Filter

How to Write an Informative Essay in Mathematics – a Guide by People Who Know Their Job

Writing an informative essay – or, in fact, any essay at all – in mathematics may look like a weird job that has little to do with what one expects to do in relation to this discipline. However, you should understand that an informative essay is noticeably different from most other types of academic writing, and is excellently suited to the nature of mathematics and related subjects. In an informative essay, you do not have to prove anything or try to persuade the audience that your point of view on the subject matter is the right one. You simply have to tell about the subject, providing relevant, specific and correct information. There is nothing to prove in mathematics (at least nothing a college student may expect to prove), so this approach suits the discipline perfectly.

Mathematics is all about hardly defined rules and principles. There are no ambiguities, no vagueness – you will not have to worry about multiple different interpretations of one and the same fact. This means that, although the approach in general may be slightly unfamiliar, you are unlikely to experience serious problems once you get used to it. At least if you carefully follow the methods learned from this guide.

How to Write an Informative Essay in Mathematics: Starting Your Job

1. Choosing a Topic

The first thing you have to do, just like with any other kind of essay, is to choose what you are going to write about. However, in relation to mathematics it may be even more important than usual, because it is a highly formalized and ordered discipline. This means that it is extremely easy to choose a topic that is not very well suited for writing about it. For example, you may end up in a situation when the majority of your essay will have to consist of formulas, not leaving you much space for explaining things in your own words. Or, alternatively, it may turn out that to explain the topic in question you need no more than a couple of sentences, after which there is simply nothing more to say. Therefore, when you have freedom to write about anything you want, spend some time and choose something that meets the following requirements:

  • Has plenty of sources writing about it (this means that you will probably be able to write enough as well);
  • Covers a subject you are at least somewhat interested in (it is much easier to write, especially write something unusual and interesting, if you are genuinely fascinated by the topic);
  • Can be explored at length without excessive use of formulas and calculations (after all, you are writing an essay, not a research paper).

It may be easier to write not about mathematics per se, but about subjects that are related to mathematics (at least if the conditions of your assignment allow it), like the history of mathematical science in different countries and the study of specific mathematical and algebraic principles and concepts in different civilizations.

If you follow these suggestions, you will end up with a topic somewhat similar to these ones:

  • The Concept of Zero and Its Role in the Development of Mathematics;
  • History of Mathematical Thought in Ancient India;
  • The Idea of Negative Numbers and How It Influenced the Mathematical Thought;
  • The Role of Mathematics in Computer Science;
  • The Most Important Mathematical Theorems and Their Role in Scientific Research.

2. Review the Literature

Even if you know the topic like the back of your hand, you cannot simply give this information. Your audience does not know for sure that you are well versed in the subject and that your explanations can be trusted. In addition, there is always a likelihood that you will discover something new and unexpected while gathering information. This is why your next step is to gather as much literature about the subject as possible and study the existing body of research dedicated to your topic. At the very least, it will allow you to alter your topic if you find out that it is not very well suited for your task.

Where to look four sources? A few simple ways suggest themselves:

  • Ask your teacher/professor. He/she may recommend a few classic publications to start your search with;
  • Go to the college library and study its index. Almost all modern libraries are equipped with sophisticated indices and search systems that make it easy to find what you need;
  • Consult your local librarians. It is their job to know books dedicated to all kinds of topics. Librarians specializing in particular disciplines (many large universities have such employees) are especially useful;
  • Use online academic search engines and databases. Some of them are specialized (such as MathSciNet and zbMath), others are universal (Google Scholar and Microsoft Academic are the two most obvious examples, although they are by far not the only ones);
  • Look through the bibliography sections of the sources you find. Just like you have to use references to other works in your writing, the authors of the publications you have already found had to do the same. Some of these references are bound to cover topics that are sufficiently relevant for your essay.

3. Evaluate the Quality of the Sources You Found

Sources of information used in academic vary greatly in terms of quality and trustworthiness. Some will add credibility to your work, while others will make your writing look immediately suspicious. Therefore, you should not blindly use any piece of information on the subject you can find. Before you start planning out your essay, check if the data you found can be relied upon. Although in mathematics it is rather unlikely that an author will follow an agenda that will twist his/her perception of the subject, there are many other ways to decrease the quality of a source.

Tired of all the guides and never-ending instructions?

When studying each publication, ask yourself:

  • Who is the author? Is he/she a specialist in the subject matter? What credentials does he/she have?
  • When was the source published? Were there any significant developments in the field since then?
  • Does his/her opinion agree with those of other authorities on the subject?
  • Does the author give references for the data and statistics he/she uses?

4. Narrow Down or Broaden the Topic

Now that you have a fair understanding of what to expect in terms of coverage but before you started writing per se, you have a chance to adjust the topic. Make sure it allows you to fully use the sources you found without setting too huge a goal you will not be able to achieve in such a small assignment as an essay. Think of everything we said concerning the choice of topic and make the necessary changes before proceeding.

How to Write an Informative Essay in Mathematics: What and How to Write

1. Start with a Plan

A plan or an outline is a must when writing an informative essay in mathematics. You are expected to give a full account of a certain topic, and due to the nature of the discipline, some information may be rendered in the form of formulas and calculations. This means that you should carefully plan where you will put them and how to organize the entire thing in a way that will allow you to maintain balance between textual content and calculations. Normally, the structure of an informative essay goes as follows:

  • Introduction – a hook to draw the audience’s attention, preliminary information on the topic, background information;
  • Body – each individual paragraph covers a separate aspect of the topic. Plan in what order you introduce them and how you connect paragraphs to each other;
  • Conclusion – you sum up everything you said up to this point and repeat the information in a shortened form.

2. Stick to the Purpose of Your Essay

Remember, you are not supposed to prove something or persuade your audience. You only have to provide information – objectively and comprehensively. If there are more than one point of view on the subject (although you are unlikely to see it very often in mathematics), you have to present all of them and treat them equally, even if you personally support one of them.

3. Maintain a Stable Structure in Each Paragraph

Each paragraph should be dedicated to a single aspect of the topic – if you find yourself drifting to something related, but distinctly different, put it in a separate adjoining paragraph and provide a logical connection between them. Make sure each paragraph contains at least one major supporting detail (preferably with a quotation).
Each paragraph should start with a topic sentence – a sentence that states and explains the main idea of the paragraph while establishing a logical connection with the preceding one. Also, make sure each paragraph is coherent in itself – i.e., it does not contain self-contradictory or irrelevant information.

4. Write a Rough Draft

Do not try to write an ideal essay the first time around – it may slow you down and prevent you from putting all the necessary information into the text. Instead, allow yourself to simply follow the plan and write down all your thoughts without worrying about how they tie in with each other. Your purpose right now is to create a more or less coherent whole to see if your work is going to need any serious alterations later.

5. Edit and Rewrite

Now that you have finished a rough draft, you can see if you need to make drastic changes: add more paragraphs, remove unnecessary parts, find additional information about some details, change the order of paragraphs and so on. Before you finish editing, ask yourself:

  • Did you provide comprehensive information on the subject?
  • Is all your information relevant?
  • Is the flow of your essay logical and smooth?
  • Did you cite enough sources?

If everything is alright, you may write a final draft, introducing final touches along the way.

How to Write an Informative Essay in Mathematics: Avoiding Common Mistakes

Half of the time success is not about achieving any particular qualities, but about avoiding common mistakes. You should keep an eye out for these while you write and spend some time hunting for them after you finish.

1. Rambling

The purpose of an informative essay is to provide definite, specific information about its topic. It is assumed that the audience is fully or partially ignorant about the subject matter, and you are expected to fill in the gaps in their knowledge. This means that your essay should be:

  • Focused – you may find interesting data about the subjects related to the topic but not dealing with it directly. Before you include it, ask yourself, “Is it really necessary to explain the topic”? If not, set it aside, no matter how fascinating it may be;
  • Organized – each paragraph should cover a single aspect of the topic, then you move on to another one and so on, finally summing things up in the conclusion. Do not jump all over the place, moving from one thing to another and getting back to what you started with;
  • Purposeful – all the information you include should follow a single goal.

2. Verbosity

An informative essay is supposed not just to teach and inform the audience about its subject matter. It should also do it in as laconic and concise a manner as possible. Your purpose is not to show how beautifully you can write. You should boil down what you know about the topic to as concentrated a state as possible and make sure there is nothing excessive about it. Therefore:

  • Cut everything you do not need to explain the nature of your topic. If you can explain something in a short formula instead of writing a few sentences, do it;
  • Prefer simple and short words to long and complicated ones;
  • Eliminate unnecessary words, phrases and sentences. Most adverbs and adjectives can be removed without any adverse effects for the bigger picture.

3. Imbalance

When you want to give a comprehensive account of something, it is very easy to pay too much attention to certain aspects of the topic and not enough to others. It is especially bad if you provide too much detail on minor issues while neglecting major ones. It can happen due to the lack of planning – you start writing with a certain level of detail and expect to maintain it throughout the essay, but discover halfway through that you already too close to your word limit and have to either omit certain aspects or give them a much more perfunctory description. To avoid it, start with important issues and plan ahead how much space you will dedicate to each of them. When proofreading, add or subtract content from individual paragraphs as necessary.

4. Failure to Cite Important Sources

Any topic has landmark works dedicated to it, and it is impossible to discuss this subject without mentioning and referring to them. When writing an informative essay on mathematics, it is your goal to identify them early on and make sure you rely on them in your work. If on rereading the essay you notice that you failed to mention some of them, find ways to do so and, preferably, insert quotations from them.

At a glance, writing an informative essay in mathematics may look like a confusing task. However, you can relatively easy deal with it if you carefully follow this guide.