Computational Mathematics · Quick Reference

Mathematical Visualization Cheat Sheet

Computational Mathematics · Lesson 5/6

In one line: turning numbers and equations into pictures — graphs, plots, and charts — often reveals patterns and insights that raw numbers alone can hide.

Key Ideas

1Why Visualize Math. A well-made graph can reveal trends, outliers, and relationships far faster than scanning a table of numbers.

2Line Plots. Show how a value changes continuously, ideal for functions like y=sin(x) or a dataset changing over time.

3Scatter Plots. Show individual data points without connecting them, ideal for spotting correlation or clusters between two variables.

4Bar Charts and Histograms. Bar charts compare categories; histograms show the distribution of a single numeric variable by grouping values into bins.

5Common Plotting Tools. Python's matplotlib is the most widely used plotting library; plt.plot() draws line plots, plt.scatter() draws scatter plots, and plt.hist() draws histograms.

Worked Examples

You want to plot y=x^2 for x from -5 to 5. What type of plot is most appropriate?

A line plot (using plt.plot())

You have exam scores for 100 students and want to see the distribution. What type of plot is best?

A histogram (using plt.hist())

You want to check if there's a relationship between study hours and exam scores for 50 students. What plot type is best?

A scatter plot (using plt.scatter())

Formulas

plt.plot(x, y) draws a line plot

plt.scatter(x, y) draws a scatter plot

plt.hist(data) draws a histogram

Practice Yourself

What plot type is best for showing a continuous function like y=sin(x)?

A line plot

What plot type is best for comparing sales across 5 different products?

A bar chart

What plot type shows the distribution of a single numeric variable?

A histogram