What Does Active Learning Mean For Mathematicians?
the Conference Board of the Mathematical Sciences (CBMS) an umbrella organization consisting of the American Math- ematical Society and sixteen other
ON PROOF AND PROGRESS IN MATHEMATICS This essay on the
Responses to the Jaffe-Quinn article have been invited from a number of math- ematicians and I expect it to receive plenty of specific analysis and
SAT Study Guide 2020 - Chapter 20: Sample Math Questions
Sample Math. Questions: Multiple-Choice. In the previous chapters you learned about the four areas covered by the SAT Math Test. On the test
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Mordad 11 1389 AP SSPI Torlakson consulted the Mathematics Curriculum Framework and Evaluation Criteria Committee regarding modifications to the CA CCSSM and the.
SCCCR Standards for Mathematics Final - Print on One Side
Additionally South Carolina College- and Career-Ready Standards for. Mathematics contains SCCCR Mathematical Process Standards
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Tennessee students have various mathematical needs that their K-12 education should address. All students should be able to recall and use their math education
LaTeX-Math-Symbols.pdf
Khordad 11 1379 AP The guide assumes that you have some experience in using TEX for typeset- ting mathematics
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Mehr 10 1396 AP Therefore
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Ordibehesht 20 1400 AP Mathematics is an essential part of a comprehensive PK-12 education for all students. Wisconsin students learn to use mathematics to understand ...
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Mordad 14 1391 AP We know you'll learn a lot of mathematics ... the appropriate mathematics rather than requiring it. ... a math teacher she calls it x.
3/29/17, 10*20 AMLaTeX Math Symbols
Page 1 of 9http://www.math.ubc.ca/~cautis/tools/latexmath.htmlLaTeX Math Symbols
The following tables are extracted from The Not So Short Introduction to LaTeX2e, aka. LaTeX2e in 90 minutes, by Tobias Oetiker, Hubert
Partl, Irene Hyna, and Elisabeth Schlegl. It can be located here.3/29/17, 10*20 AMLaTeX Math Symbols
Page 2 of 9http://www.math.ubc.ca/~cautis/tools/latexmath.html3/29/17, 10*20 AMLaTeX Math Symbols
Page 3 of 9http://www.math.ubc.ca/~cautis/tools/latexmath.html3/29/17, 10*20 AMLaTeX Math Symbols
Page 4 of 9http://www.math.ubc.ca/~cautis/tools/latexmath.html3/29/17, 10*20 AMLaTeX Math Symbols
Page 5 of 9http://www.math.ubc.ca/~cautis/tools/latexmath.html3/29/17, 10*20 AMLaTeX Math Symbols
Page 6 of 9http://www.math.ubc.ca/~cautis/tools/latexmath.html3/29/17, 10*20 AMLaTeX Math Symbols
Page 7 of 9http://www.math.ubc.ca/~cautis/tools/latexmath.html3/29/17, 10*20 AMLaTeX Math Symbols
Page 8 of 9http://www.math.ubc.ca/~cautis/tools/latexmath.html3/29/17, 10*20 AMLaTeX Math Symbols
Page 9 of 9http://www.math.ubc.ca/~cautis/tools/latexmath.htmlLast modified: Wed May 31 14:04:55 CDT 2000
X Y -picUser'sGuideKristo!erH.R ose !krisrose@ens-lyon.fr"
Version3.7,February 16,1999
Abstract
X Y -picisapack agefort ypesetting graphsanddiagrams usingKnuth's T EXtyp esettingsystem.X
Y -picworkswith mostofthe manyformats available; e.g.,plainT E X, L A T EX,andA
M S-T EX.Severalstyles ofinputforvarious
diagramtyp esaresupported;theyallshareamnemonic notationbasedon thelogicalcomposition ofvisualcom- ponents.Thisguide concentrateson howto typeset "matrix-like"diagrams,suchascomm utativediagrams, inthefollo wingstyle: U y x (x,y)##X!ZY q p%% X f Yg Z wastypesetb ytheX Y -picinputlines \xymatrix{U\ar@/_/[ddr]_y\ar@/^/[drr]^x
\ar@{.>}[dr]|-{(x,y)}\\ &X\times_Z Y\ar[d]^q\ar[r]_p &X\ar[d]_f \\ &Y\ar[r]^g &Z}Suchdiagramshave thefollo wingcharacteristics:
•Specifiedasamatrixof entriesthat areautomati- callyalignedin rowsand columns. •Anyentrymaybe connectedtoanyother en- tryusinga variety ofarro wstylesallrotatedand stretchedasrequired. •Arrowsmaybedecoratedwith labelsthataretied toasp ecifiedpoin talongthearrow andextendin aparticulardirection; andarrows may bepaired, cross,andvisit/b endaroundother entries"onthe way." Severalotherstylesof inputare supported;ashortsurvey ofthep ossibilitiesisincluded lastattheendalong with informationonho wX Y -piccanbeobtained.Contents
Preface2
1Basics 2
1.1Loading. ... .. ... ... ... ..2
1.2Entrie s........ ... ... .. ..2
1.3Arrows ...... ... ... ... .. .2
1.4Labe ls........ ... ... .. ..3
1.5Bre aks........ ... ... .. ..3
1.6Curving. ... ... ... ... .. ..4
1.7Spe edinguptypesetting.. ... ...4
2MoreA rrowsand Labels4
2.1Explicit labelpos itioning.......4
2.2Labe lingwithanyobject ... .....5
2.3Morearro wst yles.... ........5
2.4Slidingarro wsside ways.. ......6
2.5Moretarge ts.. ..... ... ... .6
2.6Changingthe target. ... ...... 7
2.7Arrows passingunder ......... 7
2.8Moreb endingarro ws....... ...8
2.9Defining newarrowtyp es.... ...8
3MoreEn tries9
3.1Manual entryformatting ........9
3.2Extrae ntries outsidethematrix...9
3.3Spacing androtation... ... ... .9
3.4Entry style.. ......... ... .10
3.5Naming forlateruse astargets ....10
3.6Groupingob jec ts........... .10
4Av ailabilityandFurtherInformation11
4.1Getting X
Y -pic.. ... .. ... ... .114.2Bac kwardscompatibility..... ...11
4.3Furthe rreading...... ...... .12
4.4Credits ..... ... ... ... ... .13
AAnsw erstoallexercises13
References14
Index15
Laboratoiredel'InformatiqueduP arall´elisme, EcoleNormaleSup ´erieure deLyon;46,All´eed'Italie;F-69364Lyon7, France.
1Preface
Thisguidee xplainssom efeaturesof X
Y -picthatare relevanttotypesettingof"matrix-lik ediagrams "as usedin,forexample, cate gorytheory; pleasereferto therefe rencemanual[8]forcompleteinformationon thedes cribedconstructions.Theguideassumesthat youhaves omeexperiencein usingT EXfort ypes et-
tingmathe matics,e.g.,hav estudied[2,ch.16-19], [3, sec.3.3],or[9],andthatX Y -picisins talledon your T EXsys temasdescribedinthe INSTALLfileacc om-
panyingthedistribution.Thefirst sectiondes cribeswhatyouneedto get
started,inparticularallthatis neede dtotypes et thediagramin theabstrac t.Se ction2 and3explain advanceduseofarrowsande ntries,res pec tively.Fi- nally,section 4explainswhereandunderwhatcondi- tionsX Y -picisa vailable, givestherelationofversion3.7topre viousve rsions,andlis tsfurthersourcesof
information.Throughoutwe giveexerc isesthatyou shouldbe
abletos olveas yougoalong;allexerc ises arean- sweredattheendjustpriortothere ferenc esand index.1Basics
Thisse ctionexplainstheX
Y -diagramcons truction conceptsneededtoget startedwithtypesetting matrix-likediagrams.1.1Loading
TheX Y -picse tupusedinthisguideis loadedbyin- sertingthelines \inputxy \xyoption{all} inthede finitionspartof yourdocume nt.1Ifyou wish
toloadonly thefeature syou use, oryouwishtouse non-standardfacilitieslik ethev2backwardscompat- ibilitymode 2 orthepsPostScript 3 backendthen thisisals opos sibleasdes cribedinthereferencem an- ual[8].1.2Entries
Adiagramis create db ythecommand
\xymatrix{...}wherethe"... "should bereplacedbyentriestobe alignedinrowsandcolumnswhere •entriesinarowarese paratedb y&, 4 and •entirerowsareseparate dby\\.Forexample,
A m i=n i 2 D wastypes etby \xymatrix{A&*+[F]{\sum_{i=n}^m{i^2}} \\
&{\bullet}& D\ar[ul]}Noticethefollowing:
•entriesaretypeset asmathe matics(using"text style");entriesshouldnots tartwithamacro (asillustrate dbytheuseof{}around\bullet. •allen triesarecenteredandthe separation be- tweenrowsandcolumnsisusuallyquite large inadiagram , •emptyentriesatthee ndofrowsmaybeomit- ted, •"X Y -decorations"(here\ar[ul])ine ntries al- lowdrawingofarro wsandsuch relative tothe entrieswithoutchangingtheove ralllay out,and •"X Y -modifiers"(here*+[F])first inentriesal- lowchangingtheform atandshape inman y ways.1.3Arrows
An"arrow" inanX
Y -picdiagramis agene ricte rm forthedra wndec orationsbetw eentheentriesof the basicmatrixstruc ture.InX Y -picallarro wsmus tbe specifiedalongwiththeentryinwhichthey start;this iscalle dtheirbaseentry.Each particulararrowcom - mandthenrefe rsexplicitlytoits targetentry.This isobtained usingthe\arcommandwhichaccepts manyoptionsofwhichwe willde scrib eafewhere andsom emoreinsection2. Initssimples tform an arrowisente red as\ar[hop]wherehopisas equenc e ofsingle letters:uforup,dfordown, lforleft, and rforright, e.g.,thearro w\ar[ur]reads"types etan arrowfromthecurre nt entry tothatoneupandone right." 1 L A T E X2 [3]userscan use\usepackage[all]{xy}. 2Ifyou usetheversion2loading command\inputxypic(orthexypicdocumentstyleoption)thenthe v2optiondescribed in
section4.2will beloaded automatically. 3 PostScriptisaregistered Trademarkof Adobe, Inc.[1]. 4ThuswhenusingX
Y -constructionsinv olving&insideothertabular constructionsthenenclose theX Y -picconstructionin anextra pairofbraces! 2Exercise1:Whichentrydo es[]referto?
Therelativ ecoordinatesspec ifiedinthiswayare
purelylogical,e.g.,ifthe diagramcon tainsv erywide entriesthen"diagonal"arrowswillbe nearlyhorizon- tal.Thec onstructe darrowsarealignedalongtheline betweenthecentersofthebaseandtarget entrie s; theywillnotautomatic allydisapp ear underentries thatthey cross(wedis cusshowthisisac hievedin section2.7).Thearrow stylekan bechangedbywritingthe
commandas\ar@style[hop].Thiswill bede sc ribed inmore detailinsec tion2.3;herewe justlis tthemost common@styles(obvious variationsalsow ork):Exercise2:Typeset
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