B GIO DC V O TO TRNG I HC BCH KHOA H NI

CHNG TRNH O TO TIN SCHUYN NGNH

M BO TON HC CHO MY TNH V H THNG TNH TONM S: 62.46.35.01

c Hi ng Xy dng Chng trnh o to bc Tin s thng qua ngy ....... thng ....... nm .............

H NI

MC LC

Trang PHN I 1 1.1 1.2 2 3 4 4.1 4.2 4.3 5 6 7 7.1 7.2 7.2.1 7.2.2 7.2.3 7.3 7.3.1 7.3.2 7.3.3 7.4 8 PHN II 9 9.1 9.2 10 TNG QUAN V CHNG TRNH O TO Mc tiu o to Mc tiu chung Mc tiu c th Thi gian o to Khi lng kin thc i tng tuyn sinh nh ngha Phn loi i tng ngnh ph hp Phn loi i tng ngnh gn ph hp Quy trnh o to, iu kin cng nhn t Thang im Ni dung chng trnh Cu trc Hc phn b sung, chuyn i Danh mc hc phn b sung, chuyn i M t tm tt hc phn b sung, chuyn i Thi hn hon thnh cc hc phn b sung, chuyn i Hc phn trnh Tin s Danh mc hc phn trnh Tin s M t tm tt hc phn trnh Tin s K hoch hc tp cc hc phn trnh Tin s Chuyn Tin s Danh sch Tp ch / Hi ngh Khoa hc CNG CHI TIT CC HC PHN Danh mc hc phn chi tit ca chng trnh o to Danh mc hc phn b sung, chuyn i Danh mc hc phn trnh Tin s cng chi tit cc hc phn trnh Tin s 3 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 10 10 12

2

PHN I

TNG QUAN V CHNG TRNH O TO

3

TRNG I HC BCH KHOA H NI KHOA TON TIN NG DNG

CNG HA X HI CH NGHA VIT NAM c lp - T do - Hnh phc

CHNG TRNH O TO TIN S CHUYN NGNH M BO TON HC CHO MY TNH V H THNG TNH TON Tn chng trnh: Chng trnh o to Tin s chuyn ngnhM BO TON HC CHO MY TNH V H THNG TNH TON

Trnh o to: Tin s Chuyn ngnh o to: M BO TON HC CHO MY TNH V H THNG TNH TON (Mathematical Foundation of Computer Science- MFCS) M chuyn ngnh: 62.46.35.01 (Ban hnh theo Quyt nh s ......... / Q-HBK-SH ngy ....... thng ....... nm ........... ca Hiu trng trng H Bch Khoa H Ni) 1 Mc tiu o to 1.1 Mc tiu chung o to Tin s chuyn ngnh M BO TON HC CHO MY TNH V H THNG TNH TON c trnh chuyn mn su cao, c kh nng nghin cu v lnh o nhm nghin cu cc lnh vc ca chuyn ngnh, c t duy khoa hc, c kh nng tip cn v gii quyt cc vn khoa hc chuyn ngnh, c kh nng trnh by - gii thiu cc ni dung khoa hc, ng thi c kh nng o to cc bc i hc v Cao hc. 1.2 Mc tiu c th Sau khi kt thc thnh cng chng trnh o to, Tin s chuyn ngnh HC CHO MY TNH V H THNG TNH TON:

M BO TON

C kh nng pht hin v trc tip gii quyt cc vn khoa hc thuc cc lnh vc m bo ton hc cho my tnh v cc h thng tnh ton v cc lnh vc lin quan v Ton Tin l thuyt v ng dng v Cng ngh thng tin. C kh nng dn dt, lnh o nhm nghin cu thuc cc lnh vc m bo ton hc cho my tnh v cc h thng tnh ton v cc lnh vc lin quan v Ton Tin l thuyt v ng dng v Cng ngh thng tin. C kh nng nghin cu, xut v p dng cc gii php cng ngh thuc cc lnh vc ni trn trong thc tin. C kh nng cao trnh by, gii thiu (bng cc hnh thc bi vit, bo co hi ngh, ging dy i hc v sau i hc) cc vn khoa hc thuc cc lnh vc ni trn.4

2 Thi gian o to Vn dng khon 4 iu 81 Quy nh v t chc v qun l o to sau i hc do Hiu trng H Bch Khoa H Ni ban hnh theo quyt nh s 1492/Q-HBK-SH ngy 30/9/2009, thi gian o to Tin s chuyn ngnh M BO TON HC CHO MY TNH V H THNG TNH TON s l: 3 nm tp trung lin tc i vi NCS c bng ThS v 4 nm tp trung lin tc i vi NCS c bng H.

Trng hp NCS khng theo hc tp trung lin tc c v c Trng, Khoa chp nhn th NCS phi c tng thi gian hc tp v nghin cu tp trung l 3 nm i vi NCS c bng ThS v 4 nm i vi NCS c bng H. Trong c t nht mt gian on 12 thng tp trung lin tc ti B mn o to, thc hin trong phm vi 3 nm u k t ngy k quyt nh cng nhn NCS. 3 Khi lng kin thc Khi lng kin thc bao gm khi lng ca cc hc phn trnh Tin s v khi lng ca cc hc phn b sung, hc phn chuyn i c xc nh c th cho tng loi i tng ti mc 4. NCS c bng ThS: 12 tn ch + khi lng b sung, chuyn i (nu c). NCS mi c bng H: 12 tn ch + 28 tn ch (khng k lun vn) ca Chng trnh Thc s Khoa hc chuyn ngnh M BO TON HC CHO MY TNH V H THNG TNH TON v Ton ng dng, . i vi NCS c bng H ca cc h 4 hoc 4,5 nm (theo quy nh) s phi thm cc hc phn b sung ca Chng trnh Thc s Khoa hc chuyn ngnh M BO TON HC CHO MY TNH V H THNG TNH TON v Ton ng dng,

4 i tng tuyn sinh i tng tuyn sinh l cc th sinh c bng Thc s vi chuyn ngnh tt nghip ph hp hoc gn ph hp vi chuyn ngnh M BO TON HC CHO MY TNH V H THNG TNH TON.. Ch tuyn sinh mi c bng H vi chuyn ngnh tt nghip ph hp. Mc ph hp hoc gn ph hp vi chuyn ngnh M BO TON HC CHO MY TNH V H THNG TNH TON, c nh ngha c th mc 4.1 sau y. 4.1 nh ngha Ngnh ph hp: L nhng hng o to chuyn su theo ngnh M BO TON HC CHO MY TNH V H THNG TNH TON , hay Ton ng dng hoc cc hng Khoa hc my tnh K Thut My Tnh, H thng Thng Tin, Mng my tnh v Truyn s liu.. trong lnh vc Cng ngh Thng Tin.. m ngun vo ly t nhng hc vin hon thnh chng trnh o to Thc s cc Trng i hc v Vin nghin cu v o to . Ngnh gn ph hp: L nhng hng o to chuyn su thuc cc ngnh sau: + Ton hc tnh ton + L thuyt ti u + L thuyt xc sut v thng k ton hc5

+ Ton Lgic + i s v S hc + Ton Gii Tch + Phng trnh vi phn v tch phn 4.2 Phn loi i tng ngnh ph hp C bng ThS Khoa hc (nh hng nghin cu) nhng thi gian tt nghip (tnh ti thi im ra quyt nh cng nhn trng tuyn nghin cu sinh) cha qu 7 nm. y l i tng khng phi tham gia hc b sung/chuyn i, gi tt l i tng A1. C bng ThS Khoa hc (nh hng nghin cu) nhng thi gian tt nghip (tnh ti thi im ra quyt nh cng nhn trng tuyn nghin cu sinh) qu 7 nm. y l i tng phi tham gia hc b sung, gi tt l i tng A2. C bng H. y l i tng phi tham gia hc b sung, gi tt l i tng A4. Trng hp c bit: Nghin cu sinh c bng ThS Khoa hc khng phi ca H Bch Khoa H Ni. Sau y gi tt l i tng A5.

4.3 Phn loi i tng ngnh gn ph hp C bng ThS Khoa hc nhng thi gian tt nghip cha qu 7 nm. y l i tng phi tham gia hc chuyn i, gi tt l i tng B1. C bng ThS Khoa hc nhng thi gian tt nghip qu 7 nm. y l i tng phi tham gia hc b sung v hc chuyn i, gi tt l i tng B2.

5 Quy trnh o to, iu kin cng nhn t Quy trnh o to c thc hin theo hc ch tn ch, tun th Quy nh 1492/2009 v t chc v qun l o to sau i hc ca H Bch Khoa H Ni. Cc hc phn b sung, hc phn chuyn i phi t mc im C tr ln (xem mc 6). Cc hc phn trnh Tin s phi t mc im B tr ln (xem mc 6).

6 Thang im Khon 6a iu 62 ca Quy nh 1492/2009 quy nh: Vic chm im kim tra - nh gi hc phn (bao gm cc im kim tra v im thi kt thc hc phn) c thc hin theo thang im t 0 n 10, lm trn n mt ch s thp phn sau du phy. im hc phn l im trung bnh c trng s ca cc im kim tra v im thi kt thc (tng ca tt c cc im kim tra, im thi kt thc nhn vi trng s tng ng ca tng im c quy nh trong cng chi tit hc phn). im hc phn c lm trn n mt ch s thp phn sau du phy, sau c chuyn thnh im ch vi mc nh sau: im s t 8,5 10 chuyn thnh im A (Gii) im s t 7,0 8,4 chuyn thnh im B (Kh)6

im s t im s t im s di

5,5 6,9 4,0 5,4 4,0

chuyn thnh im C (Trung bnh) chuyn thnh im D (Trung bnh yu) chuyn thnh im F (Km)

7 Ni dung chng trnh 7.1 Cu trc Cu trc chng trnh o to trnh Tin s gm c 3 phn nh bng sau y.Phn 1 Ni dung o to HP b sung HP chuyn i HP trnh Bt buc TS T chn CTSBt buc T chn

A1 0 0

A2 12TC 0

22)

A4 A5 5) 28TC NHD1) 0 0 3TC (1HP) 9TC (3HP)3) 2TC 4TC3)

B1 0 12TC

B2 3TC 12TC

32)1) 2) 3) 4)

TLTQ4) NC khoa hc4) Lun n4)

NHD: vit tt ca ngi hng dn Ging nhau cho mi loi i tng y l phn dnh cho NCS t chn y l cc ni dung gn vi ti NCKH v cc trnh by ca lun n nn s c quy nh ring v khng c cp n trong phn chng trnh o to mang tnh ging dy ny 5) Ngoi 28 tn ch ca chng trnh o to bc Cao hc, i tng A4 tt nghip h H 4-4,5 nm cn phi hc cc hc phn b sung ca chng trnh o to bc Cao hc theo quy nh

7.2 Hc phn b sung, chuyn i 7.2.1 Danh mc hc phn b sung, chuyn iI TNG HC PHN M S MI6010 MI6110 TN HC PHN TN CH 3 3 KHI LNG 3(2-2-0-6) 3(2-2-0-6)

A2

B sung

A4

B sung

A5

B sung

i s ng dng Ti u t hp Nhng ch hin i trong ngn 3 3(2-2-0-6) MI6190 ng hnh thc 3 3(2-2-0-6) MI6160 phc tp tnh ton Ton b 28 TC + cc hc phn b sung cho h 4-4,5 nm ca chng trnh o to Thc s Khoa hc chuyn su Ton ng dng, chuyn ngnh Ton Tin (khng k 15 TC ca lun vn tt nghip) 3 3(2-2-0-6) MI6160 phc tp tnh ton Thut ton nng cao v tnh ton 3 3(2-2-0-6) MI6050 song song Nhng ch hin i trong ngn 3 3(2-2-0-6) MI6190 ng hnh thc7

MI6160 MI6170 B1 Chuyn i MI6190 MI6180 MI6010 MI6160 MI6170 MI6190 MI6180

B sung B2

Chuyn i

phc tp thut ton Bo mt v an ton d liu Nhng ch hin i trong ngn ng hnh thc Nhn dng nng cao i s ng dng phc tp thut ton Bo mt v an ton d liu Nhng ch hin i trong ngn ng hnh thc Nhn dng nng cao

3 3 3 3 3 3 3 3 3

3(2-2-0-6) 3(2-2-0-6) 3(2-2-0-6) 3(2-2-0-6) 3(2-2-0-6) 3(2-2-0-6) 3(2-2-0-6) 3(2-2-0-6) 3(2-2-0-6)

7.2.2 M t tm tt hc phn b sung, chuyn i Cc hc phn b sung, chuyn i c m t trong quyn Chng trnh o to Thc s chuyn ngnh Ton-Tin ca trng H Bch khoa H Ni, c Hi ng Khoa hc v o to Khoa Ton-Tin ng dng chnh thc thng qua ngy .../.../2009 v c Hiu trng ban hnh theo quyt nh s 1452/Q-HBK-SH ngy 26/08/2009. 7.2.3 Thi hn hon thnh cc hc phn b sung, chuyn i Cc i tng A2, A3, A5 phi hon thnh cc hc phn b sung trong thi hn 2 nm k t ngy c quyt nh cng nhn l NCS. i tng A4 phi hon thnh cc hc phn b sung trong thi hn 2 nm k t ngy c quyt nh cng nhn l NCS. Cc i tng B1, B2, B3 phi hon thnh cc hc phn chuyn i trong thi hn 2 nm k t ngy c quyt nh cng nhn l NCS. Cc hc phn b sung phi c hon thnh trong hc k k tip sau khi hon thnh phn chuyn i.

7.3 Hc phn trnh Tin s 7.3.1 Danh mc hc phn trnh Tin sNI DUNG

M S MI7500 MI7510 MI7511

TN HC PHN L thuyt tnh ton v cc otomat Mch lng t v cc Thut ton lng t M phng ngu nhin

GING VIN PGS. TS. Phan Trung Huy GS.TSKH. Long Vn TS. Nguyn Th Thanh Huyn PGS. TS. Phan Trung Huy PGS. TS Tng nh Qu TS. Nguyn Minh Tun

TN CH 3 3 3

KHI LNG 3(3-0-0-6) 3(3-0-0-6) 3(3-0-0-6)

Bt buc

8

T chn

MI7512

Cc phng php Ton hc trong l thuyt nhn dng C s Ton hc ca lnh vc bo mt v an ton thng tin Cc thut ton nng cao trong l thuyt th Ha My Tnh Lp trnh Tin ha Tnh ton song song My hc i s v Otomat

MI7513

MI7514 MI7515 MI7516 MI7517 MI7518 MI7519

PGS.TS. Ng Quc To PGS.TSKH Bi Cng Cng PGS.TS. Nguyn Thanh Thu TS. Nguyn Minh Tun TS. Nguyn ng Tun PGS. TS. Phan Trung Huy GS.TSKH. Long Vn TS. V Thnh Nam PGS. TS. Nguyn c Ngha GS.TS Ng c Tn PGS. TS. Phan Trung Huy GS. TSKH. . L Hng Sn PGS. TS. Hong Lan PGS. TS. Nguyn Thanh Thy PGS. TS. Nguyn c Ngha PGS. TS. Nguyn c Ngha PGS. TS. Nguyn Thanh Thy PGS. TS. Tng nh Qu PGS. TS. Nguyn Thanh Thy PGS. TS. Phan Trung Huy GS.TSKH. Long Vn TS. V Thnh Nam

3

3(3-0-0-6)

3

3(3-0-0-6)

3 3 3 3 3 3

3(3-0-0-6) 3(3-0-0-6) 3(3-0-0-6) 3(3-0-0-6) 3(3-0-0-6) 3(3-0-0-6)

7.3.2 M t tm tt hc phn trnh Tin s MI7500 L thuyt tnh ton v cc otomat Mn hc trang b cc kin thc c bn v gii thiu mt s ch nng cao trong ngn ng hnh thc, l thuyt tnh ton v otomat, lm c s cho cc kin thc sau ny theo cc hng khc nhau ca chng trnh (kha cnh thut ton, phn tch cu trc ton hc qua vn phm, quy tc tnh ton hay otomat, nh gi h thng my hnh thc, phn bc, phn cp ca mt h hnh thc v kha cnh thut ton quyt nh, cc kha cnh ng dng a dng. MI7510 Mch lng t v cc Thut ton lng t Mn hc trang b nhng kin thc c bn v nng cao v l thuyt mch lng t, thut ton lng t v phc tp tnh ton lng t.MI7511 M phng ngu nhin

Mn hc trang b cc kin thc ton hc c bn trong m phng ngu nhin v thi s phc v nghin cu lnh vc m phng ngu nhin v kh nng p dng thc tin ca m phng ngu nhin trong cc lnh vc a dng ca ton, tin v khoa hc, cng ngh . MI7512 Cc phng php Ton hc trong l thuyt nhn dng Mn hc trang b cc kin thc ton hc c bn lm nn tng cho cc phng php hin i trong nhn dng v cc bi ton p dng in hnh.9

MI7513 C s Ton hc ca lnh vc bo mt v an ton thng tin Mn hc trang b cc kin thc ton hc c bn lm nn tng cho cc phng php hin i trong lnh vc bo mt v an ton d liu v mt s bi ton p dng in hnh. MI7514 Cc thut ton nng cao trong l thuyt th Mn hc trang b cc kin thc ton hc, cc thut ton c bn v nng cao lm nn tng cho cc phng php hin nay c s dng lm cng c nghin cu hay p dng thc tin trong nhiu lnh vc khc nhau ca ton hc, cng ngh thng tin v truyn thng, khoa hc cng ngh.. MI7515 Ha My Tnh Mn hc trang b cc kin thc ton hc c bn v nng cao lm nn tng cho cc phng php hin i trong lnh vc l thuyt v ng dng ha my tnh. MI7516 Lp trnh Tin ha Mn hc trang b cc kin thc ton hc v phng php lun c bn hin i v l thuyt v mt s bi ton ng dng in hnh ca Lp trnh Tin ha. MI7517 Tnh ton song song Mn hc trang b cc kin thc ton hc, cc thut ton c bn nn tng cho cc thut ton v m hnh tnh ton song song v gii thiu mt s bi ton thc tin MI7518 My hc Mn hc trang b cc kin thc v phng php lun c bn hin i ca l thuyt my hc v mt s bi ton ng dng in hnh ca my hc. MI7519 i s v Otomat Mn hc trang b cc kin thc ton hc c bn v mi quan h gia i s v otomat, i s cc otomat, cu trc i s ca otomat, cc thut ton c bn v gii thiu mt s bi ton in hnh v l thuyt v vai tr ng dng thc tin. 7.3.3 K hoch hc tp cc hc phn trnh Tin s Cc hc phn trnh Tin s c thc hin linh hot, ty theo cc iu kin thi gian c th ca ging vin. Tuy nhin, nghin cu sinh phi hon thnh cc hc phn trnh Tin s trong vng 24 thng k t ngy chnh thc nhp trng. 7.4 Chuyn Tin s Mi nghin cu sinh phi hon thnh 2 chuyn Tin s theo cc nguyn tc sau: 01 chuyn theo hng chuyn su bt buc, 01 chuyn cn li c th ty chn t danh sch hng chuyn su t chn. Mi hng chuyn su u c ngi hng dn do Hi ng Xy dng chng trnh o to chuyn ngnh ca Khoa Ton Tin ng dng xc nh.

10

Ngi hng dn khoa hc lun n ca nghin cu sinh s xut ti c th theo hng bt buc v hng chn. u tin xut ti gn lin thit thc vi ti ca lun n Tin s. Sau khi c ti c th, NCS thc hin ti di s hng dn khoa hc ca ngi hng dn chuyn .

Danh mc hng chuyn su cho Chuyn Tin sNI DUNG Bt buc T chn M S HNG CHUYN SU NGI HNG DN TS. L Cng Thnh PGS. TS. Phan Trung Huy PGS. TS. Phan Trung Huy GS.TSKH. Long Vn TS. L Cng Thnh GS. TSKH L Hng Sn PGS. TS ng Vn c PGS. TS. Phan Trung Huy PGS. TS. Phan Trung Huy TS. Nguyn Th Thanh Huyn PGS. TS. Phan Trung Huy GS.TSKH. Long Vn TS. V Thnh Nam PGS. TS. Nguyn Bch Kim TS. Nguyn Cnh Nam PGS. TS. Nguyn c Ngha PGS. TS. Phan Trung Huy PGS. TS. Hunh Quyt Thng TS. Nguyn Linh Giang PGS. TS Tng nh Qu PGS. TS. Nguyn Thanh Thy PGS.TSKH Bi Cng Cng PGS. TS. Phan Trung Huy TS. Nguyn Minh Tun PGS.TSKH Bi Cng Cng TS. Nguyn Minh Tun TS. Nguyn c Tun PGS.TSKH Bi Cng Cng PGS. TS. Phan Trung Huy TS. Nguyn Minh Tun PGS. TS. Phan Trung Huy TS. V Thnh Nam TN CH 2 2

MI7505 Thut ton v phc tp MI7550 Lgic Ton

MI7551 C s Ton hc ca GIS MI7552 MI7553 Cc thut ton tm kim nng cao trn xu - n v a mu L thuyt v cc m c di bin i Thut ton nng cao trong ti u t hp C s ton hc ca x l nh v k thut giu tin

2 2 2

MI7554

2

MI7555

2 2 2

MI7556 Khai ph d liu MI7557 C s Ton hc nng cao ca H m Nguyn l mng nron, mng nron m v ng dng

MI7558

2

MI7559 Lgic m, lp lun m v ng dng MI7560 Truyn thng lng t v m ha lng t

2 2

11

MI7561 Tnh Ton Khoa hc MI7562 Fractal, c s ton hc v ng dng MI7563 Na nhm, dn v ng dng t hp MI7564 L thuyt a tp ca ngn ng t hu hn v ca t v hn

GS. TSKH. L Hng Sn TS. Nguyn Cnh Nam TS. Nguyn Thiu Huy GS. TSKH. L Hng Sn PGS. TS. Phan Trung Huy GS.TSKH. Long Vn TS. Phan H Dng PGS. TS. Phan Trung Huy GS.TSKH. Long Vn

2 2 2 2

8 Danh sch Tp ch / Hi ngh khoa hc Cc din n khoa hc trong nc trong bng di y l ni NCS c th chn cng b (c th m rng- khng bt buc gii hn do mt s hi ngh quc t v quc t ti Vit nam v ang xut hin .. ) cc kt qu nghin cu khoa hc phc v hon thnh lun n Tin s.S TT 1 Tn din n Tp ch Tin hc v iu Khin hc Journal of Computer Science and Cybernetics Chuyn san: Tp ch Cng ngh thng tin v Truyn thng (Special issue: Post, Telecommunications & Information Technology Journal) Hi tho Mt s vn chn lc ca CNTT v Truyn thng Hi tho FAIR Acta Mathematica Vietnamica Vietnam Journal of Mathematics Hi ngh Ton hc Ton quc Journal of Sciences Journal of Sciences Tp ch Ton hc ng dng Tp ch Khoa hc v Cng ngh Tp ch Thng bo khoa hc cc trng i hc a ch lin h nh k xut bn / hp 3 thng/k

70 Trn Hng o, H ni

2

57A Hunh Thc Khng, H ni (18 Nguyn Du H ni) chuyensanbcvt@mic.gov.vn tapchibcvt@hn.vnn.vn Vin Cng Ngh Thng Tin- Vin hn lm khoa hoc v Cng ngh Vit nam Hi Ton hc Vit Nam Hi Ton hc Vit Nam Hi Ton hc Vit Nam i hc Khoa hc T nhin H S Phm H Ni Hi Ton hc Vit Nam i hc Bch Khoa H Ni B Gio dc v o to 1 nm 1 nm 4 thng 3 thng 5 nm 2-3 thng 2-3 thng 3 thng Hng thng

3 4 5 6 7 8 9 10 11 12

12

MI7500

L thuyt tnh ton v cc otomatTheory of Computation and Automata

1. Tn hc phn: L thuyt tnh ton v cc otomat 2. M hc phn: MI7500 3. Tn ting Anh: Theory of Computation and Automata 4. Khi lng: 3(3-0-0-6) - L thuyt: 45 tit - Bi tp: - Th nghim: 5. i tng tham d: Tt c NCS thuc chuyn ngnh m bo Ton hc cho my tnh v h thng tnh ton. 6. Mc tiu ca hc phn: Hc phn ny nhm mang li cho NCS: - Cc kin thc nng cao v chuyn mn trong lnh vc tnh ton, c bit s dng cc kin thc v otomat v cc m hnh my. - Rn luyn kh nng t duy logic v phng php lun h thng cht ch. - Rn luyn k nng xy dng cc thut ton tin tin phc v nghin cu l thuyt v ng dng. 7. Ni dung tm tt: NCS c trang b cc kin thc c bn v ch nng cao trong ngn ng hnh thc, l thuyt tnh ton v otomat, lm c s cho cc kin thc sau ny theo cc hng khc nhau ca chng trnh o to NCS (kha cnh thut ton, phn tch cu trc ton hc qua vn phm, quy tc tnh ton hay otomat, nh gi h thng my hnh thc, phn bc, phn cp ca mt h hnh thc v kha cnh thut ton quyt nh, cc kha cnh ng dng a dng.) 8. Nhim v ca NCS: - D lp: - Bi tp: - Th nghim: 9. nh gi kt qu: - Mc d gi ging: - Kim tra nh k: - Thi kt thc hc phn: 10. Ni dung chi tit hc phn: PHN M U Gii thiu mn hc Gii thiu cng mn hc Gii thiu ti liu tham kho Chng 1. Ngn ng hnh thc 2.1 Na nhm v v nhm t do 2.2 Ngn ng hnh thc, cc php ton trn ngn ng 2.3. Mt s phng php nh ngha ngn ng hnh thc 2.4. Vn phm v h vit li 2.5. Tnh ton hnh thc13

2.5. Phn bc Chomsky Chng 3. Lun Turing- Church 3.1. My Turing v thut ton 3.2. phc tp tnh ton ca thut ton 3.3. Hm quy v quy v quy b phn 3.4. Tp quy, quy k c 3.5. Lun Turing-Church Chng 4. Ngn ng chnh quy v otomat hu hn 4.1. Ngn ng chnh quy v biu thc chnh quy 4.2. Otomat hu hn 4.3. Tng ng gia otomat hu hn a nh v n nh 4.4. Cc c trng tng ng ca ngn ng chnh quy qua vn phm, otomat v i s 4.5. Otomat ti tiu ca ngn ng chnh quy 4.6. Mt s thut ton v bi ton quyt nh trn lp ngn ng chnh quy 4.7. Tnh ng ca lp ngn ng chnh quy 4.8. Xy dng v nhm c php t ngn ng, otomat on nhn ngn ng Chng 5. Mt s ch m rng 5.1. Otomat thc hin hm bin i ngn ng bo ton di 5.2. Otomat v ng dng trong cc bi ton snh mu 5.3. Mt s m hnh tnh ton s dng otomat nng cao: otomat xc sut, fuzzy, lng t 5.4 Otomat, my bin i c trng s v ng dng 5.5 Cellular automata 11. Ti liu hc tp: [1] [2] [3] [4] [5] [6] [7] [8] Autebert L.M.,Theorie des langages et des automates, Masson, 1994, Paris-MilanBarcolone. S. Eilenberg, Automata, Languages and Machines, Academic Press, New york, Vol. A 1974, Vol. B 1976 Garey, M. R., and Johnson, D. S. Computers and Intractability - A Guide to the Theory of NP-completeness. W. H. Freeman, 1979. Harrison M.A., Introduction to Formal Language Theory, Addison-Wesley, 1978, Massachusetts-California-London-Amsterdam-Ontario-Sydney. J.E. Hopcroft, J.D. Ulman, Intoduction to automata theory, languages and computation, Addison Wesley, 1979. Phan nh Diu, L thuyt otomat v thut ton, H ni, 1990. A. Salomaa, Nhp mn tin hc l thuyt - tnh ton v cc otomat, (bn dch ting Vit Ngi dch: Nguyn Xun My- Phm Tr n) NXB KHKT, H ni, 1992. Wim van Dam, Quantum Cellular Automata, citeseer.nj.nec.com/vandam96quantum.html, 1996.14

MI7510

Mch lng t v cc Thut ton lng tQuantum Circuits and Quan tum Algorithms

1. Tn hc phn: Mch lng t v cc thut ton lng t 2. M hc phn: EE7510 3. Tn ting Anh: Quantum Circuits and Quan tum Algorithms 4. Khi lng: 3(3-0-0-6) - L thuyt: 45 tit - Bi tp: - Th nghim: 5. i tng tham d: Tt c NCS thuc chuyn ngnh m bo Ton hc cho my tnh v h thng tnh ton. 6. Mc tiu ca hc phn: Hc phn ny nhm mang li cho NCS: - Cc kin thc c s v nng cao v tnh ton lng t, cc thut ton lng t v truyn thng lng t. - Rn luyn kh nng t duy tru tng c th lnh hi c kin thc chuyn ngnh hin i v kh ca lnh vc. - Rn luyn k nng phn tch h thng mch v thut ton lng t, bc u nm c phng php m phng v s dng cc cng c trong lnh vc tnh ton lng t. 7. Ni dung tm tt: Mn hc trang b nhng kin thc c bn v nng cao v l thuyt mch lng t, thut ton lng t v phc tp tnh ton lng t. 8. Nhim v ca NCS: - D lp: - Bi tp: - Th nghim: 9. nh gi kt qu: - Mc d gi ging: - Kim tra nh k: - Thi kt thc hc phn: 10. Ni dung chi tit hc phn: PHN M U Gii thiu mn hc Gii thiu cng mn hc Gii thiu ti liu tham kho Chng 0. Gii thiu tng quan Chng 1. C s ton hc v vt l 1.1 Mun v Tensor 1.2 Khng gian Hilbert 1.3 Nguyn l c hc lng t 1.4 Hm mt 1.5 Biu din thng tin bit v qubit15

Chng 2. Mch v cng lng t 2.1. Cng lng t 2.2. Tp cng lng t ph dng 2.3. Tnh ton o ngc 2.3. Mch lng t thc hin cc php ton c bn 2.4. hm f- Oracle 2.5 Thut ton lng t 2.6. phc tp ca thut ton lng t v phn lp phc tp Chng 3. Cc thut ton quan trng 3.1 Bi ton D. Simon 3.2. Thut ton Deutsch-Rozsa 3.3. Thut ton Grover 3.4. Thut ton bin i Fourier lng t 3.5. Thut ton P.Shor phn tch hp s ph h mt RSA 3.6. Thut ton P. Shor tm chu k n trn nhm v bi ton ph h mt logarith 3.7. Thut ton Quantum Random Walk 3.8. Cc thut ton ti u t hp lng t Chng 4. M ha v truyn thng tin lng t 4.1. Mt m hc lng t 4.2. Mt s s m ha lng t 4.3. M sa sai lng t 4.4. Nguyn l truyn thng tin lng t 11. Ti liu hc tp: 12. Ti liu tham kho: [1] D. Aharonov, Quantum computation, arXiv: quant-Ph/9810237, 12/1998 [2] A. Barenco, C. H. Bennett, R. Cleve, D. P. D. Divicenzo, N. Margolus, P. W. Shor, T. Sleator, J. Smolin, H. Weinffurter, Elementary gates for quantum computation, arXiv: quant-Ph/950316, 3/1995. [3] A. Ekert, P. Hayden, H. Inamori, Basic concepts in quantum computation, 11/2000, arXiv: quant-ph/0011013 [4] R. Feynman, Quantum mechanical Computers, Foundations of Physics, 16, No.6. March 1985. [5] L. Grover, A fast Quantum Mechanical Algorithm for Database Search, Proceedings, STOC 1996.

16

MI7511

M phng ngu nhin Stochastic simulation

1. Tn hc phn: M phng ngu nhin 2. M hc phn: MI7511 3. Tn ting Anh: Stochastic simulation 4. Khi lng: 3(3-0-0-6) - L thuyt: 45 tit - Bi tp: - Th nghim: 5. i tng tham d: Tt c NCS thuc chuyn ngnh m bo Ton hc cho my tnh v h thng tnh ton 6. Mc tiu ca hc phn: Hc phn ny nhm mang li cho NCS: - Cc kin thc c s v nng cao v m phng ngu nhin - Cc phng php m phng bin ngu nhin v m phng cc m hnh xc sut v qu trnh ngu nhin thng dng - Bc u nm c kh nng ng dng ca m phng ngu nhin vo gii cc bi ton thc t 7. Ni dung tm tt: Tng quan v m phng ngu nhin, m phng cc m hnh ngu nhin, m phng qu trnh ngu nhin, mt s ng dng ca m phng ngu nhin. 8. Nhim v ca NCS: - D lp hc y - Lm bi tp ln v m phng mt m hnh xc sut c th 9. nh gi kt qu: - Mc d gi ging: 5% - Kim tra nh k hoc bi tp ln: 35% - Thi kt thc hc phn hoc bi tiu lun: 60% 10. Ni dung chi tit hc phn: M phng ngu nhin ch thc s pht trin thnh mt ngnh khoa hc sau s bng n ca cng ngh thng tin v s ra i ca cc th h my tnh hin i. Vi s tr gip ca cc my tnh in t, cc thut ton m phng ngu nhin tr thnh mt cng c hiu qu cho vic gii nhiu bi ton thc t c t ra t cc lnh vc rt khc nhau ca i sng x hi. Hc phn ny nhm trang b cc kin thc c s c bn cho NCS v cc phng php ca m phng ngu nhin. PHN M U Gii thiu mn hc Gii thiu cng mn hc Gii thiu ti liu tham kho Chng 1. Tng quan v m phng ngu nhin 1.1.Bi ton m phng ngu nhin v qu trnh hnh thnh phng php m phng s MONTE-CARLO17

1.2.Cc ni dung c bn ca phng php MONTE-CARLO 1.3.Sai s phng c v nh gi tin cy ca cc phng c Chng 2. M phng cc m hnh ngu nhin c bn 2.1.S ngu nhin v cc phng php to ra s ngu nhin 2.2.S gi ngu nhin v cc phng php to ra s gi ngu nhin 2.3.Cc phng php m phng cc i lng ngu nhin c phn phi xc sut cho trc 2.3.1. Phng php nghch o hm phn phi 2.3.2. Phng php loi tr VON-NEUMANN 2.3.3. Phng php m phng cc i lng ngu nhin ri rc 2.3.4. Phng php m phng cc s kin ngu nhin 2.3.5. Phng php m phng i lng ngu nhin c s dng hm phn phi xc sut trn (ri rc v lin tc) 2.3.6. Phng php i bin m phng i lng ngu nhin 2.4.M phng vc t ngu nhin 2.4.1. M phng vc t ngu nhin c hm mt ng thi cho trc 2.4.2. M phng vc t ngu nhin c vc t k vng v ma trn hip phng sai cho trc 2.5.M phng cc i lng ngu nhin c phn phi xc sut thng dng 2.5.1. M phng i lng ngu nhin c phn phi u (mt v nhiu chiu) 2.5.2. M phng i lng ngu nhin c phn phi chun (mt v nhiu chiu) 2.5.3. M phng i lng ngu nhin c phn phi m v phn phi Bta (mt v nhiu chiu) Chng 3. M phng mt qu trnh ngu nhin 3.1.M phng qu o ca mt xch MARKOV thun nht vi thi gian ri rc 3.2.Cc phng php m phng mt qu trnh POISSON khng thun nht 3.3.Cc phng php m phng qu trnh GAUSS Chng 4. Mt s ng dng ca m phng ngu nhin 4.1.Tnh tch phn bi 4.2.Tnh tng ca mt chui s, chui hm s 4.3.Tnh o hm ca mt hm s 4.4.Gii phng trnh i s tuyn tnh 11. Ti liu hc tp: 12. Ti liu tham kho: [1] Sheldon M. Ross (2000) Introduction to Probability Models, Academic Press, New York [2] Fishman, G. S. (1996) Monte-Carlo: Concepts, Algorithms and Applications, Edition Springer, Berlin [3] Szobol, I. M. (1981) Foundations of Monte-Carlo methods (Hungarian Edition).18

MI7512

Cc phng php ton trong l thuyt nhn dngMathematical Methods in Pattern Recognition

1. Tn hc phn: Cc phng php ton trong l thuyt nhn dng 2. M hc phn: MI7512 3. Tn ting Anh: Mathematical Methods in Pattern Recognition 4. Khi lng: 3(3-0-0-6) - L thuyt: 45 tit - Bi tp: - Th nghim: 5. i tng tham d: Tt c NCS thuc chuyn ngnh m bo ton hc cho my tnh v h thng tnh ton. 6. Mc tiu ca hc phn: Hc phn ny nhm mang li cho NCS: - Cc kin thc ton hc c th nng cao v l thuyt nhn dng - Rn luyn kh nng t duy phn tch v s dng hiu qu cc m hnh ton hc trong l thuyt nhn dng - Rn luyn k nng xy dng v p dng cc thut ton tin tin; - C kh nng bc u thit k c cc chng trnh ng dng thc t. 7. Ni dung tm tt: Mn hc trang b cc kin thc ton hc c bn lm nn tng cho cc phng php hin i trong nhn dng v cc bi ton p dng in hnh. 8. Nhim v ca NCS: - D lp: - Bi tp: - Th nghim: 9. nh gi kt qu: - Mc d gi ging: - Kim tra nh k: - Thi kt thc hc phn: 10. Ni dung chi tit hc phn: PHN M U Gii thiu mn hc Gii thiu cng mn hc Gii thiu ti liu tham kho Chng 1. Gii thiu chung v nhn dng 1.1. S cn thit ca nhn dng 1.2. Phn loi cc cc bi ton nhn dng 1.3. Cc ng dng ca nhn dng Chng 2. C s ton hc 2.1 Cc php ton trn ma trn 2.2 Tr ring, vc t ring Chng 3 Hm quyt nh 3.1. Hm quyt nh tuyn tnh19

3.2. Hm quyt nh phi tuyn Chng 4. Phn loi theo khong cch 4.1. Gii thiu 4.2 Khong cch clid 4.3 Cc thut ton nhn dng 4.4. Cc thut ton phn loi c trng Chng 5. phn lp da trn L thuyt quyt nh Bayes Chng 6. B phn lp tuyn tnh Chng 7. B phn lp phi tuyn 7.1. Gii thiu. 7.2. Bi ton XOR. 7.3. Perceptron hai lp (layer). 7.4. Perceptron ba lp. 7.5. Thut ton da trn s phn loi chnh xc tp training. 7.6. Thut ton lan truyn ngc. 7.7. Bin dng trn s lan truyn ngc. 7.8. La chn hm pht 7.9. Cc b phn lp tuyn tnh tng qut. Chng 8. Tin x l, trch chn v la chn du hiu 8.1. Gii thiu 8.2. o khong cch 8.3. Cc bin i phn cm v tm quan trng ca cc du hiu 8.4. Phn cm da trn la chn du hiu 8.5. La chn da c trng vo Entropy 8.6. Khai trin trc giao 8.7. La chn c trng da vo xp x hm 8.8. Divergence Chng 9. Support Vector Machines (SVM) 9.1. Gii thiu 9.2. Hm kernel a. iu kin cn ca hm kernel b. nh l Mercer c. Xy dng cc hm Kernel 9.3. Nhc li mt s l thuyt Lagrange. 9.4 SVM (Support Vector Machines) Chng 10. Kt hp m hnh Markov n (HMM) v phng php phn tch thnh phn chnh vo ng dng trong nhn dng 10.1 M hnh Markov n (Hidden Markov Model) 10.1.1. nh ngha m hnh Markov n (Theory of hidden markov model) 10.1.2. Ba bi ton c bn ca m hnh Markov n.20

10.2. Phng php php phn tch thnh phn chnh (KL) 10.2.1. Mt s nh ngha v khi nim. 10.2.2. C s l thuyt ca phng php phn tch thnh phn chnh. 10.3 Kt hp m hnh Markov n v phng php phn tch thnh phn chnh trong nhn dng. 10.3.1.Qu trnh nhn dng. 10.3.2 Qu trnh hc cc tham s cho cc HMM Chng 11: Mng N ron 11.1 Gii thiu 11.2 Cc mng n ron nhn to 11.2.1 Mng Hopfield 11.2.2 Mng ABAM 11.2.3 Mng Cohonen 11.3 ng dng ca mng neuron trong nhn dng nh v hiu chnh nh 11. Ti liu hc tp: 12. Ti liu tham kho: [1] Norton Nadler et al. Pattern Recognition Engineering, John Wiley & Son Inc., NewYork 1993 [2] Julious T. Tou, Rafael C. Gonzalez, Pattern Recognition Principles , addison Wesley, 1974 [3] Nello Cristianini and John Shawe-Taylor, An Introduction to Support Vector Machines and other kernel-based learning methods, Cambridge University Press, 2000.

21

MI7513

C s Ton hc ca lnh vc bo mt v an ton thng tinMathematical Foundation of Cryptography and Data Safe

1. Tn hc phn: C s ton hc ca lnh vc bo mt v an ton thng tin 2. M hc phn: MI7513 3. Tn ting Anh: Mathematical Foundation of Cryptography and Data Safe 4. Khi lng: 3(3-0-0-6) - L thuyt: 45 tit - Bi tp: - Th nghim: 5. i tng tham d: Tt c NCS thuc chuyn ngnh m bo Ton hc cho my tnh v h thng tnh ton 6. Mc tiu ca hc phn: Hc phn ny nhm mang li cho NCS: - Cc kin thc c s ton hc nng cao phc v cho nghin cu v trin khai ng dng trong lnh vc bo mt v an ton thng tin. - Rn luyn kh nng t duy phn tch, bc u c kh nng t tm hiu, t ra bi ton v phc ha nhng im chnh gii quyt. - Rn luyn k nng t nghin cu v xy dng cc n v s ng dng. 7. Ni dung tm tt: Mn hc trang b cc kin thc ton hc c bn lm nn tng cho cc phng php hin i trong lnh vc bo mt v an ton d liu v mt s bi ton p dng in hnh 8. Nhim v ca NCS: - D lp: - Bi tp: - Th nghim: 9. nh gi kt qu: - Mc d gi ging: - Kim tra nh k: - Thi kt thc hc phn: 10. Ni dung chi tit hc phn: PHN M U Gii thiu mn hc Gii thiu cng mn hc Gii thiu ti liu tham kho M u- vai tr ca bo mt v an ton thng tin 1. Vai tr ca bo mt v an ton d liu, nhng vn c lin quan. 2. Mt s ch c bn, c cu chng trnh. Phn I. L thuyt m di bin i. Chng 1. L thuyt m. 1.1 Lch s, mi lin quan l thuyt m v mt m hc 1.2 M v v nhm t do22

1.3 Php m ha n v a tr 1.4 H sinh c s ca na nhm con ca na nhm t do 1.5. Mt s loi m, m chnh quy v phn bc Chng 2. Mt s bi ton c bn 2.1. Xc nh c s ca m 2.2. Phng php Sardinas-Patterson v Thut ton kim nh m 2.3. khng nhp nhng ca ngn ng lin quan n m 2.4. Phng php xc nh khng nhp nhng, tr ng b 2.5. Mt s o lin quan n m: tr ng b, o ca m 2.6. Bi ton lm y m 2.7. Otomat v m 2.8. M ha v mt m hc Phn II. Mt m hc Chng 1. Mt s kin thc c s ton 1.1. Mt s kin thc b tr v i s v s hc: na nhm, tng ng, dn, nhm, vnh, trng v trng hu hn, l thuyt m rng trng, cc php tnh s hc, l thuyt chia ht, phng trnh v h phng trnh nguyn, s nguyn t v phn b. 1.2. Ci t cc php ton tc cao. 1.3. Nhng yu t l thuyt quan trng lin quan ti mt: - phc tp tnh ton - Khong cch duy nht, tnh khng gii c - tr gii m, tnh a tr, mt hon thin, entropy, m tch 1.4. Cc phng php m ho - Mt s phng php m c truyn - M uniform v m c di bin i Chng 2. Mt s h mt m hin i 2.1. H m i xng DES, AES, IDEA, 2.2. H m ha cng khai RSA, Elgamal, m cng khai trn ng cong Elliptic 2.3. Mt s phng php m ho kho cng khai 2.4. Bi ton qunl kha 2.5. C ch CA Chng 3. Gii v thm m. 3.1. Bi ton gii m, Thm m, 3.2. Mt s phng php ton hc v thut ton thm m 3.3. Mt s hng nghin cu hin i, pht trin ng dng mi v m: m zigzag, m ph, m n hi.. Chng 4. Ch k s v xc thc thng tin 4.1. Ch k s 4.2. Mt s s ch k s hin i 4.3. Hm bm v ng dng 4.4. Tn cng ng yu v mnh23

4.5. Cc ng dng ca ch k s Chng 5. M sa sai 5.1. Kim tra v sa sai d liu 5.2. Bi ton truyn d liu v pht hin li 5.3. Bi ton truyn d liu v sa sai 5.4. Cc phng php ton hc sinh m sa sai v pht hin sai. Chng 6. M ha v truyn thng tin lng t 6.1. Tnh ton lng t, mch v thut ton lng t 6.2. M ha lng t, Truyn thng lng t 11. Ti liu hc tp: 12. Ti liu tham kho: [1] Andrew Binstock and John Rex, Practical Algorithms for Programmers, AdditionWesley-Publishing Company, 1995. [2] N. Koblitz, Elliptic curve cryptosystems, 48(1987)203-209, Mathematics of Computation. [3] Bernad Kolman, Robert C. Busby, Discrete Mathematical Structures for Computer Science, NewDelhi. Second Ed, 1988. [4] Julia Kempe, Quantum Algorithms, Lecture Notes -Summer School on Theory and Technology in Quantum Information, Communication,Computation and Cryptography, CNRS & LRI, Universit de Paris-Sud, ,91405 Orsay, France, June 2, 2006. [5] J.H. Van Lint, Coding Theory, Lecture Notes in Mathematics 201, Springer 1971. [6] M.A. Nielsen and I.L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, Cambridge, UK, 2000. [7] J. Berstel, D. Perrin , Theory of codes, Academic Press. INC., New York, London, 1985. [8] M.O. Rabin, Probabilistic algorithms for testing primality, 12(1980), 128-138, Journal of Number Theory. [9] Kenneth H. Rosen, The CRC Press Series on Discrete Mathematics and Its Applications, 1995. [10] A. Saloma, Public-key Cryptography, Springer-Verlag, 1990. [11] C.E. Shannon, A Mathematical Theory of Communication, 27(1948), 379-423, 623656, Bell Systems Technical Journal. [12] P.W. Shor. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comp., 26(5):1484-1509, 1997. preliminary version in Proceedings of the 35th Ann. IEEE Symp. on the Foundations of Computer Science (FOCS), pages 124-134, 1994.

24

MI7514

Cc thut ton nng cao trong l thuyt thAdvanced Algorithms in Graph Theory

1. Tn hc phn: Cc thut ton nng cao trong l thuyt th 2. M hc phn: MI7514 3. Tn ting Anh: Advanced Algorithms in Graph Theory 4. Khi lng: 3(3-0-0-6) - L thuyt: 45 tit - Bi tp: - Th nghim: 5. i tng tham d: Tt c NCS thuc chuyn ngnh m bo Ton hc cho my tnh v h thng tnh ton 6. Mc tiu ca hc phn: Hc phn ny nhm mang li cho NCS: - Cc kin thc nng cao v l thuyt th v cc thut ton tin tin, nm c tnh hiu qu v kh nng ng dng. - Rn luyn kh nng t duy ton hc xy dng c cc m hnh c s dng l thuyt th v cc thut ton nng cao. - Rn luyn k nng phn tch, tnh ton, nh gi tnh hiu qu v thit k cc ng dng. 7. Ni dung tm tt: Mn hc trang b cc kin thc ton hc, cc thut ton c bn v nng cao lm nn tng cho cc phng php hin nay c s dng lm cng c nghin cu hay p dng thc tin trong nhiu lnh vc khc nhau ca ton hc, cng ngh thng tin v truyn thng, khoa hc cng ngh. 8. Nhim v ca NCS: - D lp: - Bi tp: - Th nghim: 9. nh gi kt qu: - Mc d gi ging: - Kim tra nh k: - Thi kt thc hc phn: 10. Ni dung chi tit hc phn: PHN M U Gii thiu mn hc Gii thiu cng mn hc Gii thiu ti liu tham kho Chng 1. Cc khi nim c bn ca l thuyt th 1.1 nh ngha th 1.2 Bc ca nh 1.3 th ng cu 1.4 th con25

1.5 1.6 1.7 1.8 1.9

Dy bc th lin thng nh r nhnh v cu Mt s th c bit th c hng

Chng 2. Biu din th 2.1. Biu din th bi ma trn 2.2. Danh sch cnh 2.3. Danh sch k Chng 3. th Euler 3.1 nh ngha 3.2 Nhn bit th Euler 3.3 Bi ton ngi a th Trung hoa (The Chinese Postman Problem) Chng 4. th Hamilton 4.1 nh ngha 4.2 Nhn bit th Hamiltonian 4.3 Bi ton ngi du lch (The Traveling Salesman Problem) Chng 5. Cc thut ton duyt th 5.1 Tm kim theo chiu su trn th 5.2 Tm kim theo chiu rng trn th 5.3. Mt s ng dng ca tm kim trn th Chng 6. th phng 6.1 Cc tnh cht ca th phng 6.2. Nhn bit th phng (Planarity Testing) Chng 7. T mu th 7.1 T mu nh 7.2 a thc sc s (Chromatic Polynomials) 7.3 T mu cnh 7.4 Bi ton bn mu (The Four Color Problem) Chng 8. Bi ton cy khung nh nht 8.1. Pht biu bi ton 8.2. S chung ca cc thut ton 8.3. Thut ton Kruskal 8.4. Thut ton Prim 8.5. Thut ton Boruvka

26

Chng 9. Bi ton ng i ngn nht 9.1 Pht biu bi ton 9.2 Cc tnh cht c bn ca ng i ngn nht 9.3. Thut ton Ford-Bellman 9.4. Thut ton Dijkstra 9.5. Thut ton Floyd Chng 10. Bi ton lung cc i trong mng 10.1 Pht biu bi ton 10.2 Lt ct v th tng lung 10.3 nh l v lung cc i v lt ct hp nht 10.4 Thut ton Ford-Fulkerson 10.5 Thut ton Edmond-Karp 10.6 Thut ton thang ho kh nng thng qua 10.7 lin kt cnh 10.8 nh l Menger Chng 11. Bi ton ghp cp 11.1 Pht biu bi ton 11.2 Bi ton ghp cp cc i trn th hai pha 11.3 Bi ton ghp cp cc i trn th tng qut 11.4 Bi ton ghp cp ln nht trn th hai pha Chng 12. Bi ton lung vi chi ph nh nht 12.1 Pht biu bi ton 12.2 Thut ton ph chu trnh m 12.3 Thut ton dy ng ngn nht Chng 13. Mt s bi ton NP-kh trn th 13.1 Bi ton phn b tm v trung v 13.2 Bi ton ph nh 13.3. Mt s bi ton ti u trn cy 13.4 Cc thut ton gn ng 11. Ti liu hc tp: 12. Ti liu tham kho: [1] [2] [3] J.A. Bondy and U.S.R Murty. Graph Theory. Springer-Verlag, 2008. Douglas B. West. Introduction to Graph Theory. 2nd edition, Prentice Hall, 2001. Nicos Christofides. Graph Theory: An Algorithmic Approach. Academic Press, New York, 1975.27

[4] [5] [6] [7]

J. Bang-Jensen and G. Gutin. Digraphs:Theory, Algorithms and Applications. SpringerVerlag, 2007 T.H. Cormen, C.E. Leiserson, R.L. Rivest, and C. Stein. Introduction to Algorithms. 2nd edition, MIT Press, Cambridge, MA, 2001. Dieter Jungnickel. Graphs, Networks and Algorithms. BI-Wissenschaftsverlag, Mannheim, 3. edition, 1994. Ravindra K. Ahuja, Thomas L. Magnanti, and James B. Orlin. Network Flows: Theory, Algorithms and Applications. Prentice Hall, 1993.

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MI7517

Tnh ton song song Parallel computation

1. Tn hc phn: Tnh ton song song 2. M hc phn: MI7517 3. Tn ting Anh: Parallel Computation 4. Khi lng: 3(3-0-0-6) - L thuyt: 45 tit - Bi tp: - Th nghim: 5. i tng tham d: Tt c NCS thuc chuyn ngnh m bo Ton hc cho my tnh v h thng tnh ton 6. Mc tiu ca hc phn: Hc phn ny nhm mang li cho NCS: - Cc kin thc c s v nng cao v tnh ton song song. - Rn luyn kh nng t duy h thng, bc u t c, nm c th mnh v nghin cu kh nng ng dng ca tnh ton song song. - Rn luyn k nng phn tch, thit k v nm c cch khai thc mt s h thng tnh ton song song. 7. Ni dung tm tt: Mn hc trang b cc kin thc ton hc, cc thut ton c bn nn tng cho cc thut ton v m hnh tnh ton song song v gii thiu mt s bi ton thc tin 8. Nhim v ca NCS: - D lp: - Bi tp: - Th nghim: 9. nh gi kt qu: - Mc d gi ging: - Kim tra nh k: - Thi kt thc hc phn: 10. Ni dung chi tit hc phn: PHN M U Gii thiu mn hc Gii thiu cng mn hc Gii thiu ti liu tham kho Chng 0. M u 0.1. S lc v lch s ra i v pht trin ca my tnh song song 0.2. Cc vn ng dng ca tnh ton song song 0.3. Mt s khi nim v thut ng Chng 1. i cng v tnh ton song song 1.1. Cc mc song song 1.2 Phn loi kin trc song song29

1.3. M hnh SIMD (PRAM) 1.4. Dng cng ngh EREW m phng CRCW v CREW 1.5. H my MIMD 1.6. M hnh tnh ton song song 1.7. Ngn ng m t thut ton song song 1.8. Mt s thut ton n gin 1.9. nh gi hiu qu ca thut ton song song Chng 2. Cc mu thit k thut ton song song 2.1. Mu cy nh phn 2.2. Pht trin bi nhn i 2.3. Con tr nhy 2.4. Chia tr 2.5. Phn chia Chng 3. Thut ton song song cho mt s bi ton n gin 3.1. Tch v hng ca hai vect 3.2. Tnh tch ma trn 3.3. Bi ton tng con 3.4. H s nh thc 3.5. Phn t nh nht ca mng con Chng 4. Tm kim v trn 4.1. Tm kim tun t 4.2. Tm kim song song trong CREW PRAM 4.3. Tm kim song song vi nhiu d liu 4.4. Tm kim trong mng khng c sp xp 4.5. Trn nh xp hng 4.6. Trn hai na n iu Chng 5. Sp xp 5.1. Bi ton sp xp 5.2. Cc thut ton sp xp tun t 5.3. Sp xp trn 5.4. Mng sp xp Chng 6. Cc thut ton th 6.1. Cc thut ton th n gin 6.2. Bi ton v tnh lin thng 6.3. Thnh phn song lin thng 6.4. Cy khung 6.5. Bi ton ng i ngn nht Chng 7. Lp trnh song song 7.1. Giao din truyn thng ip (MPI: The Message Passing Interface) 7.2. Lp trnh trong CUDA30

7.3. Tnh ton li (Grid Computing) 11. Ti liu hc tp: 12. Ti liu tham kho: [1] [2] [3] [4] [5] [6] [7] [8] [9] Guy Blelloch and Bruce Maggs. Parallel Algorithms. In the Computer Science and Engineering Handbook. CRC Press, 1996. V. Kumar et al. Designing and Building Parallel Programs. Addison Wesley, 1994. B. Bauer. Practical Parallel Programming. Academic Press, 1992. V. Kumar, A. Grama, A. Gupta, and G. Karypis. Introduction to Parallel Computing: Design and Analysis of Algorithms. Benjamin Cummings, 1993. Michael J. Quinn. Parallel Computing. McGraw-Hill Inc, Second edition, 1994. Ian T. Foster Designing and Building Parallel Programs Addison Wesley Inc 1995. N. Santoro. Design and Analysis of Distributed Algorithms. Wiley, 2007. S. Rajasekaran and J. Reif (Ed). Handbook of Parallel Computing. Models, Algorithms and Applications. Chapman & Hall/CRC, 2008. Calvin Lin, Larry Snyder, Principles of Parallel Programming. Addison-Wesley, 2009. 352pp.

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MI7519

i s v OtomatAlgebra with Automata

1. Tn hc phn: i s v Ototmat 2. M hc phn: MI7519 3. Tn ting Anh: Algebra with Automata 4. Khi lng: 3(3-0-0-6) - L thuyt: 45 tit - Bi tp: - Th nghim: 5. i tng tham d: Tt c NCS thuc chuyn ngnh m bo Ton hc cho my tnh v h thng tnh ton 6. Mc tiu ca hc phn: Hc phn ny nhm mang li cho NCS: - Cc kin thc nng cao v i s trong mi lin h vi lnh vc l thuyt otomat v kh nng ng dng. - Rn luyn kh nng t duy ton hc, bc u hnh thnh phng php t hc v nghin cu cc ch hin i ca mn hc. - Rn luyn k nng phn tch v p dng m hnh otomat vo gii mt s bi ton i s v ngc li kh nng vn dng cc kin thc i s hin i xut v gii quyt cc bi ton trong lnh vc ngn ng hnh thc v otomat. 7. Ni dung tm tt: Mn hc trang b cc kin thc ton hc c bn v mi quan h gia i s v otomat, i s cc otomat, cu trc i s ca otomat, cc thut ton c bn v gii thiu mt s bi ton in hnh v l thuyt v vai tr ng dng thc tin. 8. Nhim v ca NCS: - D lp: - Bi tp: - Th nghim: 9. nh gi kt qu: - Mc d gi ging: - Kim tra nh k: - Thi kt thc hc phn: 10. Ni dung chi tit hc phn: PHN M U Gii thiu mn hc Gii thiu cng mn hc Gii thiu ti liu tham kho Chng 1 . Mt s kin thc b sung v na nhm v dn 1.1. Php ton v phng php th tnh kt hp ca Lait 1.2. Na nhm v tp sinh 1.3. Mt s na nhm c bit 1.4. Na nhm con, ideal 1.5. Na nhm thung32

1.6. ng cu na nhm 1.7. Na dn, dn v nguyn l tng ng 1.8. Tng ng, dn cc tng ng 1.9. cc quan h Green 1.10. V nhm, v nhm con, ng cu v nhm 1.11 Na nhm v v nhm t do 1.12 Ngn ng hnh thc, cc php ton trn ngn ng Chng 2. Ngn ng hnh thc 2.1. Vn phm v h vit li 2.2. Mt s phng php nh ngha ngn ng hnh thc 2.3. Phn bc ngn ng Chomsky 2.4. My Turing v thut ton 2.5. phc tp tnh ton ca thut ton 2.6. Ngn ng quy, quy k c v thut ton 2.7. M v php m ha thng tin v ng dng 2.8. Th tc kim nh m, phc tp 2.9. Gii thiu mt s bi ton c bn trong ngn ng hnh thc v t hp trn t Chng 3. Ngn ng chnh quy v otomat hu hn 3.1. Ngn ng chnh quy v biu thc chnh quy 3.2. Otomat hu hn 3.3. Biu din Eilenberrg v ngn ng qua tnh tha ng cu na nhm v v nhm 3.4. Biu din ngn ng chnh quy qua vn phm, otomat v i s 3.5. Mt s thut ton v bi ton quyt nh trn lp ngn ng chnh quy 3.6. V nhm cc php chuyn dch ca ngn ng chnh quy 3.7 Otomat khng nhp nhng 3.8 S biu din khng nhp nhng ca ngn ng chnh quy qua m v tomat khng nhp nhng Chng 4. V nhm c php ca ngn ng 4.1. V nhm c php v na nhm c php 4.2. Xy dng v nhm c php t ngn ng, otomat on nhn ngn ng 4.3. Thut ton kim nh m theo ng cu tha ngn ng 4.4. a tp Eilenberrg ca cc v nhm v ca cc na nhm hu hn 4.4. a tp ngn ng chnh quy v nh l C bn v Tng ng a tp Eilenberg Chng 5. Mt s ch m rng 5.1. ng dng i s gii mt s bi ton t hp trn t v v tomt 5.2. ng dng tmat: Nghin cu mt s bi ton quyt nh c v khng quyt nh c v i s. 5.3. a tp cc otomat hu hn 5.4 Ngn ng t v hn v otomat hu hn 5.5. Vai tr ca cc v nhm hu hn c tch v hn vi a tp cc v nhm hu hn . 5.6. Mt s bi ton khng gii c ni ting: Bi ton th mi ca Hilbert, bi ton ng nht thc trn na nhm v nhm...33

11. Ti liu hc tp: 12. Ti liu tham kho: [1] Autebert L.M.,Theorie des langages et des automates, Masson, 1994, Paris-MilanBarcolone. [2] A.H. Clipford, G.B. Preston, The Algebraic Theory of Semigroups, Amer. Math. Soc. Vol. I (1961), Vol. II. (1967). [3] B.A. Davey and H.A. Priestley, Introduction to Lattices and Order, Cambridge University Press 1990, reprinted 1991, 1992 [4] S. Eilenberg, Automata, Languages and Machines, Academic Press, New york, [5] Vol. A 1974, Vol. B 1976. [6] Garey, M. R., and Johnson, D. S. Computers and Intractability - A Guide to the Theory of NP-completeness. W. H. Freeman, 1979. [7] Harrison M.A., Introduction to Formal Language Theory, Addison-Wesley, 1978, Massachusetts-California-London-Amsterdam-Ontario-Sydney. [8] J.E. Hopcroft, J.D. Ulman, Intoduction to automata theory, languages and computation, Addison Wesley, 1979. [9] G. Lallement, Semigroups and Combinatorial Applications, John Wiley & Sons, Inc. 1979. [10] Phan nh Diu, L thuyt otomat v thut ton, H ni, 1990.

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