When I was a graduate student, math was one of the toughest subjects for me. Solving complex calculations can be overwhelming, and writing investigations is also time-consuming if you don’t follow the correct pattern.

However, writing an error-free mathematical investigation is a skill that every graduate and post-graduate student must have.

You’re in luck if you want to know how to write a mathematical investigation. This post will help you understand all about it for easy mathematics learning.

You might also enjoy reading: Best Ways to Learn Calculus (With helpful tips)

**Prerequisites For Writing A Mathematical Investigation**

Before learning how to write a mathematical investigation, you must know the essential requirements. If you don’t follow these guidelines, the professor will reject your report, wasting all your efforts.

So here are the primary requirements for writing a mathematical investigation:

**1- Everything Must Be Typed**

A mathematical investigation must be typed regardless of whether you can properly use tech tools. This **includes all text reasoning, math calculations, graphs, and labeling. You must also type the correct symbols when creating a report**.

**Microsoft Word is the top platform for writing a mathematical investigation because you can easily insert various symbols in Word**. This app will allow you to put calculations and use math language appropriately.

**2- Graphs Must Appear Professional**

This is one of the confusing requirements of writing a math report. I initially struggled with it but improved after submitting various investigations during my education life.

By professional appearance, it means your graph must be created using the app’s tools instead of hand drawing.

The diagram must also be labeled using appropriate math terms to avoid confusion. You should also ensure that the graph and its explanation must be on the same page.

**If you’re low on space, you must ensure that the explanation is placed on the page before the graph.**

### 3- **Precise Language And Units**

**Many mathematical parameters have specific units attached to them. If you use them in your investigation, you must ensure consistency. Another important aspect is maintaining the tone of your report**.

The mathematical investigation must be typed using clear language with the correct terms. You will suffer from a low grade if you use general phrases for solving a question or describing something. **It is necessary to use conventional terms for every element.**

**How To Write A Mathematical Investigation?**

Once you understand the primary requirements, you can start writing your mathematical investigation. Your report must include:

- Title
- Abstract
- Body
- Sources
- Appendices (optional)

Here’s what you must do while writing the report:

**1- Create A Title**

You may have gotten used to getting titles for every report you were assigned during school life. However, the same does not happen at the graduate or post-graduate level. Instead, you must make an effort to form unique titles for your mathematical investigations.

It is essential to give a brief title to your report relevant to its content. Otherwise, you will lose marks unnecessarily.

Your name must also be written in this section, along with the course title. **The date of submission must also be typed on the page.**

**2- Form An Abstract**

**Another confusing part of writing a mathematical investigation is writing the abstract. This is because this report portion is written at the end but placed right after the title.** You must understand that the abstract is just a fancy name for the summary of the investigation.

Check out this quick guide on how to write an abstract.

The key points of your investigation must be emphasized in your abstract in no more than two paragraphs. One paragraph will also be sufficient if you include all the relevant things. These include the things you attempted in the investigation and if you used any special techniques.

You must also include the significant results to ensure readers can grasp the investigation’s calculations without diving into the details. However, you must not slack while writing the body.

The mathematical investigation must be easy to grasp for those who skip the abstract section. Similarly, **the summary must be clear and well-developed to allow people to comprehend the investigation even if they skip the body section.**

**3- Body**

The body of a mathematical investigation must be divided into five sections:

- Introduction
- Theory
- Analysis
- Results and Discussion
- Conclusions

It is essential to remember that these five parts must not be written as different subheadings.

Instead, the body must be written in an essay form with different paragraphs targeting these five things:

**1- Introduction**

**The introduction must include the question or problem you will explain in the investigation. You should also give the reason behind the problem.**

The information must be a general overview but interesting enough to encourage others to read further.

**It is also best to set objectives in the introduction so that your readers know what to expect from the investigation.** This is also necessary because you will have to relate your results to the objectives at the end.

#### 2- **Theory**

**Your theory section must target an overview of ideas you’ll use to explain the problem**. This part must be short but clear enough to give the readers some background information.

The theory section is also relevant to the analysis part.

**3- Analysis**

**This will be the most detailed part of your mathematical investigation because you must relate your earlier general theory to the problem you specified in the introduction**. All derived results must be referenced in this part for better understanding.

However, you don’t have to repeat the results unless they allow you to help the readers understand better. So you will have to decide whether you should derive the concepts and formulae again or not.

**4- Results And Discussion**

This is a follow-up to your analysis section and must include a summary of your results. You should also display your own interpretation of the results. For instance, **mention the things that were expected after solving the problem.**

You may also target the results that were unforeseen or interesting. It is also advisable to consider questions that may come to the reader’s mind after reading your analysis section. Then, formulate the answers to such questions and mention them in this section.

Remember, you don’t have to create questions or write them as subheadings. Instead, you should put yourself in your readers’ shoes to determine things that have not yet been answered in your investigation.

This will help you ensure that the reader will not have to make an extra effort to understand the calculations or problem-solving process.

**5- Conclusions**

**A conclusion marks the last part of your body and must explain how your solved problem meets the goals you set in the introduction**.

The main highlight of this section is that you will not write any new information in it. Instead, **it will follow the earlier parts and help the reader better understand the investigation’s purpose.**

**Sources**:**The sources section is not time-consuming and refers to the references you used for writing the report**. Sometimes it may be sections of your own text. However, you must cite external sources if you use any.**Appendices**: This optional section applies to only some mathematical investigations.**It can include calculation samples, symbols with meanings, units, and original questions.**

**What to read next: **

- 5 Best Graphing Calculators (And how to pick the best one!)
- Top 9 Teaching Strategies In Mathematics For Improved Students Engagement.
- Is Calculus Harder Than Algebra? (Here’s the definite answer!)

**Final Thoughts **

This is a detailed explanation of how to write a mathematical investigation. You must ensure that no text is plagiarized in the report because plagiarism is a serious offense.

It will also get your investigation rejected, and you may suffer other consequences.