Dot products
A PDF reader for studying on your Mac
Give yourself
a little space to think
Margin is a PDF reader specifically designed for dense technical texts where every sentence matters.
Apple silicon · M1 or newer
See how Margin works.
Finding your place
No more scattered notes
Every note organized
Your notes show up on a mini-map of the textbook for you to jump right back in.
Direction and angles
2.1 Vectors as arrows
2.2 Perpendicular vectors
Applications
3.1 Comparing vectors
3.2 Finding similar text
Click a line to explore. Choose a dot to revisit a note.
Scratchpads
Stitch hard ideas
together.
Hard topics are just many little topics chained together. Scratchpads let you collect scattered notes into a cohesive picture.
This is interactive, try it out!
Example scratchpad
I can follow the calculation. Here’s how I’ll remember it.
Note from p. 12Dot product: multiply the matching pairs, then add.
So (1, 2) · (3, 4) becomes 1 × 3 + 2 × 4 = 11.
Note from p. 18What does the dot product tell me about these vectors?
Next: draw these two vectors and compare their directions.
My explanation
A dot product gives me one number. I know how to calculate it; now I want to understand what it means.
What I’ll try next
I’ll draw two perpendicular vectors and work out their dot product. Then I’ll compare that with two vectors pointing the same way.
My prediction: changing the directions will change the result.
Editable example. Your changes stay in this demo and reset when you reload. Use the toolbar to format text. Select a linked note to remove it; Undo restores it.
Dot product: multiply the matching pairs, then add.
What does the dot product tell me about these vectors?
Draw, connect, explore — with Excalidraw.
Collect notes from different pages. Add your own thinking around them.
Built for studying on your Mac.
Familiar controls.
Use Mac shortcuts and trackpad gestures. Keep books open in tabs or separate windows.
Your work stays on your Mac.
Your PDF stays in its original location. Margin saves your notes and scratchpads on your Mac.
Study offline.
Read, write, and sketch without an internet connection or a Margin account.
Margin for Mac
One purchase.
No subscription.
Try every feature free for 14 days. Take notes in your own PDFs before you decide.
Try it for free
No credit card. No automatic charge.
Apple silicon · M1 or newer
Before you get started.
Will it work with my textbooks?
Margin opens PDFs from your Mac. PDFs with selectable text work best for placing notes precisely. Scanned pages and complex layouts may offer fewer places to add notes. It supports documents up to 2,000 pages and 300 MB.
Which Macs can run Margin?
Margin runs on Apple silicon Macs (M1 or newer). The current release does not support Intel Macs.
Where are my notes saved?
Your notes and scratchpads are saved locally in the Margin workspace on your Mac. Your PDF stays at its original location. Keep that file available and back up your workspace to keep your study work safe.
Do I need a subscription or an account?
No subscription and no Margin account. Try Margin free for 14 days, then buy it for $39 USD once if you want to keep using it. Reading and writing work offline. You’ll need an internet connection to download the app, purchase, and activate or periodically verify your license.
How does the free trial work?
Your 14-day trial starts when you first open Margin. Try all the features with your own PDFs, without an account or credit card. There is no automatic charge. After the trial, buy a $39 USD license to keep using Margin. Your work is kept, and you can still export it if you choose not to buy.
Resources
A few
good books.
Free textbooks, shared by independent authors and universities. These links take you to their websites.
With thanks to the people who make learning more accessible.
Explore all resources-
Introduction to Applied Linear Algebra — authors’ website, opens in a new tab
Build an intuition for vectors, matrices, and least squares.
stanford.eduFree PDF
-
Operating Systems: Three Easy Pieces — authors’ website, opens in a new tab
See how computers manage programs, memory, and files.
wisc.eduFree chapter PDFs
-
Algorithms — author’s website, opens in a new tab
Explore recursion, graph algorithms, and ways to solve problems.
illinois.eduFree PDF
-
The Little Book of Semaphores — author’s website, opens in a new tab
Work through concurrency puzzles, with hints along the way.
greenteapress.comFree PDF
-
Open Textbook Library — library website, opens in a new tab
Browse free, openly licensed textbooks across many subjects.
open.umn.eduFree textbook library
Your PDF textbooks
deserve an upgrade.
Bring your next book. Make room for your thinking.
$39 one-time payment. 14-day free trial.
Releases
View all releasesv1.4.0
- Notes in multicolumn PDFs: Add notes within multicolumn textbooks and research papers.
v1.3.3
- Add notes more precisely beneath headings, captions, images, and equations.
v1.3.0
- Added a two-page view for reading pages side by side.
v1.1.0
- Added a website link to About Margin.
- Improved the macOS installation experience.
v1.0.0
- Introduced Margin for Mac: read PDF textbooks with inline notes, highlights, and bookmarks.
- Connect textbook notes to scratchpads with writing and canvas views.
- Organize books in a visual library and work across multiple tabs and windows.
- Keep your notes, scratchpads, and reading progress saved locally on your Mac.