WordProLWP7.EM6QhWord Pro Text File/DFBC!@PP@ANSI (Windows, IBM CP 1252)PP-P@Using mathematics in e-mailP @ Steve Mayer4될8kQB@@ @ Steve MayerH@ASMXP p@@UNIVERSAL_ALL_OTHERS_EDITOR@FOTRX@@@q pcPP`@@q pcPP` @ Steve Mayer@ESMX@@@q pcPP`@@q pcPP`D@QEB PP p \2@M@p= \CFffp= UBXF@SfI q@Tp= `3CffSH6cf XU`ffS9z>qpjcAP6B9P6P6([DcH6BP6B(c[jH6BP6Bff (nA9A]f qAy su@@@p4CP@P@@@pPp@@@P @@@PB Po CrLH@ Default Text  @@@d@ s@@@p@@@  Dny A%@p@  3#zA:@@Hx@Hx@Hx@Hx`C\M@p= ECf&Bf&Bf&Bf&(C(EDf&BfBf&Bf€BBB +spP@P@@@pPp@@@P @@@PsoLH @ Table TextD/(C[f&BfBf&Bf€BBBC5AJ B3s LB@@B.L@5[AJYB3s[5oAJf1B33o[AJYI@oAJf5I@AJffB33AJ3]B3AJ#BffAJ(Bf&AJ3BffAJ3cB33$AJ B33$4AJf4I4$B@AJ3.B  s@ @@P@ZZ Z Z Z% pH@PZ *+' pH@P& pH@P( pH@P) pH@P-,12345ZZZZ(( /7(8(96(:(;(<(=Z3ZHZPZ@Z:ZZZZZ ZGZZZZZ Z!Z"Z#Z$0./@H@@ AAPP@P`@@P`@@Pp@P`@@Hx``@@Hx``PE q@@PB@@EField1HPP@EField2HPP@EField3HPP@EField4HPP@EField5HPP@EField6HPP@EField7HPP@EField8HP2@@PHBp= mf@@@Rl BUHp@@@R qQdHHAPHBPHBff ( AAy`XffSH63 HPHm@@@RqPHBff PHB(A'jEBBBBRBBB9nGDBAuC{@@@rffBff9pP@P@@@pPp@@@PBPP@@@PBProtLH @ Body Singlex@@@P 9P@P@@@pPp@@@PB33PP@@@PBPs_@@@Q AAyCAJ|B6M ABffbff€BBBq@AHRx 1x@@3@<@Pc@PPP<@Pc@PPP<@Pc@@A-P: x@Pp@Pp@Pp@Pp`1s @@-@<@Pc@PPP<@Pc@PPP<@Pc@@A-PB4H@AJBC@@@P@H BxAP Mff,@2xB>Bp= G 9yz{p@@@`PPpLH@EFooterp@@@P@f_m@@@Re&lKp P$@@hH@@hl@@h@@h@@h@@h@@j @jD@jh@j@j@&pP@@j@ABffbff,&pP@@j@EAAM8{u@@@RffBffBfftrzLH@EBullet_Cf@@@R^& M EAPBff4LH@EHeader&epP@@j@ztLH @GBullet 1&^pP@@j@EDH@DTitlezLH @ Number ListLH @FSubheadH$ FAFxQG @QFr%F@@EBodysBPP@EBody@p H qPt AAX@@ Default PageQ(A@IQXA @CPagemH@@Default Page Styleh$@@ Default TextJUtjz l\@@ETray 1H$9qGV@i(H@IAAP@CPageIAt-B +yAAh@Q ,@FStory Ds q@@PX @i H@IQH@A/BH@EFooterLBBtcz @\\XRnIq=tA/yW@@Default FooterQ H@BPRAAP@EFooterH@@Default Footer StyleIyy` @YXQV AxpA@P 0qh@R,@Story"gSrq@i H@IQHP@E=H@EHeaderLBBXt[z @\\XQqqyW@@Default HeaderQ H@BPRPAAP@EHeaderH@@Default Header StyleIyy` @YXQ -qh@R @StoryW M@QA@BIt is an ironic and frustrating fact that, although computers were invented by mathematicians, the one thing that is extraordinarily difficult to type on computers is mathematics. SSEndLPAD@HMATHEMATICS USING @B@ @ @ FEMAILSSEnd/h Ax @Wq@ Default TextP@@@@Y@@Default Text StyleX@@@xqDpADoq @@@a n   aD@H Steve Mayer @B@ @ @ @H8 February 2000@HESSEndJ !rKW5rI jsJ@@PEH @ Now() %Dc@F@!PYM@FA@BSMost people have come across the fact that typing a half is done using 1/2 or else HHone has to press a weird key combination, but there's no alternative for most fractions. Many sophisticated word processors and desktop publishing programs do have @Hequation editorsHH> to enter mathematical symbols but most of them are cumbersome, some are buggy and all are awkward to use especially for more than the odd formula. Specialist software is also very expensive.TPAlnADPSpcFSEndHH A@BBWorse still, these editors are absolutely no use when it comes to @ @ @ email. You have to resort to the lowest common denominator called ASCII or Text and attempt to use ordinary symbols. There's yet more bad news. With the widespread use of proportional fonts, trying to line text up using spaces can be next to useless.TPAlnADPSpcFSEndHHAM@QA@BThis is a guide to writing mathematics using only normal symbols. Much of it is a compromise and may not be satisfactory as it can be quite hard to read. @ @ @ Handwritten mathematics is still the best.TPAlnADPSpcFSEnd2HYM@(A@ATPAlnADPSpcFSEnd9s@JJY@BAATPAlnADPSpcFSEndm^yAAV@i!@JR@0@AAP @ SuperTableIAAAzA AyaXQs' AA@Q @ @ SuperTableAA D@i!H@BQJ0PAAP@DTableIAP: D@@Q @@FTableAX@BBeB@AA mjY@@ Default TableQ!H@@RB0PAAP @ SuperTableH@@Default Table StyleAy)A#)@i H@PAAb p#)Ay@i H@PyRPB#q)y@i H@PAAPB 2qD@i`A@Bp0@AAP@BRowZP 6G*@i`A@Bp0@DP@BRowHBP 7/>@i`A@Bp0@EH@BRowHBP /7C0P@i`A@Bp0@E0*H@BRowHBP C7U/Dd@i`A@Bp0@ED>H@BRowHBP U7iCVx@i`A@Bp0@EVPH@BRowHBP i7}Uj@i`A@Bp0@EjdH@BRowHBP }7i~@i`A@Bp0@E~xH@BRowHBP 7}@i`A@Bp0@EH@BRowHBP 7@i`A@Bp0@EH@BRowH BP 7@i`A@Bp0@EH@BRowH BP 7@i`A@Bp0@EH@BRowH BP 7@i`A@Bp0@EH@BRowH BP 7 @i`A@Bp0@EH@BRowH BP  7 -@i`A@Bp0@E H@BRowHBP 5w =@i`A@Bp0@EH@BRowHBP;  @i H@PR PDP@CCellIAC z=r q@i H@PR PE H@CCellLC d z ?y@i H@PR PEH@CCellL C d z[CXALyZ@@BAP1Q H@PRPAAP@CCellIAxX$@ @ Table TextAzA AzZIJ!uJ"Z" O 6iF!O6H  iF!OH\6 iF0!O\pH iFD!Op\ iFV!Op iFj!O iF~!O iF!O iF!O iF!O iF!O iF!O% iF!O%5 iF !O5r% iF!{qyZ@@ Default CellQ`H@@@R@0@AAP@CCellH@@Default Table Cell Styleh$@@ Default TextAAz )  @Q ,@@Story _ *Eyh@Q (@FStoryAYAA.ZIkB(A@DX MathematicsSSEndGBq @ Table TextP@@@@Y@p@@@A@qAAAAA@% i A@PR PE H@CCellIAD  z*=r%si H@PP @PE/%H@CCellL-D @ z%B*si H@PR PE*H@CCellL(D @d z  +y@R ,@@Story_+ZB̕B(C DXType AsSSEnd -B q@R,@@Story( W(ZB3B(CDXENoteSSEnd)x(q@R @ @GraphicA P@D.texS4 *.ArialNew Roman?A"  /PP`@G.tex Q%H@9 i A@PR PE%H@CCellIA5D  z>=r9si H@PP @PEC9H@CCellLAD @ z9B>si H@PR PE>0H@CCellL<D @d z (,-y@R% @@Story-W)))#ZB̕B(C(BD1/2SSEnd --B(q@R*,@@Story<(W...SB3B(C-ASSEnd){<-q@R @ @GraphicAYAP@D.texSX4|44ArialNew Roman?A" 5 PP`@G.tex +I%H0@K /i A@PR PE9/H@CCellIA5D  zP?rKs/i H@PR PEUKH@CCellLSD @d zKBP0s/i H@PR PEPDH@CCellLND @d z <,Ay@R9,@@StoryA-W===#ZB̕B(C<BDx/2SSEnd A-B<q@R>,@@StoryN<WBBBSB3B(CAASSEnd){NAq@R0 @ @GraphicAYAP@D.texS1488ArialNew Roman?A" =PP`@G.tex [IHD?_ Ci H@PR PEKCH@CCellIA[D  zd?r_sCi H@PR PEi_H@CCellLgD @d z_BdDsCi H@PR PEdVH@CCellLbD @d z N,Sy@RK,@@StorySAWOOO.ZB̕B(CNB1/2x or 1/(2x)SSEnd S-BNq@RP,@@StorybNWTTTaZB3BQCSB@Regard everything after / as being on the bottom of the fractionSSEnd)obSq@RD @ @GraphicAYAP@D.texSK4x8e7eArial? 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" ØUex`@G.tex QH@ i A@PR PEH@CCellIAD  z?rsi H@PR PEH@CCellLD @d zBsi H@PR PEH@CCellLD @d z ,y@R,@@StoryW#ZB̕B(CBD+/-SSEnd -Bq@R,@@StoryWSB3B(CASSEnd)|q@R @ @GraphicAYAP@D.texW84+)ArialNew Roman?A" Ĭ.PP `@G.tex IH? i H@PR PEH@CCellIAD z=rsi H@PP @PEH@CCellLD @ zBsi H@PR PEH@CCellLD @d z ,y@R,@StoryWhSB̕B(CB x = (-b +/- @ @ @ sqrt(b^2G - @ @ @ G4ac))F / 2aSSEnd -Bq@R,@@StoryWt B3BQCBQMessy. Complicated formulae should be avoided where possible. Use lots of spaces.SSEnd`rHYB3BQCB'Note the importance of brackets to get X all over C2aSSEnd)oq@R @ @GraphicAYAP@D.texS4ee,eeArial? " gex`@G.tex IH? i H@PR PEH@CCellIAD z=rsi H@PP @PEH@CCellLD @ zBsi H@PR PEH@CCellLD @d z ,y@R,@@StoryWaSB̕B(CBI x^2 @ @ @ Ddx or integral of x^2 @ @ @ CdxSSEnd -Bq@R,@@StoryWSB3B(CASSEnd)oq@R @ @GraphicAYAP@D.texS4ne,neArial? 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" ex`@G.tex IH?8 i H@PR PE(H@CCellIA4D  z=?r8si H@PR PE8H@CCellL@D @d z8B=si H@PR PE=-H@CCellL;D @d z +,0y@R(,@@Story0W,,,6ZB̕B(C+Btheta, alpha, beta, piSSEnd 0-B+q@R-,@@Story;+W111SB3B(C0ASSEnd)o;0q@R @ @GraphicAYAP@D.texS4eIyGI^EICI@I#I(KI9\I(IX+I+I(I+I+II,I\#I KI[\I+Il-I-I*I-I .I I.IIz#IJI}\I"-I/I/I,I<0Iq0IJI61I-I#EM6r@HPXHPXHPXHXXHPXHPXHPXHPXHPXH@XH@ @IA$XrBmP6'@@` ?8)EԐ8HJ\Iy/I 2I@2I2/I{2I2IIj3IHI#IJI\I1I@4It4I}1I4I 5II5IcI#IJI\I3I~6I6I3I6I7I I7II#IlJI\I46I8I8I5I59Ij9I9IF I:II$ILJI\IG8I;I;I8I8I ;Iq>I>I I@?IIL$I JI\I=I@IJ@IP=I{@I@I!ILAIIj$IIIl\I?I$BIXBI?IBIBIB!ICI I$IIIJ\IAI^DIDIAIDIEI!IEI'I$III(\IDIFIFICIGITGIBI$III\IcFIGI$HIFIQHIHI IIPIoTILIKIKI5I|KIQIGUIUI{QII IKIIII IgImI I2I(I IIII+QI ITII8 IUIXItXIXIIISIWI [IZII I]OITIXI1[IIW IS IAZI II I IUIKIQI III IIII{I8 III,OISIFI^TIIIWII;IUIIIIOI2IIPIIOItSIDVIrUI[IUIXIQI[INI I I I I I I7 I[I9RII In I~[I,TIWIyPI8IZIRI I"VIPI8SII]I/]I\]In]I}]I]$GM6qJIZaIdHM6P6Ԑ8?8Arial,34,12,0,0,0,0,0 $$\sin ^2x$$X-"EPSON EPL-5200 (PCL)2BM 6(2OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOϠOOOOOOOOOOOOOOOOOOArial,34,12,0,0,0,0,0 $\overrightarrow{AB},\ $\underline{$a$}$,\ \BF a$XGL!"EPSON EPL-5200 (PCL)BM%6(GĕArial,34,12,0,0,0,0,0 $$\theta ,\ \alpha ,\ \beta ,\ \pi $$XS"EPSON EPL-5200 (PCL)2BM 6(2Arial,34,12,0,0,0,0,0 $$e^x$$X"EPSON EPL-5200 (PCL)2BM 6(2Arial,34,12,0,0,0,0,0 $$P\left( A\cap B\right) \text{, }P(A\cup B)$$Xj"EPSON EPL-5200 (PCL)2BM 6(2Arial,34,12,0,0,0,0,0 $$\int_1^2x^2\ dx$$X/A "EPSON EPL-5200 (PCL)ZcBM6(/$cArial,34,12,0,0,0,0,0 $$\int x^2\ dx$$X8"EPSON EPL-5200 (PCL)2BM 6(2Arial,34,12,0,0,0,0,0 TCIformat{2}$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$X^-"EPSON EPL-5200 (PCL)~BM16(^HArial,34,12,0,0,0,0,0 $$\pm $$X "EPSON EPL-5200 (PCL)2BM 6(2Arial,34,12,0,0,0,0,0 $$^3\sqrt{x}\text{, }^4\sqrt{x}$$XX'"EPSON EPL-5200 (PCL)4BM= 6(4Arial,34,12,0,0,0,0,0 $$\sqrt{x}$$XY'"EPSON EPL-5200 (PCL)4BM= 6(4Arial,34,12,0,0,0,0,0 $$x^2\text{, }x^3\text{ etc}$$XR"EPSON EPL-5200 (PCL)2BM 6(2Arial,34,12,0,0,0,0,0 TCIformat{2}$\dfrac 1{2x}$X/"I"EPSON EPL-5200 (PCL)ZcBM6(/$cArial,34,12,0,0,0,0,0 TCIformat{2}$\frac 12x$X%"EPSON EPL-5200 (PCL)2BM 6(2Arial,34,12,0,0,0,0,0 TCIformat{2}$\frac 12$X%"EPSON EPL-5200 (PCL)2BM 6(2&("@ @ @@@@@`@```@@@@ @ @ @ @@ @ @ ` @` ` ` @ @ @ @ @@@@@ @@ @ @ @@@@@@@@@@`@@`@`@`@@@@@@@@@@@@@@@@@@@@@`@``` `@ ` ` `@`@@`@`@```@```````@````@````@````@```@ @ @@@@@`@```@@@@@ @ @@@@@`@```@@@@@ @ @@@@@`@```@@@@@ @ @@@@@`@```@@@@ myy+6+mm%+%+>++mmm+Imm+>mmm%>ImIm#  m m#+>>>>+>!:m!m mm m! +>+> mmm >Immm >m+>+>!>>>+>+>">">+>#>Im m>m>+>>m>>+>+>+4+4+>+  +m ++>m + m +mm++>mm   ,mmmmm +>+>+>&>'>+> >>>+>!4!mm!+>+>#  mm mm+>+>+  m+ !m+>   m m+>+>m%>%>+>+>+>%>%>+>%>mm m8m 8km mmmm m  $( mmm mmmmm9mmmmmmm mmammmmmmmm m$h mmmmmmm m 0$Pmm mmFG=(&mmmmmmm mm 4mmmmmmmmmB3mmmmm /m  mm m  Vmm mm< <4     mmmmm  mmmmmmam mmmmmmmmcmmm mbUsing mathematics in e-mail Miscellaneous6Using mathematics in e-mailMiscellaneousFileProtectionGrAC,36E14DD5-DGrAC,36E14DD5-SGrAD,36E14DD5-DGrAD,36E14DD5-SGrAE,36E14DD5-DGrAE,36E14DD5-SGrAF,36E14DD5-DGrAF,36E14DD5-SGrB0,36E14DD5-DGrB0,36E14DD5-SGrB1,36E14DD5-DGrB1,36E14DD5-SGrB2,36E14DD5-DGrB2,36E14DD5-SGrB3,36E14DD5-DGrB3,36E14DD5-SGrB4,36E14DD5-DGrB4,36E14DD5-SGrB5,36E14DD5-DGrB5,36E14DD5-SGrB6,36E14DD5-DGrB6,36E14DD5-SGrB7,36E14DD5-DGrB7,36E14DD5-SGrB8,36E14DD5-DGrB8,36E14DD5-SGrB9,36E14DD5-DGrB9,36E14DD5-SGrBA,36E14DD5-DGrBA,36E14DD5-SHeaderLWPStreamTypePreviewWordProData $  hh#h33H0W2< 233 e f33 GE 33*c0'033cGAd+;+33n^8^O5#O5g5331c`.`33 -!E33"x&#w '7G W g w  '7GWgw !"#CMHdr