By Rozita Rashtchi, PhD Student Systems & Computer Engineering

It is almost impossible to write a thesis in a scientific or engineering discipline without mathematical expressions. These expressions may contain mathematical functions, symbols, parameters, numbers, units or any combination of them.  For those of you who are writing your thesis, here are some brief guidelines on how to write these mathematical expressions

Keep in mind that your discipline may have slightly different or additional requirements, so always doublecheck with your supervisor.

Formatting Mathematical Equations

A mathematical expression usually contains several parameters.  All the parameters in the thesis have to be defined on their first appearance. However, they shouldn’t be the first word of any sentence. The following tips on formatting equations can help you in writing your mathematical expressions.

  • Mathematical parameters should be written in italics, (not only in the equation itself but everywhere in the thesis), but not units, numbers and mathematical functions like logarithms.
  • Use the same font size for mathematical expressions as the font size of the text.
  • The equations that are written on a separate line are either indented or centred, but done consistently throughout the thesis.
  • Some equations are long and tend to be multi-line equations. If an equation breaks to multiple lines, align them properly and use only one number for the whole equation as far to the right as possible.
  • Provide some vertical space above and below the equations that are displayed in separate lines.
  • Equations are regarded as being a part of the text, and are punctuated accordingly. If it is the end of a sentence, there should be a period at the end of the equation; otherwise put a comma at the end of it.
  • Do not capitalize or indent “where” or “with” when listing variables following an equation.

Numbering

There are two types of equations in a thesis: those which are going to be referred and those which are not. The first type of equation should be numbered consecutively (or chapter-based) through the whole thesis, whereas the second type can be either included in the running text if they are short and don’t break the flow of the sentence, or in a separate line without an equation number, if they are long and more complex. For numbering the first type of equations, i.e., those which are going to be referred somewhere in the thesis, here are some useful tips:

  • The equation numbers should be enclosed by parentheses and placed at the right-hand side of the page.
  • If you are referring to an equation in the text, use eq. (3) (or other abbreviations). If it is the first word in a sentence, capitalize it, i.e., Eq. (3). It is also pretty normal to refer to an equation in the text with only its number within parentheses, like “(3)”. In this case, if it is the first word in the sentence, spell out “Equation” before the number, like “Equation (3)”.

Units

In a scientific or engineering thesis, it is very common to present the result of experiments, measurements or simulations. In all these cases, you need to provide numbers with their units. The following tips can help you to write them properly:

  • The number and its unit should be followed on the same line.
  • There should be a space between the number and the unit. There should also be a separator (space or /) between units when they appear together (as a product or division). However, there should be no space between the letters of units like millimeter “mm”.
  • There shouldn’t be a space between a number and the percent, angular degree, angular minute, or angular second symbols (e.g. 35%, 90°, 15′, 4″).
  • Use proper characters (sometimes special characters) for mathematical symbols.
  • Units that accompany numbers should be abbreviated, like “10 m” but they should be spell out when they do not accompany numbers, like “a few meters”.

Writing mathematical expressions without using an appropriate editor is difficult and sometimes impossible. Also, the result of not using it nearly always looks unprofessional. Microsoft Word comes with an equation editor which makes it easy to write almost any kind of equation. The other possibility is to use LaTex which is a document preparation system developed specially for mathematical writing.

For more information on LaTex formatting check out this document .

Other articles in this series can be found in our Grad Student Blog section.

4 thoughts on “How to Use Mathematical Equations in Your Thesis”

  1. It’s surprising to find on carleton.ca a resource so precious about equations.

    We will note your page as a benchmark for How to Use Mathematical Equations in Your Thesis.

    We also invite you to link and other web resources for equations like http://equation-solver.org/ or https://en.wikipedia.org/wiki/Equation.
    Thank you ang good luck!

  2. gta 5 hack says:

    Good post. I learn something totally new and challenging on sites I stumbleupon everyday.

    It’s always useful to read through articles from other writers and use a little something from their websites.

  3. ind on carleton.ca a resource so precious about equations.
    We will note your page as a benchmark for How to Use

  4. Paul says:

    Thanks for creating this… its really helpful –
    I think there’s just a slight mistake when it comes to the percent sign:
    https://english.stackexchange.com/questions/3281/should-there-be-a-space-before-a-percent-sign

    Best way to do it is afaik the LaTex small space holder “\,”

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