP deadline: Wednesday, 18th December 2030, 5:00 pm
About the Matrix Masters Quiz
Don't panic, this is meant to be fun! The quiz is divided into four rounds, each one a chance to show off what you know, help out your teammates, and maybe discover that augmented matrices are actually not so bad after all.
Round 1: It All Starts with a System
We kick things off with the basics: setting up systems of linear equations and building augmented matrices. Think of it as a warm-up: straightforward questions to get the team talking and the competitive spirit flowing.
Round 2: Eliminate to Accumulate
This is where it gets serious. Row operations, pivots, and the satisfying crunch of reducing a matrix to reduced row echelon form; the round that rewards everyone who stayed awake during the Gaussian elimination lectures. Points are there for the taking!
Round 3: What's the Solution?
A unique solution? No solution at all? Infinitely many solutions with free variables running wild? This round is all about reading the story that a reduced matrix is trying to tell you. The team that interprets the solution set most clearly takes home the points.
Round 4: Transformers
The grand finale. Rotations, reflections, chained transformations, and the all-important question of why [latex]AB[/latex] is usually not the same as [latex]BA[/latex]. Expect geometry, expect surprises, and expect at least one moment where the whole room gasps.
How to Register
Getting involved is easy:
- Round up three to five friends and choose a team name; mathematics-themed names are warmly encouraged. Last year's winning team was called The Gaussian Eliminators, so the bar has been set.
- Email mss@westmere.edu.ac.uk with your team name and the full names of all members.
- Confirm your place by Wednesday, 18th December at 5:00 pm.
Coming alone? No problem at all. Just let us know when you register and we will match you up with a team. Some of the best quiz partnerships have started exactly that way.
Prizes
- 🥇 First place: £50 vouchers per team member + the MSS Trophy (held for one academic year)
- 🥈 Second place: £25 vouchers per team member
- 🥉 Third place: MSS merchandise
A Best Team Name prize will also be awarded on the night, so even if matrices are not your strong suit, a great name might still earn you glory.
A Word from Sophie
"We designed the Matrix Masters Quiz because we wanted to mark the end of term in a way that feels true to who we are: people who actually enjoy this stuff, even when it is hard. Systems of equations and matrices have challenged all of us this term, and that is worth celebrating together. Come for the quiz, stay for the company, and leave knowing that reduced row echelon form is, in fact, your friend."
Sophie Hartley, MSS Academic Committee Chair
Food, Drinks & Good Company
Hot drinks, soft drinks, and plenty of snacks will be available throughout the evening. After the prize-giving, the social carries on informally; no agenda, just a chance to relax, catch up with friends, and mark the end of what has been a genuinely hard-working term. Everyone is welcome, whatever your quiz result turns out to be.
We cannot wait to see you there. It is going to be a great night!
The Mathematics Student Society Committee
mss@westmere.edu.ac.uk | @MSSWestmere | www.mss.westmere.edu.ac.uk
The Mathematics Student Society is a student-run organisation affiliated with the Department of Mathematics, Westmere University. All students enrolled on mathematics programmes are automatically eligible for MSS membership.
Activity 2: 'Light-hearted language' and 'the language of information'
This text is a well-written invitation. Part of the success of this text is that it blends two distinct kinds of language throughout. We will call these:
- Light-hearted language: language designed to be amusing and engaging. This kind of language may serve several purposes: setting the tone for the event, attracting people to attend through the use of humour, and making the serious study of mathematics feel slightly less formal, at least in the context of a social event. This language is typically informal.
- The language of information: language designed to provide the audience with the details they need in order to attend and participate fully. This language tends to be more formal, though it may be less formal than in other kinds of academic or professional writing.
Worked example: Consider the first paragraph of the text reproduced below:
You made it! The end of term is finally here, and the Mathematics Student Society (MSS) wants to celebrate with you in style.
In this short paragraph, light-hearted language and the language of information are blended together. We take each part in turn.
- You made it! This very informal expression carries a sense of congratulation. It means something like Well done for reaching the end of term. It is therefore an example of light-hearted language.
- The end of term is finally here … This phrase restates the meaning of You made it! in a more standard way, confirming that the term has ended. It also connects forward to the clause that follows.
- … and the Mathematics Student Society (MSS) wants to celebrate with you in style. This clause blends both kinds of language: it provides information (the MSS is holding a celebration) while the phrase in style is an example of light-hearted language, suggesting that the event will be special and enjoyable.
Question 1: Consider the rest of the opening section, reproduced below. There are three sentences in this extract. For each sentence, identify examples of the language of information and light-hearted language. Next, select the ‘Answer’ button below.
We are absolutely delighted to invite you to our End of Term Celebration, this year featuring the very first Matrix Masters Quiz, a fun, team-based evening dedicated to the topic that has kept us all busy this term: systems of equations and matrices. Whether row reduction has become your best friend or Gaussian elimination is still giving you nightmares, this is the perfect occasion to laugh about it with your fellow students over hot drinks and snacks.
Bring your friends, form a team, and get ready for a brilliant evening!
Answer
Sentence 1: This sentence is largely an example of the language of information, written in a fairly standard level of formality. It informs the reader of the name of the event (End of Term Celebration), the name of the quiz (Matrix Masters Quiz), its format (team-based), and its subject matter (systems of equations and matrices). However, the phrase kept us all busy this term is an example of light-hearted language. Note in particular the use of us, which creates a sense of inclusivity between the writer and the reader; the writer presents themselves as someone who has also been working hard on the same material.
Sentence 2: This sentence is divided between light-hearted language and the language of information. The opening clause, Whether row reduction has become your best friend or Gaussian elimination is still giving you nightmares, uses a whether … or … balanced structure. This is a common rhetorical device in English used to acknowledge two contrasting possibilities. Here, both halves of the structure use light-hearted language: your best friend and giving you nightmares are informal expressions that make the mathematics seem less intimidating. This light-hearted opening leads into the main clause, which provides information about what the event will offer (a perfect occasion to laugh about it with your fellow students over hot drinks and snacks). Note, however, that even this informational clause contains light-hearted elements: a perfect occasion and to laugh about it both contribute to the celebratory tone.
Sentence 3: This sentence consists of three imperative verb forms: Bring, form, and get ready. In ordinary contexts, imperative forms are used to give instructions or orders. Here, however, they function as enthusiastic invitations rather than commands. Note that the same meaning could be expressed more tentatively, for example, Why not bring your friends? or How about forming a team? — but the imperative form creates energy and excitement, which is appropriate for this kind of text. While the sentence does convey information (attendees may bring friends and the evening will involve teams), this information is presented through a structure that is itself an example of light-hearted language.
Question 2: The same balance of light-hearted language and the language of information appears throughout the text. Consider the opening sentences of the section About the Matrix Masters Quiz, reproduced below:
Don't panic, this is meant to be fun! The quiz is divided into four rounds, each one a chance to show off what you know, help out your teammates, and maybe discover that augmented matrices are actually not so bad after all.
Sentence 1 is entirely light-hearted. We see again the playful suggestion that while mathematics can be demanding, the event described here is enjoyable. Sentence 2 is largely informational and more formal; however, it ends with the same playful idea with which Sentence 1 began: …that augmented matrices are actually not so bad after all.
Your task: Now read each of the four rounds below and identify examples of light-hearted language and the language of information. Next, select the ‘Answer’ button below.
Answer
Round 1: It All Starts with a System
We kick things off with the basics: setting up systems of linear equations and building augmented matrices. Think of it as a warm-up: straightforward questions to get the team talking and the competitive spirit flowing.
Both sentences consist of two parts separated by a colon (:). In English, a colon typically introduces an explanation, a list, or an elaboration of what has just been stated. Sentence 1 blends light-hearted language (we kick things off) with the language of information (the description of the mathematical content). Sentence 2 follows the same pattern: the opening clause (Think of it as a warm-up) is light-hearted and informal, while the second clause provides more specific information about what the round will involve. Note, however, that even the informational part ends informally: get the team talking and the competitive spirit flowing is relatively informal. A more formal equivalent might be: to provide team members with an opportunity to discuss together and engage competitively.
Round 2: Eliminate to Accumulate
This is where it gets serious. Row operations, pivots, and the satisfying crunch of reducing a matrix to reduced row echelon form; the round that rewards everyone who stayed awake during the Gaussian elimination lectures. Points are there for the taking!
Sentence 1 is short and entirely light-hearted. The statement this is where it gets serious is playful; since the entire event is light-hearted, presenting one round as suddenly serious is itself a joke. Sentence 2 is structured around a semicolon (;), which in English typically separates two closely related independent clauses. The first part of Sentence 2 consists of a triad: a group of three items listed together (row operations, pivots, and the satisfying crunch of reducing a matrix to reduced row echelon form). We will return to the triad as a structural feature of this text in a later activity. The phrase satisfying crunch is a humorous and informal way of describing the process of row reduction. The second part of Sentence 2 is also light-hearted: the reference to stay[ing] awake during the Gaussian elimination lectures is a self-aware joke about the difficulty of the subject. Sentence 3 is an informal construction meaning something like the points are available to anyone who attempts the questions.
Round 3: What's the Solution?
A unique solution? No solution at all? Infinitely many solutions with free variables running wild? This round is all about reading the story that a reduced matrix is trying to tell you. The team that interprets the solution set most clearly takes home the points.
Sentences 1, 2, and 3 together form a triad of questions; note that each is a sentence fragment rather than a complete sentence, which contributes to the energetic, informal tone. As noted above, we will return to the triad as a structural feature in a later activity. Sentences 4 and 5, by contrast, are relatively formal and informational. However, the phrase reading the story that a reduced matrix is trying to tell you is an example of light-hearted language embedded within an otherwise formal sentence; it personifies the matrix, presenting it as if it were a living thing with something to communicate. This is a common technique in informal academic writing to make abstract ideas feel more accessible.
Round 4: Transformers
The grand finale. Rotations, reflections, chained transformations, and the all-important question of why [latex]AB[/latex] is usually not the same as [latex]BA[/latex]. Expect geometry, expect surprises, and expect at least one moment where the whole room gasps.
Sentence 1 is a sentence fragment (The grand finale) consisting of a single noun phrase. This is an example of light-hearted language that uses exaggeration for humorous effect, presenting the final round as a dramatic climax. Sentence 2 consists of a four-part list rather than a triad. The first three elements (rotations, reflections, chained transformations) are largely informational, while the fourth (the all-important question of why [latex]AB[/latex]is usually not the same as [latex]BA[/latex]) blends information with light-hearted exaggeration through the phrase all-important. Sentence 3 is a triad of imperative clauses (Expect geometry, expect surprises, and expect at least one moment where the whole room gasps). The first element is informational; the second and third are light-hearted, with the third using further exaggeration (the whole room gasps) for comic effect.
Language Focus 1: examples of informal verb structures
As you have seen in Activity 1 and Activity 2, the light-hearted nature of this text means that it contains many examples of informal language. This Language Focus collects four examples of informal verbal structures and invites you to examine the meaning of each in context. Two of the examples are phrasal verbs; if you would like to practice on phrasal verbs before completing this activity, see Sections 3.6 and 4.5.
Your task: Match the four examples of informal verbal structures below to their paraphrases. The verbal element is underlined. For each example, write a short note explaining what makes the language informal or unusual. Next, select the ‘Answer’ button below.
| Example from the text | Paraphrase | |
|---|---|---|
| You made it! | There is kudos and fame for a noteworthy team name. | |
| We kick things off with … | Get together with … / form groups with … | |
| A great name might still earn you glory. | You've got there! You've completed the task! You did it! | |
| Round up three to five friends … | We start things off with …We begin with … We get going with … |
Answer
| Example from the text | Paraphrase |
|---|---|
| You made it! | You've got there! You've completed the task! You did it! |
| We kick things off with … | We start things off with … We begin with … We get going with … |
| A great name might still earn you glory. | There is kudos and fame for a noteworthy team name. |
| Round up three to five friends … | Get together with three to five friends / gather three to five friends. |
Comment on You made it! : This is a complete phrase in itself. It is close to You did it! or You've got there! in structure and formality. The pronoun it here is sometimes called 'empty it': it does not refer to any specific thing but simply completes the grammatical structure of the sentence. Other common informal expressions with empty it include Go for it!, That's it!, and Give it a go! It may be useful to collect further examples of informal expressions containing empty it and note them in your vocabulary book.
Comment on we kick things off with …: This is a phrasal verb. The verb kick combines with the particle off to produce the meaning to begin or to start. Note that kick off can be used both transitively (we kick things off) and intransitively (the quiz kicks off at 7pm). Other phrasal verbs with kick include kick up a fuss (to complain loudly or cause a disturbance) and kick out (to force someone to leave). As with many phrasal verbs, the meaning of kick off cannot easily be predicted from the individual meanings of kick and off taken separately.
Comment on A great name might still earn you glory. : The verb earn is not itself informal; it is a standard English verb meaning to receive something in return for effort or merit, as in to earn a salary or to earn a qualification. What makes this example informal and light-hearted is the choice of object: in everyday English we would more naturally say earn you recognition or earn you points. The word glory is an example of deliberate exaggeration for humorous effect; it elevates a small reward (a team name prize) to something heroic and grand. This technique of comic exaggeration is consistent with the light-hearted tone of the text throughout.
Comment on Round up three to five friends … : This is a phrasal verb. The verb round combines with the particle up to mean to gather people together, often with the suggestion of collecting them from different places. Note that round up and its opposite round down also have a precise mathematical meaning: to round a number up means to increase it to the nearest convenient value, while to round it down means to decrease it. For example, 7.2 rounded to the nearest whole number gives 7 (rounded down), whereas 7.8 rounded to the nearest whole number gives 8 (rounded up). This is a good example of a term that has both a general, everyday meaning and a distinct technical meaning in mathematics; a feature of mathematical English that is worth paying close attention to throughout this book.
Activity 3: Triads (or trios or groups of three) in the text
This activity has a similar theme to Activity 3 in Section 6.6. A triad is a group of three items listed together. Triads are an extremely common structural feature of English, in both formal and informal writing. They are used to create rhythm, emphasis, and a sense of completeness. Consider the final sentence of the opening section, reproduced below with each of the three parts labelled:
[i] Bring your friends, [ii] form a team, [iii] and get ready for a brilliant evening!
This triad consists of three instructions or invitations. Each element is verbal, that is, the key word in each element is a verb: Bring; form; get (ready for). Note the use of and before the third element, which is the standard pattern in English for listing three items. Triads can also be nominal, that is, the key word in each element is a noun rather than a verb. We will see examples of both types below.
Your task: Re-read the text and identify all the triads. For each one, decide whether it is verbal or nominal. It can be useful (and fun) to try to memorise these triads. You may wish to work with a partner and test each other on how many you can recall. Next, select the 'Answer' button below.
Answer
Here are the triads or three-part language structures in the rest of the text.
- … each one a chance to [i] show off what you know, [ii] help out your teammates, [iii] and maybe discover that augmented matrices are actually not so bad after all. This is verbal: show off; help out; discover
- [i] Row operations, [ii] pivots, [iii] and the satisfying crunch of reducing a matrix to reduced row echelon form; … This is nominal: row operations; pivots; the satisfying crunch
- [i] A unique solution? [ii] No solution at all? [iii] Infinitely many solutions with free variables running wild? This is nominal: a solution; no solution; many solutions
- [i] Expect geometry, [ii] expect surprises,[iii] and expect at least one moment where the whole room gasps. This is verbal: expect; expect; expect
- The How to register section consists of three bullet points.
- The Prizes section consists of three bullet points.
- [i] Come for the quiz, [ii] stay for the company, [iii] and leave knowing that reduced row echelon form is, in fact, your friend. This is verbal: come; stay; leave
- [i] Hot drinks, [ii] soft drinks, [iii] and plenty of snacks. This is nominal: drinks; drinks; snacks
- no agenda, just a chance to [i] relax, [ii] catch up with friends, [iii] and mark the end of what has been a genuinely hard-working term. This is verbal: relax; catch up with; mark
Language Focus 2: Metaphors
In previous activities, we discussed the use of light-hearted language, informal phraseology, and exaggeration for humorous effect. A further feature of the light-hearted tone of this text is the use of metaphor (language that describes one thing in terms of another in order to create a particular effect). This kind of language is also called non-literal language, since the words are not meant to be taken at face value. Next, select the 'Answer' button below. The answers include some explanation.
| Example from the text | Paraphrase of the underlined metaphorical element | |
|---|---|---|
| The bar has been set | a strength or a talent | |
| If matrices are not your strong suit | moving, acting | |
| The team that interprets the solution set most clearly takes home the points. | the satisfaction; the sense of achievement from | |
| Get the competitive spirit flowing | the standard or expected level of attainment | |
| The satisfying crunch of reducing a matrix to reduced row echelon form. | to win; to collect |
Answer
| Metaphor | Paraphrase | Explanation and comments |
|---|---|---|
| The bar has been set | The standard or expected level of attainment | The literal meaning refers to a bar that an athlete jumps over, for example in the high jump. We use this metaphorically to refer to a level of performance. Related expressions include raise the bar (increase the standard) and lower the bar (reduce it). |
| If matrices are not your strong suit | A strength or a talent | The literal meaning refers to a suit in a deck of cards (clubs, diamonds, hearts, spades). We use this metaphorically to refer to personal strengths and weaknesses. For example: Algebra isn't my strong suit means Algebra isn't my greatest strength. |
| The team that interprets the solution set most clearly takes home the points. | To win, to collect | The literal meaning refers to carrying something physically back to one's home. We use this metaphorically to mean winning or receiving a reward. A related expression: The most important thing to take home from today's lecture is X means The key thing to remember from today's lecture is X. |
| Get the competitive spirit flowing | Moving, acting | The literal meaning of flow is to move like a liquid. We use this metaphorically to describe energy or ideas moving freely. Related uses: the discussion is really flowing (it is going well); to be in the flow (to be thinking clearly or working easily). |
| The satisfying crunch of reducing a matrix to reduced row echelon form. | The satisfaction; the sense of achievement from | The literal meaning of crunch refers to a sharp sound or physical sensation, such as the sound of eating crisps. We use this metaphorically to suggest that completing a mathematical process can feel, and even sound, satisfying. Note also that a crunch moment means a decisive or critical moment: That exam was a real crunch moment for me, meaning it was a significant turning point. |
Language Focus 3: Whether … or … + sentence
In Activity 2, Question 1, we noted the structure whether … or … + main clause. This is a relatively complex but very useful structure in academic and semi-formal English. We will now look at it in more detail. The example from the text is reproduced below:
Whether row reduction has become your best friend or Gaussian elimination is still giving you nightmares, this is the perfect occasion to laugh about it with your fellow students over hot drinks and snacks.
A second analogous example now follows:
Whether it is the intrinsic motivation of the challenge of mathematics or the extrinsic motivation of a high-paying career, applications for mathematics degrees are up across the board.
The meaning of this second example is something like: Applications for mathematics degrees are increasing, and this may be due to intrinsic motivation, extrinsic motivation, or indeed other factors. Note an important feature of this structure: the whether … or … element does not necessarily restrict the possibilities to exactly two options. Instead, it often signals something like here are two possible examples of a wider range of reasons or situations. This makes it a particularly useful structure for academic writing, where it is common to acknowledge multiple possibilities without listing them all explicitly.
Question 1: The nine segments below form three complete sentences using the whether … or … + main clause structure. Using both meaning and grammatical cues, match the segments to form three correct sentences. Note that each sentence consists of three segments. Next, select the 'Answer' button below.
| Part 1 | Part 2 | Part 3 |
|---|---|---|
| Whether it's down to great teaching … | … just a bag of sweets, we … | … results for the Year 1 Statistics module are significantly better than last year. |
| Whether it's a brand new textbook or … | … or the revised format for the exam … | … vital to work out how to manage the pressures of exam your way! |
| Whether listening to music is your thing, … | … or you prefer a trip to the gym or a quick walk, it's … | … need to get some kind of prize for the quiz night. |
Answer
- Whether it's down to great teaching or the revised format for the exam, results for the Year 1 Statistics module are significantly better than last year.
- Whether it's a brand new textbook or just a bag of sweets, we need to get some kind of prize for the quiz night.
- Whether listening to music is your thing, or you prefer a trip to the gym or a quick walk, it's vital to work out how to manage the pressures of exam in your way!
Question 2: Working with a partner, try to write two or three of your own examples using the whether … or … + main clause structure. Try to use contexts that are relevant to your studies — for example, referring to mathematics, university life, or the topics covered in this chapter.
Language Focus 4: Points are there for the taking!
In the text, we saw the sentence Points are there for the taking! This is an example of a fixed construction in English. Schematically, the structure is: X is/are there for the taking. The meaning is that X is available and can be obtained by anyone who makes the effort to try. It often carries a sense of encouragement; the speaker is suggesting that success is within reach.
Consider the three further examples below, each from a different context.
- With the recent increase in financial investment in UG students, summer scholarships are there for the taking.
- Tutor to students: 'If you've done the revision and worked through the worksheets, the marks on this exam are pretty much there for the taking. Good luck!'
- Student to a student: 'I thought the problem sheet was fairly straightforward. I wouldn't say the right answer was always just there for the taking or was going to fall out of the sky, but with a bit of thought, the solutions could be found pretty easily.'
Activity 4: Production Activity 1 - Roleplay
This activity invites you to respond to the text through spoken communication, giving you the opportunity to use some of the language you have encountered in this chapter.
Setup: Work in pairs. Imagine that you and your partner are both students in the Mathematics Department at Westmere University. You have both just read the invitation to the Matrix Masters Quiz.
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Student A wants to attend the quiz night and will try to persuade Student B to come along.
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Student B does not want to attend and will put forward reasons for not going.
Variations:
- In a group of three, a third student (Student C) plays someone who is undecided. Students A and B each try to bring Student C round to their point of view (note that this means to persuade Student C to agree).
- In a group of four, two students take the role of Student A and two take the role of Student B.
How to begin:
Student A might begin with something like: Have you seen this invitation to the Matrix Masters Quiz? It looks like a lot of fun — and it's a great chance to go over some of the material from this term in a relaxed setting. Shall we go?
Student B might respond with something like: I don't know, I've got a lot on at the moment, and honestly the last thing I want to do is spend an evening thinking about matrices...
Language to use: As you roleplay, try to use some of the following language from the text and from the Language Focus sections in this chapter:
- Persuading: Whether you find it easy or not, it's going to be a great evening; The prizes are there for the taking; It'll be a chance to relax and catch up with friends
- Making excuses: It's not really my strong suit; I've got other things on; I'm not sure it's for me
- Responding to persuasion: I suppose you have a point; That's a fair argument; I'm still not convinced
After the roleplay: Discuss the following questions with your partner or group:
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Which arguments did Student A use that were most persuasive? Why?
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Did Student B use any language from the text or Language Focus sections? Which expressions worked well in spoken conversation?
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Were there any expressions from the text that felt unnatural to use in spoken conversation? Why might that be?
Activity 5: Production Activity 2 - writing
This activity gives you a second opportunity to respond to the text, this time through writing. Working alone or with a partner, write a shorter invitation to a mathematics quiz night of your own design. Your invitation does not need to include all the sections present in the original text.
Suggested structure: Consider organising your invitation using some or all of the following components:
- A title and an introductory paragraph that establishes the tone and audience of the event.
- A short section giving the essential information, for example, the date, time, location, and how to register.
- A description of the nature of the quiz, for example, the number of rounds, the topics covered, and the format of the questions.
- A section on prizes, including what participants can win and how the winner is decided.
Things to consider: Before you begin writing, discuss the following questions with your partner or think about them on your own:
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Who is your audience? Are you writing for the same audience as the original text, or a different one?
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What tone do you want to establish; very informal and playful, or closer to a balance between formal and informal?
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Which mathematical topics will your quiz cover? You might choose topics from this chapter (systems of equations, row reduction, matrix multiplication) or from elsewhere in your studies.
After writing: When you have finished, exchange your invitation with another student or pair. Read their invitation and consider the following:
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Can you identify any triads, metaphors, or whether … or … structures in their text?
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Does their invitation successfully blend light-hearted language with the language of information?
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Is there anything you would suggest they change or add?
In this section, you have focused on longer written mathematical communication. To conclude the chapter, the final section provides a glossary of important mathematical terms from the chapter.
