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.
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:
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:
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:
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.
When studying each publication, ask yourself:
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.
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:
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.
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.
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.
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:
If everything is alright, you may write a final draft, introducing final touches along the way.
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.
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:
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:
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.
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.