free course · five live interactives
Open the Scottish Book
Mathematics and history, with live interactives you can play with.
Follow the mathematicians of the Lwów School through the problems they set each other, and try the ideas yourself in live interactives.
- Level
- Beginner
- Length
- Self-paced
- Topics
- 47in 11 lessons
Five interactives
Play with the mathematics
Each one runs in your browser and has a text version.
Explore
The Ulam spiral
Wind the integers into a square spiral and look at where the primes fall.
Simulate
Monte Carlo
Estimate pi by throwing random points and watch the estimate settle.
Experiment
Cellular automata
Change a rule and see what a grid of cells grows into.
Read
The Scottish Book
Browse problems from the notebook, with their statements and sources.
Travel
The Lwów map
Follow a route through the city where the problems were written.
Notebooks
The course, notebook by notebook
Short notebooks you can read in order or jump between.
11 lessons · 47 topics · about 6 h of material
- MOD 0013 min
Welcome
What the course is, how to read it and how every fact is checked.
ReadingInteractive
- MOD 0131 min
Lwów
A boy from Lemberg and a student of Kuratowski, up to the invitation to Princeton in 1935.
- 1.1 A boy from Lemberg
- 1.1 Lwów on the map
- 1.2 Kuratowski's student
- Timeline: from 1909 to 1935
- Quiz: Lwów
ReadingInteractiveQuiz
- MOD 021 h 2 min
The Lwów School and the Scottish Café
The mathematicians of the Lwów School, the café where they met and the notebook of problems they filled.
- 2.1 The Lwów School
- Seven people of the Lwów School
- 2.2 The café and the book
- 2.2 Cards from a notebook
- 2.3 Famous problems
- 2.3 Guess the outcome
- Quiz: the café and the book
ReadingInteractiveQuiz
- MOD 0343 min
America and the war
Princeton, Harvard, the last weeks in Poland and the years in Madison, until the call to Los Alamos.
- 3.1 Princeton and Harvard
- 3.1 Princeton and Cambridge
- 3.2 August 1939
- Why sources differ
- 3.3 Madison and the family's fate
- 3.3 Madison and Los Alamos
- Quiz: America and the war
ReadingInteractiveQuiz
- MOD 0448 min
Monte Carlo
A game of solitaire, an early computer and a method that estimates answers by chance. Then throw the points yourself.
- 4.1 From solitaire to the ENIAC
- 4.1 The idea: ask the dice
- 4.2 Estimate π yourself
- 4.2 Throw the points
- Practice: estimate the error after N throws
- Quiz: Monte Carlo
ReadingInteractiveQuiz
- MOD 0512 min
Los Alamos, briefly: the Teller–Ulam design
Who proposed what in 1951, when it was first tested and why credit was disputed. Short and factual.
ReadingInteractiveQuiz
- MOD 0656 min
Patterns: the spiral and cellular automata
The prime spiral, Ulam's growth rule and the grids that grow by simple rules. Build them yourself.
- 6.1 The prime spiral
- 6.1 Build the spiral
- Steps: draw a spiral by hand
- 6.2 Grids that grow
- 6.2 Rules that grow
- Quiz: the spiral and growing grids
ReadingInteractiveQuiz
- MOD 0724 min
Fermi–Pasta–Ulam–Tsingou
One of the first experiments done on a computer, a surprise, and the name of the programmer that was added in 2008.
- 7.1 The first numerical experiment
- 7.1 A program as an experiment
- Timeline: from Fermi's death to the new name
- Quiz: Fermi–Pasta–Ulam–Tsingou
ReadingInteractiveQuiz
- MOD 0833 min
Legacy and the name
Other ideas that carry Ulam's name, his later career and why this product is called ulams.
- 8.1 Other ideas that carry his name
- 8.1 The last stops
- Six ideas that carry his name
- 8.2 Why ulams
- Quiz: legacy and the name
ReadingInteractiveQuiz
- MOD 0920 min
The final test
Fourteen questions across the eight modules. You need 70% and have two attempts.
Quiz
- MOD 1010 min
Sources and licence
Where every statement comes from, the licence of the course text, the credits of the photographs and how to report a mistake.
Reading
In the course
Free, cited, certified
Open to everyone in this demo.
Badge 1
Free
No payment and no card.
Badge 2
Cited
Every historical claim links to a source.
Badge 3
Certificate
A certificate when you finish the course.
Where the history comes from
Every statement of a lesson is checked against a published source and cited
Where sources disagree the lesson says so, and the quizzes never ask about the disputed point
The last lesson lists every source and credits every photograph
Course text is licensed CC BY 4.0
Questions
Before you start
Is the course free?
Yes. Every lesson, quiz, the final test and the certificate are free.
Do I need advanced mathematics?
No. The interactives let you meet each idea by doing it first, and the text explains it in plain language.
Where do the facts come from?
From published sources, named in every lesson and listed together in the last one. Where careful sources disagree, the lesson says so.
Why is the product called ulams?
ULAMS is named in tribute to the mathematician Stanisław Ulam (1909–1984), the subject of this course. The project is not affiliated with or endorsed by his estate, Los Alamos National Laboratory or any institution associated with him.