HUOM! OPINTOJAKSOJEN TIETOJEN T=C3= =84YTT=C3=84MIST=C3=84 KOORDINOIVAT KOULUTUSSUUNNITTELIJAT HANNA-MARI PEURA= LA JA TIINA HASARI

=20

- =20
- 1. Course title =20
- 2. Course code =20
- 3. Course status: optional =20
- 4. Course level (first-, = second-, third-cycle/EQF levels 6, 7 and 8) =20
- 5. Recommended time/stage of studies f= or completion =20
- 6. Term/teaching period when the cou= rse will be offered =20
- 7. Scope of the course in credits =20
- 8. Teacher coordinating the course =20
- 9. Course learning outcomes =20
- 10. Course completion methods =20
- 11. Prerequisites =20
- 12. Recommended optional studies =20
- 13. Course content =20
- 14. Recommended and required literature = =20
- 15. Activities and teaching metho= ds in support of learning =20
- 16. Assessment practices and criteria= , grading scale =20
- 17. Teaching language =20

Fysiikan matemaattiset menetelm=C3=A4t IIIb

Fysikens matematiska meto=
der IIIb

Mathematical Methods of Physics IIIb

TCM305

Aikaisemmat leikkaavat opintojaksot 53713 Fysiikan matemaattiset menetel= m=C3=A4t III, 10 op.

3. Course status: optional

*-Which degree programme is responsible for the course?*Maste=
r=E2=80=99s Programme in Theoretical and Computational Methods

4. Course level (first-, se= cond-, third-cycle/EQF levels 6, 7 and 8)

Master=E2=80=99s level, degree programmes in medicine, dentistry and vet=
erinary medicine =3D secondcycle

degree/EQF level 7

Doctoral level =
=3D third-cycle (doctoral) degree/EQF level 8*-Does the course b=
elong to basic, intermediate or advanced studies (cf. Government Decree on University Degrees)?Advanced studies*

5. Recommended time/stage of studies for= completion

-The recommended time for completion may be, e.g., after certain rel=
evant courses have

been completed.

6. Term/teaching period when the cours= e will be offered

The course is offered in the autumn term, during II period.

<=
/p>

5 cr

Esko Keski-Vakkuri

-Description of the learning outcomes provided to students by the co=
urse

- See the competence map (https://fla=
mma.helsinki.fi/content/res/pri/HY350274).

After the course, the student will be familiar with basic concepts of ca= lculus on differentiable manifolds and Riemannian geometry, which are mathe= matical tools used in physics e.g. in the contexts of general relativity an= d gauge field theories. The student will also be familiar with basics of Li= e algebra representation theory, which is used e.g. in particle physics and= condensed matter theory. The student can work with differential forms, exp= ress metrics in different coordinates and compute metric tensors of general= relativity. He also understands basic representations of Lie algebras used= e.g. in the theory of strong interactions.

-Will the course be offered in the form of contact teaching, or can =
it be taken as a distance

learning course?

-Description of attendance=
requirements (e.g., X% attendance during the entire course or

during pa=
rts of it)

-Methods of completion

The course is lectured as contact teaching, but it is also possible to p= ass the course by studying it independently (e.g. by a final exam), if so a= greed with the lecturer. In the course form, the completion is based = on a final exam and weekly homework performance.

11. Prerequisites

-Description of the courses or modules that must be completed before=
taking this course or

what other prior learning is required

The student should be familiar with and understand the concepts of= the course Mathematical Methods of Physics IIIa. In addition it is recomme= nded to be familiar with linear algebra, differential and integral calculus= , and (partial) differential equations. It is also helpful to know basic ph= ysics such as classical mechanics, electrodynamics, some quantum mechanics,= and theory of special relativity.

12. Recommended optional studies

-What other courses are recommended to be taken in addition to this =
course?

-Which other courses support the further development of the comp=
etence provided by this

course?

13. Course content

-Description of the course content

Differentiable manifolds and calculus on manifolds: differentiable manif= olds, manifolds with boundary, differentiable maps, vector fields, 1-form f= ields, tensor fields, differentiable map and pullback, flow generated by a = vector field, Lie derivative, differential forms, Stokes' theorem

Riemannian geometry: metric tensor, induced metric, connections, paralle= l transport, geodesics, curvature and torsion, covariant derivative, isomet= ries, Killing vector fields

Semisimple Lie algebras and representation theory: SU(2), roots and weig= hts, SU(3), introduction to their most common unitary irreducible represent= ations

-What kind of literature and other materials are read during the cou=
rse (reading list)?

-Which works are set reading and which are recommend=
ed as supplementary reading?

The course follows "Mathematical methods of physics III", lecture notes = by E. Keski-Vakkuri, C. Montonen and M. Panero. Supplementary reading is li= sted in the lecture notes. The students are encouraged to actively search f= or additional supplementary material from the Web (e.g., from Wikipedia and= other such pages.)

15. Activities and teaching methods= in support of learning

-See the competence map (https://flamm=
a.helsinki.fi/content/res/pri/HY350274).

-Student activities

-Des=
cription of how the teacher=E2=80=99s activities are documented

Weekly contact lectures, independent = work of the student including solving weekly homework problem sets. The

solutions to the problem sets will be= submitted weekly, graded by the teaching assistant and discussed in weekly= exercise sessions. In these sessions the students may also discuss and get= tutoring for

next week's homework.

16. Assessment practices and criteria, = grading scale

-See the competence map (https://flamm=
a.helsinki.fi/content/res/pri/HY350274).

-The assessment practices u=
sed are directly linked to the learning outcomes and teaching

methods of=
the course.

The grade is determined in a way agreed in the beginning of the course.<= /p>

English