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Archived teaching schedules 2016–2017
You are browsing archived teaching schedule. Current teaching schedules can be found here.
Master´s Programme in Mathematics

Periods

Period I (29-Aug-2016 – 23-Oct-2016)
Period III (9-Jan-2017 – 5-Mar-2017)
Period (29-Aug-2016 - 23-Oct-2016)
Advanced Studies in Mathematics [Period I]

Prerequisities

Familiarity with first-order logic.

Topics for lectures

1st LESSON

Henkin quantifiers:
-informal presentation of Skolem semantics -a sentence expressing infinity Syntax of IF logic, free and bound variables. Game-theoretical semantics.

2nd LESSON

Hodges' signalling sentence. The correct notion of Skolemization.

Expressive power of sentences:
-the Walkoe-Ehrenfeucht theorem. Panoramic of model-theoretic properties.

3rd LESSON

The debate on compositionality. Team semantics. 1-coherence of first-order logic. The Cameron-Hodges theorem.

Expressive power of open formulas (Kontinen-Vaananen).

4th LESSON

Downward monotonicity, non-contradiction. Substitution Truth equivalence:
-dummy variables in teams (cartesian extension) and in slash sets -locality of sentences

5th LESSON Equivalence in context (1):
-substitution of equivalents
-propositional laws
-shrinking of slash sets
-distribution of quantifiers

6th LESSON

Equivalence in context (2):
-vacuous quantifiers and requantification -quantifier swapping -quantifier extraction -renaming

7th LESSON Equivalence in context (3):
-prenex normal form
-strong regularization

An application: the perfect recall fragment

Enrolment for University Studies
Enrolment time has expired
Teaching
5-Sep-2016 – 20-Oct-2016
Periods: I
Language of instruction: English
Further information:

Course can be a part of advanced studies in mathematics.

For details, course description and learning outcomes, see TUT Curricula.

Enrolment for University Studies

Registration through Tampere3 Service for Cross-Institutional Studies.

Periods: I
Language of instruction: English
Further information:

Course is organized by Tampere University of Technology and it is a part of the cross-institutional studies of Tampere3 universities.

Course can be a part of advanced studies in mathematics.

Period (9-Jan-2017 - 5-Mar-2017)
Advanced Studies in Mathematics [Period III]
Enrolment for University Studies
Enrolment time has expired
Teaching
9-Jan-2017 – 5-Mar-2017
Periods: III
Language of instruction: English
Further information:

Note. You can not include both MAT-72006 Advanced Algorithms and Data Structures  7 ECTS (TUT) and this course in your M.Sc. degree (120 ECTS).