Analysis and Geometry

Cycle

Terceiro ciclo

Degree

Doutor

This path is an option of

• Mathematics

Coordinator

Oleksiy Karlovych

Structure

1.º Semester
Code	Name	ECTS

1.º Semester - Opção I
Code	Name	ECTS
Options
11628	Numerical Analysis of Partial Differential Equations	6.0
9623	Universal Algebra	6.0
9635	Calculus of Variations and Applications	6.0
11632	Decision Sciences	6.0
11630	Complements of Functional Analysis	6.0
9644	Complements of Computational Complexity	6.0
11631	Complements of Ordinary Differential Equations	6.0
9645	Complements of Logic	6.0
11633	Population Dynamics	6.0
11634	Partial Differential Equations	6.0
11635	Stochastic Differential Equations	6.0
11636	Modeling in Operations Research	6.0
9631	Numerical Semigroups	6.0
11637	Additive Number Theory	6.0
11638	Combinatorial Group Theory	6.0
9632	Graph Theory	6.0
11639	Operator Theory	6.0
11641	Topics of Advanced Analysis	6.0
11640	Topics of Commutative Algebra and Algebraic Geometry	6.0
11642	Topics of Mathematical Physics	6.0
9646	Topics of Mathematical Logic	6.0
11643	Topics of Combinatorial Optimization	6.0
11644	Topics of Non-Linear Optimization	6.0
11696	Topics of Semigroups	6.0
9648	Topics of the Theory of Computation	6.0
11645	Topics of Topology and Geometry of Manifolds	6.0
11646	Topics of General And Algebraic Topology	6.0
O aluno deverá obter 6.0 créditos nesta opção.

1.º Semester - Opção II
Code	Name	ECTS
Options
11628	Numerical Analysis of Partial Differential Equations	6.0
9623	Universal Algebra	6.0
9635	Calculus of Variations and Applications	6.0
11632	Decision Sciences	6.0
11630	Complements of Functional Analysis	6.0
9644	Complements of Computational Complexity	6.0
11631	Complements of Ordinary Differential Equations	6.0
9645	Complements of Logic	6.0
11633	Population Dynamics	6.0
11634	Partial Differential Equations	6.0
11635	Stochastic Differential Equations	6.0
11636	Modeling in Operations Research	6.0
9631	Numerical Semigroups	6.0
11637	Additive Number Theory	6.0
11638	Combinatorial Group Theory	6.0
9632	Graph Theory	6.0
11639	Operator Theory	6.0
11641	Topics of Advanced Analysis	6.0
11640	Topics of Commutative Algebra and Algebraic Geometry	6.0
11642	Topics of Mathematical Physics	6.0
9646	Topics of Mathematical Logic	6.0
11643	Topics of Combinatorial Optimization	6.0
11644	Topics of Non-Linear Optimization	6.0
11696	Topics of Semigroups	6.0
9648	Topics of the Theory of Computation	6.0
11645	Topics of Topology and Geometry of Manifolds	6.0
11646	Topics of General And Algebraic Topology	6.0
O aluno deverá obter 6.0 créditos nesta opção.

1.º Semester - Opção III
Code	Name	ECTS
Options
11628	Numerical Analysis of Partial Differential Equations	6.0
9623	Universal Algebra	6.0
9635	Calculus of Variations and Applications	6.0
11632	Decision Sciences	6.0
11630	Complements of Functional Analysis	6.0
9644	Complements of Computational Complexity	6.0
11631	Complements of Ordinary Differential Equations	6.0
9645	Complements of Logic	6.0
11633	Population Dynamics	6.0
11634	Partial Differential Equations	6.0
11635	Stochastic Differential Equations	6.0
11636	Modeling in Operations Research	6.0
9631	Numerical Semigroups	6.0
11637	Additive Number Theory	6.0
11638	Combinatorial Group Theory	6.0
9632	Graph Theory	6.0
11639	Operator Theory	6.0
11641	Topics of Advanced Analysis	6.0
11640	Topics of Commutative Algebra and Algebraic Geometry	6.0
11642	Topics of Mathematical Physics	6.0
9646	Topics of Mathematical Logic	6.0
11643	Topics of Combinatorial Optimization	6.0
11644	Topics of Non-Linear Optimization	6.0
11696	Topics of Semigroups	6.0
9648	Topics of the Theory of Computation	6.0
11645	Topics of Topology and Geometry of Manifolds	6.0
11646	Topics of General And Algebraic Topology	6.0
O aluno deverá obter 6.0 créditos nesta opção.

1.º Semester - Opção IV
Code	Name	ECTS
Options
11628	Numerical Analysis of Partial Differential Equations	6.0
9623	Universal Algebra	6.0
9635	Calculus of Variations and Applications	6.0
11632	Decision Sciences	6.0
11630	Complements of Functional Analysis	6.0
9644	Complements of Computational Complexity	6.0
11631	Complements of Ordinary Differential Equations	6.0
9645	Complements of Logic	6.0
11633	Population Dynamics	6.0
11634	Partial Differential Equations	6.0
11635	Stochastic Differential Equations	6.0
11636	Modeling in Operations Research	6.0
9631	Numerical Semigroups	6.0
11637	Additive Number Theory	6.0
11638	Combinatorial Group Theory	6.0
9632	Graph Theory	6.0
11639	Operator Theory	6.0
11641	Topics of Advanced Analysis	6.0
11640	Topics of Commutative Algebra and Algebraic Geometry	6.0
11642	Topics of Mathematical Physics	6.0
9646	Topics of Mathematical Logic	6.0
11643	Topics of Combinatorial Optimization	6.0
11644	Topics of Non-Linear Optimization	6.0
11696	Topics of Semigroups	6.0
9648	Topics of the Theory of Computation	6.0
11645	Topics of Topology and Geometry of Manifolds	6.0
11646	Topics of General And Algebraic Topology	6.0
O aluno deverá obter 6.0 créditos nesta opção.

1.º Semester - Opção V
Code	Name	ECTS
Options
11628	Numerical Analysis of Partial Differential Equations	6.0
9623	Universal Algebra	6.0
9635	Calculus of Variations and Applications	6.0
11632	Decision Sciences	6.0
11630	Complements of Functional Analysis	6.0
9644	Complements of Computational Complexity	6.0
11631	Complements of Ordinary Differential Equations	6.0
9645	Complements of Logic	6.0
11633	Population Dynamics	6.0
11634	Partial Differential Equations	6.0
11635	Stochastic Differential Equations	6.0
11636	Modeling in Operations Research	6.0
9631	Numerical Semigroups	6.0
11637	Additive Number Theory	6.0
11638	Combinatorial Group Theory	6.0
9632	Graph Theory	6.0
11639	Operator Theory	6.0
11641	Topics of Advanced Analysis	6.0
11640	Topics of Commutative Algebra and Algebraic Geometry	6.0
11642	Topics of Mathematical Physics	6.0
9646	Topics of Mathematical Logic	6.0
11643	Topics of Combinatorial Optimization	6.0
11644	Topics of Non-Linear Optimization	6.0
11696	Topics of Semigroups	6.0
9648	Topics of the Theory of Computation	6.0
11645	Topics of Topology and Geometry of Manifolds	6.0
11646	Topics of General And Algebraic Topology	6.0
O aluno deverá obter 6.0 créditos nesta opção.

2.º Semester
Code	Name	ECTS
Options
11623	Analysis and Geometry Seminar	3.0

2.º Year
Code	Name	ECTS
11626	Thesis on Analysis and Geometry	147.0