Module 24-B-HA Advanced Analysis

Faculty

Person responsible for module

Regular cycle (beginning)

Every summer semester

Credit points and duration

10 Credit points

For information on the duration of the modul, refer to the courses of study in which the module is used.

Competencies

Non-official translation of the module descriptions. Only the German version is legally binding.

Students master the fundamental principles of complex analysis and functional analysis, i.e: Students can deal with the basic concepts and methods of complex analysis and functional analysis in a technically correct manner, successfully transfer them to new problems in different areas (such as number theory, analysis, probability theory or mathematical statistics) and independently carry out proofs in these areas.
In the tutorials, students demonstrate the acquisition of skills in the basic techniques of mathematical work in the field of complex analysis and functional analysis, the ability to apply the methods and conduct mathematical proofs under supervision as well as presentation and communication skills and perseverance as basic mathematical skills in through the study requirements. Further understanding of the contexts and concepts, independent proofs and confidence in applying the methods to new problems are demonstrated in the final exam.

Content of teaching

1. complex analysis: holomorphic functions, Cauchy's integral theorem, Cauchy's integral formula, power series expansion theorem, singularities, calculus of residues
2. functional analysis: Banach and Hilbert spaces, Hahn-Banach theorem with applications, continuous linear operators, Baire type theorems, duality, notions of convergence, Hilbert-Schmidt theorem, spectral theory

(optional and connecting: Fourier analysis)

Recommended previous knowledge

Competencies in analysis and linear algebra (cf. 24-B-MG1 and 24-B-MG2 or 24-B-AN and 24-B-LA) as well as in measure and integration theory (cf. 24-B-AN3 or 24-B-MI)

Necessary requirements

—

Explanation regarding the elements of the module

The module cannot be studied together with module 24-B-HA-5.

Module structure: 1 SL, 1 bPr 1

Courses

Advanced Analysis
Type lecture
Regular cycle SoSe
Workload5 60 h (60 + 0)
LP 2 [Pr]
Tutorials for Advanced Analysis
Type exercise
Regular cycle SoSe
Workload5 90 h (30 + 60)
LP 3 [SL]

Study requirements

Allocated examiner Workload LP2
Teaching staff of the course Tutorials for Advanced Analysis (exercise)

Regular completion of the exercises, each with a recognisable solution approach, as well as participation in the exercise groups for the module's lecture. As a rule, participation in the exercise group includes presenting solutions to exercises twice after being asked to do so as well as regular contributions to the scientific discussion in the exercise group, for example in the form of comments and questions on the proposed solutions presented. The organiser may replace some of the exercises with face-to-face exercises.

 see above see above

Examinations

e-portfolio with final oral examination o. e-portfolio with final written examination o. portfolio with final oral examination o. portfolio with final written examination
Allocated examiner Teaching staff of the course Advanced Analysis (lecture)
Weighting 1
Workload 150h
LP2 5

The (e-)portfolio is passed if

  • a sufficient number of correctly solved exercises, which are completed as part of the study requirements , are demonstrated, usually by at least 50% of the points achievable in the semester for solving the exercises, and
  • a final exam in the form of a final written exam (usually 90 min) or a final oral exam (usually 30 min) is passed. The final exam relates to the content of the lecture and the tutorial and is used for assessment.

A remote electronic written examination is not permitted as a final exam.

The module is used in these degree programmes:

Degree programme Version Profile Recom­mended start 3 Duration Manda­tory option 4
Mathematical and Theoretical Physics / Master of Science [FsB vom 26.04.2024 mit Änderungen vom 29.05.2024 und 10.12.2024 und der Berichtigung vom 01.04.2025] Admission Track Profile B 1. o. 2. one semester Compul­sory optional subject
Mathematics / Bachelor of Science [FsB vom 28.02.2025] Major Subject (Academic) 4. o. 5. o. 6. one semester Compul­sory optional subject
Mathematics / Bachelor of Science [FsB vom 28.02.2025] Major Subject (Academic) Strukturierte Ergänzung des fw Bachelor KF 4. o. 5. o. 6. one semester Compul­sory optional subject
Mathematics / Bachelor [FsB vom 28.02.2025] Minor Subject (Academic), 60 CPs 5. o. 6. one semester Compul­sory optional subject
Mathematical Economics / Bachelor of Science [FsB vom 28.02.2025 mit Berichtigung vom 30.04.2025] Bachelor with One Core Subject (Academic) 3. o. 4. o. 5. o. 6. one semester Compul­sory optional subject

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Legend

1
The module structure displays the required number of study requirements and examinations.
2
LP is the short form for credit points.
3
The figures in this column are the specialist semesters in which it is recommended to start the module. Depending on the individual study schedule, entirely different courses of study are possible and advisable.
4
Explanations on mandatory option: "Obligation" means: This module is mandatory for the course of the studies; "Optional obligation" means: This module belongs to a number of modules available for selection under certain circumstances. This is more precisely regulated by the "Subject-related regulations" (see navigation).
5
Workload (contact time + self-study)
SoSe
Summer semester
WiSe
Winter semester
SL
Study requirement
Pr
Examination
bPr
Number of examinations with grades
uPr
Number of examinations without grades
This academic achievement can be reported and recognised.

Sidebar

Elements of the module

Courses

Study requirements

Examinations

Programme of lectures (eKVV)

Programme of lectures (eKVV)

Show lists of modules

Mathematical and Theoretical Physics / Master of Science // Admission Track Profile B

Mathematics / Bachelor of Science: Major Subject (Academic)

Mathematics / Bachelor of Science: Major Subject (Academic) // Strukturierte Ergänzung des fw Bachelor KF

Mathematics / Bachelor: Minor Subject (Academic), 60 CPs

Mathematical Economics / Bachelor of Science: Bachelor with One Core Subject (Academic)