Beginner · 11 notebooks
Stanisław Ulam and the Lwów School of Mathematics
Problems from the Scottish Book, worked with live interactives
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
- 47
- Language
- EN
Elena Marsh
Program
The notebooks
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
Open the Scottish Book. This free course follows Stanisław Ulam and the mathematicians of the Lwów School from the Polish city of Lwów (today Lviv) to Los Alamos, through the problems they set each other, and lets you try the ideas yourself in live interactives before you read the explanation.
How the course works
- Play. Each lesson starts from an interactive you can work with: a map of the journey, a set of notebook cards, a spiral of primes, a random experiment, a grid that grows.
- Read. A short story and explanation say what you found and where it came from. Every statement is checked against a published source and cited, and where careful sources disagree the lesson says so.
- Check yourself. Short quizzes tell you straight away what you got right.
What is in it
Eight modules: Lwów, the Lwów School and the Scottish Café, America and the war, Monte Carlo, the Teller–Ulam design (briefly), the prime spiral and cellular automata, Fermi–Pasta–Ulam–Tsingou, and Ulam's legacy and why this product is called ulams. A final test of 14 questions, a certificate, and a last lesson that lists every source and credits every photograph.
The course is free, open to everyone and takes about three and a half hours. The text is licensed CC BY 4.0.