,,,UNIFI$ 5GLI% BRL,' ,,,GUIDEL9ES = TE*NICAL MAT]IAL,' #BJJH V].N UPDAT$ ,AUGU/ #BJAD ,PRODUC$ #BJJH BY ,A3ESSIBLE ,=MAT ,PRODUC;N ,,RNZFB1 ,AUCKL&1 ,NEW ,Z1L& ,UPDAT$ #BJAD BY ,PHYLLIS ,L&ON ,9 #A ,VOLUME ,BRL PAGES P#A-P#AJ & #A-#ACC ,PR9T PAGES #A-#HG P#A P#B ,TE*NICAL ,GUIDEL9ES ,AB ? ,DOCU;T ,? DOCU;T HAS BE5 PRODUC$ BY ! ,MA?S ,FOCUS ,GR\P1 A SUBGR\P ( ! ,,UEB ,RULES ,COMMITTEE )9 ! ,9T]NA;NAL ,C\NCIL ON ,5GLI% ,BRL "<,,ICEB">4 ,AT ! ,,ICEB ,G5]AL ,ASSEMBLY 9 ,APRIL #BJJH X 0 AGRE$ T ! DOCU;T %D 2 REL1S$ = USE 9T]NA;NALLY1 & T FE$BACK %D 2 GA!R$ ) A VIEW TO PRODUC+ A NEW $I;N PRIOR TO ! #BJAB ,G5]AL ,ASSEMBLY4 ,! PURPOSE ( ? DOCU;T IS TO GIVE TRANSCRIB]S 5 9=MA;N & EXAMPLES TO PRODUCE ,MA?S1 ,SCI;E & ,COMPUT] NOTA;N 9 ,UNIFI$ ,5GLI% ,BRL4 ,? DOCU;T IS AVAILABLE 9 ! FOLL[+ FILE =MATS3 PDF1 DOC1 DXP OR BRF4 ,^! FILES C 2 S\RC$ "? ! ,,ICEB REPRES5TATIVES ON YR LOCAL ,BRL ,AU?ORITIES4 ,PL1SE S5D FE$BACK ON ? DOCU;T TO ,,ICEB1 AG "? ! ,BRL ,AU?OR;Y 9 YR [N C.TRY4 P#C ,TE*NICAL ,GUIDEL9ES ,,,SPECIAL SYMBOLS US$ 9 ? VOLUME,' ,? BOOK HAS BE5 PRODUC$ 9 ,UNIFI$ ,5GLI% ,BRL4 ,MA!MATICAL SYMBOLS DEF9$ AT ! />T ( EA* *APT] H N BE5 9CLUD$ 9 ! LI/ 2L4 .= DOT LOCATOR .=.2 ITALIC SYMBOL .=^2 BOLDFACE SYMBOL .=,- DA% .=_4 BULLET .="< OP5 R.D BRACKET "

5!SIS"> .="> CLOSE R.D BRACKET "

5!SIS"> .=@.< OP5 TRANSCRIB]'S NOTE SYMBOL .=@.> CLOSE TRANSCRIB]'S NOTE SYMBOL .=; GRADE #A SYMBOL .=;; GRADE #A ^W .=;;; GRADE #A PASSAGE .=;' GRADE #A T]M9ATOR P#D ,TE*NICAL ,GUIDEL9ES ,,3T5TS @.<,PAGE NUMB]S REF] TO PR9T PAGE NUMB]S4@.> #A ,G5]AL ,PR9CIPLES """""""""""""""" #A #A4A ,SPAC+ """"""""""""""""""""""" #A #A4B ,"ULY+ RULES = NUMB]S & LRS "" #B #A4C ,PR9T ,SYMBOLS """"""""""""""" #C #A4D ,=MAT """""""""""""""""""""""" #C #A4E ,TYPE=MS """"""""""""""""""""" #D #A4F ,CAPITALISA;N """""""""""""""" #D #A4G ,USE ( ,GRADE #A 9DICATORS """ #E #B ,NUMB]S & ,A2REVIA;NS """""""""""" #H #B4A ,:OLE NUMB]S """"""""""""""""" #H #B4B ,DECIMALS """""""""""""""""""" #I #B4C ,DATES """"""""""""""""""""""" #I #B4D ,"T """"""""""""""""""""""""" #AJ #B4E ,ORD9AL NUMB]S """""""""""""" #AJ #B4F ,ROMAN ,NUM]ALS """"""""""""" #AA #B4G ,EMPHASIS ( ,DIGITS """"""""" #AA #B4H ,ANCI5T ,NUM]A;N SY/EMS """"" #AA #B4I ,HEXADECIMAL NUMB]S """"""""" #AB P#E ,TE*NICAL ,GUIDEL9ES #B4AJ ,A2REVIA;NS """""""""""""""" #AB #C ,SIGNS ( ,OP]A;N1 ,COMP>ISON & ,OMIS.N """""""""""""""""""""""" #AE #C4A ,EXAMPLES """"""""""""""""""" #AF #C4B ,ALGEBRAIC ,EXAMPLES """""""" #AG #C4C ,USE ( ! BRL HYPH5 """""""""" #AG #C4D ,POSITIVE & NEGATIVE NUMB]S #AH #C4E ,CALCULATOR KEYS """""""""""" #AH #C4F ,OMIS.N M>KS 9 MA!MATICAL EXPRES.NS """""""""""""""""""" #AI #D ,SPATIAL ,LAY\T & ,DIAGRAMS """"" #BJ #D4A ,SPATIAL CALCULA;NS """"""""" #BJ #D4B ,TALLY M>KS """"""""""""""""" #BE #D4C ,TABLES """"""""""""""""""""" #BF #D4D ,DIAGRAMS """"""""""""""""""" #BG #E ,GR\P+ ,DEVICES "<,BRACKETS"> """ #CJ #F ,FRAC;NS """""""""""""""""""""""" #CA #F4A ,SIMPLE NUM]IC FRAC;NS """""" #CA #F4B ,MIX$ NUMB]S """""""""""""""" #CA #F4C ,FRAC;NS WRITT5 9 L9E> =M 9 PR9T """"""""""""""""""""""""" #CB #F4D ,G5]AL FRAC;N 9DICATORS """"" #CB #F4E ,EXTRA ,EXAMPLES """""""""""" #CC P#F ,TE*NICAL ,GUIDEL9ES #G ,SUP]SCRIPTS & SUBSCRIPTS """"""" #CD #G4A ,DEF9I;N ( AN ITEM """""""""" #CD #G4B ,SUP]SCRIPTS & SUBSCRIPTS )9 LIT]>Y TEXT """""""""""""""""" #CE #G4C ,ALGEBRAIC EXPRES.NS 9VOLV+ SUP]SCRIPTS """""""""""""""""" #CE #G4D ,MULTIPLE LEVELS """""""""""" #CG #G4E ,NEGATIVE SUP]SCRIPTS """"""" #CG #G4F ,EXAMPLES F ,*EMI/RY """""""" #CH #G4G ,SIMULTANE\S SUP]SCRIPTS & SUBSCRIPTS """"""""""""""""""" #CH #G4H ,LEFT-4PLAC$ SUP]SCRIPTS OR SUBSCRIPTS """"""""""""""""""" #CH #G4I ,MODIFI]S DIRECTLY ABV OR 2L #CI #H ,SQU>E ,ROOTS & O!R RADICALS """" #DJ #H4A ,SQU>E ROOTS """""""""""""""" #DJ #H4B ,CUBE ROOTS ETC """"""""""""" #DA #H4C ,SQU>E ROOT SIGN ON XS [N """ #DA #I ,FUNC;NS """""""""""""""""""""""" #DB #I4A ,SPELL+ & CAPITALISA;N """""" #DB #I4B ,ITALICS """""""""""""""""""" #DB #I4C ,SPAC+ """""""""""""""""""""" #DC #I4D ,TRIGONOMETRIC FUNC;NS """""" #DD P#G ,TE*NICAL ,GUIDEL9ES #I4E ,LOG>I?MIC FUNC;NS """""""""" #DE #I4F ,! ,LIMIT FUNC;N """""""""""" #DF #I4G ,/ATI/ICAL FUNC;NS """""""""" #DF #I4H ,COMPLEX NUMB]S """"""""""""" #DG #AJ ,SET ,!ORY1 ,GR\P ,!ORY & ,LOGIC """"""""""""""""""""""""" #DH #AA ,MISCELLANE\S ,SYMBOLS """"""""" #EJ #AA4A ,SPAC+ """"""""""""""""""""" #EA #AA4B ,UNUSUAL ,PR9T SYMBOLS """"" #EA #AA4C ,GRADE #A 9DICATORS """""""" #EA #AA4D ,SYMBOLS : H M ?AN "O M1N+ 9 PR9T """"""""""""""""""""""" #EA #AA4E ,EXAMPLES """""""""""""""""" #EB #AA4F ,EMBELLI%$ CAPITAL LRS """"" #EE #AA4G ,GREEK LRS """"""""""""""""" #EF #AB ,B>S & DOTS ETC4 OV] & "U """""" #EG #AB4A ,! DEF9I;N ( AN ITEM """"""" #EG #AB4B ,TWO 9DICATORS APPLI$ TO ! SAME ITEM """""""""""""""""""" #EI #AC ,>R[S """""""""""""""""""""""""" #FJ #AC4A ,SIMPLE >R[S """"""""""""""" #FJ #AC4B ,>R[S ) UNUSUAL %AFTS & A /&>D B>B$ TIP """""""""""""""" #FA P#H ,TE*NICAL ,GUIDEL9ES #AC4C ,>R[S ) UNUSUAL TIPS """"""" #FB #AD ,%APE ,SYMBOLS & ,COMPOSITE ,SYMBOLS """"""""""""""""""""""" #FE #AD4A ,USE ( ! %APE T]M9A;N 9DICATOR """"""""""""""""""""" #FF #AD4B ,TRANSCRIB] DEF9$ %APES """" #FF #AD4C ,COMB9$ %APES """""""""""""" #FG #AE ,MATRICES & VECTORS """""""""""" #FI #AE4A ,5L>G$ GR\P+ SYMBOLS """"""" #FI #AE4B ,MATRICES """""""""""""""""" #FI #AE4C ,DET]M9ANTS """""""""""""""" #GJ #AE4D ,OMIS.N DOTS """"""""""""""" #GJ #AE4E ,D1L+ ) WIDE MATRICES """""" #GA #AE4F ,VECTORS """"""""""""""""""" #GB #AE4G ,GR\P+ ( EQUA;NS """"""""""" #GC #AF ,*EMI/RY """"""""""""""""""""""" #GD #AF4A ,*EMICAL "NS """"""""""""""" #GE #AF4B ,*EMICAL =MULAE """""""""""" #GE #AF4C ,ATOMIC MASS NUMB]S """""""" #GF #AF4D ,ELECTRONIC 3FIGURA;N """""" #GF #AF4E ,*EMICAL ,EQUA;NS """""""""" #GG #AF4F ,ELECTRONS """"""""""""""""" #GH #AF4G ,/RUCTURAL ,=MULAE """"""""" #GH P#I ,TE*NICAL ,GUIDEL9ES #AG ,COMPUT] ,NOTA;N """"""""""""""" #HC #AG4A ,DEF9I;N ( COMPUT] NOTA;N "" #HC #AG4B ,L9E >RANGE;T & SPAC+ )9 COMPUT] NOTA;N """"""""""""""" #HC #AG4C ,GRADE ( BRL 9 COMPUT] NOTA;N """"""""""""""""""""""" #HF P#AJ ,,,UNIFI$ 5GLI% BRL,' #A ,,,GUIDEL9ES = TE*NICAL MAT]IAL,' #BJJH V].N UPDAT$ ,AUGU/ #BJAD #A ,G5]AL ,PR9CIPLES #A4A ,SPAC+ #A4A4A ,! LAY\T ( ! PR9T %D 2 PRES]V$ Z NE>LY Z POSSIBLE4 ,H["E C>E %D 2 TAK5 9 COPY+ PR9T SPAC+ AL;G A L9E Z ? IS (T5 SIMPLY A MATT] ( PR9T+ /YLE4 ,SPAC+ %D 2 US$ TO REFLECT ! /RUCTURE ( ! MA!MATICS4 ,SPAC+ 9 PR9T "?\T A "W IS (T5 9CONSI/5T & X IS N DESIRABLE 9 ! BRL TRANSCRIP;N T ? 9CONSI/5CY %D 2 PRES]V$4 #A4A4B ,= EA* "W1 A DECI.N M/ 2 MADE ON ! SPAC+ ( OP]A;N SIGNS " & COMP>ISON SIGNS "4 ,:5 PRES5T+ BRL MA!MATICS TO "Y] *N1 9CLUDE SPACES 2F & AF OP]A;N SIGNS & 2F & AF COMP>ISON SIGNS4 ,= OLD] /UD5TS :O >E TACKL+ L;G] ALGEBRAIC EXPRES.NS "! NE$S TO 2 A BAL.E 2T CL>;Y & COMPACT;S4 ,A GD APPROA* IS TO H ! OP]A;N SIGNS UNSPAC$ ON BO? SIDES B #A #A ,G5]AL ,PR9CIPLES A#A / 9CLUDE A SPACE 2F & AF COMP>ISON SIGNS4 ,? IS ! APPROA* US$ 9 MO/ ( ! EXAMPLES 9 ? DOCU;T4 #A4A4C ,"! >E AL SITUA;NS ": X IS PREF]ABLE TO UNSPACE A COMP>ISON SIGN4 ,"O IS :5 UNSPAC+ ! SIGN WD AVOID DIVID+ A COMPLEX EXPRES.N 2T L9ES 9 A COMPLICAT$ MA!MATICAL >GU;T4 ,ANO!R IS :5 ! COMP>ISON SIGN IS N ON ! BASE L9E "<= EXAMPLE SIGMA NOTA;N ": I EQUALS #A IS 9 A SMALL FONT DIRECTLY 2L">4 #A4A4D ,:5 ISOLAT$ CALCULA;NS APPE> 9 A LIT]>Y TEXT1 ! PR9T SPAC+ C 2 FOLL[$4 --------------------------------------#B #A4B ,"ULY+ RULES = NUMB]S & LRS ,LI/$ 2L IS A SUMM>Y ( ! RULES = ,GRADE #A MODE & ,NUM]IC MODE Z !Y APPLY TO ! BRAILL+ ( NUMB]S & LRS 9 MA!MATICS4 ,REF] TO ! COMPLETE V].NS ( ^! RULES = M DETAIL4 #A4B4A ,GRADE #A MODE ,A BRL SYMBOL MAY H BO? A GRADE #A M1N+ & A 3TRAC;N " #B #A ,G5]AL ,PR9CIPLES A#B M1N+4 ,"S SYMBOLS MAY AL H A NUM]IC M1N+4 ,A GRADE #A 9DICATOR IS US$ TO SET GRADE #A MODE :5 ! GRADE #A M1N+ ( A SYMBOL CD 2 MISR1D Z A 3TRAC;N M1N+ OR A NUM]IC M1N+4 ,NOTE T IF A S+LE LR " O3URS 9 AN ALGEBRAIC EXPRES.N1 X C 2 MISR1D Z A 3TRAC;N IF X IS 8/&+ AL"O0 S MAY NE$ A GRADE #A 9DICATOR4 ,! SAME IS TRUE ( A SEQU;E ( LRS 9 BRL T CD REPRES5T A %ORT=M1 S* Z ;AB OR ;AC1 IF X IS 8/&+ AL"O04 ,A LR1 OR UNBROK5 SEQU;E ( LRS IS 8/&+ AL"O0 IF ! SYMBOLS 2F & AF ! LR OR SEQU;E >E SPACES1 HYPH5S1 DA%ES1 OR ANY COMB9A;N1 OR IF ON BO? SIDES ! ONLY 9T]V5+ SYMBOLS 2T ! LR OR SEQU;E & ! SPACE1 HYPH5 OR DA% >E COMMON LIT]>Y PUNCTUA;N OR 9DICATOR SYMBOLS4 ,SEE ! ,G5]AL ,RULE = A FULL DEF9I;N ( 8/&+ AL"O04 #A4B4B ,NUM]IC MODE ,NUM]IC MODE IS 9ITIAT$ BY ! #C #A ,G5]AL ,PR9CIPLES B#B 8NUMB] SIGN0 " FOLL[$ BY "O ( ! T5 DIGITS1 ! COMMA OR ! DECIMAL PO9T4 ,! FOLL[+ SYMBOLS MAY O3UR 9 NUM]IC MODE3 ! T5 DIGITS2 FULL /OP2 COMMA2 ! NUM]IC SPACE "2 SIMPLE NUM]IC FRAC;N L9E2 & ! L9E 3T9UA;N 9DICATOR4 ,A SPACE OR ANY SYMBOL N LI/$ "H T]M9ATES NUM]IC MODE1 = EXAMPLE ! HYPH5 OR ! DA%4 ,A NUM]IC MODE 9DICATOR AL SETS GRADE #A MODE4 ,GRADE #A MODE1 :5 9ITIAT$ BY NUM]IC MODE1 IS T]M9AT$ BY A SPACE1 HYPH5 OR DA%4 ,"!=E :ILE GRADE #A MODE IS 9 E6ECT1 A GRADE #A 9DICATOR IS N REQUIR$ EXCEPT = ANY "O ( ! L[]CASE LRS A-;J IMMLY FOLL[+ A DIGIT1 A FULL /OP OR A COMMA4 "<,NOTE T ,GRADE #A MODE1 :5 9ITIAT$ BY NUM]IC MODE1 IS N T]M9AT$ BY ! M9US SIGN1 "-4"> --------------------------------------#C #A4C ,PR9T ,SYMBOLS ,"O ( ! "ULY+ DESIGN F1TURES ( ,,UEB IS T EA* PR9T SYMBOL %D H "O & ONLY #D #A ,G5]AL ,PR9CIPLES A#C "O BRL EQUIVAL5T4 ,= EXAMPLE ! V]TICAL B> IS US$ 9 PR9T TO REPRES5T ABSOLUTE VALUE1 3DI;NAL PROBABIL;Y & ! ^WS 8S* T01 TO GIVE J ?REE EXAMPLES4 ,! SAME BRL SYMBOL %D 2 US$ 9 ALL ^! CASES1 & ANY RULES = ! USE ( ! SYMBOL 9 BRL >E 9DEP5D5T ( ! SUBJECT >EA4 ,IF A PR9T SYMBOL IS N DEF9$ 9 ,,UEB1 X C 2 REPRES5T$ EI US+ "O ( ! SEV5 TRANSCRIB] DEF9$ PR9T SYMBOLS 9 ,SEC;N #AA1 OR BY US+ ! TRANSCRIB] DEF9$ %APE SYMBOLS 9 ,SEC;N #AD4 #A4D ,=MAT .=" 3T9UA;N 9DICATOR #A4D4A ,9 PR9T1 MA!MATICAL EXPRES.NS >E "S"TS EMB$D$ 9 ! TEXT & "S"TS SET A"P4 ,:5 AN EXPRES.N IS SET A"P1 ! BRL =MAT %D 9DICATE ? BY SUITABLE 9D5TA;N1 = EXAMPLE CELL #C ) OV]RUNS 9 #E OR CELL #E ) OV]RUNS 9 #G4 ,AN EMB$D$ EXPRES.N : DOES N FIT ON ! CURR5T BRL L9E %D ONLY 2 DIVID$ IF "! IS AN OBVI\S DIVID+ #E #A ,G5]AL ,PR9CIPLES B#C PO9T4 ,(T5 X IS BETT] TO MOVE ! :OLE EXPRES.N TO ! NEXT BRL L9E4 #A4D4B ,:5 DIVID+ A MA!MATICAL EXPRES.N1 *OICE ( A RUNOV] SITE %D FOLL[ MA!MATICAL /RUCTURE3 _4 2F COMP>ISON SIGNS _4 2F OP]A;N SIGNS "E )9 "O ( ! MA!MATICAL UNITS 2L"> _4 2F A MA!MATICAL UNIT S* Z _4 FRAC;NS "<& )9 ! FRAC;N 3SID] ! NUM]ATOR & D5OM9ATOR Z UNITS"> _4 FUNC;NS _4 RADICALS _4 ITEMS ) MODIFI]S S* Z SUP]SCRIPTS OR B>S _4 %APES OR >R[S _4 ANY?+ 5CLOS$ 9 PR9T OR BRL GR\P+ SYMBOLS _4 A NUMB] & XS A2REVIA;N OR COORD9ATES ,USUALLY ! BE/ PLACE TO BR1K IS 2F A COMP>ISON SIGN OR AN OP]A;N SIGN4 #F #A ,G5]AL ,PR9CIPLES C#C ,BR1K+ 2T BRL PAGES %D 2 AVOID$4 --------------------------------------#D #A4D4C ,:5 AN EXPRES.N W N FIT ON "O BRL L9E & HAS TO 2 DIVID$1 ! USE ( 9D5TA;N Z SU7E/$ 9 #A4D4A %D MAKE X CLE> T ! OV]RUN IS "P ( ! SAME EXPRES.N4 ,H["E 9 ! UNLIKELY CASE ": ! TWO POR;NS CD 2 R1D Z TWO SEP>ATE EXPRES.NS ! 3T9UA;N 9DICATOR " %D 2 PLAC$ IMMLY AF ! LA/ CELL ( ! 9ITIAL L9E4 ,! SUM ( A1 ;B1 ;C1 ;D & ;E1 "TS ! SUM ( ;F1 ;G1 ;H1 I & ;J1 EQUALS ! SUM ( #A TO #E "TS ! SUM ( #F TO #AJ EQUALS #FJJ4 "" "7 "<#A"6#B"6#C"6#D"6#E">" "<#F"6#G"6#H"6#I"6#AJ"> "7 #FJJ #A4E ,TYPE=MS ,9 MA!MATICS1 ALGEBRAIC LRS >E FREQU5TLY ITALICIS$ Z A 4T9C;N F ORD9>Y TEXT4 ,X IS G5]ALLY N NEC TO #G #A ,G5]AL ,PR9CIPLES A#D 9DICATE ? 9 BRL4 ,H["E1 :5 BOLD OR O!R TYPEFACE IS US$ TO 4T+UI% DI6]5T TYPES ( MA!MATICAL LRS OR SIGNS F ORD9>Y ALGEBRAIC LRS1 E4G4 = VECTORS OR MATRICES1 ? 4T9C;N %D 2 RETA9$ 9 BRL BY US+ ! APPROPRIATE TYPE=M 9DICATOR4 ,SEE ,SEC;N #B4G = ! EMPHASIS ( 9DIVIDUAL DIGITS )9 NUMB]S4 #A4F ,CAPITALISA;N ,9 MA!MATICS & SCI;E1 /R+S ( CAPITAL LRS (T5 O3UR1 = EXAMPLE 9 A GEOMETRICAL "N1 9 A PHYSICS =MULA OR 9 G5ETICS4 ,S* /R+S %D ALW 2 UNCONTRACT$4 ,CAPITAL ^W 9DICATORS " >E NORMALLY US$4 ,SEE ,SEC;N #AF = ADVICE ON CAPITAL LRS 9 *EMICAL =MULAE4 ,X IS PREF]ABLE TO AL USE ? APPROA* 9 G5ETICS OR O!R TOPICS ": "! >E FREQU5T *ANGES ( CASE )9 A SEQU;E ( LRS4 RECTANGLE ,,ABCD ;,V "7 ,,IR ,TRIANGLE ,,RST N ,,R/ #H #A ,G5]AL ,PR9CIPLES B#D ,,AB;9#B @.<,9 PR9T1 CAPITAL ,A1 CAPITAL ;,B1 SUP]SCRIPT #B4@.> ;,,AB1 ,,BC & ;,,AC ,,III,'RD @.<,ROMAN CAPITAL ?IRD4@.> ,H,H,HH @.<,PR9T %[S #C CAPITAL ;H'S & A L[] CASE ;H4@.> --------------------------------------#E #A4G ,USE ( ,GRADE #A 9DICATORS .=; GRADE #A SYMBOL 9DICATOR .=;; GRADE #A ^W 9DICATOR .=;;; GRADE #A PASSAGE 9DICATOR .=;' GRADE #A PASSAGE T]M9ATOR .=""=;;; GRADE #A PASSAGE 9DICATOR ON A L9E ( XS [N .=""=;' GRADE #A PASSAGE T]M9ATOR ON A L9E ( XS [N #A4G4A ,GRADE #A 9DICATORS W N 2 NE$$ = SIMPLE >I?METIC PROBLEMS 9VOLV+ NUMB]S1 OP]A;N SIGNS1 NUM]ICAL FRAC;NS & MIX$ NUMB]S4 #I #A ,G5]AL ,PR9CIPLES A#E ,EVALUATE ! FOLL[+3 #C M9US #B & A HALF EQUALS ,EVALUATE ! FOLL[+3 #C "- #B#A/B "7 #A4G4B ,SIMPLE ALGEBRAIC EQUA;NS : 9CLUDE LRS B NO FRAC;N OR SUP]SCRIPT 9DICATORS MAY NE$ GRADE #A SYMBOL 9DICATORS ": LRS /& AL"O OR FOLL[ NUMB]S4 "<,SEE ,SEC;N #A4B = ! "ULY+ RULES & ,SEC;N #C4B = M EXAMPLES4"> ;Y EQUALS ;X PLUS #D;C ;Y "7 X"6#D;C --------------------------------------#F #A4G4C ,M COMPLEX ALGEBRAIC EQUA;NS >E BE/ 5CLOS$ 9 GRADE #A PASSAGE 9DICATORS4 ,? W 5SURE T ISOLAT$ LRS & 9DICATORS S* Z SUP]SCRIPT1 SUBSCRIPT1 FRAC;NS1 RADICALS1 >R[S & %APES >E WELL DEF9$ )\T ! NE$ = GRADE #A SYMBOL 9DICATORS4 ,3SID] ! FOLL[+ EQUA;N3 #AJ #A ,G5]AL ,PR9CIPLES A#F #CX M9US #DY PLUS ;Y SQU>$ EQUALS ;X SQU>$ ,3SID] ! FOLL[+ EQUA;N3 ;;;#CX"-#DY"6Y9#B "7 X9#B;' ,NOTE T ? "PICUL> EQUA;N CD AL 2 WRITT5 #CX"-#DY"6Y9#B "7 X;9#B 2C ! LEFT H& SIDE ( ! EQUA;N IS 9 GRADE #A MODE FOLL[+ ! NUM]IC 9DICATOR "4 ,SIMIL>LY FRAC;N3 ;X SQU>$ PLUS #BX ALL OV] #A PLUS ;X SQU>$ CLOSE FRAC;N C 2 SAFELY WRITT5 Z ;;;(X9#B"6#BX./#A"6X9#B) "7 #A;' B CD AL 2 WRITT5 ;;(X9#B"6#BX./#A"6X9#B) "7 #A ,SEE ,SEC;N #AA4E = M EXAMPLES ( ! USE ( GRADE #A PASSAGE 9DICATORS4 #AA #A ,G5]AL ,PR9CIPLES B#F #A4G4D ,IF A COMPLEX ALGEBRAIC EXPRES.N DOES N 9CLUDE A COMP>ISON SIGN " !N X IS UNLIKELY TO 9CLUDE 9T]IOR SPACES 9 BRL "4 ,9 ? CASE A GRADE #A ^W 9DICATOR W 2 5 TO 5SURE T SUP]SCRIPT1 SUBSCRIPT1 FRAC;NS1 RADICALS1 >R[S & %APE 9DICATORS >E WELL DEF9$ )\T ! NE$ = GRADE #A SYMBOL 9DICATORS4 ,EVALUATE ! SQU>E ROOT ( OP5 R.D BRACKET ;Y M9US ;X SUP]SCRIPT #B CLOSE R.D BRACKET4 ,EVALUATE ;;%"+4 ,SEE ,SEC;N #G4C = M EXAMPLES ( ! USE ( GRADE #A ^W 9DICATORS4 --------------------------------------#G #A4G4E ,:5 5TIRE "W$ EXAMPLES OR SETS ( EX]CISES >E 5CLOS$ 9 GRADE #A PASSAGE 9DICATORS1 ! GRADE #A 9DICATORS C 2 PREC$$ BY ! 8USE 9DICATOR0 & PLAC$ ON A L9E ( _! [N4 #AB #A ,G5]AL ,PR9CIPLES A#G ,SOLVE ! FOLL[+ QUADRATIC EQUA;NS3 ""=;;; #A4 X9#B"-X"-#B "7 #J #B4 X9#B"-#DX"-#C "7 #J #C4 #BX9#B"-X "7 #A ""=;' #A4G4F ,:5 ONLY A FEW 3TRACT$ ^WS >E 9VOLV$1 ! GRADE #A PASSAGE 9DICATOR C 2 US$ TO 5CLOSE 5TIRE "W$ EXAMPLES & SETS ( EX]CISES4 ,9 ? SITUA;N ANY ^WS O3URR+ 9 ! EX]CISES W 2 WRITT5 9 UNCONTRACT$ BRL & ISOLAT$ LRS W N NE$ LR SIGNS4 ,": "! IS M TEXT 9VOLV$ X IS BETT] TO /AY 9 GRADE #B & USE GRADE #A PASSAGE1 ^W OR SYMBOL 9DICATORS ONLY Z REQUIR$4 #A4G4G ,9 ! EXAMPLES 9 ? DOCU;T1 GRADE #B MODE IS ASSUM$ TO 2 9 E6ECT1 & GRADE #A 9DICATORS H BE5 9CLUD$ AC TO ! GUIDEL9ES 9 ? SEC;N4 ,M9IMIS+ ! NUMB] ( 9DICATORS M/ 2 BAL.ED AG/ R$UC+ CLUTT] )9 ! EXPRES.N XF4 ,A GRADE #A SYMBOL 9DICATOR : O3URS HALF WAY "? AN EXPRES.N MAY 2 M 4RUPTIVE TO ! R1D] ?AN A #AC #A ,G5]AL ,PR9CIPLES B#G ^W OR PASSAGE 9DICATOR1 EV5 IF ^! TAKE UP M CELLS4 ,X IS AL IMPORTANT TO USE A 3SI/5T APPROA* :5 TRANSCRIB+ A "PICUL> TEXT4 ,OV]ALL ! FOCUS %D 2 ON MA!MATICAL CL>;Y = ! R1D]4 ,FUR!R GUID.E W 2 GIV5 :5 M FE$BACK HAS BE5 RCVD F /UD5TS4 --------------------------------------#H #B ,NUMB]S & ,A2REVIA;NS ,REF] TO ,SEC;N #A4B = A SUMM>Y ( ! RULES = ,GRADE #A MODE & ,NUM]IC MODE Z !Y APPLY TO ! BRAILL+ ( NUMB]S & LRS 9 MA!MATICS4 ,! BRL REPRES5TA;N ( NUMB]S S* Z DATES & "TS %D REFLECT ! PUNCTUA;N US$ 9 PR9T4 #B4A ,:OLE NUMB]S #DEF #C1JJJ "ATOR 9 PR9T"> #E"JJJ"JJJ "ATOR 9 PR9T"> ,CALL+ S1T NUMB]S #CJ-#EI4 ,9 ! #FJ'S #AD #B ,NUMB]S & ,A2REVIA;NS A#H ,9 ! #FJS ,9 ! '#FJS ,PH"O #JI-#ECG"JHIA ,= NEGATIVE NUMB]S SEE #D4B4 --------------------------------------#I #B4B ,DECIMALS #H4IC #J4G #4G ,IS ! NUMB] 9 ! RANGE #B-#E4E8 #4H IS A DECIMAL FRAC;N4 ,= RECURR+ DECIMALS SEE ,SEC;N #AB "S1 DOTS ETC4 OV] & "U"> #B4C ,DATES #BH-#E-#BJJA #E-#BH-#JA #BJJA_/#E_/#BH #BJJA4E4BH #BH_/#E-#CA_/#E -------------------------------------#AJ #AE #B ,NUMB]S & ,A2REVIA;NS A#AJ #B4D ,"T #E3#CJ PM #E4CJ #JH4JJ #ACJJ #F-#G A4M4 #F3#AE-#G3#DE #B4E ,ORD9AL NUMB]S #AST #BND OR #B;D #CRD OR #C;D #DTH #A;ER -------------------------------------#AA #B4F ,ROMAN ,NUM]ALS ,ROMAN NUM]ALS %D 2 BRLD Z IF !Y 7 NORMAL LRS US+ ! RULES = GRADE #A MODE4 ,NOTE T ;V & ;X W H GRADE #A 9DICATORS B I W N4 ,R1D "PS ,I1 ,,II & ;,V4 ,ANSW] "QS I1 VI & ;X4 #AF #B ,NUMB]S & ,A2REVIA;NS A#AA ;,,CD #B4G ,EMPHASIS ( ,DIGITS ,IF A TYPE=M 9DICATOR APPLIES TO A DIGIT OR DIGITS )9 A NUMB]1 ! NUM]IC 9DICATOR NE$S REP1T+ AF ANY TYPE=M 9DICATOR4 ,IF ! F/ DIGIT IS A6ECT$ !N ! TYPE=M 9DICATOR %D 2 PLAC$ 2F ! NUM]IC 9DICATOR4 #FG^2#HDE @.<,! DIGIT #H IS 9 BOLD4@.> #FG^1#HDE @.<,! LA/ ?REE DIGITS >E 9 BOLD4@.> #FG^1#HD^'#E @.<,DIGITS #H & #D >E 9 BOLD4@.> _1#FGH_'#DE @.<,! F/ ?REE DIGITS >E "UL9$4@.> _2#FGHDE @.<,DIGIT #F IS "UL9$4@.> ,= RECURR+ DECIMALS SEE ,SEC;N #AB "S1 DOTS ETC4 OV] & "U"> #AG #B ,NUMB]S & ,A2REVIA;NS B#AA #B4H ,ANCI5T ,NUM]A;N SY/EMS ,BRL SYMBOLS TO REPRES5T NUM]ALS F O!R NUMB] SY/EMS MAY 2 DEVIS$ = EA* SITUA;N US+ TRANSCRIB] DEF9$ PR9T SYMBOLS4 ,^! %D 2 DEF9$ EI ON ! SPECIAL SYMBOLS PAGE OR 9 A TRANSCRIB]'S NOTE4 "<,SEE EXAMPLE 9 ,SEC;N #AA4E4G"> -------------------------------------#AB #B4I ,HEXADECIMAL NUMB]S ,HEXADECIMAL NUMB]S O3UR 9 A COMPUT] SETT+ & >E MADE UP ( ! DIGITS #J TO #I & ! LRS ,A TO ;,F4 ,!Y %D 2 TR1T$ ! SAME Z ANY O!R /R+ ( LRS & NUMB]S4 ,FATAL EXCEP;N #J,E HAS O3URR$ AT #JJBH3,C#JJJHB,,CD #B4AJ ,A2REVIA;NS ,! FOLL[+ SIGNS >E US$ = SPECIAL PR9T SYMBOLS3 .=@C C5T .=@E EURO .=@F FRANC #AH #B ,NUMB]S & ,A2REVIA;NS A#AB .=@L P.D " .=@S DOLL> .=@Y Y5 "<,JAPAN"> .=@N NAIRA "<,NIG]IA"> .=.0 P]C5T .=^J DEGREE .=7 FOOT OR M9UTE "<%[N Z A PRIME SIGN"> .=77 9* OR SECOND "<%[N Z A D\BLE PRIME SIGN"> .=,^$A ANG/ROM "<,A ) SMALL CIRCLE ABV"> ,NOTE T ! ,R& "<,S\? ,AFRICA"> IS WRITT5 9 PR9T Z A NORMAL CAPITAL ;,R S WD 2 BRLD Z S*4 ,NOTE T ! FOOT OR M9UTE MAY 2 %[N 9 PR9T BY AN APO/ROPHE "<'"> & ! 9* OR SECOND BY A NONDIREC;NAL D\BLE QUOTE "<,7">4 ,? USAGE C 2 FOLL[$ 9 BRL4 -------------------------------------#AC ,FOLL[ PR9T = ORD]1 SPAC+1 CAPITALISA;N & PUNCTUA;N ( A2REVIA;NS4 "<,IF X IS UNCLE> 9 PR9T :E!R "! IS A SPACE 2T A NUMB] & XS UNIT1 OR IF #AI #B ,NUMB]S & ,A2REVIA;NS A#AC PR9T SPAC+ IS 9CONSI/5T1 !N X IS RECOMM5D$ T A SPACE IS 9S]T$ 9 ! BRL4"> ,": %D ,I WRITE ! DOLL> SIGN1 ,,US@S OR @S,,US8 #CJ C5TS C 2 WRITT5 Z @S#J4CJ1 #CJ;C OR #CJ@C4 ,9 ,S\? ,AFRICA1 ? WD CO/ ,R#AC4EA4 ,2F DECIMALISA;N1 @L#A4GE 0 @L#A #AES S HALF ( X 0 #AGS #F;D OR #AG_/#F4 ,HALF A Y>D IS #A FT #F 9 OR #A7 #F77 : IS AB #DE CM OR #J4DE ;M4 #A ;,L ( WAT] WEIE #CFJ^J 9 A REVOLU;N1 #FJ7 9 A DEGREE & #FJ77 9 A M9UTE4 ,"O COMPLETE ORBIT LA/S #BYR #EM #AE;D #G;H #AGMIN & #DES4 #BJ #B ,NUMB]S & ,A2REVIA;NS A#AD ,A #F ;,V BATT]Y W CAUSE A CURR5T ( #C ,A TO FL[ "? A RESI/.E ( #B ,.W4 ,! R1D+ 0 #AE M,HZ4 ,! PATT]N SAYS K#D P#A SL#A K#A PSSO4 #A ,^$A "7 #A/AJ1JJJ .M -------------------------------------#AE #C ,SIGNS ( OP]A;N1 ,COMP>ISON & ,OMIS.N ,OP]A;N SIGNS3 .="6 PLUS .="- M9US "<:5 4T+UI%$ F HYPH5"> .="8 "TS " .="/ DIVID$ BY " .=_6 PLUS OR M9US " .=_- M9US OR PLUS " .="4 MULTIPLICA;N DOT ,COMP>ISON SIGNS3 .="7 EQUALS .=@< LESS ?AN1 OR OP5+ ANGLE BRACKET .=@> GRT] ?AN1 OR CLOS+ ANGLE BRACKET .=_@< LESS ?AN OR EQUAL TO #BA #C ,OP]A;N & ,COMP>ISON A#AE .=_@> GRT] ?AN OR EQUAL TO .="7@: N EQUAL TO " .=_9 APPROXIMATELY EQUAL TO " .=^9 APPROXIMATELY EQUAL TO " ,LESS COMMON SIGNS ( COMP>ISON3 .=.@< IS M* LESS ?AN .=.@> IS M* GRT] ?AN .="_9 TILDE OV] EQUALS SIGN " .=."7 EQUALS SIGN DOTT$ ABV & 2L " .=^"7 EQUALS SIGN ) BUMP 9 TOP B> " .=_= EQUIVAL5T TO " .=_"7 IS PROPOR;NAL TO ,RATIO .=3 RATIO SIGN " #BB #C ,OP]A;N & ,COMP>ISON #AF "ISON US$ 9 SET !ORY1 GR\P !ORY & LOGIC"> #C4A ,EXAMPLES ,9 MO/ ( ! EXAMPLES 2L1 OP]A;N SIGNS >E UNSPAC$ F PREC$+ & FOLL[+ T]MS B COMP>ISON SIGNS >E SPAC$4 ,! F/ TWO EXAMPLES %[ ! USE ( EXTRA SPACE = ! "Y] LE>N]4 ,FOLL[ ! GUIDEL9ES 9 ,SPAC+ "<,SEC;N #A4A4B">4 #C "6 #E "7 #H #H "- #E "7 #C #C"8#E "7 #E"8#C "7 #AE #B CM"6#D CM "7 #F CM #BJJ;G"8#E "7 #AKG #E4GB M"/#AJ "7 #EG4B CM #AE_6#J4E ,>EA "7 BH "7 #E"4#C "7 #AE #C4I"8#D4A _9 #AF #E"-#C "7@: #C"-#E -------------------------------------#AG ,A SCALE ( #A3#BJJ "ISON A#AG SIGN IS US$ TO COMP>E TWO NUMB]S1 X IS BE/ TR1T$ Z AN OP]A;N SIGN = PURPOSES ( SPAC+"> #B3#D "7 #F3#AB #C4B ,ALGEBRAIC ,EXAMPLES ,9 ! ALGEBRAIC EXAMPLES 2L NOTE ! USE ( ! GRADE #A 9DICATOR :5"E A LR IS 8/&+ AL"O0 AC TO ! DEF9I;N 9 ,SEC;N #A4B & S CD R1D Z A 3TRAC;N4 ,9 ! LA/ EXAMPLE1 ! COLON XF CD R1D Z ! CC 3TRAC;N4 ,IF ;Y _"7 ;X !N ;Y "7 KX ,F9D .? IF #J _@< .? _@< #B.P ;Y "7 X"6#D #BY "7 #B;C"-#D D"6AB "7 ;AC ,! RATIO X;3Y #C4C ,USE ( ! BRL HYPH5 ,IF ! M9US SIGN & HYPH5 >E 9DI/+UI%ABLE 9 PR9T !N ! BRL HYPH5 C 2 US$ = BO?4 ,H["E MO/ MA?S & SCI;E TEXTS %[ ! M9US SIGN Z SLIISON B#AG A HYPH5 9 PR9T S ! DOT #E =M IS BE/ US$ "?\T4 -------------------------------------#AH 9T]E/-RATE"-9FLA;N-RATE ,! TEMP]ATURE 0 #AE-#AG4 " #C4D ,POSITIVE & NEGATIVE NUMB]S ,"S"TS POSITIVE & NEGATIVE NUMB]S1 Z OPPOS$ TO ADD$ OR SUBTRACT$ NUMB]S1 >E %[N 9 PR9T BY A PLUS SIGN OR A M9US SIGN 2+ WRITT5 Z A LEFT SUP]SCRIPT "4 ,? C 2 %[N 9 BRL US+ ! SUP]SCRIPT 9DICATOR4 "<,SEE ,SEC;N #G"> ,GRADUATE ! ;X AXIS F "-#D TO "6#E4 "<) ! PLUS & M9US SIGNS 9 ! C5TRAL POSI;N 9 PR9T"> ,EVALUATE ;9"-#B"69"-#C "<) ! M9US SIGNS 9 ! SUP]SCRIPT POSI;N 9 PR9T"> #BE #C ,OP]A;N & ,COMP>ISON A#AH #C4E ,CALCULATOR KEYS ,:5 NUMB]S & OP]ATORS >E 5CLOS$ 9 BOXES TO %[ T CALCULATOR KEYS >E TO 2 PRESS$1 X MAY N 2 HELP;L TO USE ! %APE 5CLOSURE 9DICATORS 9 ,SEC;N #AD4C4 ,IF ! BOXES NE$ TO 2 %[N !N AN ALT]NATIVE APPROA* IS TO USE ! "UL9E 9DICATOR & A TRANSCRIB]'S NOTE4 #C "6 #D "7 #G @.<,"UL9+ %[S T ! SYMBOL 0 BOX$ 9 PR9T4@.> _2#C _2"6 _2#D _2"7 _2#G -------------------------------------#AI #C4F ,OMIS.N M>KS 9 MA!MATICAL EXPRES.NS .=",- L;G DA% .=.- "USCORE .=+ VISIBLE SPACE .=$#D SQU>E " #C"6#G "7 ",- " #BF #C ,OP]A;N & ,COMP>ISON A#AI #C"6#G "7 .- " #C"6#G "7 ;8 "K 9 PR9T"> #C$#D:#G "7 #AJ "E 9 PR9T"> #C+#G "7 #AJ "K$ GAP 9 PR9T"> #I/AB "7 ;(#C./+) " ,NOTE T ! VISIBLE SPACE IS ! SAME SYMBOL Z ! CLOS+ ROOT 9DICATOR "4 ,IF ! RADIC& IS TO 2 FILL$ 9 !N ! SYMBOL WD 2 REP1T$ TO T]M9ATE ! ROOT4 #E "7 ;;%++ -------------------------------------#BJ #D ,SPATIAL ,LAY\T & ,DIAGRAMS #D4A ,SPATIAL CALCULA;NS .="3 2G9 HORIZONTAL L9E MODE .=_ V]TICAL L9E SEG;T #BG #D ,SPATIAL & ,DIAGRAMS A#BJ .=# SPAC$ NUM]IC 9DICATOR .=## NUM]IC PASSAGE 9DICATOR .=#' NUM]IC PASSAGE T]M9ATOR ,": HORIZONTAL L9ES >E NE$$ )9 *N'S SUMS1 HORIZONTAL L9E MODE %D 2 US$4 ,! LAY\T ( ! CALCULA;N C FOLL[ PR9T1 ?\< FE$BACK F T1*]S "W+ ) /UD5TS %D AL 2 TAK5 9TO A3.T4 ,^! GUIDEL9ES C AL 2 APPLI$ = O!R SPATIAL >RANGE;TS S* Z F9ANCIAL /ATE;TS OR A3.TANCY TEXTS4 ,COLUMNS TO 2 ADD$ %D N 3TA9 NUM]IC 9DICATORS OR OP]A;N SIGNS4 ,? C 2 A*IEV$ BY ALIGN+ NUM]IC 9DICATORS V]TICALLY,-A NUM]IC 9DICATOR FOLL[$ BY A SPACE / 9ITIATES NUM]IC MODE4 ,ALT]NATIVELY USE ! NUM]IC PASSAGE 9DICATOR & ! NUM]IC T]M9ATOR : SET NUM]IC MODE & GRADE #A MODE = ! 5CLOS$ TEXT4 ,9 A NUM]IC PASSAGE NUM]IC 9DICATORS >E N US$1 & ANY L[]CASE LR A TO ;J IS PREC$$ BY A GRADE #A 9DICATOR4 ,! L9E ABV & 2L SPATIAL CALCULA;NS %D EI 2 BLANK1 OR %D ONLY 3TA9 ! #BH #D ,SPATIAL & ,DIAGRAMS B#BJ NUM]IC PASSAGE 9DICATOR OR T]M9ATOR4 #D4A4A ,ADDI;N OR SUBTRAC;N #DEF "6# CD "333 #DIJ -------------------------------------#BA ,! SECOND V].N 2L ILLU/RATES ! USE ( ! NUM]IC PASSAGE 9DICATOR4 ,! PLACE;T ( ! OP]A;N SIGN DOES N NE$ TO FOLL[ PR9T1 B C 2 ADJU/$ TO SUIT LOCAL T1*+ PRACTICES4 ,9D5TA;N HAS BE5 US$ TO KEEP ! COLUMNS ( ! CALCULA;N CLE> ( NUM]IC 9DICATORS4 ## DEF "6 CD "33 DIJ #' #BI #D ,SPATIAL & ,DIAGRAMS A#BA #D4A4B ,L;G MULTIPLICA;N ## ABC "8 AB "333 BDF ABC "333 ADGF #' -------------------------------------#BB #D4A4C ,DIVI.N ,! SPAC$ V]TICAL L9E SEG;T " C 2 US$ TO REPRES5T ! CURV$ OR /RAI #CA #D ,SPATIAL & ,DIAGRAMS B#BB ## IC "3333 E _ DFE DE "33 AE AE "33 #' ## E _ DFE DE _I "33 AE _C AE "33 #' ,ANS3 #IC #CB #D ,SPATIAL & ,DIAGRAMS #BC #D4A4D ,SPATIAL FRAC;NS = T1*+ PURPOSES TWO ?IRDS #B "3 #C "O ?IRD PLUS "O HALF EQUALS TWO SIX?S PLUS ?REE SIX?S EQUALS FIVE SIX?S ## A A B C E "3 "6 "3 "7 "3 "6 "3 "7 "3 C B F F F #' #CC #D ,SPATIAL & ,DIAGRAMS A#BC #D4A4E ,C>RYOV]S ,9S]T SPACES 2T ! DIGITS 9 BRL S T ! SMALL NUMB]S C 2 PLAC$ ON _! [N R[ ABV OR 2L ! C5TRAL CALCULA;N4 ,! LAY\T ( ? TYPE ( EXAMPLE C 2 ADJU/$ TO SUIT LOCAL T1*+ PRACTICES4 ,?IRTY-TWO M9US F\RTE5 EQUALS EI4 @.<,! SMALL NUMB]S >E A "O TO ! LEFT & ABV ! NUMB] TWO 9 ! TOP L9E1 & A "O TO ! "R & 2L ! NUMB] "O 9 ! SECOND L9E4@.> ## A C B "- A D A "333 A H #' #CD #D ,SPATIAL & ,DIAGRAMS #BD #D4A4F ,C.ELLA;N .=@: L9E "? PREVI\S ITEM " ,:5 C.ELLA;N ( NUMB]S OR EXPRES.NS IS %[N 9 PR9T1 X IS "S"TS BETT] TO PRES]VE ! USUAL BRL =M & EXPLA9 ! PROCESS 9 A TRANSCRIB]'S NOTE4 ,TAKE ! AGE ( ! /UD5T 9TO A3.T & *ECK ) LOCAL T1*+ PRACTICES4 ,= ! FRAC;N EXAMPLE 2L1 TWO POSSIBLE APPROA*ES >E %[N4 ,?REE FIF?S "TS EI #CE #D ,SPATIAL & ,DIAGRAMS A#BD ,SPATIAL >RANGE;T ## A C@: H H "333 "8 "333 "7 "33 E I@: AE C #' ,US+ C.ELLA;N L9ES )9 G5]AL FRAC;N 9DICATORS "<,SEE ,*APT] #F"> ;(#C@:#A./#E)"8(#H./#I@:#C) "7 #H/AE #D4A4G ,NUMB]$ CALCULA;NS ,IF A S]IES ( CALCULA;NS >E NUMB]$1 !N NUM]IC PASSAGE 9DICATORS C 2 US$ TO 5CLOSE ! :OLE S]IES4 ,H["E X IS RECOMM5D$ T ! NUM]IC 9DICATOR IS AL US$ 2F EA* ITEM NUMB]4 ,EX3 #CF #D ,SPATIAL & ,DIAGRAMS #BE ## #A #B AB "6 CF "6 CD EB "33 "33 #C #D FC "6 AED "6 AI GF "33 "33 #' #D4B ,TALLY M>KS .=_ TALLY M>K " .=____3 #D TALLY M>KS ) /RIKE "? " ,! HORIZONTAL OR DIAGONAL /RIKE-"? REPRES5TS ! C.T+ ( A FIF? ITEM4 ,? C EI 2 %[N Z A FIF? TALLY M>K 9 BRL OR ! 8#D TALLY M>KS ) /RIKE-"?0 SYMBOL C 2 US$4 ,EX3 #CG #D ,SPATIAL & ,DIAGRAMS A#BE ,EIKS ) /RIKE-"?S1 & "O GR\P ( ?REE TALLY M>KS4@.> ,EIE LEFT 2T COLUMNS4 ,IF NUMB]S >E TO 2 ADD$ !Y %D 2 "R ADJU/$4 ,EX3 #CH #D ,SPATIAL & ,DIAGRAMS A#BF ;;;Y "7 X9#B"-#C;' ;X ;Y "333 "333 "-#A "-#B #J "-#C #A "-#B #B #A #C #F ,X IS AL A3EPTABLE TO 9CLUDE A BOX+ L9E ABV & 2L ! TABLE4 -------------------------------------#BG #D4D ,DIAGRAMS ,? SEC;N DOES N ATTEMPT TO GIVE ADVICE ON ! DESIGN ( TACTILE DIAGRAMS OR ON ! RANGE ( PRODUC;N ME?ODS AVAILABLE4 #D4D4A ,HORIZONTAL ,L9E ,MODE ,MO/ TRANSCRIB]S H EXP]I;T$ ) ! USE ( BRL SYMBOLS = DRAW+ SIMPLE BOX %APES OR FAMILY TREES4 ,AL? ^! >E (T5 N Z #CI #D ,SPATIAL & ,DIAGRAMS A#BG R1DABLE Z A RAIS$ L9E DRAW+1 !Y / H _! USES4 ,IF AN UNBROK5 BRL L9E 2G9S ) ! HORIZONTAL L9E MODE 9DICATOR "3 !N ALL ! O!R CELLS 9 T L9E W 2 R1D Z %APES R ?AN SYMBOLS4 ,IF V]TICAL L9ES >E AL %[N US+ ! V]TICAL L9E SEG;T _ !N A BACK TRANSLA;N PROCESS OR A TUN$ 9 R1D] C 2 CLE> T ? IS A DIAGRAM R ?AN A /R+ ( TEXT4 "3333433334 _ _ _ _ _ _ "3333J3333J H5RY ;M M>Y _ "333333W33333334 _ _ _ SUE DAVE PAT #DJ #D ,SPATIAL & ,DIAGRAMS B#BG ,REF] TO ! .7,RULES ( ,UNIFI$ ,5GLI% ,BRL1 ,SEC;N #AF3 ,L9E ,MODE1 ,GUIDE ,DOTS.' = SYMBOLS TO USE 9 L9E MODE4 ,SPECIAL M5;N IS MADE ( >R[ SYMBOLS : C 2 US$ )\T T]M9AT+ HORIZONTAL L9E MODE4 ,! FOLL[+ TWO EXAMPLES ILLU/RATE ! USE ( >R[ SYMBOLS & AL 9CLUDE UNLI/$ DOT PATT]NS = ! %APES ( ! HOLL[ & SOLID CIRCLES US$ 9 PR9T TO REPRES5T ! OP5 OR CLOS$ 5D ( AN 9T]VAL4 -------------------------------------#BH ,9 ! PR9T EXAMPLE 2L A NUMB] L9E IS GRADUAT$ F "-#B TO #C & AN 9T]VAL IS M>K$ ABV X />T+ AT #J & F9I%+ ) AN OP5 CIRCLE AT #B4 ,9 ! BRL V].N 2L1 ,,UEB >R[ MODE IS US$ = ! LEFT & "R PO9T+ >R[S "<,SEE ,SEC;N #AC"> & HORIZONTAL L9E MODE IS US$ 2T !M4 ,! 9T]VAL XF IS %[N Z A L9E F9I%+ ) ! DOT PATT]N .=Y = ! EMPTY CIRCLE4 "333333333Y \["33W3333W3333W3333W3333W3333W333\O "-#B "-#A #J #A #B #C #DA #D ,SPATIAL & ,DIAGRAMS A#BH ,9 ! SECOND EXAMPLE 2L ! 9T]VAL />TS ) A SOLID CIRCLE AT "-#B & F9I%ES AT #J4 ,9 ! BRL V].N1 ! DOT PATT]N .== HAS BE5 US$ = ! SOLID CIRCLE4 =3333333333 \["33W3333W3333W3333W3333W3333W333\O "-#B "-#A #J #A #B #C ,NOTE T 9 ? SECOND BRL EXAMPLE1 ! HORIZONTAL L9E MODE 9DICATOR .="3 CD N PREC$E ! CIRCLE SYMBOL )\T OBSCUR+ ! POSI;N ( T />T PO9T ON ! NUMB] L9E4 ,9 ANY DIAGRAM1 TACTUAL CL>;Y MAY 2 DEEM$ M IMPORTANT ?AN TE*NICAL AMBIGU;Y4 ,ALW BE> 9 M9D T A WELL EXECUT$ RAIS$ L9E DRAW+ W G5]ALLY 2 M R1DABLE ?AN A DIAGRAM CR1T$ US+ BRL CELL PATT]NS4 ,SEE ,SEC;N #AF = EXAMPLES ( *EMI/RY /RUCTURES DRAWN US+ HORIZONTAL L9E MODE & V]TICAL & DIAGONAL L9E SEG;TS4 #DB #D ,SPATIAL & ,DIAGRAMS #BI #D4D4B ,LABELL+ DIAGRAMS ,? SEC;N DOES N ATTEMPT TO GIVE ADVICE ON H[ TO E6ECTIVELY LABEL A DIAGRAM 9 BRL S T X IS CLE> TO ! R1D] : "P ( ! DIAGRAM EA* LABEL REF]S TO4 ,R1 X LI/S CODE A3OMMODA;NS : C 2 MADE )9 ! 3T5T ( C]TA9 LABELS :5 SPACE IS AT A PREMIUM4 _4 ,:5 LABELL+ PO9TS1 L9ES ETC4 ) S+LE LRS1 ^! C 2 3SI/5TLY %[N Z TWO CELLS BY OMITT+ ! GRADE #A 9DICATOR = ALL CAPITAL LRS & 9CLUD+ X = ALL L[]CASE LRS 9CLUD+ A1 I & O4 _4 ,:5 GRADUAT+ AN AXIS ) NEGATIVE NUMB]S1 ! HYPH5 CD 2 US$ 9/1D ( ! M9US SIGN "4 ,9CLUDE A TRANSCRIB]'S NOTE4 _4 ,:5 WRIT+ COORD9ATES S* Z "<#B1 -#C">1 ANY ( ! FOLL[+ CD 2 3SID]$3 OMITT+ ! SPACE2 OMITT+ ! DOT #E PREFIX F ! R.D BRACKETS2 OMITT+ ! DOT #E PREFIX F ! M9US SIGN4 ,9CLUDE A TRANSCRIB]'S NOTE4 #DC #D ,SPATIAL & ,DIAGRAMS A#BI _4 ,:5 LABELL+ A L9E OR CURVE ) XS EQUA;N1 ! SPACE EI SIDE ( ! EQUALS SIGN CD 2 OMITT$4 _4 ,:5 LABELL+ ANGLES1 ! DEGREE SIGN CD 2 OMITT$4 ,9CLUDE A TRANSCRIB]'S NOTE4 -------------------------------------#CJ #E ,GR\P+ ,DEVICES "<,BRACKETS"> .="< OP5+ R.D P>5!SIS .="> CLOS+ R.D P>5!SIS .=.< OP5+ SQU>E BRACKET .=.> CLOS+ SQU>E BRACKET .=_< OP5+ CURLY BRACE .=_> CLOS+ CURLY BRACE .=@< OP5+ ANGLE BRACKET .=@> CLOS+ ANGLE BRACKET .=_\ V]TICAL B> " .=,"< BIG " OP5+ R.D P>5!SIS .=,"> BIG " CLOS+ R.D P>5!SIS .=,.< BIG " OP5+ SQU>E BRACKET #DD #E ,GR\P+ ,DEVICES A#CJ .=,.> BIG " CLOS+ SQU>E BRACKET .=,_< BIG " OP5+ CURLY BRACE .=,_> BIG " CLOS+ CURLY BRACE .=,_\ BIG " V]TICAL B> ,PR9T BRACKETS >E USUALLY UNSPAC$ F ! ITEMS !Y 5CLOSE & ! SAME %D 2 D"O 9 BRL4 ,SEE ,SEC;N #AE = ! LAY\T ( MATRICES & VECTORS4 ,LET ! MIDPO9T ( ,A"<#C1 "-#E"> & ,B"<#J1 #D"> ; ! PO9T "<;X1 ;Y">4 .<#B".>"/#D @< #AJ _\"-#F_\ "7 _\#F_\ "7 #F " ,3SID] ! SEQU;E @<,T;5N@>4 "<;,T SUB ;N 5CLOS$ 9 ANGLE BRACKETS"> #DE #F ,FRAC;NS #CA #F ,FRAC;NS .=/ SIMPLE NUM]IC FRAC;N L9E .=./ G5]AL FRAC;N L9E .=( G5]AL FRAC;N OP5 9DICATOR .=) G5]AL FRAC;N CLOSE 9DICATOR #F4A ,SIMPLE NUM]IC FRAC;NS ,A SIMPLE NUM]IC FRAC;N IS "O ^: NUM]ATOR & D5OM9ATOR 3TA9 ONLY DIGITS1 DECIMAL PO9TS1 COMMAS OR SEP>ATOR SPACES & ^: FRAC;N L9E 9 PR9T IS DRAWN 2T ! TWO V]TICALLY "LY V]TICALLY"> >RANG$ NUMB]S4 ,9 S* A CASE A NUM]IC FRAC;N L9E SYMBOL MAY 2 US$ 2T ! NUM]ATOR & D5OM9ATOR & 3T9UES ! NUM]IC MODE4 ,FIVE EIE BOYS4 #E/H ( ! CLASS >E BOYS4 ,CALCULATE #E4G OV] #B1JJJ ,CALCULATE #E4G/B1JJJ #DF #F ,FRAC;NS A#CA #F4B ,MIX$ NUMB]S ,MIX$ NUMB]S %D 2 TR1T$ Z TWO UNSPAC$ NUM]IC ITEMS4 ,TWO & A HALF CUPS ( SUG> #B#A/B CUPS ( SUG> #AGEJ CM "7 "O & ?REE QU>T] ;M #AGEJ CM "7 #A#C/D ;M -------------------------------------#CB #F4C ,FRAC;NS WRITT5 9 L9E> =M 9 PR9T ,! NUM]IC FRAC;N L9E NE$ N 2 US$ :5 ! PR9T IS EXPRESS$ L9E>LY US+ AN ORD9>Y SLA% " SYMBOL4 ,9 S* A CASE ! SAME SYMBOLS C 2 US$ Z 9 PR9T4 #C_/#H ( ! CLASS >E GIRLS4 #F4D ,G5]AL FRAC;N 9DICATORS ,IF ! NUM]ATOR OR D5OM9ATOR IS N 5TIRELY NUM]IC Z DEF9$ 9 #F4A1 !N ! G5]AL FRAC;N 9DICATORS %D 2 US$4 #DG #F ,FRAC;NS A#CB ,AF ! OP5+ 9DICATOR ! NUM]ATOR EXPRES.N IS WRITT51 !N ! G5]AL FRAC;N L9E SYMBOL1 !N ! D5OM9ATOR EXPRES.N & F9ALLY ! CLOS+ 9DICATOR4 ,BO? NUM]ATOR & D5OM9ATOR MAY 2 ANY K9D ( EXPRES.N :AT"E1 9CLUD+ FRAC;NS ( EI SIMPLE NUM]IC OR G5]AL TYPE4 ,9 ! V]BALISA;NS 2L1 QUOTA;N M>KS H BE5 US$ TO REFLECT ! SPATIAL >RANGE;T US$ 9 PR9T4 ;Y EQUALS 8;X OV] #B0 ;;;Y "7 (X./#B);' TWO & A HALF OV] 8;X PLUS ;Y0 ;(#B#A/B./X"6Y) TWO SLA% ?REE ALL OV] #E ;(#B_/#C./#E) FRAC;N 8;X OV] #B0 PLUS 8;Y OV] #C0 ALL OV] 8;X PLUS ;Y0 ;;((X./#B)"6(Y./#C)./X"6Y) #DH #F ,FRAC;NS #CC SPE$ EQUALS 4T.E OV] "T1 %[+ ALT]NATIVE USAGE ( GRADE #A 9DICATORS ;;;SPEED "7 (DISTANCE./TIME);' SPE$ "7 ;;(DISTANCE./TIME) SPE$ "7 ;(DI/.E./"T;) #F4E ,EXTRA ,EXAMPLES ,^! EXAMPLES >E 9CLUD$ TO FUR!R ILLU/RATE ! DI6];E 9 PR9T 2T SIMPLE NUM]IC FRAC;NS Z DEF9$ 9 #F4A1 & FRAC;NS : W NE$ G5]AL FRAC;N 9DICATORS 9 BRL Z DEF9$ 9 #F4D4 ,SIMPLE NUM]IC FRAC;NS3 #C OV] #D #C/D #GC OV] #D #GC/D #C OV] #D4B #C/D4B #DI #F ,FRAC;NS A#CC #E4C OV] #D1BJJ #E4C/D1BJJ #E & ?REE-QU>T]S #E#C/D #F & 8#C OV] #AJ"JJJ0 "ATOR 9 PR9T"> #F#C/AJ"JJJ ,FRAC;NS NE$+ G5]AL FRAC;N 9DICATORS 2C !Y 3TA9 LRS3 ;X OV] ;Y ;;(X./Y) ;X OV] #D ;(X./#D) #C OV] ;B ;(#C./B) A OV] 8;B PLUS ;C0 ;;(A./B"6C) #EJ #F ,FRAC;NS B#CC #CX OV] #D ;(#CX./#D) ;X OV] #D1JJJ ;(X./#D1JJJ) ,FRAC;NS NE$+ G5]AL FRAC;N 9DICATORS 2C !Y 3TA9 "S?+ M ?AN DIGITS1 COMMAS OR DECIMAL PO9TS3 #C SQU>$ OV] #F ;(#C9#B./#F) @S#EE OV] #E ;(@S#EE./#E) #BDM OV] #C;CM ;(#BDM./#C;CM) "Q M>K OV] #D ;(8./#D) #EA #F ,FRAC;NS C#CC TWO-?IRDS OV] #D ;(#B/C./#D) 8#B M9US #E0 OV] #C ;(#B"-#E./#C) -------------------------------------#CD #G ,SUP]SCRIPTS & SUBSCRIPTS .=5 LEVEL *ANGE D[N " .=9 LEVEL *ANGE UP " .=.5 EXPRES.N DIRECTLY 2L .=.9 EXPRES.N DIRECTLY ABV .=< BRL GR\P+ OP5 .=> BRL GR\P+ CLOSE #G4A ,DEF9I;N ( AN ITEM ,! SCOPE ( ANY ( ! F\R LEVEL *ANGE 9DICATORS1 T IS1 ! SYMBOL" A6ECT$ BY X1 IS ! NEXT 8ITEM04 ,AN ITEM IS DEF9$ Z ANY ( ! FOLL[+ GR\P+S IF IMMLY AF ! LEVEL *ANGE 9DICATOR3 #A4 ,AN 5TIRE NUMB]1 I4E4 ! #EB #G SUP]SCRIPT SUBSCRIPT A#CD 9ITIAT+ NUM]IC SYMBOL & ALL SU3E$+ SYMBOLS )9 ! NUM]IC MODE ?US E/ABLI%$ "<: WD 9CLUDE ANY 9T]IOR DECIMAL PO9TS1 COMMAS1 SEP>ATOR SPACES1 OR SIMPLE NUM]IC FRAC;N L9ES">4 #B4 ,AN 5TIRE G5]AL FRAC;N1 5CLOS$ 9 FRAC;N 9DICATORS "4 #C4 ,AN 5TIRE RADICAL EXPRES.N1 5CLOS$ 9 RADICAL 9DICATORS "4 #D4 ,AN >R[ "4 #E4 ,AN >BITR>Y %APE "4 #F4 ,ANY EXPRES.N 5CLOS$ 9 MAT*+ PAIRS ( R.D P>5!SES1 SQU>E BRACKETS OR CURLY BRACES "4 #G4 ,ANY EXPRES.N 5CLOS$ 9 ! BRL GR\P+ 9DICATORS4 #H4 ,IF N"O ( ! =EGO+ APPLY1 ! ITEM IS SIMPLY ! NEXT 9DIVIDUAL SYMBOL4 -------------------------------------#CE #G4B ,SUP]SCRIPTS & SUBSCRIPTS )9 LIT]>Y TEXT ,NOTE T IF A SUP]SCRIPT OR SUBSCRIPT APPE>S )9 A GRADE #B PASSAGE1 X W NE$ A GRADE #A 9DICATOR4 #EC #G SUP]SCRIPT SUBSCRIPT A#CE ,! >EA IS #F ;M SQU>$ ,! >EA IS #F M;9#B ,! PO9TS ;,P SUB #A & ;,P SUB #B ,! PO9TS ,P;5#A & ,P;5#B ,SMI? WROTE A PAP] SUP] #EF : SAYS 444 " ,SMI? WROTE A PAP];9#EF : SAYS 444 ,! =MULA = WAT] IS ;,H SUB #B ,O ,! =MULA = WAT] IS ,H;5#B,O #G4C ,ALGEBRAIC EXPRES.NS 9VOLV+ SUP]SCRIPTS ,REF] TO ! DEF9I;N ( AN ITEM 9 ,SEC;N #G4A TO DECIDE :5 BRL GR\P+ SYMBOLS >E REQUIR$4 ,NOTE T ! BRL GR\P+ SYMBOLS !MVS H AN ALT]NATIVE GRADE #B M1N+4 ,9 ! V]BALISA;NS 2L1 QUOTA;N M>KS H BE5 US$ TO REFLECT ! SPATIAL >RANGE;T US$ 9 PR9T4 #ED #G SUP]SCRIPT SUBSCRIPT B#CE ;X SQU>$ X;9#B ;X SQU>$ "TS ;Y X;9#BY ;X TO ! #BY ;;X9<#BY> -------------------------------------#CF 8;X TO ! ;Y0 PLUS #A X;9Y"6#A ;X TO ! 8;Y PLUS #A0 ;;X9 ;X TO ! 8;Y PLUS #A0 PLUS #C ;;X9"6#C ;X TO ! TWO ?IRDS X;9#B/C ;X SQU>$ OV] #C ;;(X9#B./#C) #EE #G SUP]SCRIPT SUBSCRIPT A#CF ;X TO ! 8HALF ;Y0 ;;X9<#A/BY> 8;X TO ! HALF0 ;Y X;9#A/BY ;X SUP]SCRIPT 8A OV] ;B0 5D SUP]SCRIPT ;Y EQUALS ;X ;;;X9(A./B)Y "7 X;' ,IF FRAC;N 8;X SQU>$ PLUS #BX0 ALL OV] 8#A PLUS ;X SQU>$0 5D FRAC;N EQUALS #A ;X SQU>$ PLUS #BX EQUALS #A PLUS ;X SQU>$ ;X EQUALS #A OV] #B ;;;,IF (X9#B"6#BX./#A"6X9#B) "7 #A X9#B"6#BX "7 #A"6X9#B X "7 #A/B;' -------------------------------------#CG #G4D ,MULTIPLE LEVELS ,NOTE T A SUP]SCRIPT : XF HAS A SUP]SCRIPT DOES N FIT ! ABV #EF #G SUP]SCRIPT SUBSCRIPT A#CG DEF9I;N ( AN ITEM4 ,9 S* CASES BRL GR\P+ SYMBOLS >E REQUIR$4 ;E TO ! ;X SQU>$ ;;E9 ;E TO ! OP5 P>5!SIS ;X SQU>$ CLOSE P>5!SIS ;;E9" ;,P ) AN ;X SUB I 9 ! SUBSCRIPT POSI;N ;;,P5 #G4E ,NEGATIVE SUP]SCRIPTS ,NEGATIVE SUP]SCRIPTS M/ 2 5CLOS$ 9 BRL GR\P+ SYMBOLS4 "<,? IS 2C A M9US SIGN C 2 AN ITEM 9 XS [N "R1 Z 9 #G4F 2L4"> #J4JJDE EQUALS #D4E "TS #AJ TO ! M9US #C #J4JJDE "7 #D4E"8#AJ9<"-#C> ;V EQUALS #FJ MS TO ! M9US #A ;;;V "7 #FJ MS9<"-#A>;' #EG #G SUP]SCRIPT SUBSCRIPT B#CG A TO ! M9US #B;B P[] ;;A9<"-#B;B> -------------------------------------#CH #G4F ,EXAMPLES F ,*EMI/RY ,SEE ,SEC;N #AF = M EXAMPLES4 ,,CH SUB #D PLUS #B ,CL EQUALS ,,CH SUB #C ,CL PLUS ,H,CL ;;;,C,H5#D"6#B,CL "7 ,C,H5#C,CL"6,H,CL;' ,IONS ;,H SUP] PLUS1 ,CL SUP] M9US & ,CA SUP] 8#B PLUS0 ,IONS ,H;9"61 ,CL;9"- & ;;,CA9<#B"6> #G4G ,SIMULTANE\S SUP]SCRIPTS & SUBSCRIPTS ,IF M ?AN "O SUP]SCRIPT OR SUBSCRIPT APPLY1 "W F BOTTOM TO TOP1 OR LEFT TO "R4 ,IF ! PR9T 9DICATES BY ! PLAC+ ( ! SUBSCRIPT T X IS 2+ APPLI$ AF ! SUP]SCRIPT !N ! ORD] C 2 REV]S$4 ;X SUB #A SQU>$ EQUALS ;Y SUB #B CUB$ ;;;X5#A9#B "7 Y5#B9#C;' #EH #G SUP]SCRIPT SUBSCRIPT A#CH ;X SQU>$ SUB ;K ;;X9#B5K #G4H ,LEFT-4PLAC$ SUP]SCRIPTS OR SUBSCRIPTS ,"S"TS 9 PR9T A SUP]SCRIPT OR SUBSCRIPT IS WRITT5 TO ! LEFT ( ! BASE SYMBOL 9/1D ( TO ! "R4 ,^! >E H&L$ SIMPLY BY US+ ! CORRESPOND+ ORD9>Y 9DEX EXPRES.N PRIOR TO ! BASE SYMBOL4 ;,U ) #IB WRITT5 2L LEFT & #BCH WRITT5 ABV LEFT ;;5#IB9#BCH,U M9US #B PLUS M9US #C EQUALS M9US #E "<) M9US SIGNS 9 ! SUP]SCRIPT POSI;N"> ;;;9"-#B"69"-#C "7 9"-#E;' -------------------------------------#CI #G4I ,MODIFI]S DIRECTLY ABV OR 2L ,IF "S?+ IS WRITT5 DIRECTLY ABV OR 2L A T]M R ?AN TO ! "R OR LEFT1 USE ! DIRECTLY ABV 9DICATOR OR DIRECTLY 2L 9DICATOR 9/1D ( ! SUP]SCRIPT OR #EI #G SUP]SCRIPT SUBSCRIPT A#CI SUBSCRIPT 9DICATOR4 ,COMMON MODIF]S S* Z ! B>1 >R[1 DOT1 TILDE1 HAT OR >C >E TR1T$ SEP>ATELY 9 ,SEC;N #AB4 ,! SUM F ;X EQUALS #A TO ;N ( ;X SUB I SQU>$ ) SUMMA;N LIMITS DIRECTLY 2L & ABV A CAPITAL SIGMA 22,.S.5.9NX5I9#B ,! LIMIT1 Z ;X T5DS TO A1 ( ;F ( ;X1 EQUALS #A1 ) ;X >R[ A DIRECTLY 2L LIM ;;;LIM.5F" "7 #A;' ;X ) B> OV] X X;: " -------------------------------------#DJ #H ,SQU>E ,ROOTS & O!R RADICALS .=% OP5 RADICAL " .=+ CLOSE RADICAL " .="% SQU>E ROOT SIGN )\T V9CULUM #FJ #H ,SQU>E ,ROOTS A#DJ #H4A ,SQU>E ROOTS ,! EXPRES.N 9SIDE ! SQU>E ROOT SIGN 9 PR9T " %D 2 PREC$$ BY ! OP5 RADICAL SIGN & FOLL[$ BY ! CLOSE RADICAL SIGN4 ,! RADIC& XF MAY 2 ANY EXPRES.N :ATSO"E1 & MAY "!=E 3TA9 RADICALS Z WELL Z O!R MA!MATICAL /RUCTURES4 ,NOTE T BO? ! OP5+ & CLOS+ RADICAL SIGNS H ALT]NATIVE GRADE #B M1N+S S MAY NE$ GRADE #A 9DICATORS4 ! SQU>E ROOT ( #I EQUALS #C ;%#I+ "7 #C "<,NOTE T ! SQU>E ROOT ( A SIMPLE NUMB] / NE$S TO 2 T]M9AT$ BY ! CLOSE RADICAL SIGN4"> ;R EQUALS ! SQU>E ROOT ( ;X SQU>$ PLUS ;Y SQU>$ 5D ROOT ;;;R "7 %X9#B"6Y9#B+;' #FA #H ,SQU>E ,ROOTS B#DJ ! SQU>E ROOT ( FRAC;N #GHC4B "TS #F4EDG OV] #J4DFBH 5D FRAC;N 5D ROOT ;;%(#GHC4B"8#F4EDG./#J4DFBH)+ ;X EQUALS ! FRAC;N3 M9US ;B PLUS-OR-M9US ! SQU>E ROOT ( ;B SQU>$ M9US #D;AC 5D ROOT ALL OV] #B;A ;;;X "7 ("-B_6%B9#B"-#D;AC+./#B;A);' -------------------------------------#DA #H4B ,CUBE ROOTS ETC ,9 PR9T ! RADICAL 9DEX1 IF PRES5T1 IS PR9T$ ABV & TO ! LEFT ( ! RADICAL SIGN4 ,? 9DEX IS PLAC$ 9 BRL Z A SUP]SCRIPT EXPRES.N IMMLY FOLL[+ ! OP5+ RADICAL SYMBOL4 ! CUBE ROOT ( #H EQUALS #B ;;%9#C#H+ "7 #B ;Q EQUALS ! CUBE ROOT ( ;X CUB$ PLUS ;Y CUB$ PLUS ;Z CUB$ 5D ROOT ;;;Q "7 %9#CX9#C"6Y9#C"6Z9#C+;' #FB #H ,SQU>E ,ROOTS A#DA ! MN-TH ROOT ( XY ;;%9XY+ #HA TO ! ?REE-QU>T]S EQUALS " CUB$ EQUALS "E ROOT ( ! SQU>E ROOT ( #HA"> CUB$ EQUALS "E ROOT ( #I"> CUB$ EQUALS ?REE CUB$ EQUALS #BG ;;;#HA9#C/D "7 "<%9#D#HA+">9#C "7 "<%%#HA++">9#C "7 "<%#I+">9#C "7 #C9#C "7 #BG;' #H4C ,SQU>E ROOT SIGN ON XS [N ,"S"TS PR9T OMITS ! HORIZONTAL L9E " ABV ! RADIC&4 ,9 OLD] BOOKS1 @. CD M1N ! SQU>E ROOT ( #D1 B 9 "S MOD]N 3TEXTS CD 2 J A SEQU;E ( SYMBOLS4 ,:5 9TRODUC+ SIMPLE ROOTS TO "Y] *N1 X IS BETT] TO 9TRODUCE ! 3CEPT ( OP5+ & CLOS+ 9DICATORS F ! />T4 ,IF X IS CLE> F ! 3TEXT T ? IS A SQU>E ROOT1 !N X IS BE/ TO ASSUME AN 9T5D$ V9CULUM & TO USE ! /&>D =M4 ,IF1 H["E1 ! SQU>E ROOT #FC #H ,SQU>E ,ROOTS B#DA SIGN IS 2+ US$ Z AN ISOLAT$ GRAPHIC SYMBOL !N ! DOT #E =M C 2 US$4 ,EX4 #D )9 SQU>E ROOT ) V9CULUM EQUALS #B ;%#D+ "7 #B SQU>E ROOT SIGN )\T V9CULUM FOLL[$ BY #D EQUALS #B ;%#D+ "7 #B ,! 8SQU>E ROOT )\T V9CULUM0 SIGN ,! "% SIGN -------------------------------------#DB #I ,FUNC;NS ,IF A FUNC;N "N IS PREC$$ OR FOLL[$ BY A LR ( ! SAME FONT & ALPHABET1 X MAY N 2 CLE> ": ! FUNC;N "N 2G9S OR 5DS4 ,9 PR9T ? IS CL>IFI$ US+ A V>IETY ( TE*NIQUES4 ,TAKE ! EXAMPLE A "TS ! COS9E ( ;T4 ,9 PR9T ? IS (T5 WRITT5 .7A COS ;T.'4 ,NOTICE T "H ! .2A & .2;T >E WRITT5 9 ITALICS TO %[ !Y >E V>IABLES1 & A SMALL SPACE IS 9CLUD$ EI SIDE ( ! FUNC;N #FD #I ,FUNC;NS A#DB "N4 ,? TE*NIQUE IS AL US$ 9 PR9T TO 4T+UI% ^W FRAG;TS O!R ?AN FUNC;NS4 ,! EXAMPLES 9 ? SEC;N >E TAK5 F SECOND>Y S*OOL SCI;E & MA!MATICS B ! SAME RULES %D 2 FOLL[$ :5 D1L+ ) FUNC;NS )9 ANY SUBJECT >EA4 #I4A ,SPELL+ & CAPITALISA;N ,FOLL[ PR9T = ! SPELL+ & CAPITALISA;N ( FUNC;N "NS4 ,F9D ! VALUE ( ,COS9E ;,B4 #I4B ,ITALICS ,": LRS 2F OR AF ! FUNC;N "N >E WRITT5 9 ITALICS TO 9DICATE !Y >E V>IABLES1 ! ITALICS %D 2 OMITT$ 9 A3ORD.E ) RULE #A4C4 -------------------------------------#DC #I4C ,SPAC+ ,": ! FUNC;N "N IS PREC$$ OR FOLL[$ BY A LR1 A SPACE MAY 2 NE$$1 TO REMOVE AMBIGU;Y Z TO ": ! FUNC;N "N 2G9S & 5DS4 ,! SPACE IS N NE$$ IF ! FUNC;N "N #FE #I ,FUNC;NS A#DC IS ALR SEP>AT$ BY A BRACKET OR BY A BRL 9DICATOR S* Z A CAPITALISA;N 9DICATOR1 A ,GREEK LR 9DICATOR OR A FRAC;N 9DICATOR4 ,C>E %D 2 TAK5 :5 A CAPITAL LR PREC$ES A FUNC;N "N4 ,? IS SUMM>IS$ 2L4 #I4C4A ,IF A FUNC;N "N IS DIRECTLY PREC$$ OR FOLL[$ BY A NUMB]1 !N ! NUMB] %D 2 WRITT5 UNSPAC$ F ! FUNC;N "N4 ,S9#CJ #CTAN#DE^J "<#C TAN #DE DEGREES"> #D;COS#EX #I4C4B ,9S]T A SPACE IF A FUNC;N "N IS FOLL[$ DIRECTLY BY A L[] CASE ,LAT9 LR ) NO 9T]V5+ BRL 9DICATORS OR BRACKETS4 LOG ;Y S9.? " ,SEC,A LOG" ;;,LIM(X./#B) "<,LIM 8;X OV] #B0"> -------------------------------------#DD #I4C4C ,9S]T A SPACE IF A FUNC;N #FF #I ,FUNC;NS A#DD "N IS PREC$$ DIRECTLY BY A L[] OR UPP] CASE ,LAT9 LR ) NO 9T]V5+ BRL 9DICATORS OR BRACKETS4 ,NOTE T LRS ISOLAT$ BY ^! EXTRA SPACES MAY NE$ GRADE #A 9DICATORS4 ;X S9#FJ X,S9#FJ ;,X LOG ;Y X,LOG ;Y S9 "<,A PLUS ;,B"> EQUALS S9 ,A COS ;,B PLUS COS ,A S9 ;,B S9"<,A"6,B"> "7 S9,A COS,B"6COS,A S9,B S9 #B 2TA EQUALS #B S9 2TA COS 2TA S9#B.B "7 #BSIN.BCOS.B #I4D ,TRIGONOMETRIC FUNC;NS ,COMMON TRIGONOMETRIC FUNC;NS >E ,S9E1 ,COS9E1 ,TANG5T1 ,SECANT1 ,COSECANT & ,COTANG5T1 USUALLY A2REVIAT$ 9 PR9T TO S91 COS1 TAN1 SEC1 COSEC & COT4 ,_! 9V]SES MAY 2 WRITT5 9 PR9T Z #FG #I ,FUNC;NS B#DD S9 SUP] M9US #A1 COS SUP] M9US #A1 TAN SUP] M9US #A1 SEC SUP] M9US #A1 COSEC SUP] M9US #A & COT SUP] M9US #A1 OR LESS COMMONLY Z >CS91 >CCOS1 >CTAN1 >CSEC1 >CCOSEC & >CCOT4 ,Y MAY AL MEET ! ASSOCIAT$ HYP]BOLIC FUNC;NS S9H1 CO%1 TANH1 SE*1 COSE* & CO? & _! 9V]SES4 ,IF S9 !TA EQUALS O OV] ;H EQUALS #B OV] #D !N !TA EQUALS S9 TO ! M9US #A ( #J4E EQUALS #CJ DEGREES ,IF ;;;SIN.? "7 (O./H) "7 #B/D;' !N ;;;.? "7 SIN9<"-#A>#J4E "7 #CJ^J;' -------------------------------------#DE ,PROVE SEC SQU>$ ;X EQUALS #A PLUS TAN SQU>$ ;X ,PROVE ;;;SEC9#BX "7 #A"6TAN9#BX;' ,F9D ! D]IVATIVE ( ;F ( ;X EQUALS FRAC;N CO% ;X OV] S9H ;X SQU>$ 5D FRAC;N ,F9D ! D]IVATIVE ( ;;;F" "7 (COSH X./SINH X9#B);' #FH #I ,FUNC;NS A#DE #I4E ,LOG>I?MIC FUNC;NS ,! LOG>I?MIC FUNC;N IS USUALLY WRITT5 LOG OR ,LOG & MAY 2 FOLL[$ BY A SUBSCRIPT 9DICAT+ ! BASE4 ,A LOG>I?M TO BASE ;E IS CALL$ A NATURAL LOG & IS (T5 A2REVIAT$ TO LN4 #C LOG ;X #CLOG ;X LOG BASE #B ( #H EQUALS #C ;;LOG5#B#H "7 #C ! NATURAL LOG ( ;E EQUALS #A LN ;E "7 #A ,LOG A PLUS ,LOG ;B EQUALS ,LOG ;AB ;;;,LOG A"6,LOG B "7 ,LOG AB;' ,! 9TEGRAL ( TAN ;X ) RESPECT TO ;X EQUALS ! NATURAL LOG ( COS ;X PLUS A 3/ANT ;;;!TAN XDX "7 LN COS X"6C;' #FI #I ,FUNC;NS B#DE ,! LOG BASE ;B ( ;X EQUALS ! LOG BASE A ( ;X OV] ! LOG BASE A ( ;B ;;;LOG5BX "7 (LOG5AX./LOG5AB);' -------------------------------------#DF #I4F ,! ,LIMIT FUNC;N ,LIMIT1 LIM1 LM1 LT >E ALL US$ TO 9DICATE LIMIT1 "S"TS ) CAPITALS1 "S"TS )\T4 ,NOTE3 SEE ,SEC;N #AC = ! REPRES5TA;N ( >R[S4 ,! LIMIT1 Z ;X T5DS TO A1 ( ;F ( ;X1 EQUALS #A1 ) ;X >R[ A DIRECTLY 2L ,LIM ;;,LIM.5F" "7 #A ,! LIMIT1 Z !TA T5DS TO #J1 ( S9 !TA OV] !TA1 EQUALS #A ;;LIMIT.5<.?\O#J>(SIN.?./.?) "7 #A #I4G ,/ATI/ICAL FUNC;NS ,PROBABIL;Y IS %[N 9 PR9T 9 _M WAYS1 9CLUD+ ;,P1 ,PROB OR ,PR4 ,O!R /ATI/ICAL FUNC;NS 9CLUDE EXPECTA;N : MAY 2 %[N 9 PR9T Z ;,E OR ,EXP4 #GJ #I ,FUNC;NS A#DF PROBABIL;Y ( ,A & ;,B EQUALS PROBABIL;Y ( ,A PLUS PROBABIL;Y ( ;,B ,PR"<,A & ;,B"> "7 ,PR,A"6,PR,B ,! EXPECTA;N ( ;,R EQUALS 8;N OV] #B0 PLUS #A ;;;,EXP"<,R"> "7 (N./#B)"6#A;' -------------------------------------#DG #I4H ,COMPLEX NUMB]S ,FUNC;NS US$ 9 COMPLEX NUMB] !ORY 9CLUDE >G "<>GU;T">1 ,RE "1 ,IM "Y "P"> & CIS4 >G ( ;Z SUB #A ;Z SUB #B EQUALS >G ;Z SUB #A PLUS >G ;Z SUB #B ;;;ARG" "7 ARG Z5#A"6ARG Z5#B;' ;Z EQUALS ;R CIS !TA EQUALS ;R COS !TA PLUS IR S9 !TA ;;;Z "7 R CIS.? "7 R COS.?"6IR SIN.?;' #GA #AJ ,SET ,!ORY #DH #AJ ,SET ,!ORY1 ,GR\P ,!ORY & ,LOGIC .=.6 UNION " .=.8 9T]SEC;N "<9V]T$ ;,U %APE"> .=@J NULL SET " .=7 COMPLE;T " .=^E IS AN ELE;T ( "IANT EPSILON"> .=@^E 3TA9S Z AN ELE;T "IANT EPSILON"> .=^< 3TA9$ IN1 IS A SUBSET ( "<;,U OP5 TO "R"> .=^> 3TA9S1 IS A SUP]SET ( "<;,U OP5 TO LEFT"> .=_^< 3TA9$ 9 OR EQUAL TO .=_^> 3TA9S OR EQUAL TO .=.^< 3TA9$ IN1 B N EQUAL TO " .=.^> 3TA9S1 B IS N EQUAL TO " .=@_< IS A NORMAL SUBGR\P ( " #GB #AJ ,SET ,!ORY A#DH .=@_> 9V]SE 8IS NORMAL SUBGR\P0 " .=__< IS NORMAL SUBGR\P ( OR EQUAL " .=__> 9V]SE 8NORMAL SUBGR\P OR EQUAL0 " .=._< NORMAL SUBGR\P B N EQUAL " .=._> 9V]SE 8NORMAL SUBGR\P B N EQUAL0 " .=@6 OR " .=@8 & "<9V]T$ ;V %APE"> .=@? 8N0 SIGN " .=_3 ASS];N "<8IS A !OREM0 SIGN2 8;,T0 LY+ ON LEFT SIDE"> .=@_3 REV]SE ASS];N "<8;,T0 LY+ ON "R SIDE"> .=^_3 8IS VALID0 SIGN " .=._3 REV]SE 8IS VALID0 SIGN #GC #AJ ,SET ,!ORY #DI ,IF ,A EQUALS ! SET #A1 #B1 #C1 #D & ;,B EQUALS ! SET #B1 #D1 #E1 #H IS #C AN ELE;T ( ,A 9T]SEC;N ;,B & IS ,A 9T]SEC;N ;,B A SUBSET ( ,A UNION ;,B8 ,IF ,A "7 _<#A1 #B1 #C1 #D_> & ;,B "7 _<#B1 #D1 #E1 #H_> IS #C ^E ,A.8,B & IS ,A.8,B ^< ,A.6,B8 ! UNION ( ,A COMPLE;T & ;,B COMPLE;T EQUALS ! COMPLE;T ( ! 9T]SEC;N ( ,A & ;,B ;;;,A7.6,B7 "7 "<,A.8,B">7;' ,= ! /ATE;TS ;P & ;Q EI ;P OR ;Q2 & N ;P2 "!=E1 ;Q ,= ! /ATE;TS ;P & ;Q ;;;.<"@8@?P.> _3 Q;' #GD #AA MISCELLANE\S SYMBOLS #EJ #AA ,MISCELLANE\S ,SYMBOLS .=! 9TEGRAL SIGN .=@! CLOS$ L9E 9TEGRAL " .=@D "PIAL D]IVATIVE " .=^D DEL1 NABLA "<9V]T$ CAPITAL DELTA"> .=7 PRIME "<:5 4T+UI%$ F APO/ROPHE 9 PR9T"> .=_"7 IS PROPOR;NAL TO "IES Z"> .=@9 TILDE " .=@5 C>ET " .="9 A/]ISK .="0 HOLL[ DOT .=_\ V]TICAL B> .=#= 9F9;Y .=6 FACTORIAL SIGN "K 9 PR9T"> .=_[ ANGLE SIGN .=._[ M1SUR$ ANGLE SIGN .=#_[ M1SUR$ "R ANGLE SIGN .=#L P>ALLEL TO .=#- P]P5DICUL> TO #GE #AA MISCELLANE\S SYMBOLS A#EJ .=,* 8"!=E0 " .=@/ 8S9CE0 " .=^5 8"! EXI/S0 " .=^A 8= ALL0 "<9V]T$ ,A"> .=@A AT SIGN .=_* BACKSLA% .=.- "USCORE .=_? CROSS HAT* .=@& AMP]S& .=.\ BROK5 V]TICAL B> -------------------------------------#EA .=? F/ TRANSCRIB]-DEF9$ PR9T SYMBOL .=#? SECOND TRANSCRIB]-DEF9$ PR9T SYMBOL .=@#? ?IRD TRANSCRIB]-DEF9$ PR9T SYMBOL .=^#? F\R? TRANSCRIB]-DEF9$ PR9T SYMBOL .=_#? FIF? TRANSCRIB]-DEF9$ PR9T SYMBOL .="#? SIX? TRANSCRIB]-DEF9$ PR9T SYMBOL .=.#? SEV5? TRANSCRIB]-DEF9$ PR9T SYMBOL #AA4A ,SPAC+ ,9 G5]AL1 ! SPAC+ ( SYMBOLS C FOLL[ PR9T4 ,H["E IF A SYMBOL IS CLE>LY 2+ US$ Z A SIGN ( OP]A;N OR COMP>ISON1 #GF #AA MISCELLANE\S SYMBOLS A#EA FOLL[ ! GUIDEL9ES 9 ,SEC;N #A4A4 #AA4B ,UNUSUAL ,PR9T SYMBOLS ,IF A PR9T SYMBOL IS N DEF9$ 9 ,,UEB1 X C 2 REPRES5T$ EI US+ "O ( ! SEV5 TRANSCRIB]-DEF9$ PR9T SYMBOLS ABV1 OR BY US+ ! TRANSCRIB]-DEF9$ %APE SYMBOLS 9 ,SEC;N #AD4 "<,SEE EXAMPLE #AA4E4G 2L"> #AA4C ,GRADE #A 9DICATORS ,IF ! BRL V].N ( A PR9T SYMBOL AL HAS A GRADE #B M1N+1 & GRADE #A MODE IS N ALR 9 =CE1 !N GRADE #A 9DICATORS W 2 NE$$4 ,SYMBOLS 9 ! LI/ ABV = : ? APPLIES >E ! 9TEGRAL SIGN1 ! PRIME SIGN & ! "!=E SIGN4 #AA4D ,SYMBOLS : H M ?AN "O M1N+ 9 PR9T ,"O ( ! "ULY+ DESIGN F1TURES ( ,,UEB IS T EA* PR9T SYMBOL %D H "O & ONLY "O BRL EQUIVAL5T4 ,= EXAMPLE ! V]TICAL B> IS US$ 9 PR9T TO REPRES5T ABSOLUTE VALUE1 3DI;NAL PROBABIL;Y & ! ^WS #GG #AA MISCELLANE\S SYMBOLS B#EA 8S* T01 TO GIVE J ?REE EXAMPLES4 ,! SAME BRL SYMBOL %D 2 US$ 9 ALL ^! CASES4 -------------------------------------#EB #AA4E ,EXAMPLES #AA4E4A ,IF ;Y "7 F" !N ! D]IVATIVE IS DY OV] DX OR ;F DA% ;X & ! "PIAL D]IVATIVE IS CURLY ;D ;Y OV] CURLY ;D ;X ,IF ;Y "7 F" !N ! D]IVATIVE IS ;;(DY./DX) OR ;;F7" & ! "PIAL D]IVATIVE IS ;;(@DY./@DX)4 #GH #AA MISCELLANE\S SYMBOLS A#EB #AA4E4B ! 9TEGRAL F #B TO #C ( "<#BX PLUS #A"> DX EQUALS .<;X SQU>$ PLUS ;X.> SUB #B SUP] #C EQUALS "<#C SQU>$ PLUS #C"> M9US "<#B SQU>$ PLUS #B"> EQUALS #AB M9US #F EQUALS #F ;;;!5#B9#C"<#BX"6#A">DX "7 .5#B9#C "7 "<#C9#B"6#C">"-"<#B9#B"6#B"> "7 #AB"-#F "7 #F;' ,NOTE3 ! SPAC+ ( ! 9TEGRAL SIGN 9 PR9T C 2 UNCLE> OR 9CONSI/5T4 ,9 BRL X IS BE/ TO H ! 9TEGRAL SIGN UNSPAC$ F ! FUNC;N & TR1T XS LIMITS Z SUBSCRIPTS & SUP]SCRIPTS4 ,! DX AT ! 5D M1NS 89TEGRATE ) RESPECT TO ;X01 & C AL 2 WRITT5 UNSPAC$4 #GI #AA MISCELLANE\S SYMBOLS #EC #AA4E4C "G$ BRACKETS 5CLOS+ ;N AT ! TOP & ;R AT ! BOTTOM EQUALS FRAC;N ;N FACTORIAL OV] ;R FACTORIAL "TS "<;N M9US ;R"> FACTORIAL 5D FRAC;N"> ;;;9N,C5R "7 " "7 (N6./R6"6);' ,NOTE3 ! B9OMIAL COE6ICI5T "WS BETT] Z A %APE ?AN A VECTOR "4 #AA4E4D ,A/]ISK IS 4TRIBUTIVE OV] HOLL[ DOT IF A A/]ISK "<;B HOLL[ DOT ;C"> EQUALS " HOLL[ DOT " "9 IS 4TRIBUTIVE OV] "0 IF A"9" "7 ""0" ,NOTE3 ! HOLL[ DOT %D N 2 US$ TO #HJ #AA MISCELLANE\S SYMBOLS A#EC REPRES5T ! A2REVIA;N = DEGREES1 : IS COV]$ 9 ,SEC;N #C4 -------------------------------------#ED #AA4E4E ,IF ;F F ;,X TO ;,Y IS A FUNC;N !N ! RELA;N ;F SUP] M9US #A F ;,Y TO ;,X IS XF A FUNC;N IF & ONLY IF = ALL ;Y 9 ;,Y "! EXI/S ;X 9 ;,X S* T ;F ( ;X EQUALS ;Y ,IF ;;;F3 ,X \O ,Y;' IS A FUNC;N !N ! RELA;N ;;;F9<"-#A>3 ,Y \O ,X;' IS XF A FUNC;N IF & ONLY IF ;;;^AY ^E ,Y ^5X ^E ,X;' S* T ;;;F" "7 Y;' ,NOTE3 SEE ,SEC;N #AC = ! REPRES5TA;N ( >R[S4 #AA4E4F ,! SET ( "<;X1 ;Y"> S* T ;X PLUS ;Y EQUALS #F ;;;_<" _\ X"6Y "7 #F_>;' #HA #AA MISCELLANE\S SYMBOLS A#ED #AA4E4G ,BABYLONIAN NUM]ALS USE TWO SYMBOLS1 ;? M1NS #A & #? M1NS #AJ4 ,NOTE3 ! TWO TRANSCRIB] DEF9$ SYMBOLS WD 2 DEF9$ EI ON ! SPECIAL SYMBOLS PAGE OR 9 A TRANSCRIB]'S NOTE4 -------------------------------------#EE #AA4F ,EMBELLI%$ CAPITAL LRS ,EMBELLI%$ CAPITAL LRS >E (T5 US$ TO "N COMMON SETS S* Z ! UNIV]SAL SET ;,E1 ! SET ( R1L NUMB]S ;,R OR 9TEG]S ,I4 ,^! V>Y 9 PR9T F BOOK TO BOOK B C 2 REPRES5T$ 9 BRL BY ! SCRIPT TYPE=M 9DICATORS4 ,! SET ( R1L NUMB]S @2;,R -------------------------------------#EF #AA4G ,GREEK LRS ,GREEK LRS >E US$ H1VILY 9 ,MA!MATICS4 ,! ALPHABET IS LI/$ 2L4 ,REF] AL TO ! ,RULE ON ,LRS & _! MODIFI]S4 #HB #AA MISCELLANE\S SYMBOLS A#EF .=.A ,GREEK ALPHA .=.B ,GREEK 2TA .=.G ,GREEK GAMMA .=.D ,GREEK DELTA .=.E ,GREEK EPSILON .=.Z ,GREEK ZETA .=.: ,GREEK ETA .=.? ,GREEK !TA .=.I ,GREEK IOTA .=.K ,GREEK KAPPA .=.L ,GREEK LAMBDA .=.M ,GREEK MU .=.N ,GREEK NU .=.X ,GREEK XI .=.O ,GREEK OMICRON .=.P ,GREEK PI .=.R ,GREEK RHO .=.S OR .S ,GREEK SIGMA .=.T ,GREEK TAU .=.U ,GREEK UPSILON .=.F ,GREEK PHI .=.& ,GREEK *I .=.Y ,GREEK PSI .=.W ,GREEK OMEGA #HC #AA MISCELLANE\S SYMBOLS B#EF .=,.A CAPITAL ,GREEK ALPHA .=,.B CAPITAL ,GREEK 2TA .=,.G CAPITAL ,GREEK GAMMA .=,.D CAPITAL ,GREEK DELTA .=,.E CAPITAL ,GREEK EPSILON .=,.Z CAPITAL ,GREEK ZETA .=,.: CAPITAL ,GREEK ETA .=,.? CAPITAL ,GREEK !TA .=,.I CAPITAL ,GREEK IOTA .=,.K CAPITAL ,GREEK KAPPA .=,.L CAPITAL ,GREEK LAMBDA .=,.M CAPITAL ,GREEK MU .=,.N CAPITAL ,GREEK NU .=,.X CAPITAL ,GREEK XI .=,.O CAPITAL ,GREEK OMICRON .=,.P CAPITAL ,GREEK PI .=,.R CAPITAL ,GREEK RHO .=,.S CAPITAL ,GREEK SIGMA .=,.T CAPITAL ,GREEK TAU .=,.U CAPITAL ,GREEK UPSILON .=,.F CAPITAL ,GREEK PHI .=,.& CAPITAL ,GREEK *I .=,.Y CAPITAL ,GREEK PSI .=,.W CAPITAL ,GREEK OMEGA #HD #AB ,B>S & DOTS OV] & "U #EG #AB ,B>S & DOTS ETC4 OV] & "U .=: B> OV] PREVI\S ITEM .=,: B> "U PREVI\S ITEM .=@: L9E "? PREVI\S ITEM " .=^: SIMPLE "R PO9T+ >R[ OV] PREVI\S ITEM .=,^: SIMPLE "R PO9T+ >R[ "U PREVI\S ITEM .=^4 DOT OV] PREVI\S ITEM .=,^4 DOT "U PREVI\S ITEM .=_: TILDE OV] PREVI\S ITEM .=,_: TILDE "U PREVI\S ITEM .=": HAT OV] PREVI\S ITEM .=,": HAT "U PREVI\S ITEM .=._: >C OV] PREVI\S ITEM #AB4A ,! DEF9I;N ( AN ITEM ,! DEF9I;N ( AN ITEM 2L IS ! SAME Z T GIV5 = SUP]SCRIPTS & SUBSCRIPTS 9 ,SEC;N #G4A4 #HE #AB ,B>S & DOTS OV] & "U A#EG ,Z 9 ,SEC;N #G1 AN ITEM IS DEF9$ Z ANY ( ! FOLL[+ GR\P+S3 #A4 ,AN 5TIRE NUMB]1 I4E4 ! 9ITIAT+ NUM]IC SYMBOL & ALL SU3E$+ SYMBOLS )9 ! NUM]IC MODE ?US E/ABLI%$ "<: WD 9CLUDE ANY 9T]IOR DECIMAL PO9TS1 COMMAS1 SEP>ATOR SPACES1 OR SIMPLE NUM]IC FRAC;N L9ES">4 #B4 ,AN 5TIRE G5]AL FRAC;N1 5CLOS$ 9 FRAC;N 9DICATORS "4 #C4 ,AN 5TIRE RADICAL EXPRES.N1 5CLOS$ 9 RADICAL 9DICATORS "4 #D4 ,AN >R[ "4 #E4 ,AN >BITR>Y %APE "4 #F4 ,ANY EXPRES.N 5CLOS$ 9 MAT*+ PAIRS ( R.D P>5!SES1 SQU>E BRACKETS OR CURLY BRACES "4 #G4 ,ANY EXPRES.N 5CLOS$ 9 ! BRL GR\P+ 9DICATORS4 #H4 ,IF N"O ( ! =EGO+ APPLY1 ! ITEM IS SIMPLY ! PREVI\S 9DIVIDUAL SYMBOL4 #HF #AB ,B>S & DOTS OV] & "U #EH ,EXAMPLES3 ;X B> EQUALS #AJ PLUS #AA PLUS #AB ALL OV] #C ": ;X B> IS ! >I?METIC M1N4 ;;;X: "7 (#AJ"6#AA"6#AB./#C);' ": X;: IS ! >I?METIC M1N4 ,NOTE3 ! SECOND O3UR;E ( ;X B> NE$S A GRADE #A SYMBOL 9DICATOR 2C X IS )9 A GRADE #B PASSAGE4 ;X PLUS ;Y ALL ) A B> "U 22,: EQUALS SIGN ) A L9E "? X " "7@: #J4C ) A DOT OV] ! #C,-! RECURR+ DECIMAL #J4CCCCC444 #J4<#C>^4 ,NOTE3 BRL GR\P+ SIGNS >E NE$$ "H O!RWISE ! DOT WD REF] TO ! 5TIRE NUMB]4 #HG #AB ,B>S & DOTS OV] & "U A#EH ,! RECURR+ DECIMAL #J4EFABCABCABC 444 #J4EF<#A>^4#B<#C>^4 ,2C ! DIGITS #ABC >E 2+ IMPLICITLY GR\P$ 9 PR9T ? C AL 2 WRITT5 Z3 #J4EF<#ABC>^4 D]IVATIVES ;X DOT & ;X D\BLE DOT D]IVATIVES X^4 & ;;X.9<44> ,ANGLE ,,ABC ) A HAT OR C>ET OV] ! ;,B ,ANGLE ;;,A,B":,C -------------------------------------#EI #AB4B ,TWO 9DICATORS APPLI$ TO ! SAME ITEM ,IF TWO 9DICATORS APPLY TO ! SAME ITEM1 !N BRL GR\P+ SYMBOLS M/ 2 US$ TO %[ : APPLIES F/4 ;X TO ! 8;Y B>0 ;;X9 ;X TO ! ;Y ) A B> OV] ! :OLE EXPRES.N ;;: #HH #AC ,>R[S #FJ #AC ,>R[S #AC4A ,SIMPLE >R[S .=\ >R[ 9DICATOR .=^\ BOLD >R[ 9DICATOR .=\O SIMPLE "R PO9T+ >R[ " .=\[ SIMPLE LEFT PO9T+ >R[ " .=\+ SIMPLE UP PO9T+ >R[ " .=\% SIMPLE D[N PO9T+ >R[ " .=\S SIMPLE UP & "R PO9T+ >R[ " .=\< SIMPLE D[N & "R PO9T+ >R[ " .=\: SIMPLE UP & LEFT PO9T+ >R[ " .=\> SIMPLE D[N & LEFT PO9T+ >R[ " ,A SIMPLE >R[ HAS A /&>D B>B$ TIP AT "O 5D "4 ,! %AFT IS /RAIE N SIGNIFICANT4 ,^! >R[S >E REPRES5T$ BY AN OP5+ >R[ 9DICATOR & ! APPROPRIATE CLOS+ >R[ 9DICATOR4 ,NOTICE T ALL ^! T]M9AT+ SYMBOLS H ?REE #HI #AC ,>R[S A#FJ DOTS1 >RANG$ 9 A 3SI/5T PATT]N T BE/ DESCRIBES ! DIREC;N4 ,NOTE T UN.S Y >E ALR 9 GRADE #A MODE1 ! >R[ 9DICATOR W NE$ A GRADE #A SYMBOL 9DICATOR4 ,! BOLD >R[ 9DICATOR W N NE$ "O1 Z ? TWO CELL SYMBOL DOES N H A GRADE #B M1N+4 ,BO? >R[ 9DICATORS SET >R[ MODE S NO FUR!R GRADE #A 9DICATORS W 2 NE$$4 ,>R[S >E SIGNS ( COMP>ISON S %D USUALLY 2 SPAC$4 ,AN EXCEP;N IS :5 !Y >E WRITT5 2L ! LIMIT FUNC;N "4 ,D N USE >R[ 9DICATORS :5 A SIMPLE "R PO9T+ >R[ IS ! ONLY MODIFI] ABV OR 2L AN ITEM4 ,SEE 8>R[ OV] PREVI\S ITEM0 & 8>R[ 2L PREVI\S ITEM0 9 ,SEC;N #AB4 -------------------------------------#FA ;N "R >R[ #J,-;N T5DS TO Z]O ;;;N \O #J;' 9PUT 8"R >R[0 PROCESS 8BOLD "R >R[0 \TPUT 9PUT ;\O PROCESS ^\O \TPUT #IJ #AC ,>R[S A#FA #AC4B ,>R[S ) UNUSUAL %AFTS & A /&>D B>B$ TIP ,%AFT SYMBOLS3 .=3 %ORT S+LE /RAI .=5 CURV$ OR B5T TO ! "R " .=4 %>P TURN TO ! "R "<9 L9E ( DIREC;N"> .=0 %>P TURN TO ! LEFT "<9 L9E ( DIREC;N"> ,ALL %AFT SYMBOLS C 2 EL;GAT$ BY REPETI;N4 ,! %AFT SYMBOLS >E PLAC$ 2T ! OP5+ & CLOS+ >R[ 9DICATORS4 ,>R[ L5G? ONLY NE$S TO 2 9DICAT$ 9 BRL :5 9 PR9T >R[S ( DI6]5T L5G?S H DI6]5T M1N+S4 ,^! EXAMPLES / H /&>D B>B$ TIPS4 #IA #AC ,>R[S B#FA D\BLE %AFT$ M$IUM L5G? "R PO9T+ >R[ ;\77O M$IUM >R[ PO9T+ UP ) A %>P TURN TO ! "R ;\44+ M$IUM L5G? "R PO9T+ >R[ B5D+ CLOCKWISE ;\55O -------------------------------------#FB L;G1 BROK5 LEFT PO9T+ >R[ ;\111[ %ORT1 M$IUM & L;G D[N PO9T+ SIMPLE >R[S ;\3% ;\% ;\333% #AC4C ,>R[S ) UNUSUAL TIPS ,B>B SYMBOLS3 .=R REGUL> B>B1 FULL1 9 L9E ( DIREC;N .=W REGUL> B>B1 FULL1 C.T] TO L9E ( DIREC;N .=@W REGUL> B>B1 UPP] HALF1 C.T] .=,W REGUL> B>B1 L[] HALF1 C.T] #IB #AC ,>R[S A#FB .=@R REGUL> B>B1 UPP] HALF1 9 L9E .=,R REGUL> B>B1 L[] HALF1 9 L9E .=& CURV$1 FULL1 C.T] .=Y CURV$1 FULL1 9 L9E .=@& CURV$1 UPP] HALF1 C.T] .=,& CURV$1 L[] HALF1 C.T] .=@Y CURV$1 UPP] HALF1 9 L9E .=,Y CURV$1 L[] HALF1 9 L9E .=\ /RAI .=@\ /RAI .=,\ /RAI ,IF AN >R[ HAS UNUSUAL TIPS1 DECIDE : IS ! H1D 2F Y *OOSE ! DIREC;N ( YR CLOS+ 9DICATOR4 ,! COMPLETE RULES = DECID+ >R[ DIREC;N >E3 #A4 ,IF "! >E DIREC;NAL TIPS1 & ALL L1D 9 ! SAME DIREC;N1 ! H1D IS ! 5D T LIES 9 T DIREC;N4 #B4 ,IF "! >E NO DIREC;NAL TIPS1 B "O 5D HAS A TIP & ! O!R DOES N1 ! 5D ) ! TIP IS ! H1D4 #C4 ,9 ALL O!R CASES1 ! H1D ( ! #IC #AC ,>R[S B#FB >R[ IS DEEM$ TO 2 ! 5D AT ! "R1 OR 9 ! CASE ( /RICTLY V]TICAL >R[S1 AT ! TOP4 -------------------------------------#FC ,! TIP" & %AFT SEG;T" >E TRANSCRIB$ 2T ! OP5+ & CLOS+ 9DICATORS4 ,^! ITEMS >E EXPRESS$ 9 LOGICAL ORD]1 T IS />T+ ) ! >R[ TAIL & PROGRESS+ T[>DS ! H1D1 EV5 IF T RUNS C.T] TO ! PHYSICAL ORD] "R[">4 ,C]TA9 ELE;TS >E OMITT$1 CORRESPOND+ TO ^! R1D] RULES3 #A4 ,IF NO TIP IS TRANSCRIB$1 X IS "U/OOD T AN ORD9>Y FULL B>B$ TIP O3URS AT ! >R[ H1D1 & "! IS NO O!R TIP4 #B4 ,IF NO %AFT IS TRANSCRIB$1 X IS "U/OOD T ! %AFT IS A /RAI AL APPLIES2 IF "O TIP IS TRANSCRIB$1 X IS AT ! H1D2 IF TWO TIPS >E TRANSCRIB$1 ! F/ IS AT ! TAIL & ! SECOND AT ! H1D4 #ID #AC ,>R[S A#FC O!RWISE ORD9>Y "R >R[1 ) CURV$ H1D ;\YO COMMON HORIZONTAL BIDIREC;NAL >R[ ;\WRO HORIZONTAL BIDIREC;NAL >R[1 TILT$ F L[] LEFT TO UPP] "R ;\WRS O!RWISE ORD9>Y "R >R[1 ) TAIL & H1D TIPS ;\RRO O!RWISE ORD9>Y "R >R[1 ) TWO H1D TIPS ;\33RRO O!RWISE ORD9>Y LEFT >R[1 ) TAIL & H1D TIPS ;\RR[ O!RWISE ORD9>Y LEFT >R[1 ) TWO H1D TIPS ;\33RR[ #IE #AC ,>R[S #FD "R >R[ ) A /RAIR[ UP1 FOLL[$ BY ORD9>Y >R[ D[N ^\+\% COMMON "R >R[ OV] COMMON LEFT >R[,-SEE ,SEC;N #AD4C4C REG>D+ V]TICAL JUXTAPOSI;N ;\O]\[ HALF B>B$ LEFT >R[ OV] HALF B>B$ "R >R[,-REV]SIBLE *EMICAL REAC;N ;\@R[]\,RO ,SEE ,SEC;N #AF = EQUILIBRIUM >R[S T O3UR 9 ,*EMI/RY4 #IF #AD ,%APE ,SYMBOLS #FE #AD ,%APE ,SYMBOLS & ,COMPOSITE ,SYMBOLS ,LI/+ ( %APE 9DICATORS3 .=$ %APE 9DICATOR .=_$ FILL$ " %APE 9DICATOR .=.$ %AD$ %APE 9DICATOR .=@$ TRANSCRIB]-ASSIGN$ %APE 9DICATOR .=@_$ TRANSCRIB]-ASSIGN$ FILL$ " %APE 9DICATOR .=@.$ TRANSCRIB]-ASSIGN$ %AD$ %APE 9DICATOR .=: %APE T]M9ATOR ,LI/+ ( SPECIFIC %APES3 .=$#C REGUL> " TRIANGLE .=$#D SQU>E .=$#E REGUL> P5TAGON .=$#F REGUL> HEXAGON .=$#G REGUL> HEPTAGON .=$#H REGUL> OCTAGON " POLYGONS"> .=$= CIRCLE #IG #AD ,%APE ,SYMBOLS A#FE .=$@#D P>ALLELOGRAM ,COMPOSITE ,SYMBOLS3 .=& SUP]POSI;N 9DICATOR .== HORIZONTAL JUXTAPOSI;N 9DICATOR .=] V]TICAL JUXTAPOSI;N 9DICATOR .=[ PHYSICAL 5CLOSURE 9DICATOR -------------------------------------#FF #AD4A ,USE ( ! %APE T]M9A;N 9DICATOR #AD4A4A ,IF A %APE IS FOLL[$ BY A SPACE !N NO T]M9A;N SYMBOL IS NE$$4 TRIANGLE SYMBOL SPACE ,,ABC ;$#C ,,ABC #AD4A4B ,IF ! %APE SYMBOL IS FOLL[$ BY PUNCTUA;N1 OR UNSPAC$ F A FOLL[+ SYMBOL1 !N ! %APE T]M9ATOR M/ 2 US$4 TRIANGLE ,,ABC UNSPAC$ ;$#C:,,ABC #IH #AD ,%APE ,SYMBOLS A#FF ,:AT IS ! NEXT %APE8 OP5 BRACE SQU>E1 %AD$ CIRCLE1 SOLID TRIANGLE1 %AD$ SQU>E 444 CLOSE BRACE ,:AT IS ! NEXT %APE8 _<;$#D:1 .$=:1 _$#C:1 .$#D 444_> ,NOTE T UN.S Y >E ALR 9 GRADE #A MODE1 A GRADE #A SYMBOL 9DICATOR W 2 NE$$ 2F ! %APE 9DICATOR4 ,? DOES N H["E APPLY TO ! %AD$ & FILL$ %APE 9DICATORS 2C ^! TWO CELL SYMBOLS D N H A GRADE #B M1N+4 ,ALL ! 9ITIAL %APE 9DICATORS 9ITIATE %APE MODE S NO FUR!R GRADE #A 9DICATORS W 2 NE$$4 #AD4B ,TRANSCRIB] DEF9$ %APES ,! DESCRIP;N )9 TRANSCRIB] DEF9$ %APES %D 2 A %ORT S]IES ( 9ITIALS OR A S+LE GRADE #A ^W4 ,!Y %D N 2 US$ IF ! PR9T SYMBOL IS ALR COV]$ ELSE": 9 ! CODE4 ,! DEF9I;NS ( ALL %APE SYMBOLS %D 2 AVAILABLE TO ! R1D] 9 EI A TRANSCRIB]'S NOTE OR ON A SPECIAL SYMBOLS PAGE4 #II #AD ,%APE ,SYMBOLS B#FF ,= EXAMPLE1 A SMIL+ FACE US$ Z AN ICON "?\T A BOOK CD 2 DEF9$ Z @$SF OR @$SMILE R ?AN @$ : IS TOO L;G & REQUIRES BRL GR\P+ SYMBOLS TO /OP ! SPACE T]M9AT+ ! %APE4 -------------------------------------#FG #AD4C ,COMB9$ %APES ,IF TWO PR9T SYMBOLS H BE5 COMB9$ TO =M A NEW PREVI\SLY UNDEF9$ SYMBOL1 !N X M/ 2 DECID$ :E!R ! SECOND SYMBOL IS 5CLOS$1 SUP]IMPOS$1 COMB9$ ON ! "R OR COMB9$ 2L4 ,EA* ( ! F\R COMPOSITE SYMBOL 9DICATORS SIGNALS A COMB9+ ( ! ITEM J PRIOR ) ! ITEM IMMLY FOLL[+ X1 ": 8ITEM0 IS Z DEF9$ 9 ,SEC;N #G4 ,EA* COMPOSITE SYMBOL 9DICATOR W NE$ A GRADE #A SYMBOL 9DICATOR UN.S ! :OLE EXPRES.N IS ALR 9 GRADE #A MODE4 #AD4C4A ,PHYSICAL ,5CLOSURE1 ;[ CIRCLE 5CLOS+ A PLUS SIGN ;$=["6 #AJJ #AD ,%APE ,SYMBOLS A#FG ,9 ! EXAMPLE 2L1 ! CIRCLE 5CLOS+ A PLUS SIGN IS 2+ US$ Z AN OP]A;N SIGN4 ,9 ! F/ V].N ! OP]A;N SIGN IS UNSPAC$ S A T]M9A;N SIGN IS NE$$ B NO GRADE 9DICATORS >E NE$$ 2C ! NUMB] SIGNS 9ITIATE NUM]IC MODE4 ,9 ! SECOND V].N ! OP]A;N SIGN IS SPAC$ = CL>;Y S NO T]M9A;N SIGN IS NE$$ B ! %APE SYMBOLS D NE$ GRADE #A 9DICATORS4 #B 8CIRCL$ PLUS0 #C EQUALS #C 8CIRCL$ PLUS0 #B #B$=["6:#C "7 #C$=["6:#B #B 8CIRCL$ PLUS0 #C EQUALS #C 8CIRCL$ PLUS0 #B #B ;$=["6 #C "7 #C ;$=["6 #B ,NOTE3 ,SEE ,SEC;N #C4E IF NUMB]S >E 5CLOS$ 9 A SQU>E TO REPRES5T A CALCULATOR KEY4 #AJA #AD ,%APE ,SYMBOLS #FH #AD4C4B ,SUP]POSI;N1 ;& ,NOTE T ? /RUCTURE %D N 2 US$ = NEGA;N4 ,SEE 8L9E "? PREVI\S ITEM0 9 ,SEC;N #AB4 ;,R ) SUP]IMPOS$ ;X,-PRESCRIP;N SYMBOL ,R;&X 9TEGRAL SIGN ) A SMALL CIRCLE SUP]IMPOS$ HALF WAY UP,-CLOS$ 9TEGRAL DEF9$ 9 ,SEC;N #AA4A @! 9TEGRAL SIGN ) A SMALL SQU>E SUP]IMPOS$ HALF WAY UP,-! T]M9A;N CD 2 OMITT$ IF "! 0 A FOLL[+ SPACE ;;!&$#D: #AD4C4C ,V]TICAL ,JUXTAPOSI;N1 ;] ,! UPP] SYMBOL %D 2 GIV5 F/1 FOLL[$ BY ! V]TICAL JUXTAPOSI;N 9DICATOR1 !N ! L[] SYMBOL4 ,? /RUCTURE %D N 2 US$ = B>S1 #AJB #AD ,%APE ,SYMBOLS A#FH >R[S1 DOTS1 TILDES OR HATS OV] OR "U O!R SYMBOLS "4 ,NEI %D X 2 US$ = SUP]SCRIPTS OR SUBSCRIPTS WRITT5 DIRECTLY OV] OR "U "4 A HOLL[ DOT ) AN EQUAL SIGN "UN1? "0;]"7 B9OMIAL COE6ICI5T " " #AD4C4D ,HORIZONTAL ,JUXTAPOSI;N1 ;= 8,HORIZONTAL JUXTAPOSI;N0 IS TO 2 9VOK$ ONLY :5 TWO SYMBOLS >E WRITT5 9 CLOSE PROXIM;Y & X IS CLE> F ! USAGE T A NEW S+LE SYMBOL1 4T9CT F ! ELE;T>Y SYMBOLS 3SID]$ 9 SEQU;E1 IS 9T5D$4 ,O!RWISE1 SYMBOLS WRITT5 "O AF ! O!R %D SIMPLY 2 BRLD ACLY4 #AJC #AE ,MATRICES & VECTORS #FI #AE ,MATRICES & VECTORS #AE4A ,5L>G$ GR\P+ SYMBOLS ,:5 5L>G$ BRACKETS >E US$ 9 PR9T = VECTORS1 MATRICES1 SY/EMS ( EQUA;NS1 FUNC;N DEF9I;NS ETC41 ! APPROPRIATE 5L>G$ GR\P+ SYMBOLS %D 2 US$ 9 BRL4 ,^! >E ! USUAL GR\P+ SYMBOLS PREC$$ BY A DOT #F4 ,SEE ! FULL LI/ 9 ,SEC;N #E4 ,^! %D 2 PLAC$ DIRECTLY "U EA* O!R4 ,BLANK L9ES 2F & AF S* >RANGE;TS MAY 2 NE$$ = CL>;Y4 #AE4B ,MATRICES ,! COLUMNS %D 2 LEFT ADJU/$ EXCEPT = M9US SIGNS : %D 2 BRLD TO /& \4 ,"O COLUMN ( BLANK CELLS %D 2 LEFT 2T COLUMNS4 ,MAT]IAL \TSIDE ! MATRIX1 S* Z SIGNS ( OP]A;N & COMP>ISON1 %D 2 PLAC$ ON ! TOP L9E1 EV5 IF !Y >E C5T]$ 9 PR9T4 ,I "7 ,"<#A #J,"> ,"<#J #A,"> #AJD #AE ,MATRICES & VECTORS A#FI ,.<#A #B #C,.>,.< #A #B,.> ,.<#D #E #F,.>,.<"-#C #D,.> ,.< #E "-#F,.> ,"< A "-B,"> ,"<"-C D,"> -------------------------------------#GJ #AE4C ,DET]M9ANTS ,^! H ! SAME /RUCTURE Z MATRICES B >E NORMALLY 5CLOS$ 9 PR9T ) 5L>G$ V]TICAL B>S4 ;;;_\,P_\ "7 ,_\A B_\ "7 AD"-BC;' ,_\C D_\ #AE4D ,OMIS.N DOTS ,! PLACE;T ( DOTS US$ TO 9DICATE ! OMIS.N ( "O OR M R[S OR COLUMNS C FOLL[ ! PR9T4 #AJE #AE ,MATRICES & VECTORS A#GJ ;;;,_\A5#AA A5#AB 444 A5<#AN>,_\ ,_\A5#BA A5#BB 444 A5<#BN>,_\ ,_\ 4 4 444 4 ,_\ ,_\A5 A5 444 A5 ,_\;' -------------------------------------#GA #AE4E ,D1L+ ) WIDE MATRICES ,IF A MATRIX OR DET]M9ANT IS TOO WIDE = ! BRL PAGE1 RUNOV]S )9 5TRIES MAY 2 NEC4 ,IF "! IS N ROOM TO 9D5T ^! RUNOV]S1 !Y C 2 BLOCK$ & A BLANK L9E LEFT 2T R[S4 #AJF #AE ,MATRICES & VECTORS A#GA ""=;;; ," ,"<"6B5#AX5#B "6B5#AY5#B "6B5#AZ5#B,"> ,"<"6C5#AX5#C "6C5#AY5#C "6C5#AZ5#C,"> ,"< ,"> ," ,"<"6B5#BX5#B "6B5#BY5#B "6B5#BZ5#B,"> ,"<"6C5#BX5#C "6C5#BY5#C "6C5#BZ5#C,"> ,"< ,"> ," ,"<"6B5#CX5#B "6B5#CY5#B "6B5#CZ5#B,"> ,"<"6C5#CX5#C "6C5#CY5#C "6C5#CZ5#C,"> ""=;' ,ANO!R APPROA* IS TO COMPLETE ! F/ COLUMN )\T OV]RUNS & !N TO PLACE ! NEXT COLUMN 2L ?1 9D5T$ TWO CELLS4 #AJG #AE ,MATRICES & VECTORS B#GA ""=;;; ," A5#BZ5#A"6B5#BZ5#B"6C5#BZ5#C,"> A5#CZ5#A"6B5#CZ5#B"6C5#CZ5#C,"> ""=;' ,NOTICE T 9 ! F/ EXAMPLE ! /RUCTURE ( ! MATRIX IS CLE>] B 9 ! SECOND EXAMPLE ! 9DIVIDUAL 5TRIES >E EASI] TO R1D4 ,NOTICE AL ! DI6]5T PLACE;T ( ! 5L>G$ GR\P+ SIGNS 9 ! TWO EXAMPLES4 -------------------------------------#GB ,A TRANSCRIB]'S NOTE %D 2 9CLUD$ 9 EI CASE TO EXPLA9 ! PLACE;T ( EA* 5TRY4 #AJH #AE ,MATRICES & VECTORS A#GB #AE4F ,VECTORS ,LRS REPRES5T+ VECTORS >E (T5 PR9T$ 9 BOLD FONT & MAY H >R[S OR B>S ABV OR 2L4 ,BOLDFACE ONLY NE$S TO 2 %[N 9 BRL IF X IS ! ONLY ME?OD US$4 ,= >R[S & B>S ABV & 2L SEE ,SEC;N #AB4 ,IF ! VECTOR 8#B OV] M9US #A0 0 CALL$ ;P & W5T F PO9T ,A TO PO9T ;,B "H >E "S ( ! MO/ LIKELY =MS3 ;P ) A B> "U EQUALS 5L>G$ R.D BRACKETS1 #B AT ! TOP & M9US #A AT ! BOTTOM P,: "7 ,"< #B,"> ,"<"-#A,"> ;P ) A B> OV] P;: BOLD ;P ^2;P #AJI #AE ,MATRICES & VECTORS B#GB ;,,AB ) AN >R[ OV] ;;<,,AB>^: ;,,AB ) A B> "U ;;<,,AB>,: -------------------------------------#GC #AE4G ,GR\P+ ( EQUA;NS ,OP5+ 5L>G$ CURLY BRACES >E (T5 US$ TO GR\P EQUA;NS4 ,PR9T SPAC+ %D 2 FOLL[$ ": POSSIBLE4 ,SOLVE3 ,_< X"6#BY "7 #G ,_<#BX"- ;Y "7 "-#D ;;;F" "7 ,_<#J IF X @< #J ,_ #J;' #AAJ #AF ,*EMI/RY #GD #AF ,*EMI/RY .=@_7 EQUILIBRIUM >R[1 TR5D TO ! LEFT .="_7 EQUILIBRIUM >R[1 TR5D TO ! "R .=^_7 EQUILIBRIUM >R[ "POONS"> .=,- DA% OR S+LE L9E BOND .=.,- D\BLE L9E BOND .=_,- TRIPLE L9E BOND .=@_,- QUADRUPLE L9E BOND .="5 S+LE DA%$ L9E .=."5 D\BLE DA%$ L9E .=_"5 TRIPLE DA%$ L9E .=@_"5 QUADRUPLE DA%$ L9E .="4 S+LE DOT .=."4 D\BLE DOT .=_"4 TRIPLE DOT .=@_"4 QUADRUPLE DOT .="8 S+LE CROSS .=."8 D\BLE CROSS #AAA #AF ,*EMI/RY A#GD .=_"8 TRIPLE CROSS .=@_"8 QUADRUPLE CROSS .="0 S+LE SMALL CIRCLE .=."0 D\BLE SMALL CIRCLE .=_"0 TRIPLE SMALL CIRCLE .=@_"0 QUADRUPLE SMALL CIRCLE -------------------------------------#GE #AF4A ,*EMICAL "NS CYCLOHEXANE ) ! F/ FIVE LRS 9 ITALIC .1CYCLO.'HEXANE #B COMMA #B HYPH5 ,DIME?YLPROPANE #B1B-,DIME?YLPROPANE #A HYPH5 ,HYDROXYL COMMA #B HYPH5 NITROB5Z5E #A-,HYDROXYL1#B-NITROB5Z5E ,COPP] OP5 P>5!SIS ,ROMAN CAPITAL TWO CLOSE P>5!SIS SPACE ,SULPHATE ,COPP]"<,,II"> ,SULPHATE #AAB #AF ,*EMI/RY A#GE ,COPP] SUP]SCRIPT ,ROMAN CAPITAL TWO SPACE ,SULPHATE ,COPP];;9<,,II> ,SULPHATE #AF4B ,*EMICAL =MULAE ,USE ( CAPITAL 9DICATORS & T]M9ATORS3 ,! G5]AL ,,UEB PR9CIPLES ON ! *OICE ( S+LE LR1 ^W OR PASSAGE MODE APPLY2 9 "PICUL>1 A CAPITAL T]M9ATOR %D N 2 US$ )9 A TWO-LR *EMICAL ELE;T SYMBOL4 ,US+ S+LE CAPITAL 9DICATORS = *EMICAL =MULAE PROVIDES A UNI=M APPE>.E TO ! BRL2 N"E!.S1 "! MAY 2 A CLE> ADVANTAGE 9 US+ CAPITAL PASSAGE MODE 9 "S CASES4 ,LRS REPRES5T+ *EMICAL ELE;TS %D N"E 2 3TRACT$4 ,O ,FE ,N,O ,NA,CL ;,AL OP5 P>5!SIS ,O CLOSE P>5!SIS ,CL ,AL"<,O">,CL #AAC #AF ,*EMI/RY B#GE ,O SUB #B ,O;5#B -------------------------------------#GF ;,H SUB #B ,O ,H;5#B,O ,CA "<,O ;,H"> SUB #B ,CA"<,O,H">;5#B ,CU ;,S ,O SUB #D DOT #E ;,H SUB #B ,O ,CU,S,O;5#D"4#E,H5#B,O ;,H SUP] PLUS ,H;9"6 ;,S ,O SUB #D SUP] M9US M9US ,S,O;5#D9<"-"-> ,AN EXAMPLE ( US+ CAPITAL PASSAGE MODE3 #AAD #AF ,*EMI/RY A#GF ;,R DOT ;,,,C ;H " DOT ;,C ;,H SUB #B DOT ;,C ;,H SUB #B DOT ;,C ,O SUB #B ;,H ,,,R"4CH""4CH;5#B"4CH5#B "4CO;5#B;H,' ,NOTE T ,ROMAN NUM]ALS >E CAPITALIS$ Z A S+LE GR\P3 ,FE SUP] ,,III ,CL SUB #C ;;,FE9<,,III>,CL5#C #AF4C ,ATOMIC MASS NUMB]S ,^! >E (T5 %[N ) LEFT-H& SUP]SCRIPT & SUBSCRIPT NUMB]S3 SUB #IB SUP] #BCH ;,U ;5#IB9#BCH,U #AF4D ,ELECTRONIC 3FIGURA;N ,S* NOTA;N C 9VOLVE LEFT-H& SUP]SCRIPTS1 & A SPACE OR HALF-SPACE 9 PR9T NE$S TO 2 RETA9$ 9 ! BRL TO MAKE ! ATTA*;T CLE>4 #AAE #AF ,*EMI/RY B#GF ,AR #AS SUP] #B #BS SUP] #B #BP SUP] #F #CS SUP] #B #CP SUP] #F ,AR #AS9#B#BS9#B#BP9#F#CS9#B#CP9#F SUP] #A ;,S SUB #J ;9#A,S5#J #D;D SUP] #I #ES SUP] #B SUP] #B ;,D SUB #E_/#B #D;D9#I#ES9#B ;9#B,D5<#E_/#B> -------------------------------------#GG #AF4E ,*EMICAL ,EQUA;NS #B ,NA ,O ;,H PLUS ;,H SUB #B ;,S ,O SUB #D "R >R[ ,NA SUB #B ;,S ,O SUB #D PLUS #B ;,H SUB #B ,O ;;;#B,NA,O,H"6,H5#B,S,O5#D \O ,NA5#B,S,O5#D"6#B,H5#B,O;' #AAF #AF ,*EMI/RY A#GG ;,N SUB #B "R >R[ ;,N ;,H SUB #C1 ) AN ;,H SUB #B WRITT5 ABV ! >R[ & 8,HAB] PROCESS0 WRITT5 2L ! >R[ ;;;,N5#B \O.9<,H5#B>.5<,HABER PROCESS> ,N,H5#C;' OR ""=;;; ,H5#B ,N5#B \O ,N,H5#C ,HABER PROCESS ""=;' ;,H SUB #B "<;G"> PLUS ,I SUB #B "<;S"> EQUALS #B ;,H ,I "<;G"> ;;;,H5#B ""6,I5#B " "7 #B,H,I ";' ;,,,H ;N ;C O,' PLUS ;,,,R O ;H,' "R >R[ ;,N ;,H SUB #B DOT ;,C ,O DOT ,O ;,R "R >R[ ;,N ;,H SUB #B ;,C ,O DOT ;,N ;,H DOT ;,C ,O SUB #B ;,R ;;;,,,HNCO"6ROH \O NH5#B"4CO"4OR \O NH5#B;CO"4NH"4CO5#BR,';' #AAG #AF ,*EMI/RY B#GG ,PB " PLUS #B ;E EQUILIBRIUM >R[ ,PB ;;;,PB9<"6"6>"6#B;E ^_7 ,PB;' -------------------------------------#GH #AF4F ,ELECTRONS ,ELECTRONS %[N Z DOTS1 CROSSES OR CIRCLES ATTA*$ TO ELE;T SYMBOLS MAY 2 REPRES5T$ US+ ! CORRESPOND+ ,,UEB SIGNS = S+LE1 D\BLE1 TRIPLE DOTS1 ETC4 ,H["E1 M COMPLEX CASES " >E BETT] D1LT ) US+ ORD9>Y DIAGRAM ME?ODS1 R ?AN TRY+ TO CODE !M PURELY 9 BRL4 ,CL ) A MIDL9E DOT AF ! ;L ,CL"4 #AAH #AF ,*EMI/RY A#GH ,! LRS ;,,,H O ;H,' WRITT5 9 A L9E ) ! ,O SURR.D$ BY SMALL CROSSES & CIRCLES Z FOLL[S3 TWO CROSSES ABV !N MOV+ CLOCKWISE A CROSS ABV A CIRCLE ON ! "R1 TWO CROSSES 2L1 & A CIRCLE 2L A CROSS ON ! LEFT4 ""=;;; ."8 ,H "8"0 ,O "8"0 ,H ."8 ""=;' #AF4G ,/RUCTURAL ,=MULAE ,! G5]AL ,,UEB ME?OD = L9E DRAW+ MAY 2 US$ = REPRES5T+ /RUCTURAL =MULAE4 ,REF] TO ! .7,RULES ( ,UNIFI$ ,5GLI% ,BRL1 ,SEC;N #AF3 ,L9E ,MODE1 ,GUIDE ,DOTS.' = SYMBOLS US$ TO DRAW L9ES US+ BRL CELLS4 ,9-L9E BOND SIGNS C 2 US$ 9 3JUNC;N ) ! L9E DRAW+ SYMBOLS4 ,"S EXAMPLES >E %[N 2L4 ,= M COMPLEX CASES X IS RECOMM5D$ T ! /RUCTURE 2 DRAWN \ GRAPHICALLY R ?AN US+ #AAI #AF ,*EMI/RY B#GH TRANSCRIB] DEF9$ SYMBOLS4 ""=;;; ,H _ ,H,-,C,-,H _ ,H,-,C,-,H _ ,H,-,C,-,H _ ,H ""=;' -------------------------------------#GI "37 > < > < << >> << >> "33 #ABJ #AF ,*EMI/RY A#GI ""=;;; >>< >> < "3344 _ __ __ _ __ __ << > < > <<> <> ,N ,H ""=;' #ABA #AF ,*EMI/RY B#GI ""=;;;,,, CHO _ HO "33W333 H _ H "33W333 OH _ HO "33W333 H _ CH5#BOH ""=,';' #ABB #AF ,*EMI/RY #HJ ""=;;; ><< > << > << __ _ __ _ < >> < >> ,N ""=;' ""=;;;,,, NH > < H5#B;C CH5#B < > NH ""=,';' #ABC #AF ,*EMI/RY #HA ""=;;;,,, CH5#C OH _ >< NO5#B CH5#C"4CH5#B"4CH5#B"4CH"33> <> _ _ < > <> NO5#B ""=,';' ""=;;;,,, HO"4CO,-CH5#B CH5#B,-CO"4OH < > < > N"4CH5#B"4CH5#B"4N > < > < HO"4CO,-CH5#B CH5#B,-CO"4OH ""=,';' #ABD #AF ,*EMI/RY #HB >>< ><< >> < > << _ __ _ _ __ _ << > < >> <<> <>> ,L9E> ,ME?OD ,A ME?OD IS AVAILABLE 9 : /RUCTURAL =MULAE >E REPRES5T$ 9 A COMPACT L9E> =M 9 BRL4 ,H["E1 Z YET ? HAS N BE5 DOCU;T$ Z A ,,UEB TE*NIQUE4 -------------------------------------#HC #AG ,COMPUT] ,NOTA;N .== " CURSOR 9DICATOR .=+ VISIBLE SPACE .=" " 3T9UA;N 9DICATOR .="" " 3T9UA;N 9DICATOR ) SPACE .=,7 NONDIREC;NAL D\BLE QUOTE "<,,ASCII D\BLE QUOTE"> #ABE #AG ,COMPUT] ,NOTA;N A#HC #AG4A ,DEF9I;N ( COMPUT] NOTA;N ,COMPUT] NOTA;N IS ANY TEXT WRITT5 9 A =MAL SYNTAX T IS DESIGN$ TO ALL[ COMPUT]S TO UTILIZE ! TEXT DIRECTLY = TE*NICAL PURPOSES RELAT$ TO ! COMPUT] XF4 ,EXAMPLES 9CLUDE COMPUT] PROGRAMS WRITT5 9 PROC$URAL LANGUAGES S* Z ,JAVA1 ,C"6"61 ,,COBOL1 & V>I\S 8ASSEMBLY0 LANGUAGES1 NONPROC$URAL SCRIPT+ & M>KUP LANGUAGES S* Z ,,XHTML1 & DATA FILES PREP>$ TO MEET ! 9PUT REQUIRE;TS ( SPECIFIC PROGRAMS4 ,EV5 "S %ORT ITEMS S* Z EMAIL ADDRESSES1 ,WEB SITE ,,URL,'S & FILE "NS QUALIFY Z COMPUT] NOTA;N 2C ( _! TE*NICAL PURPOSE4 ,O!R EXAMPLES MIATE F ! 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L9E 3T9U$ #ABG #AG ,COMPUT] ,NOTA;N A#HD ON ! NEXT L9E4 ,! SPECIFIC 3T9UA;N 9DICATOR US$ DEP5DS ON :E!R ! BR1K 9 E6ECT REPLACES A SPACE 9 ! ORIG9AL L9E "<: IS PREF]R$1 IF PRACTICAL1 & 9 : CASE USE DOTS #E1 #E">1 OR IS SIMPLY 9TRODUC$ AT AN >BITR>Y PO9T "<9 : CASE USE DOT #E">4 ,9 ! LATT] CASE1 :5 PRACTICAL1 X IS PREF]ABLE N TO 9TRODUCE A BR1K 2T LRS4 ,! SIGNIFIC.E ( SPACES )9 COMPUT] NOTA;N AL DEP5DS ^U ! SPECIFIC =MAL SYNTAX 9VOLV$4 ,EXACT SPAC+1 T IS A C]TA9 NUMB] ( SPACES1 MAY "S"TS 2 SIGNIFICANT1 Z 9 8/R+S0,-AL? USUALLY1 ONLY ! PRES;E OR ABS;E ( SPACE IS SIGNIFICANT4 ,IF ! PR9T PRES5TA;N MAKES ! NUMB] ( SPACES PRACTICAL TO C.T1 Z = EXAMPLE BY US+ 8VISIBLE SPACES0 " OR A MONOSPAC$ FONT1 & ! TRANSCRIB] IS N C]TA9 T EXACT SPAC+ IS N SIGNIFICANT1 !N X %D 2 ASSUM$ T EXACT SPAC+ IS SIGNIFICANT4 ,O!RWISE1 SPACES %D 2 US$ ": !Y >E 9 PR9T1 B N NECESS>ILY ! EXACT SAME NUMB]4 ,Z A "PICUL> #ABH #AG ,COMPUT] ,NOTA;N B#HD APPLICA;N ( ! LATT] CASE1 :5 ! LEFT M>G9 %[S A PATT]N ( 9D5TA;N1 S* 9D5TA;N %D 2 REPLICAT$ 9 BRL1 B G5]ALLY US+ MULTIPLES ( TWO CELLS 9/1D ( ! FIVE OR T5 POSI;NS (T5 US$ 9 PR9T4 ,9 PR9T COMPUT] NOTA;N1 A 8VISIBLE SPACE0 C 2 REPRES5T$ BY ANY ( S"EAL AD- HOC "*S1 S* Z3 ,U"6#JAHJ ,LAT9 SMALL LR ;B ) /ROKE " ,U"6#BC,B#E BOTTOM SQU>E BRACKET ,U"6#JCID ,GREEK CAPITAL LR DELTA ,U"6#BBJF ,9CRE;T ,U"6#BE,B#C ,:ITE UP-PO9T+ TRIANGLE ,:5 S* 8VISIBLE SPACES0 >E US$ 9 PR9T1 DOTS #CDF %D 2 US$ 9 BRL = EA* S* 8VISIBLE SPACE0 "4 ,LIKEWISE1 IF P] ! GUIDEL9ES ABV X IS DET]M9$ T A SEQU;E ( ?REE OR M ORD9>Y SPACES 9 PR9T IS TO 2 TR1T$ Z SIGNIFICANT1 !N EA* SIGNIFICANT SPACE 9 ! SEQU;E1 O!R ?AN ! F/ & #ABI #AG ,COMPUT] ,NOTA;N C#HD ! LA/1 %D 2 9DICAT$ BY DOTS #CDF "<) GRADE #A 9DICATORS IF NEC">4 ,EXAMPLES3 #A4 ,A 8COMM& PROMPT0 %[+ ! CURSOR IMMLY FOLL[+ "<9 GRADE #A 3TEXT">3 ,C3_*@> = -------------------------------------#HE #B;A4 ,A 8/R+0 3TA9+ EXPLICIT 8VISIBLE SPACES0 "3 ,,PR9T ,7,"N;;++++,TEL4+,NO4,7 #B;B4 ,! SAME EXAMPLE 9 GRADE #A 3TEXT3 ,,PRINT ,7,NAME++++,TEL4+,NO4,7 #C4 ,A 8/R+0 3TA9+ IMPLI$ SIGNIFICANT SPACES "3 ,,PRINT ,7,NAME ++ ,TEL4 ,NO4,7 #ACJ #AG ,COMPUT] ,NOTA;N A#HE #D4 ,RUNOV]S MADE NEC 2C ( A #CB-CELL L9E LIMIT1 )9 COMPUT] NOTA;N "3 ,Y C F9D ! /ORY AT HTTP3_/_/WWW" 4RIDBC4ORG4AU_/NEWS_//ORIES.-" *ILDR54ASP #E4 ,A RUNOV] AT A SPACE "3 ,! PROGRAM IS /OR$ 9 DIRECTORY C3_*PROGRAM FILES_*ABC"" CORPORA;N_*UTIL;Y PROGRAMS ---------------------------------#HF-#HG #AG4C ,GRADE ( BRL 9 COMPUT] NOTA;N ,A 4PLAY$ COMPUT] PROGRAM OR PROGRAM FRAG;T %D NORMALLY 2 TRANSCRIB$ 9 GRADE #A BRL2 NE>BY EXC]PTS F A PROGRAM T IS 4PLAY$ 9 GRADE #A %D PREF]ABLY AL 2 9 GRADE #A1 = 3SI/5CY4 ,O!R EXPRES.NS1 S* Z EMAIL ADDRESSES1 WEB SITES1 ,,URL,'S1 FILE"NS1 & COMPUT] EXPRES.NS N 4PLAY$ ON SEP>ATE L9ES1 %D NORMALLY 2 TRANSCRIB$ 9 GRADE #B BRL4 #ACA #AG ,COMPUT] ,NOTA;N A#HF-#HG ,EXAMPLE3 ,N[ T Y'VE SE5 ! 8,HELLO ,_W60 APPLICA;N1 Y MI ARGS"> _< ,SYSTEM4OUT4PRINTLN"<,7,HELLO"" ,WORLD6,7">2 _/_/ ,DISPLAY THE"" STRING4 _> _> ""=;' ,! CALL TO FUNC;N #ACB #AG ,COMPUT] ,NOTA;N B#HF-#HG ;;SYSTEM4OUT4PRINTLN1 PASS+ X ! 3/ANT /R+ ;;;,7,HELLO ,WORLD6,7;'1 DOES ! ESS5TIAL "W,-B ! O!R /ATE;TS & COM;TS AL PLAY A ROLE 444 ,NOTES3 ,! 9D5TA;N PATT]N ON ! LEFT ( ! 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