Residue: Mathematics

Residue is mathematics you do, not read. Every problem is generated on your device and checked before you see it, and one you have solved is not served to you again. FOUR WAYS TO PLAY • Crucible: modular powers, Diophantine equations, power sums, counting, inequalities, geometry, polynomials, trigonometry and linear algebra, at a tier that follows your recent results. Sprint puts it against the clock, with a countdown on the Lock Screen. • Chromatic Ramsey: colour every edge of a complete graph without making a forbidden shape in one colour. Hints name an edge and the reason for its colour. Two boards cannot be won, and finding out why is the lesson. • Spoof Hunt: a derivation reaches something false. Exactly one step is illegal. Find it. • Daily Conundrum: one problem a day, the same on every device, with a streak to keep. ANSWERS, NOT GUESSES • No multiple choice. Answer on the pad the problem needs: a whole number, a fraction, a root or a multiple of π. Grading is exact. • Stuck? A lemma reveals the next rung of the argument, not the answer. Once you solve, the whole ladder is yours. • Work it out on the scratchpad. Circle your answer and it goes into the pad for you to check. • Geometry problems draw their figure, and can show a helpful construction. THEOREMS Sixteen theorems behind the problems, from Euclid's primes to Ptolemy and the roots of unity, each with a proof, a step by step ladder and a sandbox to play in. Search them by what they are about. EVERYWHERE • Export a solved problem and its ladder as a PDF or a LaTeX file. • Widgets for the Home Screen, the Lock Screen and iPad. • An Apple Watch drill answered with the Digital Crown, and complications for your rating and your streak. • Your Daily record and progress follow you across devices through iCloud. • In English and Japanese. VoiceOver reads every problem. FREE, WITH PLANS Residue is free with ads, and three free lemmas a day; a short video buys one more. Two optional subscriptions, in one group: • Ad-Free (yearly) removes the ads and keeps the three free lemmas a day. • Residue Plus (monthly or yearly) removes the ads, makes lemmas unlimited, opens every theorem and exports clean copies. Prices are shown in the app before you buy. Subscriptions renew automatically unless cancelled at least 24 hours before the end of the period, and are managed in your App Store account settings. Terms of Use (EULA): https://www.apple.com/legal/internet-services/itunes/dev/stdeula/ Terms: https://marsstudio.app/residue/terms Privacy Policy: https://marsstudio.app/residue/privacy