cyto.json

{
  "nodes": {
    "000": {
      "id": "000",
      "label": "Logical Statements\nand Operations",
      "meta": " SLL01",
      "content": "Logic is the foundation to formulate proofs and to understand the language of mathematics.",
      "notes": "000-snippet.html",
      "video": "https://www.youtube.com/embed/DU4wKBDm2Z4?start=7",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/SDSU/Discrete/Logic/ttcontratautB4.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto000?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "001": {
      "id": "001",
      "label": "Sets",
      "meta": " SLS01 + SLS02 + SLS03 + SLS04 ",
      "content": "Sets are the basic building blocks for a lot of mathematics. In order to rigorously define numbers and doing real analysis, we need to know how to work with sets.",
      "notes": "001-snippet.html",
      "video": "https://www.youtube.com/embed/iA-Dtf7529M?start=14",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/Rochester/setSetTheory1/ur_st_1_5.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto001?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": "<iframe style=\"border-radius:12px\" src=\"https://open.spotify.com/embed/episode/4dhxy6YLYN7ItlWa0QgsG1?utm_source=generator&theme=0\" width=\"100%\" height=\"232\" frameBorder=\"0\" allowfullscreen=\"\" allow=\"autoplay; clipboard-write; encrypted-media; fullscreen; picture-in-picture\"></iframe><p>Courtesy of Marcus Waurick. <i>Well-defined & Wonderful podcast</i>, <a href=\"https://www.marcus-waurick.de/teaching\">marcus-waurick.de</a>.</p>"
    },
    "002": {
      "id": "002",
      "label": "Real Numbers",
      "meta": " SLR03  ",
      "content": "In a real analysis, the real numbers are the largest number set we need. They satisfy axioms that represent the idea of a number line.",
      "notes": "002-snippet.html",
      "video": "https://www.youtube.com/embed/E2MAvASTcg4?start=19",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/Mizzou/Intermediate_Algebra/Compound_Inequalities/P_02.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto002?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": "<iframe style=\"border-radius:12px\" src=\"https://open.spotify.com/embed/episode/1i62R3ZdwhjASp1TNJ2Bcy?utm_source=generator&theme=0\" width=\"100%\" height=\"232\" frameBorder=\"0\" allowfullscreen=\"\" allow=\"autoplay; clipboard-write; encrypted-media; fullscreen; picture-in-picture\"></iframe><p>Courtesy of Marcus Waurick. <i>Well-defined & Wonderful podcast</i>, <a href=\"https://www.marcus-waurick.de/teaching\">marcus-waurick.de</a>.</p>"
    },
    "003": {
      "id": "003",
      "label": "Maps",
      "meta": " SLS04 ",
      "content": "Maps are the mathematical formulation of a machine that gets inputs and generate outputs. On both sides, sets are needed.",
      "notes": "003-snippet.html",
      "video": "https://www.youtube.com/embed/JoLDwNh1lZ8?start=260",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/Mizzou/Intermediate_Algebra/Functions_Evaluating/Quad_No_Constant.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto003?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "004": {
      "id": "004",
      "label": "Natural Numbers\nand Induction",
      "meta": " SLN01 + SLN02 + SLN03 + SLN04 ",
      "content": "Using natural numbers is our first mathematical abstraction as children. Mathematical induction is an important technique of proof.",
      "notes": "004-snippet.html",
      "video": "https://www.youtube.com/embed/WMgiYh7tac0?start=13",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/MC/Proofs/EssayProofs/InductionDivisibility01.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto004?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": "<iframe style=\"border-radius:12px\" src=\"https://open.spotify.com/embed/episode/30dINCx7oSXMkCcSIOIBrv?utm_source=generator&theme=0\" width=\"100%\" height=\"232\" frameBorder=\"0\" allowfullscreen=\"\" allow=\"autoplay; clipboard-write; encrypted-media; fullscreen; picture-in-picture\"></iframe><p>Courtesy of Marcus Waurick. <i>Well-defined & Wonderful podcast</i>, <a href=\"https://www.marcus-waurick.de/teaching\">marcus-waurick.de</a>.</p>"
    },
    "005": {
      "id": "005",
      "label": "Image and\nPreimage",
      "meta": " SLS05 ",
      "content": "Via images and preimages we describe how functions work on sets.",
      "notes": "005-snippet.html",
      "video": "https://www.youtube.com/embed/twBYYTJdcjc?start=14",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/Mizzou/Algebra/functions_domain_range/fun_dom_19.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto005?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "006": {
      "id": "006",
      "label": "Injectivity, Surjectivity,\nBijectivity",
      "meta": " SLS06 ",
      "content": "These are important notions for maps.",
      "notes": "006-snippet.html",
      "video": "https://www.youtube.com/embed/CSzJchEvfpE?start=9",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/UMass-Amherst/Abstract-Algebra/PS-Functions/Functions2.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto006?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "007": {
      "id": "007",
      "label": "Composition",
      "meta": "  SLS07 ",
      "content": "The composition for maps is just applying two maps in a row.",
      "notes": "007-snippet.html",
      "video": "https://www.youtube.com/embed/NiJ1yWKM9CU?start=13",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/UMN/algebraKaufmannSchwitters/ks_8_6_18.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto007?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "008": {
      "id": "008",
      "label": "Logical Deduction",
      "meta": " SLL03",
      "content": "How to get new true proposition from other true propositions.",
      "notes": "008-snippet.html",
      "video": "https://www.youtube.com/embed/AjdIPOXRgoQ?start=10",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/ASU-topics/setDiscrete/katie5.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto008?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "009": {
      "id": "009",
      "label": "Predicates and Quantifiers",
      "meta": " SLS01 + SLS02 + SLS03 + SLS04 ",
      "content": "Formal mathematical statements are often built by predicates.",
      "notes": "009-snippet.html",
      "video": "https://www.youtube.com/embed/yIdECC6QExY?start=11",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/SDSU/Discrete/Predicates/predicateB8.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto009?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "010": {
      "id": "010",
      "label": "Operations on Sets",
      "meta": " SLL03",
      "content": "Sets can be joined or intersected in order to create new sets.",
      "notes": "010-snippet.html",
      "video": "https://www.youtube.com/embed/",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/UMN/logicAndSetTheory/prob03.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto010?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "011": {
      "id": "011",
      "label": "Sums and Products",
      "meta": " SLL03",
      "content": "An important shorthand notation for calculations.",
      "notes": "011-snippet.html",
      "video": "https://www.youtube.com/embed/S5DdXfxl3ac?start=3",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/Union/setIntSigmaNotation/an6_4_02.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto011?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "012": {
      "id": "012",
      "label": "Countable Sets",
      "meta": "",
      "content": "A notion of cardinality that covers finite sets and thos that can be enumerated via the natural numbers.",
      "notes": "012-snippet.html",
      "video": "https://www.youtube.com/embed/",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/Rochester/setSetTheory1/ur_st_1_6.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto012?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": "<iframe style=\"border-radius:12px\" src=\"https://open.spotify.com/embed/episode/6JdbJSYkihEiLJQijcPkYO?utm_source=generator&theme=0\" width=\"100%\" height=\"232\" frameBorder=\"0\" allowfullscreen=\"\" allow=\"autoplay; clipboard-write; encrypted-media; fullscreen; picture-in-picture\"></iframe><p>Courtesy of Marcus Waurick. <i>Well-defined & Wonderful podcast</i>, <a href=\"https://www.marcus-waurick.de/teaching\">marcus-waurick.de</a>.</p>"
    },
    "013": {
      "id": "013",
      "label": "Bounded Sets,\nMaxima and Minima",
      "meta": "",
      "content": "The values inside a set of real numbers can be bounded.",
      "notes": "013-snippet.html",
      "video": "https://www.youtube.com/embed/",
      "webwork": "",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto013?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "100": {
      "id": "100",
      "label": "Sequences",
      "meta": " RA02 ",
      "content": "These object are needed to define limits later on.",
      "notes": "100-snippet.html",
      "video": "https://www.youtube.com/embed/1SguKALJji8?start=17",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/UMN/calculusStewartCCC/s_11_1_5.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto100?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "101": {
      "id": "101",
      "label": "Convergence",
      "meta": " RA02 ",
      "content": "Convergent sequences have a well-defined limit.",
      "notes": "101-snippet.html",
      "video": "https://www.youtube.com/embed/1SguKALJji8?start=367",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/10_Infinite_Series/10.1_Sequences/10.1.31.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto101?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "102": {
      "id": "102",
      "label": "Bounded\nSequences",
      "meta": " RA03 ",
      "content": "Sequences can be bounded from above and from below.",
      "notes": "102-snippet.html",
      "video": "https://www.youtube.com/embed/k-Wm6gJYfrw?start=221",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/WinonaState/StewartCalcEarlyTran7ed/Chap11Section01/SCalcET7-11-1-037.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto102?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "103": {
      "id": "103",
      "label": "Limit Theorems",
      "meta": " RA04 ",
      "content": "Combining limits is a useful tool.",
      "notes": "103-snippet.html",
      "video": "https://www.youtube.com/embed/237VMLNVtQs?start=18",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/Dartmouth/setStewartCh12S1/problem_7.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto103?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "104": {
      "id": "104",
      "label": "Monotonicity and\nSandwich Theorem",
      "meta": " RA05 ",
      "content": "Sandwich a sequence by two converging sequences to get its limit.",
      "notes": "104-snippet.html",
      "video": "https://www.youtube.com/embed/Y6rRSip3QN4?start=14",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/Hope/Calc2/APEX_08_01_Sequences/Q_17.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto104?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "105": {
      "id": "105",
      "label": "Supremum and\nInfimum of Sets",
      "meta": " RA06 ",
      "content": "Bounded sets always have an supremum and infimum which are generalizations of maximum and minimum.",
      "notes": "105-snippet.html",
      "video": "https://www.youtube.com/embed/8Cyvdv7Sm2s?start=16",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=%%%&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto105?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "106": {
      "id": "106",
      "label": "Completeness",
      "meta": " RA07 ",
      "content": "Completeness says that Cauchy sequences must converge.",
      "notes": "106-snippet.html",
      "video": "https://www.youtube.com/embed/R2AFZD0jiKQ?start=14",
      "webwork": "https://bright.jp-g.de/bsom/ra/ratest07/quiz.html",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto106?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": "<iframe style=\"border-radius:12px\" src=\"https://open.spotify.com/embed/episode/2oh22JbFBcqSdfBJHEYUGo?utm_source=generator&theme=0\" width=\"100%\" height=\"232\" frameBorder=\"0\" allowfullscreen=\"\" allow=\"autoplay; clipboard-write; encrypted-media; fullscreen; picture-in-picture\"></iframe><p>Courtesy of Marcus Waurick. <i>Well-defined & Wonderful podcast</i>, <a href=\"https://www.marcus-waurick.de/teaching\">marcus-waurick.de</a>.</p>"
    },
    "107": {
      "id": "107",
      "label": "Subsequences and\nAccumulation Values",
      "meta": " RA09 ",
      "content": "A sequence that does not converge may still have converging subsequences.",
      "notes": "107-snippet.html",
      "video": "https://www.youtube.com/embed/xZ5vjdZzTUI?start=14",
      "webwork": "https://bright.jp-g.de/bsom/real_analysis/ratest09.html",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto107?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "108": {
      "id": "108",
      "label": "Bolzano-\nWeierstrass",
      "meta": "RA10 ",
      "content": "Every bounded sequence has at least one converging subsequence.",
      "notes": "108-snippet.html",
      "video": "https://www.youtube.com/embed/e2QaNklYZGg?start=10",
      "webwork": "https://bright.jp-g.de/bsom/ra/ratest10/quiz.html",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto108?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": "<iframe style=\"border-radius:12px\" src=\"https://open.spotify.com/embed/episode/4MKVAhO2q57xmMn1P7ONKg?utm_source=generator&theme=0\" width=\"100%\" height=\"232\" frameBorder=\"0\" allowfullscreen=\"\" allow=\"autoplay; clipboard-write; encrypted-media; fullscreen; picture-in-picture\"></iframe><p>Courtesy of Marcus Waurick. <i>Well-defined & Wonderful podcast</i>, <a href=\"https://www.marcus-waurick.de/teaching\">marcus-waurick.de</a>.</p>"
    },
    "109": {
      "id": "109",
      "label": "Limit Inferior and\nLimit Superior",
      "meta": "RA11+RA12 ",
      "content": "The largest and smallest limit of all convergent subsequences.",
      "notes": "109-snippet.html",
      "video": "https://www.youtube.com/embed/-y0v2V0-_8E?start=21",
      "webwork": "https://bright.jp-g.de/bsom/ra/ratest11/quiz.html",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto109?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "110": {
      "id": "110",
      "label": "Open, Closed,\nCompact Sets",
      "meta": " RA13 ",
      "content": "Important notions for subsets of real numbers.",
      "notes": "110-snippet.html",
      "video": "https://www.youtube.com/embed/Wqo4Svs4erw?start=12",
      "webwork": "https://bright.jp-g.de/bsom/ra/ratest13/quiz.html",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto110?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "111": {
      "id": "111",
      "label": "Heine-Borel\nTheorem",
      "meta": " RA14 ",
      "content": "The theorem connecting the concept of compactness with boundedness and closedness.",
      "notes": "111-snippet.html",
      "video": "https://www.youtube.com/embed/vjOefDHOVIg?start=10",
      "webwork": "https://bright.jp-g.de/bsom/ra/ratest14/quiz.html",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto111?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "112": {
      "id": "112",
      "label": "Interior, Closure,\nBoundary",
      "meta": " ",
      "content": "Topological operations on sets.",
      "notes": "112-snippet.html",
      "video": "https://www.youtube.com/embed/",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/Union/setAlgebraIntervals/ur_ab_10_1.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto112?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "113": {
      "id": "113",
      "label": "Uncountability\nof the Reals",
      "meta": " ",
      "content": "The real numbers cannot be enumerated.",
      "notes": "113-snippet.html",
      "video": "https://www.youtube.com/embed/jCiIsigwaBE",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto113?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": "<iframe style=\"border-radius:12px\" src=\"https://open.spotify.com/embed/episode/7ElhBgZebKwOXqMsWMGgGJ?utm_source=generator&theme=0\" width=\"100%\" height=\"232\" frameBorder=\"0\" allowfullscreen=\"\" allow=\"autoplay; clipboard-write; encrypted-media; fullscreen; picture-in-picture\"></iframe><p>Courtesy of Marcus Waurick. <i>Well-defined & Wonderful podcast</i>, <a href=\"https://www.marcus-waurick.de/teaching\">marcus-waurick.de</a>.</p>"
    },
    "114": {
      "id": "114",
      "label": "Convergence of Bounded Monotonic Sequences",
      "meta": " ",
      "content": "If a sequence of real numbers is bounded and monotonic, then it is convergent.",
      "notes": "114-snippet.html",
      "video": "",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/WinonaState/StewartCalcEarlyTran7ed/Chap11Section01/SCalcET7-11-1-027.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto114?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "115": {
      "id": "115",
      "label": "Cauchy\nSequences",
      "meta": " RA07 ",
      "content": "The sequence members of a Cauchy Sequence eventually become arbitrarily close to each other.",
      "notes": "115-snippet.html",
      "video": "https://www.youtube.com/embed/R2AFZD0jiKQ?start=14",
      "webwork": "https://bright.jp-g.de/bsom/ra/ratest07/quiz.html",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto106?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": "<iframe style=\"border-radius:12px\" src=\"https://open.spotify.com/embed/episode/2oh22JbFBcqSdfBJHEYUGo?utm_source=generator&theme=0\" width=\"100%\" height=\"232\" frameBorder=\"0\" allowfullscreen=\"\" allow=\"autoplay; clipboard-write; encrypted-media; fullscreen; picture-in-picture\"></iframe><p>Courtesy of Marcus Waurick. <i>Well-defined & Wonderful podcast</i>, <a href=\"https://www.marcus-waurick.de/teaching\">marcus-waurick.de</a>.</p>"
    },
    "200": {
      "id": "200",
      "label": "Partial Sums",
      "meta": "RA15",
      "content": "A series is a sequence of partial sums.",
      "notes": "200-snippet.html",
      "video": "https://www.youtube.com/embed/BgfP3riDcrc?start=13",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/10_Infinite_Series/10.2_Summing_an_Infinite_Series/10.2.3.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto200?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": "<iframe style=\"border-radius:12px\" src=\"https://open.spotify.com/embed/episode/4rf4zO7V8UJErJxgzmZFgh?utm_source=generator&theme=0&t=0\" width=\"100%\" height=\"232\" frameBorder=\"0\" allowfullscreen=\"\" allow=\"autoplay; clipboard-write; encrypted-media; fullscreen; picture-in-picture\"></iframe><p>Courtesy of Marcus Waurick. <i>Well-defined & Wonderful podcast</i>, <a href=\"https://www.marcus-waurick.de/teaching\">marcus-waurick.de</a>.</p>"
    },
    "201": {
      "id": "201",
      "label": "Geometric and\nHarmonic Series",
      "meta": "RA16",
      "content": "The most important examples of series.",
      "notes": "201-snippet.html",
      "video": "https://www.youtube.com/embed/Y4yRcz-b17A?start=12",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/ASU-topics/setSequenceandSeries/jj14.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto201?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "203": {
      "id": "203",
      "label": "Convergent Series and\nLimit Theorems",
      "meta": "RA17",
      "content": "Basic operations with convergent series.",
      "notes": "203-snippet.html",
      "video": "https://www.youtube.com/embed/lr12HwXQ3uw?start=20",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/Rochester/setSeries4Geometric/ns8_2_23.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto203?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "204": {
      "id": "204",
      "label": "Cauchy Criterion",
      "meta": "RA17",
      "content": "A series convergence if its partial sums form a Cauchy sequence.",
      "notes": "204-snippet.html",
      "video": "https://www.youtube.com/embed/lr12HwXQ3uw?start=130",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/AlfredUniv/anton8e/chapter10/10.4/prob1.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto204?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "205": {
      "id": "205",
      "label": "Leibniz Criterion",
      "meta": "RA18",
      "content": "A convergence criterion for sums based on an alternating sequence.",
      "notes": "205-snippet.html",
      "video": "https://www.youtube.com/embed/MjjMwQ6zFko?start=10",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/ma123DB/set11/s11_5_5.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto205?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "206": {
      "id": "206",
      "label": "Absolute Convergence",
      "meta": "RA19",
      "content": "A strong concept of convergence of series.",
      "notes": "206-snippet.html",
      "video": "https://www.youtube.com/embed/mI40-tAtP58?start=21",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/ma123DB/set11/s11_6_15.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto206?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "207": {
      "id": "207",
      "label": "Comparison Test",
      "meta": "RA19",
      "content": "If a series converges can be checked with different tests.",
      "notes": "207-snippet.html",
      "video": "https://www.youtube.com/embed/mI40-tAtP58?start=160",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/WinonaState/StewartCalcEarlyTran7ed/Chap11Section04/SCalcET7-11-4-002a.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto207?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "208": {
      "id": "208",
      "label": "Quotient Criterion",
      "meta": "RA20",
      "content": "An important criterion to prove absolute convergence by means of ratios of the underlying sequence's terms.",
      "notes": "208-snippet.html",
      "video": "https://www.youtube.com/embed/yLbgdL9HAeg?start=10",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/FortLewis/Calc2/9-4-Ratio-test/ratio-05.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto208?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "209": {
      "id": "209",
      "label": "Root Criterion",
      "meta": "RA20",
      "content": "An important criterion to prove absolute convergence by means of the behavior of the n-th roots of the underlying sequence's terms.",
      "notes": "209-snippet.html",
      "video": "https://www.youtube.com/embed/yLbgdL9HAeg?start=420",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/10_Infinite_Series/10.5_The_Ratio_and_Root_Tests/10.5.37.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto209?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "210": {
      "id": "210",
      "label": "Reordering",
      "meta": "RA21",
      "content": "Series can be reordered.",
      "notes": "210-snippet.html",
      "video": "https://www.youtube.com/embed/GADre0hHc4c?start=9",
      "webwork": "https://bright.jp-g.de/bsom/ra/ratest21/quiz.html",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto210?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": "<iframe src=\"https://anchor.fm/profmoppi/embed/episodes/Rearrangement-of-Series-with-Fabian-Gabel-e1iq2sr/a-a7vb2vp\" height=\"102px\" width=\"100%\" frameborder=\"0\" scrolling=\"no\"></iframe><p>Courtesy of Marcus Waurick. <i>Well-defined & Wonderful podcast</i>, <a href=\"https://www.marcus-waurick.de/teaching\">marcus-waurick.de</a>.</p>"
    },
    "211": {
      "id": "211",
      "label": "Cauchy Product",
      "meta": "RA22",
      "content": "A special way to multiply two absolutely convergent sequences.",
      "notes": "211-snippet.html",
      "video": "https://www.youtube.com/embed/tRa0Ex_0Yfo?start=10",
      "webwork": "https://bright.jp-g.de/bsom/ra/ratest22/quiz.html",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto211?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "300": {
      "id": "300",
      "label": "Sequences of\nBounded Functions",
      "meta": "RA23",
      "content": "The concept of sequences but for functions instead of real numbers.",
      "notes": "300-snippet.html",
      "video": "https://www.youtube.com/embed/RM2hytsyMpc?start=20",
      "webwork": "https://bright.jp-g.de/bsom/ra/ratest23/quiz.html",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto300?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "301": {
      "id": "301",
      "label": "Pointwise Convergence",
      "meta": "RA24",
      "content": "A notion of convergence for sequences functions that reduces the question of convergence to convergence of sequences of real numbers.",
      "notes": "301-snippet.html",
      "video": "https://www.youtube.com/embed/Kq_KZpljeXo?start=10",
      "webwork": "https://bright.jp-g.de/bsom/ra/ratest24/quiz.html",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto301?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "302": {
      "id": "302",
      "label": "Uniform Convergence",
      "meta": "RA25",
      "content": "A strong notion of convergence for sequences of functions that helps to preserve favorable properties like continuity in the limit.",
      "notes": "302-snippet.html",
      "video": "https://www.youtube.com/embed/O2HKxNcom7g?start=10",
      "webwork": "https://bright.jp-g.de/bsom/ra/ratest25/quiz.html",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto302?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "303": {
      "id": "303",
      "label": "Limits of Functions",
      "meta": "RA26",
      "content": "How function evaluations change when the argument approaches a certain point.",
      "notes": "303-snippet.html",
      "video": "https://www.youtube.com/embed/QoLlvvro6rE?start=15",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/ASU-topics/setRateChange/3-2-72.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto303?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "304": {
      "id": "304",
      "label": "Continuity",
      "meta": "RA27",
      "content": "The concept that relates functions with convergent sequences.",
      "notes": "304-snippet.html",
      "video": "https://www.youtube.com/embed/8VTG6EsyJh4?start=8",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/ASU-topics/setContinuity/4-1-57.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto304?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "305": {
      "id": "305",
      "label": "Epsilon-Delta\nDefinition",
      "meta": "RA28",
      "content": "A different notion of continuity using open intervals.",
      "notes": "305-snippet.html",
      "video": "https://www.youtube.com/embed/",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/Berkeley/StewCalcET7e/2.4/2-4-03.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto305?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "306": {
      "id": "306",
      "label": "Continuity for Sums,\nProducts, Quotients,\nand Compositions",
      "meta": "RA29",
      "content": "How combination of continuous functions leads to new continuous functions.",
      "notes": "306-snippet.html",
      "video": "https://www.youtube.com/embed/W-E4LqZyEHA?start=10",
      "webwork": "https://bright.jp-g.de/bsom/ra/ratest29/quiz.html",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto306?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "307": {
      "id": "307",
      "label": "Continuous Images\nof Compact Sets\nAre Compact",
      "meta": "RA30",
      "content": "A mapping property for continuous functions.",
      "notes": "307-snippet.html",
      "video": "https://www.youtube.com/embed/6VWTG4wlRoA?start=11",
      "webwork": "https://bright.jp-g.de/bsom/ra/ratest30/quiz.html",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto307?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "308": {
      "id": "308",
      "label": "Uniform Limits of \n Continuous Functions",
      "meta": "RA31",
      "content": "How to preserve continuity in the limit.",
      "notes": "308-snippet.html",
      "video": "https://www.youtube.com/embed/llJruZnO-t4?start=11",
      "webwork": "https://bright.jp-g.de/bsom/ra/ratest31/quiz.html",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto308?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "309": {
      "id": "309",
      "label": "Intermediate Value\nTheorem",
      "meta": "RA32",
      "content": "This theorem tells us that continuous functions don't jump. They have to attain every value between two values in their image.",
      "notes": "309-snippet.html",
      "video": "https://www.youtube.com/embed/BNLu4_3Okuk?start=9",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/Valdosta/APEX_Calculus/1.5/APEX_1.5_34.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto309?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": "<audio controls src=\"/e-10/pontifex/podcast/imvt.mp3\">Your browser does not support the <code>audio</code> element.</audio>"},
    "400": {
      "id": "400",
      "label": "Exponential\nFunction",
      "meta": "RA33",
      "content": "A special function that can be defined via a power series.",
      "notes": "400-snippet.html",
      "video": "https://www.youtube.com/embed/onmh9nzkfDA?start=25",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/UCSB/Stewart5_1_5/Stewart5_1_5_15.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto400?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": "<iframe src=\"https://anchor.fm/profmoppi/embed/episodes/Exponential-Series-with-Fabian-Gabel-e1iq43j\" height=\"102px\" width=\"100%\" frameborder=\"0\" scrolling=\"no\"></iframe><p>Courtesy of Marcus Waurick. <i>Well-defined & Wonderful podcast</i>, <a href=\"https://www.marcus-waurick.de/teaching\">marcus-waurick.de</a>.</p>"
    },
    "401": {
      "id": "401",
      "label": "Logarithm Function",
      "meta": "RA33",
      "content": "The inverse of the exponential function.",
      "notes": "401-snippet.html",
      "video": "https://www.youtube.com/embed/onmh9nzkfDA?start=213",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/ASU-topics/setLogarithmicFunctions/srw4_3_43.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
      "discussion": "https://etherpad.studiumdigitale.uni-frankfurt.de/p/discussingbridgesfromandto401?showControls=true&showChat=true&showLineNumbers=true&useMonospaceFont=false",
      "podcast": ""
    },
    "402": {
      "id": "402",
      "label": "Polynomials",
      "meta": "RA33",
      "content": "A basic class of functions that consists a linear combinations of monomials.",
      "notes": "402-snippet.html",
      "video": "https://www.youtube.com/embed/onmh9nzkfDA?start=297",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/CollegeOfIdaho/setAlgebra_05_01_IntroPolynomials/51IntAlg_03_Polynomial.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
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      "label": "Sum and Product Rule",
      "meta": "RA35",
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      "notes": "501-snippet.html",
      "video": "https://www.youtube.com/embed/wp-s9c1IKhI?start=10",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/Union/setDervProductQuotientRule/s2_2_13.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
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      "label": "Chain Rule",
      "meta": "RA36",
      "content": "How to differentiate compositions of functions.",
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      "video": "https://www.youtube.com/embed/g57hlenwvis?start=10",
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      "video": "https://www.youtube.com/embed/93i7uKScVvc?start=10",
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      "video": "https://www.youtube.com/embed/h0nBAMhdSMk?start=10",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/3_Differentiation/3.8_Derivatives_of_Inverse_Functions/3.8.7.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
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      "label": "Rolle's Theorem",
      "meta": "RA40",
      "content": "The derivatives of functions with equal boundary conditions always have at least one zero.",
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      "meta": "RA41",
      "content": "This theorem helps us to link monotonicity of a function with values of its derivative.",
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      "video": "https://www.youtube.com/embed/FQo9OYku5aY?start=10",
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      "video": "https://www.youtube.com/embed/KbS_cRToPFA?start=10",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/4_Applications_of_the_Derivative/4.5_LHopitals_Rule/4.5.40.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
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      "content": "Further scenarios in which limits can be calculated by l'Hospital's rule.",
      "notes": "509-snippet.html",
      "video": "https://www.youtube.com/embed/KuF0JRsWhBk?start=10",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/Valdosta/APEX_Calculus/6.7/APEX_6.7_27.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
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      "label": "Higher Derivatives",
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      "content": "Taking derivatives of derivatives of differentiable functions.",
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      "video": "https://www.youtube.com/embed/vyZ5ESoqsxw?start=11",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=brary/Valdosta/APEX_Calculus/3.4/APEX_3.4_13.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
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      "label": "Taylor's Theorem",
      "meta": "RA45",
      "content": "An approximation method for differentiable functions.",
      "notes": "511-snippet.html",
      "video": "https://www.youtube.com/embed/Pb390hRaLrw?start=10",
      "webwork": "https://bright.jp-g.de/bsom/ra/ratest45/quiz.html",
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      "id": "512",
      "label": "Application of\nTaylor's Theorem",
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      "content": "Calculate an approximation via Taylor's Theorem",
      "notes": "512-snippet.html",
      "video": "https://www.youtube.com/embed/zRoyHrMNOO8?start=10",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/FortLewis/Calc2/10-2-Taylor-series/Taylor-series-05.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
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      "label": "Proof of\nTaylor's Theorem",
      "meta": "RA47",
      "content": "Derive an approximation result from the generalised mean value theorem.",
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      "video": "https://www.youtube.com/embed/oZZrwKsqVro?start=10",
      "webwork": "https://bright.jp-g.de/bsom/ra/ratest47/quiz.html",
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      "content": "Splitting up an innterval in subintervals and defining functions that are constant on them.",
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      "video": "https://www.youtube.com/embed/6Pb97_7huwI?start=34",
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      "id": "603",
      "label": "Riemann Integral\nfor Bounded Functions",
      "meta": "RA51",
      "content": "Notion of integral for a large class of functions.",
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      "video": "https://www.youtube.com/embed/t8Hh73HxP1o?start=12",
      "webwork": "https://bright.jp-g.de/bsom/ra/ratest51/quiz.html",
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      "content": "Use the approximation by step functions to calculate integrals.",
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      "video": "https://www.youtube.com/embed/J9qXHzxeDN4?start=10",
      "webwork": "https://bright.jp-g.de/bsom/ra/ratest52/quiz.html",
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      "content": "Important properties of the Riemann integral of bounded functions.",
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      "video": "https://www.youtube.com/embed/h4XohuM2iK4?start=10",
      "webwork": "https://bright.jp-g.de/bsom/ra/ratest53/quiz.html",
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      "label": "Second Fundamental\nTheorem of Calculus",
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      "content": "Characterization of all antiderivatives",
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      "video": "https://www.youtube.com/embed/SJC4DGuyg4c?start=12",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/Rochester/setIntegrals4FTC/osu_in_4_15.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
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      "video": "https://www.youtube.com/embed/E4zieCbfdcs?start=12",
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      "content": "An important integration rule.",
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      "video": "https://www.youtube.com/embed/wmZCoV6Y0_c?start=12",
      "webwork": "https://jupyterhub.mat.tu-harburg.de/webwork2/html2xml?&answersSubmitted=0&sourceFilePath=Library/Valdosta/APEX_Calculus/6.1/APEX_6.1_3-6.pg&problemSeed=123567890&displayMode=MathJax&courseID=pontifex&userID=pontifexuser&course_password=ki(JH7j3m4)k_46)&outputformat=simple",
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      "content": "How to integrate rational functions.",
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      "content": "Compare improper Riemann integrals to infinite series.",
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    "001-004": {
      "source": "001",
      "target": "004",
      "label": "Natural numbers are a set of numbers."
    },
    "001-005": {
      "source": "001",
      "target": "005",
      "label": "Image and Preimage are special sets related to a mapping."
    },
    "101-102": {
      "source": "101",
      "target": "102",
      "label": "Convergent sequences are bounded."
    },
    "002-102": {
      "source": "002",
      "target": "102",
      "label": "The statement of boundedness involves a comparison of real numbers."
    },
    "001-013": {
      "source": "001",
      "target": "013",
      "label": "Bounded sets are sets of real numbers that don't get arbitrarily small or large."
    },
    "005-013": {
      "source": "005",
      "target": "013",
      "label": "If the image or preimage of a real valued map is bounded, one also calls the map bounded."
    },
    "013-300": {
      "source": "013",
      "target": "300",
      "label": "If the image of a map is a bounded set, one also calls the map bounded."
    },
    "105-300": {
      "source": "105",
      "target": "300",
      "label": "One bound to a map is given by the finite supremum of the set of the absolute function values."
    },
    "005-102": {
      "source": "005",
      "target": "102",
      "label": "Boundedness of a sequence means that the image of the sequence is a bounded set."
    },
    "100-102": {
      "source": "100",
      "target": "102",
      "label": "Boundedness is a property of sequences."