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"lensParentId": "", "pathPages": [], "learnMoreTaughtMap": {}, "learnMoreCoveredMap": {}, "learnMoreRequiredMap": {}, "editHistory": {}, "domainSubmissions": {}, "answers": [], "answerCount": 0, "commentCount": 0, "newCommentCount": 0, "linkedMarkCount": 0, "changeLogs": [], "feedSubmissions": [], "searchStrings": {}, "hasChildren": false, "hasParents": false, "redAliases": {}, "improvementTagIds": [], "nonMetaTagIds": [], "todos": [], "slowDownMap": null, "speedUpMap": null, "arcPageIds": null, "contentRequests": {} }, "2vv": { "likeableId": "1787", "likeableType": "page", "myLikeValue": 0, "likeCount": 4, "dislikeCount": 0, "likeScore": 4, "individualLikes": [ "12y", "267", "31s", "5" ], "pageId": "2vv", "edit": 1, "editSummary": "", "prevEdit": 0, "currentEdit": 1, "wasPublished": true, "type": "comment", "title": "\"Might one of the following ...\"", "clickbait": "", "textLength": 859, "alias": "2vv", "externalUrl": "", "sortChildrenBy": "recentFirst", "hasVote": false, "voteType": "", "votesAnonymous": false, "editCreatorId": "2nj", "editCreatedAt": "2016-03-26 22:11:31", "pageCreatorId": "2nj", "pageCreatedAt": "2016-03-26 22:11:31", "seeDomainId": "0", "editDomainId": "1", "submitToDomainId": "0", "isAutosave": false, "isSnapshot": false, "isLiveEdit": true, "isMinorEdit": false, "indirectTeacher": false, "todoCount": 0, "isEditorComment": false, "isApprovedComment": true, "isResolved": false, "snapshotText": "", "anchorContext": "", "anchorText": "", "anchorOffset": 0, "mergedInto": "", "isDeleted": false, "viewCount": 691, "text": "Might one of the following examples work?\n\nThe Riemann hypothesis asserts that the real part of every non-trivial zero of the Riemann zeta function $\\zeta(s) = \\sum_{n=1}^\\infty \\frac{1}{n^s}$ is equal to $\\frac{1}{2}$.\n\n(Stealing from Wikipedia): A sequence of groups and group homomorphisms $G_0 \\xrightarrow{f_1} G_1 \\xrightarrow{f_2} G_2 \\xrightarrow{f_3} \\cdots \\xrightarrow{f_n} G_n$ is called *exact* if $\\text{im}(f_k) = \\text{ker}(f_{k+1})$ for $0 \\le k < n$.\n\n(Also paraphrased from Wikipedia): Given an $n\\times n$ matrix $A$ whose elements are $a_{i,j}$, we can define the determinant $\\det(A) = \\sum_{\\sigma\\in S_n}\\text{sgn}(\\sigma) \\prod_{i=1}^n a_{i,\\sigma_i}$ where $S_n$ is the symmetric group on $n$ elements.\n\nI'm a bit worried, though, that \"standard research notation\" in one discipline is foreign to mathematicians in other disciplines.", "metaText": "", "isTextLoaded": true, "isSubscribedToDiscussion": false, "isSubscribedToUser": false, "isSubscribedAsMaintainer": false, "discussionSubscriberCount": 0, "maintainerCount": 0, "userSubscriberCount": 0, "lastVisit": "", "hasDraft": false, "votes": [], "voteSummary": null, "muVoteSummary": 0, "voteScaling": 0, "currentUserVote": -2, "voteCount": 0, "lockedVoteType": "", "maxEditEver": 0, "redLinkCount": 0, "lockedBy": "", "lockedUntil": "", "nextPageId": "", "prevPageId": "", "usedAsMastery": false, 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"learnMore": [], "requirements": [], "subjects": [], "lenses": [], "lensParentId": "", "pathPages": [], "learnMoreTaughtMap": {}, "learnMoreCoveredMap": {}, "learnMoreRequiredMap": {}, "editHistory": {}, "domainSubmissions": {}, "answers": [], "answerCount": 0, "commentCount": 0, "newCommentCount": 0, "linkedMarkCount": 0, "changeLogs": [], "feedSubmissions": [], "searchStrings": {}, "hasChildren": false, "hasParents": false, "redAliases": {}, "improvementTagIds": [], "nonMetaTagIds": [], "todos": [], "slowDownMap": null, "speedUpMap": null, "arcPageIds": null, "contentRequests": {} }, "3fr": { "likeableId": "2474", "likeableType": "page", "myLikeValue": 0, "likeCount": 2, "dislikeCount": 0, "likeScore": 2, "individualLikes": [ "267", "5" ], "pageId": "3fr", "edit": 2, "editSummary": "", "prevEdit": 1, "currentEdit": 2, "wasPublished": true, "type": "comment", "title": "\"I suggest we can assume tha...\"", "clickbait": "", "textLength": 418, "alias": "3fr", "externalUrl": "", "sortChildrenBy": "recentFirst", "hasVote": false, "voteType": "", "votesAnonymous": false, "editCreatorId": "12y", "editCreatedAt": "2016-05-06 18:04:22", "pageCreatorId": "12y", "pageCreatedAt": "2016-05-06 16:42:24", "seeDomainId": "0", "editDomainId": "1", "submitToDomainId": "0", "isAutosave": false, "isSnapshot": false, "isLiveEdit": true, "isMinorEdit": false, "indirectTeacher": false, "todoCount": 0, "isEditorComment": false, "isApprovedComment": true, "isResolved": false, "snapshotText": "", "anchorContext": "", "anchorText": "", "anchorOffset": 0, "mergedInto": "", "isDeleted": false, "viewCount": 515, "text": "I suggest we can assume that almost everyone in Math 3 is familiar with either calculus concepts or discrete math concepts, but we can't assume abstract algebra or number theory or real analysis, etc.\n\nSo the zeta function equation would be a fair example (one might want to state that $s$ is complex), but the other two would not. Another fair example might be L'Hopital's Rule or the Fundamental Theorem of Calculus.", "metaText": "", "isTextLoaded": true, "isSubscribedToDiscussion": false, "isSubscribedToUser": false, "isSubscribedAsMaintainer": false, "discussionSubscriberCount": 0, "maintainerCount": 0, "userSubscriberCount": 0, "lastVisit": "", "hasDraft": false, "votes": [], "voteSummary": null, "muVoteSummary": 0, "voteScaling": 0, "currentUserVote": -2, "voteCount": 0, "lockedVoteType": "", "maxEditEver": 0, "redLinkCount": 0, "lockedBy": "", "lockedUntil": "", "nextPageId": "", "prevPageId": "", "usedAsMastery": false, "proposalEditNum": 0, "permissions": { "edit": { "has": false, "reason": "You don't have domain permission to edit this page" }, "proposeEdit": { "has": true, "reason": "" }, "delete": { "has": false, "reason": "You don't have domain permission to delete this page" }, "comment": { "has": false, "reason": "You can't comment in this domain because you are not a member" }, "proposeComment": { 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"sortChildrenBy": "recentFirst", "hasVote": false, "voteType": "", "votesAnonymous": false, "editCreatorId": "4c1", "editCreatedAt": "2016-06-18 18:17:11", "pageCreatorId": "4c1", "pageCreatedAt": "2016-06-18 18:17:11", "seeDomainId": "0", "editDomainId": "1", "submitToDomainId": "0", "isAutosave": false, "isSnapshot": false, "isLiveEdit": true, "isMinorEdit": false, "indirectTeacher": false, "todoCount": 0, "isEditorComment": false, "isApprovedComment": true, "isResolved": true, "snapshotText": "", "anchorContext": "", "anchorText": "", "anchorOffset": 0, "mergedInto": "", "isDeleted": false, "viewCount": 439, "text": "[@12y] I think that's a fair assumption for the moment. Later as Arbital grows the requisites can be refined to Calculus 0, 1, 2, 3; abstract algebra 0, 1, 2, 3 etc. Or else pages can just make use of specific pages as requisites (e.g. do you know what a 'group homomorphism' is).", "metaText": "", "isTextLoaded": true, "isSubscribedToDiscussion": false, "isSubscribedToUser": false, "isSubscribedAsMaintainer": false, "discussionSubscriberCount": 1, "maintainerCount": 1, "userSubscriberCount": 0, "lastVisit": "", "hasDraft": false, "votes": [], "voteSummary": null, "muVoteSummary": 0, "voteScaling": 0, "currentUserVote": -2, "voteCount": 0, "lockedVoteType": "", "maxEditEver": 0, "redLinkCount": 0, "lockedBy": "", "lockedUntil": "", "nextPageId": "", "prevPageId": "", "usedAsMastery": false, "proposalEditNum": 0, "permissions": { "edit": { "has": false, "reason": "You don't have domain permission to edit this page" }, "proposeEdit": { "has": true, "reason": "" }, "delete": { "has": false, "reason": "You don't have domain permission to delete 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