NAMSSN UI Chapter

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

This page is for the student 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 the university licence or Wolfram Cloud. Ask your lecturer or NAMSSN executives for the current instructions if you are not yet set up.

  • • 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 “NAMSSN 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.