InvariantMath

Mathematica Lab • Foundations & first notebook
Foundations: from zero to first notebook

This page is for anyone who has never opened Mathematica before. By the end, you should be able to open a notebook, run cells, understand basic syntax, and save your work without fear.

Step 0
Getting access

The Mathematica Lab assumes that you have access through a university licence or Wolfram Cloud. If you are not yet set up, ask a lecturer, a tutor, or the platform maintainers for the current instructions.

  • • Install Mathematica Desktop or log in to Wolfram Cloud.
  • • Open a new blank notebook.
  • • Type your name and “Mathematica Lab foundations” on the first line as a comment.
🌱 Absolute beginner friendly 🕒 10–15 minutes
Step 1
Cells, input, and output

In Mathematica, everything happens inside cells. Each input cell starts with In[ ]:= and produces an output labelled Out[ ]= when you evaluate it.

Type the following in one cell and press Shift + Enter: 

2 + 3
2^10
Sin[Pi/4]

You should see the outputs appear directly under the input. Each time you run a cell, Mathematica updates the input and output numbers.

Keyboard habits
Shift + Enter — run current cell Alt + Enter — run and create new cell Ctrl + Z — undo
  • You can run a cell and see output without panicking.
  • You can tell which part of the notebook is “input” and which is “output”.
Step 2
Syntax: brackets, lists, and function names

Mathematica is strict but consistent:

  • • Round brackets ( ) for grouping.
  • • Square brackets [ ] for function arguments.
  • • Curly brackets { } for lists.
  • • Function names start with a capital letter: Sin, Exp, Log, Sqrt.

Try these in a new notebook:

Sqrt[2]
Exp[1]
Log[10]

{1, 2, 3, 4}
Mean[{1, 2, 3, 4}]

If you forget a bracket, Mathematica usually shows a red underline or an error message. Click at the end of the line and count the brackets carefully.

  • You understand why Sqrt[2] is correct but Sqrt(2) is not.
  • You can create a list and apply a function like Mean to it.
Step 3
Your first plots

Visual intuition is important. Mathematica makes it easy to see the shape of a function.

Type and run:

Plot[Sin[x], {x, 0, 2 Pi}]

Plot[Exp[-x^2], {x, -3, 3}]

Change the interval or the function and re-run the cell. Try to match plots with the curves you know from calculus.

📈 Connects to Calc I sketching 🕒 15 minutes of play
  • You can change the function and the interval and re-run the plot.
  • You know where to look if the plot does not appear (check for errors above).
Step 4
Getting help the right way

Instead of searching the internet blindly, start with built-in help: 

?Integrate
??Plot

Run these in a notebook. A small help window appears with usage examples. Learn to scan the examples and copy the pattern you need.

In addition, use:

  • • The Documentation Center (desktop) or “Reference” tab (cloud).
  • • Autocomplete suggestions: type Inte and pause.
  • You can find the syntax for a function you do not remember exactly.
  • You can adapt an example from the documentation to your own problem.
Step 5
Saving, naming, and reopening notebooks

A well-organised notebook is part of being a serious student.

  • • Use File → Save As… and name your file with the date and topic:
2025-UI-Mathematica-Lab-Foundations.nb
  • • Keep all Mathematica files in a single “InvariantMath Mathematica Lab” folder.
  • • When you return, open the same notebook and continue your work instead of starting a new one every time.
  • You can save, close, and reopen the notebook without losing anything.
  • You can tell which notebook belongs to which course or lab session from the file name.