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- पूर्व-प्राथमिक–कक्षा 2Boxes inside boxesWhat is inside a box that contains only an empty box? Is it empty? And can every description you can think of make a collection?यहाँ से शुरू होता है संग्रह →SetsRussell's paradox and why sets need axiomsZFC: axiomatic set theoryपथ पर चलें
- कक्षा 6–8How many infinities?There are infinitely many counting numbers and infinitely many infinite 0–1 sequences. Are these two infinities the same size?यहाँ से शुरू होता है Sets →Countability and Cantor's diagonal argumentपथ पर चलें
- कक्षा 6–8Clock arithmeticIt's 9 o'clock. What time will it be in 5 hours — and in 29 hours? Can a clock teach us a whole new kind of arithmetic?यहाँ से शुरू होता है Integers →Clock arithmetic: remainders and modular arithmeticCongruencesQuotient groups and quotient ringsपथ पर चलें
- कक्षा 6–8Inverses and structureEvery integer can be added to another integer to get . So why can almost no integer be multiplied by another integer to get ?यहाँ से शुरू होता है Integers →Algebraic structures: monoids, groups and ringsGroupsRings, ideals and fieldsपथ पर चलें
- कक्षा 6–8Remainder familiesSort every integer — positive, negative and zero — into families by its remainder after dividing by 3. If you add a member of one family to a member of another, does the family of the answer depend on which members you chose?यहाँ से शुरू होता है Integers →Relations, equivalence relations and partitionsCongruencesQuotient groups and quotient ringsपथ पर चलें
- कक्षा 9–12The product, by its mapsCan you describe the set of pairs without ever looking inside it — only by how functions go into it?यहाँ से शुरू होता है Functions →Universal propertiesLimits and colimitsपथ पर चलें
- कक्षा 9–12Arrows that composeWhat do functions between sets, maps between groups and continuous maps between shapes have in common? What if we studied only the arrows?यहाँ से शुरू होता है Composition →CategoriesFunctorsपथ पर चलें