I HC QUC GIA H NITRNG I HC KHOA HC T NHIN

KHUNG CHNG TRNH

O TO THC SChuyn ngnh: i s v l thuyt s Algebra and Number Theory M s : 60.46.05 Ngnh: Ton hc

H Ni - 2007

2

I HC QUC GIA H NITRNG I HC KHOA HC T NHIN

KHUNG CHNG TRNH O TO THC SChuyn ngnh: i s v l thuyt s Algebra and Number Theory M s : 60.46.05 Ngnh: Ton hc Khung chng trnh o to thc s ngnh Ton hc, chuyn ngnh v l thuyt s c ban hnh theo Quyt nh s: nm 2007 ca Gim c i hc Quc gia H Ni. H ni, ngy thng nm 2007CH NHIM KHOA SAU I HC

i s /SH ngy thng

GS. TSKH. Nguyn Hu Cng

H Ni - 2007

3

I HC QUC GIA H NI

CNG HO X HI CH NGHA VIT NAM

TRNG I HC KHOA HC T NHIN

c lp T do Hnh phc

_____________

_____________

KHUNG CHNG TRNH O TO THC SChuyn ngnh: i s v l thuyt s M s: 60.46.05 Ngnh: Ton hc Phn I. Gii thiu chung v chng trnh o to.1. Mt s thng tin v chuyn ngnh o to.

- Tn chuyn ngnh: i s v l thuyt s (Algebra and Number Theory). - M s chuyn ngnh: 60.46.05. - Tn ngnh: Ton hc (Mathematics).Bc o to: Thc s

- Tn vn bng: Thc s Ton hc (Master in Mathematics).n v o to: Trng i hc Khoa hc T nhin, i hc Quc gia H Ni. 2. i tng d thi v cc mn thi tuyn.

- i tng c ng k d thi: Cng dn nc CHXHCN Vit Nam c cciu kin quy nh di y c d thi vo o to thc s: 1.1 iu kin vn bng Th sinh phi c mt trong cc vn bng sau: a) C bng tt nghip ngnh ng hoc ph hp vi ngnh ng k d thi: Ton hc, Ton Tin ng dng, S phm Ton, Ton C. b) C bng tt nghip i hc chnh qui ngnh gn vi ngnh ng k d thi, hc b sung kin thc cc mn hc c trnh tng ng vi bng tt nghip i hc ngnh ng. Ni dung, khi lng (s tit) cc mn hc b sung do trng HKHTN, HQG HN quy nh.

1.2

iu kin v thm nin cng tc

a) Th sinh c bng tt nghip i hc loi kh tr ln, ngnh tt nghip ng hoc ph hp vi ngnh ng k d thi c d thi ngay sau khi tt nghip i hc.

4

b) Nhng trng hp cn li phi c t nht hai nm kinh nghim lm vic trong lnh vc chuyn mn ng k d thi k t khi tt nghip i hc (tnh t ngy Hiu trng k quyt nh cng nhn tt nghip) n ngy ng k d thi. Cc mn thi tuyn u vo: o Mn thi C bn: i s o Mn thi C s: Gii tch o Mn Ngoi ng: trnh B, mt trong nm th ting: Anh, Nga, Php, c, Trung Quc. Phn II. Khung chng trnh o to. 1. Mc tiu o to: 1.1. V kin thc: Trang b cc kin thc nng cao v c cp nht v chuyn ngnh i s v L thuyt s. 1.2. V nng lc ging dy v nghin cu khoa hc: Thc s chuyn ngnh i s v L thuyt s c kh nng ging dy cc mn Ton hc c bn v cc mn thuc chuyn ngnh i s v L thuyt s cc trng i hc, Cao ng, c kh nng tham gia nghin cu v ng dng Ton hc theo hng chuyn ngnh ca mnh cc Vin, trng i hc v cc c quan nghin cu, sn xut, kinh doanh. Thc s chuyn ngnh i s v L thuyt s c th c tip tc o to bc hc tin s theo cc m ngnh tng ng. 2. Ni dung o to: 2.1. Tm tt yu cu chng trnh o to: Tng s tn ch phi tch lu: 57 tn ch, trong : - Khi kin thc chung (bt buc): 11 tn ch. - Khi kin thc c s v chuyn ngnh: 30 tn ch. o Bt buc: 22 tn ch. o La chn: 8 tn ch/18 tn ch. - Lun vn:16 tn ch.

5

2.2. STT

Khung chng trnh: Tn mn hc S Tn ch (4) 11 4 4 3 22 2 2 2 2 2 2 2 2 S gi tn ch * S tit hc ** M s cc TS(LL/ThH/TH) TS(LL/ThH/TH) mn hc tin quyt (5) (6) (7) 60(60/0/0) 60(30/30/0) 45 (15/15/15) 180(60/0/120) 180(30/60/90) 135(15/30/90)

M mn hc

(1) (2) (3) I. Khi kin thc chung 1. MG01 Trit hc Philosophy 2. MG02 Ngoi ng chung Foreign languague for general purposes 3. MG03 Ngoi ng chuyn ngnh Foreign languague for specific purposes II. Khi kin thc c s v chuyn ngnh II.1. Cc mn hc bt buc 4. TNDS 501 o v tch phn Measure and Integration 5. TNDS 502 Gii tch phi tuyn Nonlinear Analysis 6. TNDS 503 Gii tch trn a tp Analysis on Manifolds 7. TNDS 504 L thuyt nhm v biu din nhm Theory of Groups and Group Representations 8. TNDS 505 L thuyt ton t tuyn tnh Theory of Linear Operators 9. TNDS 506 L thuyt xp x Theory of Approximation 10. TNDS 507 Hnh hc vi phn Differential Geometry 11. TNDS 508 B tc v i s tuyn tnh

30(25/5/0) 30(25/5/0) 30(25/5/0) 30(25/5/0) 30(25/5/0) 30(25/5/0) 30(25/5/0) 30(25/5/0)

90(25/10/55) 90(25/10/55) 90(25/10/55) 90(25/10/55) 90(25/10/55) 90(25/10/55) 90(25/10/55) 90(25/10/55)

12. 13. 14.

15 . 16. 17. 18. 19. 20. 21. 22. 23. III.

Advanced Linear Algebra TNDS 509 Hnh hc i s Algebraic Geometry TNDS 510 i s giao hon Commutative algebra TNDS 511 Tp i s Algebraic Topology II.2. Cc mn hc la chn TNDS 512 L thuyt s i s Algebraic Number Theory TNDS 513 Dy ph v ng dng Spectral sequences and applications TNDS 514 i s ng iu Homological algebra TNDS 515 i s Hopf v ng dng Hopf algebras and applications TNDS 516 L thuyt bt bin Modular Modular Invariant Theory TNDS 517 L thuyt vnh v m-un Theory of Rings and Modules TNDS 518 M rng nhm v i ng iu ca nhm Extension and Cohomology of Groups TNDS 519 Nhm Lie v i s Lie Lie groups and Lie algebras TNDS 520 Ton t i ng iu Cohomology Operations Lun vn Cng:

2 2 2 8/18 2 2 2 2 2 2 2 2 2 16 57

30(25/5/0) 30(25/5/0) 30(25/5/0)

90(25/10/55) 90(25/10/55) 90(25/10/55)

30(25/5/0) 30(25/5/0) 30(25/5/0) 30(25/5/0) 30(25/5/0) 30(25/5/0) 30(25/5/0) 30(25/5/0) 30(25/5/0)

90(25/10/55) 90(25/10/55) 90(25/10/55) 90(25/10/55) 90(25/10/55) 90(25/10/55) 90(25/10/55) 90(25/10/55) 90(25/10/55) TNDS504 TNDS504

Ghi ch: * Tng s gi tn ch (s gi tn ch ln lp/s gi tn ch thc hnh/s gi tn ch t hc). **Tng s tit hc (s tit ln lp/s tit thc hnh/s tit t hc). 7

2.3. STT

Danh mc ti liu tham kho: S Tn ch (4) 11 4 4 3 14 2 Danh mc ti liu tham kho (Ti liu bt buc, Ti liu tham kho thm) (5) Theo chng trnh chung Theo chng trnh chung Theo chng trnh chung

M mn Tn mn hc hc (1) (2) (3) I. Khi kin thc chung 1. MG01 Trit hc Philosophy 2. MG02 Ngoi ng chung Foreign languague for general purposes 3. MG03 Ngoi ng chuyn ngnh Foreign languague for specific purposes II. Khi kin thc c s v chuyn ngnh II.1. Cc mn hc bt buc 4. TNDS 501 o v tch phn Measure and Integration

1. Paul Halmos Measure theory 2. J Genet Mesure et intgration thorielmentaire (maitrises de mathematiques) Librairie Vuibert, 1976 3. O. Arino, Cl. Delode et J. Genet Mesure et integration (Cours de maitrises) Librairie Vuibert, 1976. 4. Vestrup, Eric M. The Theory of Measure and Integration, John Wiley & Sons, Inc., New York, 2003 [1]. Hong Ty, Hm thc v Gii tch hm, NXB DdHQG

5.

TNDS 502

Gii tch phi tuyn

2

8

Nonlinear Analysis

6.

TNDS 503

Gii tch trn a tp Analysis on Manifolds

2

2005. [2]. .H. Tn, N.T.T. H, NXB DDHSP 2003. [3]. N.T.T. H, Mt s vn v im bt ng, NXB HSP 2006. [4]. Kn m g rp, Ph min, C s l thuyt hm v gii tch hm, NXB THCN 1973. [5]. V. Trenoguine, Analyse fonctonanelle, Moscow 1985 1. M.P. do Carmo, Differential forms and Applications, Springer-Verlag, 1994. 2. V. Guillemin, A.Pollack, Differential Topology, Prentice-Hall, 1974. 3. I.H. Madsen, J. Tornehave, From calculus to hohomology, Cambridge, 1997. 4. F. Pham, Geometrie et calcul differentiel sur les varietes, InterEditions, 1992. 5. M. Spivak, Gii tch trn a tp, bn dch ting Vit, NXB HTHCN 1985.

7.

TNDS 504

L thuyt nhm v biu din nhm Theory of Groups and Group Representations

2

1.

D. J. Benson, Representations and Cohomology (I)-(II), Cambridge University Press, 1991. 2. C. W. Curtis and I. Reiner, Representation Theory of finite groups and associate algebras, Interscience Publishers, New York-London-Sedney. 1966. 3. Nguyn Hu Vit Hng: i s i cng, NXB Gio dc, H Ni, 1998, ti bn ln th nht 1999. 4. G. James and M. Liebeck, Representations and characters of groups, Cambridge Univ. Press, Cambridge 1993.

9

5.

J. P. Serre, Linear Representations of finite groups, Springer-Verlag, New York -Heidelberg- Berlin, 1977. 8. TNDS 505 L thuyt ton t tuyn tnh Theory of Linear Operators 2

1. Klaus Jochen Engel, Rainer Nagel, One parametersemigroups for linear evolution equations. 2. Jerome A. Goldstein, Semigroups of linear operators and applications. 3. Pazy, Semigroups of linear and applications to partial differential equations.

9.

TNDS 506

L thuyt xp x Theory of Approximation

2

1.R.A.

DeVore, G.G. Lorentz, Constructive Approximation, Springer, Berlin-Heidelberg, 1993 Contructive Approximation, Advance Problems, Springer, Berlin-Heidelberg, 1996

2.G.G. Lorentz, M.V.Golitschek, Yu.Makovoz,

3.E. Hernandez, G.Weiss, A First Course onWavelets, CRC Press, 1996

4.S.M. Nikolskii, Approximation of Functions ofSeveral Variables and Imbedding Theorems, Springer, Berlin-Heidelberg, 1975

5.V.M.

Tikhomirov, Some Questions of Approximation Theory, Moscow University Press, Moscow 1976. (Russian) 1965. (Russian)

6.N.I. Akhiezer, Theory of Approximation, Nauka 7.D. Hong, J. Wang, R. Garner, Real Analysis with 10

an Introduction to Wavelets and Applications, Elsevier (Academic Press) 2005. 10. TNDS 507 Hnh hc vi phn Differential Geometry 2

1. T. Aubin, A course in Differential Geometry, AMS, 2. 3. 4. 5.2000. W.M. Boothby, An introduction to differentiable manifolds and Riemannian geometry, Academic Press, 2nd edition, 1986. S. S. Chern, W. H. Chen, K. S. Lam, Lectures on Differential Geometry, World Scientific, 2000. S. Gallot, D. Hulin, J. Lafontaine, Riemannian Geometry, Springer-Verlag, 2nd edition, 1993. Khu Quc Anh v Nguyn Don Tun, L thuyt lin thng v hnh hc Riemann, NXB HSP 2004.

11.

TNDS 508

B tc v i s tuyn tnh Advanced Linear Algebra

2

1. R. Godement, Cours dalgbre, Paris 1969. 2. S.T. Hu, Modern Algebra, Inc. San. Francisco, 1968. 3. S. Lang, Algebra, Addison-Wesley, Reading, MA, 1965 (Bn dch ting Vit: "i s", NXB H v THCN, H ni, 1974). Revised third edition, Springer, New York, 2002. 4. B.L. Van Der Waerden, Modern Algebra, English translation of the original German, Volume I, Frederick Ungar Publishing Co., New York, 1949. Volume II, Frederick Ungar Publishing Co., New York, 1950. 1. Cox D. et al, Ideals, Varieties, and Algorithms, Springer-Verlag (second ed., 1996). 2. Hartshorne R., Algebraic Geometry, Springer-Verlag (1977). (Chng 1).

12.

TNDS 509

Hnh hc i s Algebraic Geometry

2

11

3. Shafarevich I.R., Basic Algebraic Geometry, Volume 1, Springer-Verlag (second ed., 1997). 4. Smith K.E. et al, An invitation to Algebraic Geometry, Springer-Verlag (2000). 13. TNDS 510 i s giao hon Commutative algebra 2

1. M. F. Atiyah and I. G. Macdonald, Introduction to 2. 3. 4. 5.Commutative Algebra, Addison-Wesley, Reading, Massachusetts, 1969. Nguyn T Cng, Gio trnh i s hin i, NXB i hc quc gia, 2003 L Tun Hoa, i s my tnh: C s Grbner, NXB i hc quc gia, 2003 H. Matsumura, Commutative Ring Theory, Cambridge Univ. Press, 1989. R. Y. Sharp, Steps in Commutative Algebra, Cambridge Univ. Press 1990.

14.

TNDS 511

Tp i s Algebraic Topology

2

1. D. J. Benson, Representations and Cohomology (I)-(II), Cambridge University Press, 1991. 2. A. Dold, Lectures on algebraic topology, SpringerVerlag, Berlin-Heidelberg-New York, 1972. 3. S. MacLane, Homology, Springer-Verlag, BerlinHeidelberg-New York, 1967. 4. E. H. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966. 5. R. W. Switzer, Algebraic Topology- Homotopy and Homology, Springer-Verlag, Berlin-Heidelberg-New York, 1975.

15.

II.2. Cc mn hc la chn TNDS 512 L thuyt s i s Algebraic Number Theory

8/18 2

1. Z. Borevich and I. Shafarevich, Teoria chisel (ting Nga), Nauka, 1975. (C bn dch ting Anh)

12

2. S. Lang, Algebra, Addison-Wesley, 1972 (C bn dch ting Vit: "i s", NXB H v THCN, H ni, 1974). 3. S. Lang, Algebraic Numbers, Addison-Wesley, 1965. 4. A. Weil, Basic Number Theory, Springer-Verlag, 1972. 16. TNDS 513 Dy ph v ng dng Spectral sequences and applications 2 1. C. A. Weibel, An Introduction to Homological Algebra, Cambridge University Press, 1994. 2. D. J. Benson, Representations and Cohomology - II: Cohomology of Groups and Modules, Cambridge University Press, 1991. 3. R. M. Switzer, Algebraic Topology - Homotopy and Homology, Berlin-Heidelberg-New York: Springer 1975. 4. S. Mac Lane, Homology, Berlin-Heidelberg-New York: Springer 1963. 5. E. Spanier, Algebraic Topology, Springer-Verlag, 1981. 6. J. McCleary, A User's Guide to Spectral Sequences, Second edition, 58. Cambridge University Press, 2001. 1. D. J. Benson, Representations and Cohomology (I)-(II), Cambridge University Press, 1991. 2. H. Cartan and S. Eilenberg, Homological Algebra, Princeton Univ. Press, Princeton, 1956. 3. A. Dold, Lectures on algebraic topology, SpringerVerlag, Berlin-Heidelberg-New York, 1972. 4. L. Evens, The cohomology of groups, Clarendon Press, Oxford - New York - Tokyo, 1991. 5. S. MacLane, Homology, Springer-Verlag, BerlinHeidelberg-New York, 1967. 6. E. H. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966. 7. R. W. Switzer, Algebraic Topology- Homotopy and Homology, Springer-Verlag, Berlin-Heidelberg-New York, 1975.

17.

TNDS 514

i s ng iu Homological algebra

2

13

18.

TNDS 515

i s Hopf v ng dng Hopf algebras and applications

2

1. D. J. Benson: Representations and Cohomology - II: Cohomology of Groups and Modules, Cambridge University Press, 1991. 2. V. Chari, A. Pressley: A Guide to Quantum Groups, Cambridge University Press, 1994. 3. S. Mac Lane, Homology, Berlin-Heidelberg-New York: Springer 1963. 4. J. W. Milnor, J. C. Moore: On the structure of Hopf algebras, Ann. Math Vol. 81, No. 2, (1965), 211--264. 5. J. W. Milnor: The Steenrod algebra and its dual, Ann. Math Vol. 67, No. 1, (1958), 150--171. 6. C. A. Weibel: An Introduction to Homological Algebra, Cambridge University Press, 1994. 7. M. E. Sweedler: Hopf Algebras, W.A.Benjamin Inc, 1968. 8. R. M. Switzer, Algebraic Topology - Homotopy and Homology, Berlin-Heidelberg-New York: Springer 1975. 1. D. Benson, Polynomial invariants of finite groups, London mathematical Society Lecture Note Series, volume 190, 1993. 2. L. Smith, Polynomial invariants of finite groups. Research Notes in Mathematics, Volume 6, A K Peters 1995. 1. F. W. Anderson and K. R Fuller, Rings and Catergories of Modules, Springer Verlag, 1974 2. C. Faith, Rings, Modules and Categories I, Springer

19.

TNDS 516

L thuyt bt bin Modular Modular Invariant Theory

2

20.

TNDS 517

L thuyt vnh v m-un Theory of Rings and Modules

2

14

Verlag, Berlin - Heidelberg - NewYork, 1981 3. N. Jacobson, Structure of Rings, Providence, 1964 4. J. Lambek, Lectures on Rings and Modules, Blaisdell Publ. Co. Waltham, Mass. Toronto - London, 1966 5. N. H. Mc Coy, The theory of rings, Macmillan, NewYork - London, 1964. 21. TNDS 518 M rng nhm v i ng iu ca nhm Extension and Cohomology of Groups 2 1. A. Adem, J. Milgram, Cohomology of finite groups, Springer-Verlag, 1995. 2. M. Hall, The theory of groups, Macmillan, 1959. 3. A.G. Kurosh, L thuyt nhm, Nauka, 1967 (Ting Nga). 4. S. Lang, Algebra, Addison-Wesley, 1965. 5. S. MacLane, Homology, Springer-Verlag, 1963. 6. J. Rotman, An introduction to the theory of groups, Springer, 1999.

22.

TNDS 519

Nhm Lie v i s Lie Lie groups and Lie algebras

2

1. Ngc Dip, L thuyt nhm Lie, gio trnh. 2. J. F. Adams, Lectures on Lie groups, Benjamin Inc, 3. 4. 5. 6.NewYork-Amsterdam 1969. N. Bourbaki, Groupes et algbres de Lie, L'eslements de mathmatiques, Hermann, Paris 1968. A. Kirillov, C s l thuyt biu din, Ting Nga, Nauka, Moskva, 1972. J. P. Serre, Lie algebras and Lie groups, Benjamin, NewYork-Amsterdam 1965. V. V. Trofimov, Bi tp l thuyt nhm Lie v i s Lie, Ting Nga, MGU, Moskva, 1990.

23.

TNDS 520

Ton t i ng iu Cohomology Operations

2

1. R. E. Mosher and M. C. Tangora, Cohomology Operations and Applications in Homotopy Theory, Harper and Row, New York, 1968.

15

2. E. H. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966. 3. N. E. Steenrod and D. B. A. Epstein, Cohomology Operations, Ann. Math. Studies 50, Princeton Univ. Press, Princeton 1962. 4. R. W. Switzer, Algebraic Topology- Homotopy and Homology, Springer-Verlag, Berlin-Heidelberg-New York, 1975. 2.4. i ng cn b ging dy: S Tn ch (4) 11 4 4 3 Cn b ging dy Chc danh, Chuyn ngnh hc v o to (6) (7) Theo s phn cng ca trng HKHTN Theo s phn cng ca trng HKHTN Theo s phn cng ca trng HKHTN

STT M mn hc

Tn mn hc

H v tn (5)

n v cng tc (8)

(1) (2) (3) I. Khi kin thc chung 1. MG01 Trit hc Philosophy 2. MG02 Ngoi ng chung Foreign languague for general purposes 3. MG03 Ngoi ng chuyn ngnh Foreign languague for specific purposes II. Khi kin thc c s v chuyn ngnh II.1. Cc mn hc bt buc 4. TNDS 501 o v tch phn Measure and Integration

22 2

Trn c Long ng Hng Thng Nguyn Duy Tin Nguyn Hu D Phan Vit Th

TS. PGS.TSKH. GS.TSKH. GS.TS. TS.

Ton hc Ton hc Ton hc Ton hc Ton hc

H KHTN H KHTN H KHTN H KHTN H KHTN

16

9.

TNDS 502

Gii tch phi tuyn Nonlinear Analysis

2

13.

TNDS 503

Gii tch trn a tp Analysis on Manifolds

2

18.

TNDS 504

L thuyt nhm v biu din nhm Theory of Groups and Group Representations L thuyt ton t tuyn tnh Theory of Linear Operators

2

Phm K Anh Nguyn Xun Tn Trn c Long Nguyn Khc Vit Ph c Ti Nguyn Vn Minh L Minh H H Huy Vui V Th Khi Nguyn Hu Vit Hng L Minh H Trn Ngc Nam Hunh Mi Trn c Long Nguyn Vn Mu V Ngc Pht Hng Tn inh Dng V Hong Linh Nguyn Thy Thanh Ph c Ti L Minh H H Huy Vui V Th Khi Phm Vit Hng L Minh H Trn Ngc Nam Nguyn c t Trn Trng Hu Ph c Ti

GS.TSKH. GS.TSKH. TS. TSKH. TS. PGS.TSKH. TS. PGS.TSKH. TS. GS.TSKH. TS. TS. GS.TS. TS. GS.TSKH. GS.TSKH. PGS.TSKH. GS.TSKH. TS. PGS.TS. TS. TS. PGS.TSKH. TS. TS. TS. TS. PGS.TS. PGS.TS. TS.

Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc

22.

TNDS 505

2

H KHTN Vin Ton hc H KHTN Vin Ton hc H KHTN H KHTN H KHTN Vin Ton hc Vin Ton hc H KHTN H KHTN H KHTN H DL Thng Long H KHTN H KHTN H KHTN Vin Ton hc H QGHN H KHTN H KHTN H KHTN H KHTN Vin Ton hc Vin Ton hc H KHTN H KHTN H KHTN H KHTN H KHTN H KHTN

26. 29.

TNDS 506 TNDS 507

L thuyt xp x Theory of Approximation Hnh hc vi phn Differential Geometry B tc v i s tuyn tnh Advanced Linear Algebra

2 2

33.

TNDS 508

38.

TNDS 509

Hnh hc i s

17

Algebraic Geometry 41. 44. TNDS 510 TNDS 511 i s giao hon Commutative algebra Tp i s Algebraic Topology

Nguyn Khc Vit Ng Vit Trung Ph c Ti L Tun Hoa Ng Vit Trung Nguyn Hu Vit Hng L Minh H Trn Ngc Nam Hunh Mi Nguyn Vit Dng

TSKH. GS.TSKH. TS. GS.TSKH. GS.TSKH. GS.TSKH. TS. TS. GS.TS. PGS.TS. TS. PGS.TS. GS.TSKH. TS. TS. GS.TS. GS.TSKH. TS. TS. GS.TS. GS.TSKH. TS. TS. GS.TS. GS.TSKH. TS.

Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc

Vin Ton hc Vin Ton hc H KHTN Vin Ton hc Vin Ton hc H KHTN H KHTN H KHTN H DL Thng Long Vin Ton hc H KHTN Vin Ton hc H KHTN H KHTN H KHTN H DL Thng Long H KHTN H KHTN H KHTN H DL Thng Long H KHTN H KHTN H KHTN H DL Thng Long H KHTN H KHTN

II.2. Cc mn hc la chn 49. TNDS 512 L thuyt s i s Algebraic Number Theory 51. TNDS 513 Dy ph v ng dng Spectral sequences and applications

8/18 L Minh H Nguyn Quc Thng Nguyn Hu Vit Hng L Minh H Trn Ngc Nam Hunh Mi Nguyn Hu Vit Hng L Minh H Trn Ngc Nam Hunh Mi Nguyn Hu Vit Hng L Minh H Trn Ngc Nam Hunh Mi Nguyn Hu Vit Hng L Minh H

55. TNDS 514

i s ng iu Homological algebra

59.

TNDS 515

i s Hopf v ng dng Hopf algebras and applications

63.

TNDS 516

L thuyt bt bin Modular Modular Invariant Theory

18

Trn Ngc Nam Hunh Mi 67. 69. TNDS 517 TNDS 518 L thuyt vnh v m-un Theory of Rings and Modules M rng nhm v i ng iu ca nhm Extension and Cohomology of Groups Nhm Lie v i s Lie Lie groups and Lie algebras Ton t i ng iu Cohomology Operations Trn Trng Hu Nguyn c t Nguyn Hu Vit Hng L Minh H Trn Ngc Nam Hunh Mi Ngc Dip Nguyn Hu Vit Hng L Minh H Trn Ngc Nam Hunh Mi 16 57

TS.

Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc Ton hc

PGS.TS. PGS.TS. GS.TSKH. TS. TS. GS.TS. GS.TSKH. GS.TSKH. TS. TS. GS.TS.

73.

TNDS 519

H KHTN H DL Thng Long H KHTN H KHTN H KHTN H KHTN H KHTN H DL Thng Long Vin Ton hc H KHTN H KHTN H KHTN H DL Thng Long

74. TNDS 520

III. Lun vn Cng

19

2.5 Tm tt ni dung mn hc: 1. Trit hc Theo chng trnh chung 2. Ngoi ng chung Theo chng trnh chung 3. Ngoi ng chuyn ngnh Theo chng trnh chung 4. o v tch phn Mn hc trang b nhng kin thc c bn v nng cao v l thuyt o v tch phn nh: Vnh, i s, - vnh, - i s cc tp con ca mt tp cho, o dng, Khng gian o c, nh x v hm o c, Tch phn (cc hm dng), Tch phn Lebesgue tru tng, Hm kh tch, Cc khng gian Lebesgue Lp v Lp (1 p +), Cc kiu hi t, o tch. o nh, o cm sinh, o thc hoc phc. Khai trin, o lin tc tuyt i, o Radon 5. Gii tch phi tuyn Mn hc ny gii thiu nhng khi nim c bn m u ca gii tch hm phi tuyn nh php tnh vi phn trong khng gian Banach, p dng ca php tnh vi phn vo vic nghin cu bi ton cc tr ca cc phim hm kh vi c bit l cc bi ton ca php tnh bin phn. Ngoi ra mn hc cng trnh by mt s nh l v im bt ng ca cc nh x lin tc trong cc khng gian metric, cu trc hnh hc ca cc khng gian Banach cng nh mt s nh l v im bt ng ca cc nh x khng gin trong khng gian Banach v khng gian Hilbert cng vi mt vi p dng ca cc nh l . 6. Gii tch trn a tp Mn hc trang b nhng kin thc c bn v php tnh vi tch phn trn a tp kh vi: cc a tp con trong Rn, trng vc t, a tp kh vi v tch phn trn a tp. 7. L thuyt nhm v biu din nhm Mn hc trang b nhng kin thc c bn v nng cao v l thuyt nhm v biu din nhm: Biu din nhm, Vnh nhm, Mun trn vnh nhm, ng cu mun trn vnh nhm, Mun con v tnh kh quy, nh l Maschke, B Schur, Mun bt kh quy, Phn tch vnh nhm thnh cc mun con bt kh quy, Cc lp lin hp, c trng ca biu din, Tch v hng ca cc c trng, S cc biu din bt kh quy ca mt nhm, Bng c trng v cc quan h trc giao, Nhm con chun tc v nng cc c trng, Mt s bng c trng s cp, Tch tenx ca cc biu din, Hn ch biu din xung nhm con, Mun v c trng cm sinh. 8. L thuyt ton t tuyn tnh

Mn hc trang b nhng kin thc c bn v l thuyt na nhm ton t, l thuyt nhiu lon v xp x. 9. L thuyt xp x Mn hc trang b kin thc hin i v l thuyt xp x hm thc bng a thc lng gic, a thc i s, sng nh v cc cng c khc. Phn c bn ca mn hc l xp x bng phng php tuyn tnh. Tuy nhin mn hc cng cp n mt s vn hin i ca xp x phi tuyn. T y, sinh vin c th vn dng nhng kin thc c tip thu trong cc lnh vc ca gii tch s, x l v nn tn hiu 10. Hnh hc vi phn Gii thiu hnh hc vi phn, trng tm v a tp Riemann: a tp kh vi, khng gian tip xc, tch phn ca trng vc t v dng vi phn, lin thng tuyn tnh, hnh hc Riemann. 11. B tc v i s tuyn tnh Kin thc chun b v phm tr v hm t. Ma trn v K-ng cu. Cu trc cc dng song tuyn tnh. Tch a tuyn tnh. 12. Hnh hc i s Gii thiu cc kin thc c bn v hnh hc i s: a tp i s afin, a tp x nh, hnh hc song hu t, gii k d, c v cc dng vi phn, s giao. 13. i s giao hon Vnh v m un, vnh v m un c iu kin hu hn, phn tch nguyn s, a phng ha, nhp mn l thuyt chiu. 14. Tp i s Phm tr. ng lun, nhm c bn v ng dng. ng iu k d v ng dng. Cc tch. 15. L thuyt s i s nh gi v gi tr tuyt i, cc vnh s hc v vnh Dedekind, m rng r nhnh v khng r nhnh, s hc ca cc m rng ton phng v cu phn, nh l Fermat ln. 16. Dy ph v ng dng Mn hc trang b kin thc c bn v k thut dy ph dng trong i s v Tp. Trng tm ca mn hc l dy ph Leray-Serre ca cc phn th v cc ng dng trong vic tnh i ng iu ca cc nhm c bn, xy dng cc lp Chern v Stiefel-Whitney, v tnh ton i ng iu ca cc khng gian Eilenberg-MacLane. 17. i s ng iu M u v l thuyt phm tr, mun v gii thc ca mun, ng iu ca phc dy chuyn, nhm cc ng cu v hm t m rng, tch tenx v hm t xon. 18. i s Hopf v ng dng i s v i i s, i s Hopf, cc v d v i s Hopf, i s Steenrod v i ngu.

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19. L thuyt bt bin Modular L thuyt bt bin trn trng c s 0. Tnh hu hn sinh ca vnh bt bin. Xy dng cc bt bin. Chui Poincar v nh l Molien. Cc tnh cht ng iu ca bt bin. Nhm sinh bi cc php phn x. Bt bin modular. a thc tenx vi i s ngoi. i s Dickson, nhm tuyn tnh c bit, nhm tam gic trn v bt bin. L thuyt bt bin v tp i s. i s Steenrod v l thuyt bt bin modular. 20. L thuyt vnh v mun Cc khi nim i s c bn. L thuyt vnh giao hon. Vnh v mun Noether, Artin. L thuyt vnh kt hp. 21. M rng nhm v i ng iu ca nhm Nhm, mun v dy khp, m rng nhm v i ng iu ca nhm. ng dng vo bi ton phn loi nhm cp thp. M rng ca nhm khng abel - cn tr ca m rng. ng dng vo bi ton phn loi nhm cp 16. 22. Nhm Lie v i s Lie Khi nim v nhm Lie v i s Lie, cc v d c bn. i s Lie ca nhm Lie, nhm Lie con v nhm Lie thng. L thuyt Lie: nh x m, nh l n o, v d phn loi nhm Lie v i s Lie chiu thp. Cc lp i s Lie v nhm Lie c bit. 23. Ton t i ng iu Xy dng i s Steenrod theo tin . i ngu ca i s Steenrod, ng dng: Nhng cc khng gian vo mt cu. Xy dng cc ton t Steenrod. Quan h Adem v nh l v tnh duy nht.

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