Post on 05-Feb-2018
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 1/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=0/>0
Cmsgak, Odktrdf `kc Gktmar`tgdk dn
Kmxt Amkmr`tgdk d!mr `kc"kmra# $#stm%s
B`ol Irduwmr, Xe.C.
@ssdog`tmCgrmotdr
Gkstgtutm ndr "kmra# "&ogmko#'O $`kt` (`r)`r`
*`roe +, 980=
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 2/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=9/>0
utfgkm
• Gktrdcuotgdk
• $g%-fm $-`tg`f $NO *dcmf
• C#k`%go Numf Omff *dcmfs . Odktrdfs $#stm%s
Cmmfd-%mkt
• "kmra# $#stm%s . gae Ymkm!`)fm mkmtr`tgdkC#k`%gos
• "kmra# $#stm%s . 'tgfgt# Argc Kmt!dr G%-`ots• $u%%`r#
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 3/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=?/>0
KNOYO 3dr `kc ssdog`tmc "x-mrgmkom• Nukc`%mkt`f `kc `--fgmc rmsm`roe ndr cmmfd-gka `kc
ukcmrst`kcgka numf omff s#stm%s sogmkom, gktmar`tmc s#stm%scmmfd-%mkt `kc `--fgo`tgdk td tem )ugft mkgrdk%mkt `kcmegofms ‟ "%-e`sgs dk egae tm%-mr`turm numf omffs
‟ Gktmar`tmc s#stm% cmmfd-%mkt ndr `ff numf omff t#-ms
‟ $t`tgdk`r# numf omff s#stm%s `kc gknr`struoturm
‟ "x-mrg%mkt`f `kc ku%mrgo`f
• Ymodakgmc "x-mrtgsm gk1
‟ Numf Omff C#k`%gos `kc Odktrdf ‟ O#ofm Odkom-tu`fg`tgdk `kc k`f#sms
‟ Numf Omff Gktmar`tgdk !gte A`s 5ur)gkms `kc Numf rdomssgka
‟ (ugft "kgrdk%mkt Gktmar`tgdk
‟ Numf Omff `kc fua7gk #)rgc 2megofm 5mstgka `kc k`f#sms
‟ Ymkm!`)fm Numf Omff $#stm%s
‟ #crdamk Gknr`struoturm Cmmfd-%mkt`kc "`fu`tgdk
‟ gr <u`fgt# G%-`ots dn Numf Omffs
• "cuo`tgdk `kc utrm`oe ‟ Ngrst '6$6 'kgmrsgt# Ar`cu`tm Numf Omff Odursm :9880;
‟ $edrt odursms :NO $m%gk`r, GO"A, NO5G;
‟ O`fgndrkg` $t`tgdk`r# Numf Omff Odff`)dr`tgm
Srg-Amkmr`tgdk2E9, Em`t & Xdwmr
Ymkmw`ifm !"#stm$s
E#irg% !AS
! 'megofms& E9 "t`tgdk
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 4/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=+/>0
K`tgdk`f Numf Omff Ymsm`roe Omktmr
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 5/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980==/>0
Gktrdcuotgdk
• "kmra# $#stm%s `rm orgtgo`f td1 ‟ "odkd%gms . `ff smotdrs
‟ <u`fgt# dn 4gnm
‟ Nrmmcd% dn *d)gfgt#
• nm! g%-drt`kt `s-mots dn "kmra# $#stm%s ‟ 5emr%dc#k`%gos
‟ m`t 5r`ksnmr ‟ Nfugc C#k`%gos
‟ Oem%gstr#
‟ "fmotrdoem%gstr#
‟ *`tmrg`fs $ogmkom
‟ C#k`%gos
‟ Odktrdfs
‟ $#stm%s Gktmar`tgdk
• Odksgcmr ff• *`m sg%-fgn#gka `ssu%-tgdks• Ygadrdusf# `k`f#m tem
g%-drt`kt -e#sgos/oem%gstr#/mto6gk `k gktmar`tmc n`segdk
"(`tg`f & Sm$(dr`f rmsdfutgdk g$(drt`kt (e#sgos, oem$gstr#,
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 6/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=>/>0
utfgkm
• Gktrdcuotgdk
• $g%-fm $-`tg`f $NO *dcmf
• C#k`%go Numf Omff *dcmfs . Odktrdfs $#stm%s
Cmmfd-%mkt• "kmra# $#stm%s . gae Ymkm!`)fm mkmtr`tgdk
C#k`%gos
• "kmra# $#stm%s . 'tgfgt# Argc Kmt!dr G%-`ots• $u%%`r#
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 7/82© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=H/>0
Gktmar`tmc A`sg@o`tgdk Numf Omff f`kt
GANO Odkom-t Gktrdcuotgdk
Od`frm-6
Od`fA`sg@o`tgd
k
$#ka`sOfm`k7u- $NO
A`s 5ur)gkm
$tm`% 5ur)gkm
O9 $m-`r`tgdk Ymo#ofm
o`t`f#tgo e#crd7a`sg@mr GANO s#stm% te`t t`ms `c`kt`am dntem -dtmktg`f )mkm@ts dn O+7rgoe s#ka`s numf o`k `oegmm %drm
te`k >8I m&ogmko# !egfm mk`)fgka o`r)dk cgdxgcm sm-`r`tgdkndr smumstr`tgdk
4g, mt `f6, durk`f dn d!mr$duroms, 2df6 0M=, Gss6 0H, --6
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 8/82© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=/>0
*dcmf Cmmfd-%mkt
• *dst s#stm% cmmfd-%mkt `kc `k`f#sms `rm )`smcu-dk )uf :87cg%mksgdk`f; %dcmfs
• $mmr`f g%-drt`kt d-mr`tgka odkstr`gkts o`kkdt )m`ssmssmc !gtedut sd%m amd%mtrgo rmsdfutgdk dn tem$NO ‟ m` tm%-mr`turm, tm%-mr`turm ar`cgmkts
‟ Numf dxgc`kt utgfg`tgdk
• 3m cmsgrm td rmsdfm sd%m nm`turms dn %dcmrk $NOd-mr`tgdk ‟ kmmc od%-ut`tgdk`f sg%-fgogt#/m&ogmko# su&ogmkt td
gkodr-dr`tm tem %dcmf gktd cmt`gfmc gktmar`tmc a`sg@o`tgdks#stm%s k`f#sgs
‟ "x-fgogtf# m`fu`tm `otg`tgdk, de%go, `kc cgusgdk fdssms `s!mff `s gkmtgos dn e#crdo`r)dk rm`otgdks
‟ rmcgot -mrndr%`kom nm`turms suoe `s tem gktmrk`f
tm%-mr`turm, ourrmkt/-d!mr cmksgt# `kc Ed! od%-dsgtgdk-rd@fms, numf `kc dxgc`kt utgfg`tgdk, ndr m`fu`tgdk dn numf omff
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 9/82© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=M/>0
f`k`r $NO *dcmf Amd%mtr#
<u`sg79C od/oduktmr Ed! -f`k`r $NO %dcmf
4g, *6, d!mrs, 6C6, `kc (rdu!mr, 6, durk`f dnNumf Omff
7 7
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 10/82© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=08/>0
Ku%mrgo`f $oem%m
4g, *6, d!mrs, 6C6, `kc (rdu!mr, 6, durk`f dnNumf Omff
$ogmkom `kc 5moekdfda#, 2df6 H, --6 8+080H70709, 9808
"K
$Y $Y $Y
$Y $Y $Y
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 11/82© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=00/>0
07C *dcmf Gktmar`tgdk gktd $#stm%s k`f#sgs
O`t`f#tgo e#crd7a`sg@mr GANO s#stm%
$NO m`t"xoe`kam $#stm%:07C, 862, H?I ½n ;
4g, mt `f6, durk`f dn d!mr$duroms, 2df6 0M=, Gss6 0H, --6
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 12/82© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=09/>0
07C oduktmr7Ed! $NO %dcmf gk gktmar`tmc GANO`k`f#sgs
• Gktmrk`f rmndr%gka1 -m` tm%-mr`turms %dm tdgktmrgdr
• Gkfmt dutfmt tm%-mr`turms kd fdkamr rm-rmsmkt-m` C5
• utfmt numf/`gr tm%-mr`turms `rm cmorm`smc .cgs`)fgka cd!kstrm`% em`t usm
• gr Ed! rmugrmc ndr 5%`xB988LO gs +F te`t dn 87C
%dcmf
Oe`ffmkams Gcmktg@mc1 87C s6 07C
numf dut:>=8 J 988; LO
`gr dut:>=8 J 988; LO
numf gk>=8 LO
`gr gk
>=8 LO
+$(fgogt@ssu$(tgdk-
C numf dut:>=8 J +8; LO
`gr dut:>=8 J H8; LO
numf gk>=8 LO
`gr gk>=8 LO
-C
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 13/82© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=0?/>0
GANO mrndr%`kom Od%-`rgsdk
+tm$ -C d%mf -C "gk/fm "t`/m!duktmr-8dw"0!
Od`f mkmra# gk-ut 0,?MH A/e :2; 0,?MH A/e :2;
$NO d-mr`tgdk -rmssurm 08 t% 08 t%
Ardss -d!mr dut-ut
$NO mfmotrgo`f -d!mr 9+H6 *3 9+H6? *3
O`tedcm mxe`ust mx-`kcmr >?6+ *3 0H6> *3
$tm`% tur)gkm 96> *3 06M *3
$#ka`s rm`otdr/mx-`kcmrtd--gka o#ofm
M6? *3 H6> *3
5dt`f ardss -d!mr amkmr`tmc ?9?6? *3 +?=6> *3
uxgfg`r# -d!mr odksu%-tgdk :gkod%-fmtm fgst;
$' 9,0> 3 9,0> 3
$NO gr od%-rmssdr/)fd!mr >>,M8> 3 9+9,+MM 3
Ymo#ofmc 9 od%-rmssdr ,9?= 3 ,9? 3
5dt`f gktmrk`f -d!mrodksu%-tgdk `kc fdssms
+6H *3 9>86= *3
Kmt mfmotrgo -d!mr 9?6> *3 0H=60 *3 DDD
mr`ff temr%`f m&ogmko# >06=I :2; +=60I :2;DDD
4g, *6, Y`d, 6C6, (rdu!mr, 6, `kc $`%umfsmk, durk`f dn d!mr $duroms, 2df60M=, Gss6 0H, --6=H8H7=H0, 98086
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 14/82© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=0+/>0
$tr`tma# ndr *gtga`tgka gae ∎ 5 Oe`ffmkam
O`so`cm $NO st`os
mr`ff'n B 86H9H
'` B 86+==
gr gk>=8LO
Numf gk>=8LO
Numf dut>H0LO
]n : 8.18
'` B 860=
gr ccgtgdk??8LO
grH0?LO
Numf gk>=8LO
Numf dut>MLO
]n : 8.1?
'` B 860>
gr ccgtgdk??8LO
grH?9LO
Numf gk>=8LO
Numf dutH8+LO
]n : 8.1?
'`B860H
gr ccgtgdk??8LO
grH+9LO
Numf gk>=8LO
Numf dutH0MLO
]n : 8.13
'` B 860H
gr dutH=?LO
4g, *6, Y`d, 6C6, (rdu!mr, 6, `kc $`%umfsmk, durk`f dn d!mr $duroms, 2df60M=, Gss6 0H, --6=H8H7=H0, 98086
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 15/82© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=
0=/>0
GANO mrndr%`kom Od%-`rgsdk
+tm$ -C d%mf -C !`so`%gk/!duktmr-8dw"0!s
Od`f mkmra# gk-ut 0,?MH A/e :2; 0,?MH A/e :2;$NO d-mr`tgdk -rmssurm 08 t% 08 t%
Ardss -d!mr dut-ut
$NO mfmotrgo`f -d!mr 9+H6 *3 9+H6 *3
O`tedcm mxe`ust mx-`kcmr >?6+ *3 H960 *3
$tm`% tur)gkm 96> *3 96H *3
$#ka`s rm`otdr/mx-`kcmrtd--gka o#ofm
M6? *3 H6> *3
5dt`f ardss -d!mr amkmr`tmc ?9?6? *3 ??86+ *3
uxgfg`r# -d!mr odksu%-tgdk :gkod%-fmtm fgst;
$' 9,0> 3 9,0> 3
$NO gr od%-rmssdr/)fd!mr >>,M8> 3 +,H+ 3 Ymo#ofmc 9 od%-rmssdr ,9?= 3 M,HM9 3
5dt`f gktmrk`f -d!mrodksu%-tgdk `kc fdssms
+6H *3 08+6? *3
Kmt mfmotrgo -d!mr 9?6> *3 99>60 *3 D
mr`ff temr%`f m&ogmko# >06=I :2; =69I :2; D
4g, *6, Y`d, 6C6, (rdu!mr, 6, `kc $`%umfsmk, durk`f dn d!mr $duroms, 2df60M=, Gss6 0H, --6
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 16/82© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=
0>/>0
utfgkm
• Gktrdcuotgdk
• $g%-fm $-`tg`f $NO *dcmf
• C#k`%go Numf Omff *dcmfs . Odktrdfs $#stm%s
Cmmfd-%mkt• "kmra# $#stm%s . gae Ymkm!`)fm mkmtr`tgdk
C#k`%gos
•"kmra# $#stm%s . 'tgfgt# Argc Kmt!dr G%-`ots
• $u%%`r#
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 17/82© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=
0H/>0
C#k`%go $g%uf`tgdk --rd`oe
C#k`%go "kmra# $#stm%s $g%uf`tgdk Nr`%m!dr
• *54(/$g%ufgkX mkgrdk%mkt smfmotmc ‟ 'smr nrgmkcf#, !gcmf# ``gf`)fm/usmc, gcm`f ndr odktrdfs
cmmfd-%mkt `kc tmstgka
• *`gk `ssu%-tgdks1 ‟ u`sg7stm`c# st`tm oem%gstr# `kc mfmotrdoem%gstr# :m6a6,
oe`r`otmrgmc )# Kmrkst -dtmktg`f `kc fdssms;
‟ $g%-fg@mc amd%mtr# :)ut gkofucgka sd%m amd%mtrgo rmsdfutgdk;• Ndous dk c#k`%go sdfutgdk dn tem mssmktg`f NO `kc
dtemr od%-dkmkt nm`turms suoe `s1 ‟ Kmrkst -dtmktg`f
‟ "fmotrdoem%go`f fdssms
‟ $-mogms odkomktr`tgdks `kc *`ss odksmr`tgdk ‟ "kmra# odksmr`tgdk
‟ *d%mktu% odksmr`tgdk
‟ m`t 5r`ksnmr
‟ Oem%go`f Ym`otgdk Am%%mk, Y, 4gmsm, "6, Ygmr`, 6, `))`rg, N,`kc (rdu!mr, 6, $*" `-mr Ku%)mr 98887
A57==+, 98886
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 19/82© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=
0M/>0
Xf`k`r `kc Suiuf`r _DNO gsormtg!`tgdk " #$ Kdcms
• %kdcm &`s
• O`tedcm &`s
"x`%-fm C#k`%go $g%uf`tgdk *dcufms
• Omff _dfgc
• 'ktmrodkkmot Xf`tms
#$ KDM_
(MND(JM
N)MF
O%S*DM &%_
OMFF _DF' 'KSM(ODKKMOS
%KDM &%_
OMFF S)+M
%'( _)XXF, X'XM
O%S*DM &%_
O(D__ _MOS'DK
(MND(JM
N)MF
X(M-
*M%SM
%'(
f g g f g c f
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 20/82© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=
98/>0
"x`%-fm C#k`%go $g%uf`tgdk *dcufms
f`k`r Kdc`f $NO m`t 5r`ksnmr Ymsgst`koms
'KSM(ODKKMOS
XF%SM
KDM k KDM k.#
/
((%
(ODK^
(ODK^
(ODK^
(ODK
(ODK(ODK (ODK
(ODK
((%
(ODK
(ODK^
(ODK^
(ODK^
%KDM
'K
%KDM
D)S
O%S*DMD)S
O%S*DM'K
(ODK^(ODK^
((% ((%
OMFF
(ODK(ODK (ODK
'KSM(ODKKMOS
XF%SM
C g * c fg 5 f 2 g@ c
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 21/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=90/>0
C#k`%go *dcmfgka 5ddfs 2mrg@mc
$gm%mks Gktmar`tmc$NO $#stm%$gkafm Omff *ONO 5mst$t`kc
$gm%mks/$O" 998 3$NO/A5 #)rgc
" f $ cc C n
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 22/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=99/>0
"x`%-fm1 $uccmk Cmorm`sm dn d!mr
#)rgc $NO/A5 $#stm%
• *`kg-uf`tm1 ‟ Ymogro6 )fd!mr -d!mr
‟ Numf Ed!
‟ gr -rmem`t )#-`ss `fm
‟ $NO `gr )#-`ss `fm
• Odktrdf1 ‟ $#stm% -d!mr
‟ m` $NO tm%-mr`turm
‟ $NO tm%-mr`turm ar`cgmkt
‟ xgcgmr tm%-mr`turm
• mrtur)`tgdk1 ‟ $uccmk cmorm`sm nrd% 088I
td =8I nuff -d!mr*o4`rt#, C6N6, $`%umfsmk, $6, `kc
(rdu!mr, 6 $*" `-mr NO98087???9, ukm, 9808
" f $ cc C n
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 23/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=9?/>0
"x`%-fm1 $uccmk Cmorm`sm dn d!mr
#)rgc $NO/A5 $#stm%
• *mt succmk cmorm`smgk -d!mr cm%`kc
• Pm-t $NO -m`tm%-mr`turm 08H? Pcurgka tr`ksgmkt
• Pm-t $NO tm%-mr`turmar`cgmkt 0=8 P curgka tr`ksgmkt
*o4`rt#, C6N6, $`%umfsmk, $6, `kc
(rdu!mr, 6 $*" `-mr NO98087???9, ukm, 9808
" f $ cc G g
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 24/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=9+/>0
Gktmar`tmc $t`kc7fdkm $NO s#stm%
• *`kg-uf`tm1 ‟ Numf Ed!
‟ (fd!mr -d!mr
‟ (#-`ss `fm
• Odktrdf1 ‟ $#stm% -d!mr
‟ m` $NO tm%-mr`turm
‟ $NO tm%-mr`turm -rd@fm
• mrtur)`tgdk1 ‟ 9= td H8 `%- ourrmkt gkorm`sm !gte "K tm%-mr`turm
nmmc)`o
"x`%-fm1 $uccmk Gkorm`sm gk d!mr
*umffmr, N6, `))`rg, N6, (rdu!mr, 6,
durk`f dn d!mr $duroms, 2df6 0H, Gss69, --6 +=97+>8, 988M
" f $ cc G g
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 25/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=9=/>0
"x`%-fm1 $uccmk Gkorm`sm gk d!mr
Gktmar`tmc$NOs#stm%
9= td H8 `%-ourrmkt
gkorm`sm-mrtur)`tgdk
Odktrdf `otgdks1
?`tgdk`f umf !mff Ymsm`roe
*umffmr, N6, `))`rg, N6,(rdu!mr, 6, durk`f dn d!mr$duroms, 2df6 0H, Gss6 9, --6
+=97+>8, 988M
" f $ cc G g
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 26/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=9>/>0
"x`%-fm1 $uccmk Gkorm`sm gk d!mr
Gktmar`tmc $NO s#stm% 7 9= td H8 `%- ourrmktgkorm`sm !gte "K tm%-mr`turm nmmc)`o
*umffmr, N6, `))`rg, N6, (rdu!mr, 6, durk`f dn d!mr $duroms, 2df6 0H, Gss6
9, --6 +=97+>8, 988M
5 g A tg O t
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 27/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=9H/>0
80$ 9? *SNO
9?s SD
MFMOS('O FD%3
0$=
*,(D&MK3
8$=
*M%S SD
+)'F'K&_
S*M(J%F FD%3
#0=>$=
5rg7Amkmr`tgdk Odkom-t
4m`f, "6*6, (rdu!mr, 6, 6 Numf Omff$og6
Ymkm!`)fm 5rg Amk dn d!mr m`t
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 28/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=9/>0
$5YA"
5KP
CA
535"Y
"5
"FOKA"Y K"Y(GO CGA"$5GK A$ 4C"Y
$4'CA"
CGA"$5"Y
(G4"Y
_CYA"K_CYA"K$5YA"
_CYA"KCG$"K$"Y
N'"4 5Y"5*"K5
O3"Y
GA75N'"4 O"44
NGY$5 4GO5GK
• r`kam Odukt# $`kgt`tgdk Cgstrgot
• "uofgc "xgt, G+8=, Ndukt`gk 2`ffm#
• $u--drt1 C", Y(, <*C• Cmom%)mr 9808
K`tgdk`f Numf Omff Ymsm`roeOmktmr
]kgvmrsgty dn O`fgndrkg`, Grvgkm
Ymkm!`)fm 5rg7Amk dn d!mr, m`t 9
O$C rdSmot 3drfc]s Ngrst 5rg Amk
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 29/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=9M/>0
O$C rdSmot . 3drfc]s Ngrst 5rg7Amk
• =+I 9 d!mr -rdcuotgdk m&ogmko#
• ^ ?,888 Ymkm!`)fm 9 megofm rm@ffs
Ymkm!`)fm 9
Ngffgka $t`tgdk
CA numfmc
CNO79 Xrdcuotgdk 'kgt
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 30/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=?8/>0
kdcm"xe`ust
$gc
CNO:Cgrmot NumfOmff;
CA
Ofm`k7u-$gc
$#ka`s
Od%-rmssdr$gc$ $gc
:-rmssurm s!gka
`)sdr-tgdk;
Od%-rmssdr $gc
#crdamk$tdr`am 5u)ms
Gkmrtmr "fmotrgo`f (d
*moe`kgo`f (d
*`ra`fmn, mt `f6, 6 Numf Omff $og6 5moekdf6, 2df6 ?, Gss6 9, --6 0?H70+? 988>
5rg Amkmr`tgdk C#k`%go k`f#sms
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 31/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=?0/>0
5rg7Amkmr`tgdk C#k`%go k`f#sms
• Cgurk`f c#k`%go d-mr`tgdk dn 5rg7Amkmr`tgdk s#stm%
• #crdamk t`k @ffs ndrogka mkc dn 5rg7amkmr`tgdk
• Odktrdf dn s#stm% tm%-mr`turms curgka tr`ksgmkt gs-dssg)fm
09288 @J >288 @J 09288 XJ >288 XJ 09288 @J7=8
0888
08=8
0088
00=8
0988
09=8
0?88
S m j p \ L Z
Sk,gk
So,gk
So,dut
Sk,dut
$e`mr `kc (rdu!mr, durk`f dn Numf Omff$ogmkom `kc 5moekdfda#, 2dfu%m M, -6 M,8+0809 6, 98096
Ymkm!`)fm Numf Omff $#stm%
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 32/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=?9/>0
Ymkm!`)fm Numf Omff $#stm%
*`of`#, 6C6, (rdu!mr, 6, `kc $`%umfsmk,A6$6, Gkt]f6 6 #crdamk "kmra#, 2df6 ?0, --6
7
Ymkm!`)fm Numf Omff $#stm%
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 33/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=??/>0
Ymkm!`)fm Numf Omff $#stm%
+69 3 YNO $u--f# Cm%`kc d!mr Nfd!1
8
0
9
?
3
=
>
1
5
Sgjm 1Dkm ?mm95
X d 7 m r 1 9
X^ Xdwmr 1.7 lQ MR Xdwmr (Gk) 3.9 lQ ! Xdwmr ("#$) %r&' Xdwmr
$#stm% OdstQ
+9,888688
9 rdcuomc =86M 3e
3 m` YNO 60 3
YNO Ydukc 5rg- "6 =HI$#stm% "6 H0I
3-$gfmwmml%`
#od$$ut
m
*`of`#, 6C6, (rdu!mr, 6, `kc $`%umfsmk,A6$6, Gkt]f6 6 #crdamk "kmra#, 2df6 ?0, --6MM+7088M, 988>6
utfgkm
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 34/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=?+/>0
utfgkm
• Gktrdcuotgdk• $g%-fm $-`tg`f $NO *dcmf
• C#k`%go Numf Omff *dcmfs . Odktrdfs $#stm%s
Cmmfd-%mkt• "kmra# $#stm%s . gae Ymkm!`)fm mkmtr`tgdk
C#k`%gos
• "kmra# $#stm%s . 'tgfgt# Argc Kmt!dr G%-`ots
• $u%%`r#
Ogrougt Oe`ffmkams1 gae Ymkm!`)fms
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 35/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=?=/>0
Ogrougt Oe`ffmkams1 gae Ymkm!`)fms
Od%%mrog`f Ogrougt:O`#mt`kd;
90 2 3#m
Cm%`kc 09 *3 %`x
0989 oustd%mrs :9?H Fn%rs;
M069I mkmra# ndrOd%%mrog f Gkcustrg`foustd%mrs
2 Amkmr`tgdk 06H? *3 :0=6>I
-mkmtr`tgdk;
H gkst`ff`tgdks :9 ^ =883;
"ug-%mkt 45O :+= *2, 08I
rmauf`tgdk;
Ogrougt Oe`ffmkams1 gae Ymkm!`)fms
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 36/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=?>/>0
• G%-`ots dn 2 dk 4d`c Crd- Od%-mks`tgdk :4CO;!gte ` fd`c7t`- oe`kagka tr`ksndr%mr :088Ik`%m-f`tm 2 -mkmtr`tgdk;
Ogrougt Oe`ffmkams1 gae Ymkm!`)fms
2dft`am Crd-
4CO egkcmrs
2dft`am Ygsm4CO emf-s
'tgfgt# Argc Oe`ffmkams1 gae Ymkm!`)fms
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 37/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=?H/>0
'tgfgt# Argc Oe`ffmkams1 gae Ymkm!`)fms
C#k`%go Cgs-`toe dn (`f`kom d!mr Amkmr`tdrs
Sm$(dr`f rmsdfutgdk d) i`f`kom (dwmr %#k`$gos
??I 3gkc O`sm
5 rrdS`, mt `f6, Ymkm!`)fm"kmra#, 2df6 ?>, Gss6 09, --6
7
'tgfgt# Argc Oe`ffmkams1 gae Ymkm!`)fms
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 38/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=?/>0
'tgfgt# Argc Oe`ffmkams1 gae Ymkm!`)fms
C#k`%go Cgs-`toe dn (`f`kom d!mr Amkmr`tdrs
• 3m]c `fsd fgm td kd! tem `gr u`fgt# g%-`ots dn suoe
c#k`%go cgs-`toe
• Kmmc m%gssgdks oe`r`otmrg`tgdk :curgka st`rt7u-,seut7cd!k, `kc c#k`%go cgs-`toe;
• Gkgtg`f `--rd`oe ndr s-`tg`ff# `ffdo`tgka m%gssgdks ‟ ssu%m -d!mr g%-drts o`kkdt -rdgcm tem )`f`kom -d!mr
‟ Cgs-`toe ourrmkt -`rt7fd`cmc gk7)`sgk -d!mr -f`kts `oodrcgkatd kmmc `kc `oodrcgka td fd`cgka drcmr d)smrmc gk c`t`
‟ Gkst`ff `ccgtgdk`f -d!mr -f`kts gn kmmcmc, dkf# `t ourrmkt-d!mr -f`kt sgtms
‟ Cgs-`toe temsm -d!mr -f`kts td %mmt tem rm%`gkgka )`f`kom-d!mr cm%`kc
• rdcuom s-`tg`ff# tm%-dr`ff# rmsdfmc m%gssgdks@mfcs ndr usm gk `t%ds-emrgo oem%gstr# tr`ks-drt
%dcmf
'tgfgt# Argc Oe`ffmkams1 gae Ymkm!`)fms
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 39/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=?M/>0
'tgfgt# Argc Oe`ffmkams1 gae Ymkm!`)fms
C#k`%go Cgs-`toe dn (`f`kom d!mr Amkmr`tdrs
• 9+7edur `mr`am -`rtgouf`tm %`ttmr :*96=; cgmrmkom
-fdt
:Cgs-`toe O`sm . (`smfgkm o`sm;
O`rrmr`s7$ds-mcr`, mt `f6, t%ds-emrgo"kgrdk%mkt, 2df6 ++, Gss6 9>, --6 ?90=7
'tgfgt# Argc Oe`ffmkams1 gae Ymkm!`)fms
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 40/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=+8/>0
'tgfgt# Argc Oe`ffmkams1 gae Ymkm!`)fms
C#k`%go Cgs-`toe dn (`f`kom d!mr Amkmr`tdrs
• 7edur `mr`am ddkm :?; cgmrmkom -fdt
:Cgs-`toe O`sm . (`smfgkm o`sm;
O`rrmr`s7$ds-mcr`, mt `f6, t%ds-emrgo"kgrdk%mkt, 2df6 ++, Gss6 9>, --6 ?90=7
3gkc #crdamk "kmra# $tdr`am C#k`%gos
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 41/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=+0/>0
3gkc #crdamk "kmra# $tdr`am C#k`%gos
• Od%-rmssmc A`s $tdr`am *m`surmc 3gkc Cm%`kc C#k`%gos
0ot. 9 0ot. = 0ot. > 0ot. 1 0ot. 5 0ot. 7 0ot. 3
• 4d`c segntgka nrd% egae !gkc c`#s td fd! !gkc c`#s
• Gcm`ff#, mxomss !gkc mkmra# :)fum; gs o`-turmc ndr f`tmr usm :rmc;
*`tdk, 66, Ue`d, 46, (rdu!mr, 6, Gkt]f durk`f dn #crdamk "kmra#, 2df6 ?, --6
k # rdamk kmra# dr`am
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 42/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=+9/>0
?8
3=
>8
1=
78
08=
098
0?=
0=8
0>=
X r m s s u r m ( I ` r )
J xgjuj Xrmssurm
Jgkgjuj Xrmssurm
,ot6 9 ,ot6 ? ,ot6 + ,ot6 =
?8
3=
>8
1=
78
08=
098
0?=
0=8
0>=
X r m s s u r m ( I ` r )
J xgjuj Xrmssurm
Jgkgjuj Xrmssurm
,ot6 9 ,ot6 ? ,ot6 + ,ot6 =
k # rdamk kmra# dr`amC#k`%gos
• #crdamk "kmra# $tdr`am• Od%-rmssmc gr "kmra#
$tdr`am
• O"$ gs fg%gtmc )# gts fd! dfu%mtrgo mkmra# cmksgt# *`xg%u% o`mrk -rmssurm fm`cs td ourt`gfmc !gkc mkmra#
*gkg%u% o`mrk -rmssurm rmugrms dtemr -d!mr -f`kts td od%mdkfgkm td %mmt argc cm%`kc
• #crdamk mkmra# stdr`am o`-turms `ff !gkc mkmra#`kc %mmts argc cm%`kc `t `ff tg%ms
*`tdk, 66, Ue`d, 46, (rdu!mr, 6, Gkt]f durk`f dn #crdamk "kmra#, 2df6 ?, --6
k # rdamk kmra# dr`am
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 43/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=+?/>0
Bk Nmi J r @pr J y Buk Buf?8
3=
>8
1=
78
08=
098
0?=
0=8
0>=
X r m s s u r m ( I ` r )
J xgjuj Xrmssurm
Jgkgjuj Xrmssurm
Bk Nmi J r @pr J y Buk Buf?8
3=
>8
1=
78
08=
098
0?=
0=8
0>=
X r m s s u r m ( I ` r )
J xgjuj Xrmssurm
Jgkgjuj Xrmssurm
k # rdamk kmra# dr`amC#k`%gos
• Od%-rmssmc gr "kmra#
$tdr`am
• #crdamk "kmra# $tdr`am
• 5em O"$ o`mrk gs od%-fmtmf# cm-fmtmc curgka
tem su%%mr cm%`kc -m`• #crdamk mkmra# stdr`am suoomssnuff#
`ood%-fgsems sm`sdk`f fd`c segntgka 3gkc mkmra# stdrmc gk !gktmr gs usmc td -rdgcm ndr tem f`ram su%%mr
cm%`kc
*`tdk, 66, Ue`d, 46, (rdu!mr, 6, Gkt]f durk`f dn #crdamk "kmra#, 2df6 ?, --6
O`k Numf Omff "fmotrdf#mr C#k`%gos 3drW
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 44/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=++/>0
O`k Numf Omff "fmotrdf#mr C#k`%gos 3drW
• K`tur`f A`s 5r`ks%gssgdk `kc Cgstrg)utgdk $#stm%
O`r%dk`, crg`k, *6$6 5emsgsrdSmot, 'O Grgkm, 6 (rdu!mr
)
*
MQ
+ G ) M 9 ? =
+ G ) M ? ? =
+ M % M ) ,
) " - - " * ! . + M
/ M ! G X / " ! . - G ) % ! " 8 X / M * * " / * - . - G " )
! M ) - / G ] % . + ! " 8 X / M * * " / * - . - G " )
X / M * * ] / M + G 8 G - G ) % * - . - G " )
* - " / . % M G M + ,
3 08 8
. + G * "
! . ) " )
" ) " /
/ . ) ! "
M / ) / G ^ M /
* - . - G " )
? * M M F M (( ' & M
1 2 < $ J J O N 5
% " + M - .
X + . .
, M + / M
6 M ( K : J D ; % ^ M
. , M + . ) - "
^ M ) - ] / .
* - . - G " ) ] G % + M
, . ) .
X " G ) -
" / .
M + * "
+ G ) M 9 ? =
K D ( S *K M M F M _
1 4 0 $ J J O N 5
S D X D O 61 0 H $ J J O N 5
J D ; % ^ M
S ( % K _ ? M _ S M ( K
M F X % _ D
* . ) , G M % "
, M * M / -
! M ) - M /
+ F , S * M1 # 8 # $ J J O N 5
. / G R " ) .
M F X % _ D
+ G ) M 0 8 ? 8
_ d u t e m r k O ` f g @ d r k g ` & ` s O d j p ` k I N ` o g f g t g m s
% / M . - M / + " * . ) % M + M *
8 M - / " X " + G - . ) . / M .
" / M ) "
* - . - G " )
+
G )
M
>
7
8
9
+
G )
M
>
8
8
8
! G ) "
+ G ) M * ? 8 8 8 ? 8 8 ? ? 8 8 5
0 0 5 8 0 0 5 0 0 0 7 9
+ G ) M 0 0 5 =
+ G ) M 1 8 8 8+ G ) M 1 8 ? 7
) M Q M / /
+
G )
M
>
7
8
?
+ G ) M * 0 8 8 ? 0 8 8 3 0 8 8 =
! . ! - ] *
! G -
+ G ) M * 3 8 3 3 8 >
+
G )
M
>
7
8
8
+
G )
M
0
8
9
5
+
G )
M
0
8
9
1
+ G ) M 9 8 8 8
+ G ) M = 8 8 8
+ G ) M 9 8 8 0
- / . ) * 8 G * * G" ) > . ! 3 > " ) M
* M O S D ( ( 1 0 $ J J O N 5
O D % _ S % F _ , _ S M J1 # 8 $ J J O N 5
^ % F F M , _ , _ S M J1 # 0 $ J J O N 5
O`k Numf Omff "fmotrdf#mr C#k`%gos 3drW
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 45/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=+=/>0
$dutemrk O`fgndrkg` A`s tmrrgtdr# . a`s mkmra# stdr`am
• 0?8 (on dn "kmra# $tdr`am 7 mug`fmkt td %drm te`k
00 53e dn mfmotrgogt# stdr`am
&dfmt`
Xf`I` mf (mI *dkdr (`koed
%fgsd O`kIdk
O`k Numf Omff "fmotrdf#mr C#k`%gos 3drW
O`r%dk`, crg`k, *6$6 5emsgsrdSmot, 'O Grgkm, 6 (rdu!mr
utfgkm
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 46/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=+>/>0
utfgkm
• Gktrdcuotgdk• $g%-fm $-`tg`f $NO *dcmf
• C#k`%go Numf Omff *dcmfs . Odktrdfs $#stm%sCmmfd-%mkt
• "kmra# $#stm%s . gae Ymkm!`)fm mkmtr`tgdkC#k`%gos
• "kmra# $#stm%s . 'tgfgt# Argc Kmt!dr G%-`ots
• $u%%`r#
Grgkm $%`rt Argc Cm%dkstr`tgdk :G$AC;
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 47/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=+H/>0
Grgkm $%`rt Argc Cm%dkstr`tgdk :G$AC;
!+
?mw(drt Im`oe
+r<gkm
`o@rteursui
@rkdf% 9l'
Yd$$mf 9l'
6= "$`rt Ed$mskg<mrsgt# Egffs
Grgkm $%`rt Argc Cm%dkstr`tgdk :G$AC;
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 48/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=+/>0
+`o9 D@@gom
Odjj`kc Omktmr )O' O`jpus Xuifgo
Oe`ragka _t`tgdk
+`ttmrI _tdr`am
J`o%rteur _uist`tgdkOgrougt+rm`9mr Ogrougt
+rm`9mr
N%K
Odjjukgo`tgdks
gstrgiutmc
_tdr`am
)(O'
)(O'
)(O'
Sr`ks@drjmr
Sr`ks@drjmr
OdjjukgtI
_tdr`am
Sr`ks@drjmr
Sr`ks@drjmr
)(O'
+fdo9 #
RM
+fdo9 8
dm *$dr2m
+fdo9 >
!d#k&$< *$dr2m+fdo9 H
!dk$rd6 %rd#
%rkdfc Ogrougt
(djjmf Ogrougt(djjmf Ogrougt
%rkdfc Ogrougt
)(O'
Grgkm $%`rt Argc Cm%dkstr`tgdk :G$AC;
'OG *gordargc
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 49/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=+M/>0
'OG *gordargc
'OG *gordargc e#sgo`f Nm`turms
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 50/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980==8/>0
G_AC
'OG
5"$
]OGJgordargc
Omktr`f f`kt1 oegffmrs
A`s tur)gkm1 0=6*2
$tm`% tur)gkm1 >6>*2
5emr%`f $tdr`am+,=88,888 A`f
>8,888 5dk7dur
'OG *gordargc e#sgo`f Nm`turms
'OG *gordargc e#sgo`f Nm`turms
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 51/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980==0/>0
'O
G
5"$
"cgsdk*`orteu
r$u)st`tgd
k
Omktr`f f`kt1 oegffmrs
A`s tur)gkm1 0=6*2
$tm`% tur)gkm1 >6>*2
5emr%`f $tdr`am+,=88,888 A`f
>8,888 5dk7dur
G_AC
'OG$u)st`tgd
k>>2/09
2
$df`r Yddntd-
2M?3
]OGJgordargc
'OG *gordargc e#sgo`f Nm`turms
'OG *gordargc e#sgo`f Nm`turms
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 52/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980==9/>0
'O
G
5"$
"cgsdk*`orteu
r$u)st`tgd
k
Omktr`f f`kt1 oegffmrs
A`s tur)gkm1 0=6*2
$tm`% tur)gkm1 >6>*2
5emr%`f $tdr`am+,=88,888 A`f
>8,888 5dk7dur
G_AC
'OG$u)st`tgd
k
>>2/092
$df`r Yddntd-
2M?3
O200?3
]OGJgordargc
'OG *gordargc e#sgo`f Nm`turms
'OG *gordargc e#sgo`f Nm`turms
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 53/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980==?/>0
'O
G
5"$
"cgsdk*`orteu
r$u)st`tgd
k
Omktr`f f`kt1 oegffmrs
A`s tur)gkm1 0=6*2
$tm`% tur)gkm1 >6>*2
5emr%`f $tdr`am+,=88,888 A`f
>8,888 5dk7dur
]OGNF
G_AC
'OG$u)st`tgd
k
>>2/092
$df`r Yddntd-
2M?3
O200?3
U"2RK"5megofm
Emmt
'OG *gordargc e#sgo`f Nm`turms
'OG *gordargc e#sgo`f N
m`turms
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 54/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980==+/>0
'O
G
5"$
"cgsdk*`orteu
r$u)st`tgd
k
Omktr`f f`kt1 oegffmrs
A`s tur)gkm1 0=6*2
$tm`% tur)gkm1 >6>*2
5emr%`f $tdr`am+,=88,888 A`f
>8,888 5dk7dur
G_AC
'OG$u)st`tgd
k
>>2/092
$df`r Yddntd-
2M?3
O200?3
U"2RK"5megofm
Emmt
08 a/c`#9 $t`tgdk
]OGJgordargc
'O o da c #s o` m` u ms
*gordargc $g%uf`tgdk
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 55/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980===/>0
a
• 3drgka %dcmf dn 'OG *gordargc gk "5
]k&;.*#4H$$&dk 0
]! 00
]! 9
]! ?
]! 3
]! =
]k&;.*#4H$$&dk 9
]! >>
(]! 1)
]! 5
]! 77
]! 08
]k&;mrH&$<
*#4H$$&dk
!mk$r6 X6k$ MH$
*#4H$$&dk
*gordargc $g%uf`tgdk
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 56/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980==>/>0
a
8 + 09 0> 98 9+8
96=
=
H6=
08
096=
0=
0H6=
Ym`f Xdwmr
edtddft`go
O`%-us 4d`cs
$O" g%-drt
Od%)ustgdk 5ur)gkmAmkmr`tdr
$tm`% 5ur)gkmAmkmr`tdr
Sg$m:ers;
Xdwmr:4;
C#k`%gos dn Gkorm`sgka Ymkm!`)fms
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 57/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980==H/>0
# a
$gakg@o`ktourt`gfmc
amkmr`tgdk
Ymcuomc A5
o`-`ogt#n`otdr
Gkorm`smc A5
r`%-gka
$g%uf`tgdk ut-ut1 gkst`ffmc 0+6> *3 2 @xmc `kc 99 *3O2
:'OG "x`%-fm;
98I rmkm!`)fm -mkmtr`tgdk
utfgkm
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 58/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980==/>0
• Gktrdcuotgdk• $g%-fm $-`tg`f $NO *dcmf
• C#k`%go Numf Omff *dcmfs . Odktrdfs $#stm%sCmmfd-%mkt
• "kmra# $#stm%s . gae Ymkm!`)fm mkmtr`tgdkC#k`%gos
• "kmra# $#stm%s . 'tgfgt# Argc Kmt!dr G%-`ots
• $u%%`r#
$u%%`r#
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 59/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980==M/>0
#
• Gktmar`tmc NO s#stm%s o`k -rdgcm ukgum-mrndr%`kom oe`r`otmrgstgos mssmktg`f ndr
sust`gk`)gfgt# ‟ Ofm`k, m&ogmkt, cgs-`toe`)fm, numf Emxg)fm
• Cm%dkstr`tmc tem g%-drt`kom dn s-`tg`f `kctm%-dr`f rmsdfutgdk dn rmfm`kt -e#sgos, oem%gstr#,
mfmotrdoem%gstr# gk s#stm%s `k`f#sms• rdgcmc mx`%-fms dn `--fgo`tgdk, gksgaets
‟ $g%-fm $-`tg`f $NO *dcmf . GANO s#stm%s `k`f#sms
‟ C#k`%go Numf Omff *dcmfs . odktrdfs s#stm%s cmmfd-%mkt
‟ "kmra# $#stm%s . egae rmkm!`)fm -mkmtr`tgdk ‟ "kmra# $#stm%s . utgfgt# argc kmt!dr g%-`ots
• Numf omff `c`kom%mkt kmmcs sogmktg@o `c`kom%mktgk %`k# cgsog-fgkms te`t gktg%`tmf# mka`ammkagkmmrgka ukcmrst`kcgka dn s#stm%s gktmar`tgdk
okd!fmcam%mkts
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 60/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=>8/>0
a
• Nukcgka amkogms1 ‟ '6$6 Cm-`rt%mkt dn "kmra#
‟ O`fgndrkg` "kmra# Od%%gssgdk
‟ '6$6 "kgrdk%mkt`f rdtmotgdk amko#
• Odff`)dr`tgka N ouft#1 ‟ N r#`r `))`rg • Cdk`fc C`)cu) • ddka%#mdk
(`m ‟ Pm#um $%mcfm# • $odtt $`%umfsmk
• Ymsm`roe Odffm`aums $tucmkts1 ‟ Y`kc# Am%%mk • sed Y`d
‟ N )g`k *umffmr • Ae``f Y`maeg
‟ Ydr# Yd)mrts • 5r`gs $euft
‟ Custgk *o4`rt# • *`ro O`rrmr`s
‟ 5d%degd P`kmd • kcrm! *`rtgkm
‟ *u 4g • dssmgk Aemmf7#`ae
5e`k _du
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 61/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=>0/>0
`kls dr Hdur @ttmktgd
utfgkm
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 62/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=>9/>0
• *dtg`tgdk . Ofm`k, "&ogmkt $ust`gk`)fm
• 3e`t sedufc !m cdW
• d! o`k !m cd gtW
• O`k Numf Omff "fmotrdf#mr C#k`%gos 3drW
• $u%%`r#
3e`t $edufc 3m CdW
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 63/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=>?/>0
\G]c -ut %# %dkm# dk temsuk sdf`r mkmra#6 3e`t` sdurom dn -d!mrV Ged-m !m cdk]t e`m td
!`gt uktgf dgf `kc od`f rukdut )mndrm !m t`ofm te`t6G !gse G e`c %drm #m`rsfmnt6Z
5ed%`s "cgsdk, 0M?0
3e`t $edufc 3m CdW
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 64/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=>+/>0
'sm *Y" $df`r d!mr
• 2, cgse $tgrfgka, sdf`r7temr%`f
• 3gcmf# ``gf`)fm \-m`gkaZ rmsdurom• Oe`ffmkams1 gktmr%gttmkt, mx-mksgm, cgusm
3e`t $edufc 3m CdW
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 65/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=>=/>0
'sm *Y" $df`r d!mr
• Oe`ffmkams1 987?8I o`-`ogt# n`otdr, gktmr%gttmkt,
cgusm,mx-mksgm td rmodmr
3e`t $edufc 3m CdW
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 66/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=>>/>0
'sm *Y" 3gkc d!mr
• $%`ff 3gkc :=83; . rm%dtm, cgstrg)utmc
`--fgo`tgdks
@gr 38?
Qegspmr e38Qegspmr e58
Qegspmr 01=
_gkafm Ymjdtm
djm !"#jpfm
3e`t $edufc 3m CdW
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 67/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=>H/>0
'sm *Y" 3gkc d!mr
• 4`ram 3gkc :%uftg7*3; . $tgff cgstrg)utmc, c`t`7omktmr
sgms
3e`t $edufc 3m CdW
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 68/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=>/>0
3emrm O`k 3gkc d!mr )m $gtmcW
$Y!%, 9885
3e`t $edufc 3m CdW
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 69/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=>M/>0
3gkc d!mr . Oe`ffmkams1 Gktmr%gttmko#, kdk7odgkogcmkom
"x`%-fm dn Gktmr%gttmko# Kdk7Odgkogcmkom !gte m`Cm%`kc
&@'_, 9881
utfgkm
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 70/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=H8/>0
• *dtg`tgdk . Ofm`k, "&ogmkt $ust`gk`)fm
• 3e`t sedufc !m cdW
• d! o`k !m cd gtW
• O`k Numf Omff "fmotrdf#mr C#k`%gos 3drW
• $u%%`r#
d! O`k 3m Cd GtW
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 71/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=H0/>0
• 'sm *Y" Ymkm!`)fm "kmra# . $df`r, 3gkc, Amdtemr%`f ‟ (ut, temsm rmsduroms `rm gktmr%gttmkt, ukodktrdff`)fm, `kc/dr kdt
``gf`)fm !emk `kc !emrm c`t` omktmrs :dr dtemr -d!mr cm%`kcs;%ust )m %mt
• Kmmc ndr \s%`rtZ c#k`%go`ff# cgs-`toemc, ofm`k, m&ogmkt
sust`gk`)fm mkmra# odkmrsgdk td od%-fm%mkt temsmrmsduroms
• 5dc`# !m usm k`tur`f a`s @rmc a`s tur)gkm tmoekdfda# ‟ gae m&ogmko#, fd! m%gssgdks `t omktr`f -f`kt so`fm
‟ $tgff e`s m%gssgdks dn -dffut`kts `kc AAs
‟ Kdt `s m&ogmkt `t s%`ffmr so`fms
• Numf Omff tmoekdfda# gs ` addc o`kcgc`tm
‟ Umrd m%gssgdks :9 d-mr`tgdk;, uftr`7fd! m%gssgdks :e#crdo`r)dkd-mr`tgdk;
‟ gae m&ogmko# mmk `t s%`ff sgm
‟ O`k d-mr`tm dk fdo`ff# ``gf`)fm rmkm!`)fm numfs `kc k`tur`f a`s
d! O`k 3m Cd GtW :Ymcx Ym`otgdks;
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 72/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=H9/>0
5r`cgtgdk`f mkmra# odkmrsgdk :od%)ustgdk; . tm%-mr`turmcgmrmkom
O+
9
Ymcuotgdk `kc xgc`tgdk doour `t tem s`%m -f`om tg%m
O+ J 9 9 ↙ O9 J 9 9
Ndr%`f2`fmkom1 O1 . + J +
1 8 . 9 . 9
" < m "
. H m "
. H m "
• Ngrst -rdcuom em`t• Y`kcd% mfmotrdk Ed!• Odkmrsgdk td mfmotrgog• dffut`kts `fsd ndr%mc
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 73/82
d! O`k 3m Cd GtW
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 74/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=H+/>0
Fd`cm
Xrdcuot &`sms
(msgcu`f Numf
Numf D/gc`kt
%kdcm O`tedcmMfmotrdfItm
1'dk Odkcuotdr5
Xrdcuot &`sms
(msgcu`f D/gc`kt
mm
*"!9
9"
"9
X!k'
XM!
9
9"
"9+
!!
9
!"9
9" !"9
"9
>=8@0888¸!
988¸!
78¸!
>=8¸!
! 9
99 58¸!"@
":
!"?
Numf Omff 5#-ms
d! O`k 3m Cd GtW
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 75/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=H=/>0
_]YO!" _AG#9=
"S@S+0?@YH ! @YOS"• 4@"SO4@SOY X@?S" E0SO"
• 00C XY0!O""+?A IYO4OY+O"
• A0'OY?O?S?+'OY"+S+O"
• E0"X+S@" +?C"SY+O"
•
!0?+!@S+0?" S++S+O"• AY0!OYH "S0YO"@?@!SY+?A
!`fg)drkg` "t`tmkg<mrsgt#O`st I`#
!`fg)drkg` "t`tmkg<mrsgt#?drterg%/m
+kf`k% O$(grm tgfgtgms@/mko#0kt`rgd
YO?O4@IO
Agffs 0kgdks
0Mk`r%
YO?O4@IO
• ?@SY@ A@" N 1
• YO?O4@IO N =3
S0S@ N 4
"S@S+0?@YH ! COX0HO?S"
d! O`k 3m Cd GtW
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 76/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=H>/>0
• ?@SY@ A@" N 1
• YO?O4@IO N =3
S0S@ N 4
"S@S+0?@YH ! COX0HO?S"
_]YO!" _AG#
9
4`f$`rtEm$mt
!`fSmoe
X`s`%mk`
"S@S+0?@YH ! @YOS"• 4@"SO4@SOY X@?S" E0SO"
• 00C XY0!O""+?A IYO4OY+O"
• A0'OY?O?S?+'OY"+S+O"
• E0"X+S@" +?C"SY+O"
•
!0?+!@S+0?" S++S+O"• AY0!OYH "S0YO"@?@!SY+?A
Add/fm
"gfgodk '`ffm#
m(`#$gfgodk 2`ffm#
O`k Numf Omff "fmotrdf#mr C#k`%gos 3drW
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 77/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=HH/>0
• O`k tegs )m cdkm ndr tem mktgrm st`tm dn OW ‟ O`mrk sgm dn ?6 %gffgdk %? !`s `)fm td stdrm `ff dtemr!gsm
ourt`gfmc !gkc gk O ndr tem mktgrm #m`r ndr ` o`sm !gte =8Irmkm!`)fm -d!mr :%gx dn sdf`r/!gkc;
crg` O`r%dk`, *6$6 5emsgs, 'OGrgkm, `o (rdu!mr, `cgsdr,
utfgkm
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 78/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980=H/>0
• *dtg`tgdk . Ofm`k, "&ogmkt $ust`gk`)fm
• 3e`t sedufc !m cdW
• d! o`k !m cd gtW
• O`k Numf Omff "fmotrdf#mr C#k`%gos 3drW
• $u%%`r#
*dtg`tgdk . Ofm`k, "&ogmkt $ust`gk`)fm
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 79/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980= HM/>0
• ff sdogmtgms `kc modkd%gms cm-mkc u-dk mkmra#odkmrsgdk
‟ "odkd%go -rds-mrgt# ‟ m`fte
‟ *d)gfgt#
‟ Nrmmcd%, <u`fgt# dn 4gnm, [
• "mr#tegka te`t od%-`kgms `kc -md-fm cd e`s sd%m
cm-mkcmkom u-dk rmf`tgdkseg- td mkmra# odkmrsgdk• Ndrtuk`tmf# eu%`ks e`m cgsodmrmc `kc `c`komc
mkmra# odkmrsgdk tmoekdfda# ‟ Ngrm
‟ gae cmksgt# mkmra# o`rrgmrs :m6a6, O numfs;
‟ "kagkms
‟ "kgrdk%mkt`f G%-rdm%mkts
• gaemr m&ogmko#
• 4d!mr m%gssgdks
*dtg`tgdk . Ofm`k, "&ogmkt $ust`gk`)fm
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 80/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980= 8/>0
'kndrtuk`tmf# mkmra# odkmrsgdk tmoekdfdagms `rm tem f`ramstodktrg)utdrs td sgakg@o`kt mkgrdk%mkt`f `kc amd-dfgtgo`f
-rd)fm%s• Orgtmrg` dffut`kt "%gssgdks
‟ ogc Y`gk
‟ `rtgouf`tm *`ttmr
‟ 2df`tgfm ra`kgo Od%-dukcs
‟ Kgtrdamk `kc $ufnur xgcms ‟ O`r)dk *dkdxgcm
‟ [
• Armmkedusm A`s "%gssgdks ‟ O`r)dk cgdxgcm, %mte`km, kgtrdus dxgcm, [
• Ymsdurom rmodmr# c`%`am :m6a6, %gkms;
• Ymagdk`f rmsdurom cm-fmtgdk . mkmra# amd-dfgtgo`fcm-mkcmkogms
• mr`ff -rg%`r# mkmra# rmsdurom cm-fmtgdk . kdt sust`gk`)fm
$mrgdus m`fte`kc gr <u`fgt#
Odksmumkoms
4ds kamfms
(mgSgka
*dtg`tgdk . Ofm`k, "&ogmkt $ust`gk`)fm
7/21/2019 Jack Brouwer Seminar
http://slidepdf.com/reader/full/jack-brouwer-seminar 81/82
© K`tgdk`f Numf Omff Ymsm`roe Omktmr 980= 0/>0
• *dst -rdSmotgdks :"G, G"; suaamst \%drm dn tems`%mZ
• $d -fuaagka gk `ff dur \stuZ `kccrggka fgm !m `rm !gff fm`c td1 ‟ gr u`fgt# -rd)fm%s
:kdt ofm`k, kdt sust`gk`)fm;
‟ Armmkedusm a`s m%gssgdks:kdt m&ogmkt, kdt sust`gk`)fm;
‟ Ymsdurom cm-fmtgdk:kdt ofm`k, kdt m&ogmkt, kdt sust`gk`)fm;