3000

MATE-3000 Seminario Electivo

Credits

2

Distribution

-

Instructor

Ferri Stefano

- MATE-3002

MATE-3101 Algebra Abstracta 2

Rings, integral domains and fields. Algebraic and transcendental extensions. Unique factorization domains and Euclidean domains. Field automorphisms, Galois’ theory and solvability of equations.

Credits

3

Distribution

-

MATE-3105 Teoría Algebráica de Números

Credits

3

Distribution

-

MATE-3112 Geometria Discreta

Credits

3

Distribution

-

MATE-3116 Combinatoria de Determinantes

Credits

3

Distribution

-

MATE-3120 Logica 1

This course is an introduction with mathematical emphasis to logic. The minimum content of the course includes the study of the calculation of propositions and predicates: symbolization, syntax, semantics, formal deduction, validity and completeness theorems for these calculations. It gives an introduction to calculations: recursive functions, Turing-calculable functions, equivalence between them. We study some links between calculation and formal properties of logical calculations studied.

Credits

3

Distribution

-

MATE-3121 Capitalism and Entrepreneurship in the Global Economy

Credits

3

Distribution

-

- MATE-3125

MATE-3126 Teoria de Recursion

Credits

3

Distribution

-

MATE-3129 Topología Dócil y Estructuras O-Minimales

Credits

3

Distribution

-

- MATE-3130

MATE-3131 Sustainable Business Models - Challenges and Future Tendencies

Credits

3

Distribution

-

MATE-3132 MATE-3132

Distribution

-

- MATE-3134

- MATE-3135

- MATE-3136

- MATE-3144

- MATE-3145

- MATE-3146

MATE-3147 MATE-3147

Distribution

-

- MATE-3156

MATE-3157 Introducción A Las Representaciones de Grupos Finitos

Credits

3

Distribution

-

MATE-3158 Geometría Algebraica Computacional

Credits

3

Distribution

-

- MATE-3159

MATE-3162 MATE-3162

Distribution

-

- MATE-3163

- MATE-3164

- MATE-3169

- MATE-3171

- MATE-3172

MATE-3175 Introduccion a la Geometria Algebraica

Credits

3

Distribution

-

- MATE-3177

MATE-3181 Complejidad Computacional

Credits

3

Distribution

-

MATE-3182 La Paradoja de Banach-Tarski

Credits

3

Distribution

-

MATE-3205 Teoría Ergodica

Credits

3

Distribution

-

MATE-3210 Análisis Complejo

Credits

3

Distribution

-

MATE-3211 Teoría Analitica de Números

Credits

3

Distribution

-

- MATE-3212

- MATE-3213

- MATE-3214

- MATE-3215

- MATE-3216

MATE-3302 Ecuaciones de la Física Matemática

Credits

3

Distribution

-

MATE-3361 Análisis Asintótico

Credits

3

Distribution

-

MATE-3401 Geometría Riemanniana

Introduce students to the basic tools provided by the differential geometry (Riemannian) for the study of differential varieties with metrics. Specially, study in depth fundamental notions as parallel transport, curvature and geodesic and its properties. Study the key results on Riemannian varieties and get to know the classic examples from which we can study the mentioned concepts.

Credits

3

Distribution

-

Instructor

Vargas Dominguez Andres

MATE-3410 Geometria Diferencial 2

Credits

3

Distribution

-

MATE-3414 Variedades Toricas I

Credits

3

Distribution

-

- MATE-3415

MATE-3420 Topologia 1

Topological spaces, bases and sub-bases, sub-spaces, continuous functions. Order topology, product topology, quotient topology and metric topology. Connected spaces, arc-connected spaces and local connectedness. Compact and locally compact spaces, compactifications, Tychonoff’s Theorem. Axioms of enumerability. Regular and completely regular spaces. Normal spaces, Urysohn’s Lemma, Tietze’s Theorem of extension. Metrizability.

Credits

3

Distribution

-

MATE-3422 MATE-3422

Distribution

-

- MATE-3423

MATE-3426 Grupos de Lie

Credits

3

Distribution

-

MATE-3441 Haces Fibrados

Credits

3

Distribution

-

MATE-3510 Procesos Estocásticos

Introduction. Stochastic processes specifications. Some important classes of processes such as stationary processes. Processes with stationary increments and processes with independent increments. Markov processes. Martingales. MARKOV CHAINS: definitions and examples. Features. Finite Markov chains. Classification of states and chains. Markov chains accounting. Limit theorems. Stationary distribution. POISSON PROCESSES: generalizations of Poisson processes. not homogeneous process. Compound Poisson processes. Conditional processes. Processes of birth and death. MARTINGALA in discrete time: conditional expected value. Definition and examples. Time to Stop. Optional stopping theorem. Inequalities of the Doob Martingale. Convergence Theorem of Martingala. RENEWAL PROCESSES : Renewal Equation. Laws of large numbers. Age and residual life. Applications to the theory of the tail. Brownian motion: Preliminaries. Simple Features of standard Brownian motion. Variations in the Brownian motion. Brownian motion with drift. Kolomogorov equations. Ornstein-Uhlenbeck process.

Credits

3

Distribution

-

Instructor

Arunachalam Viswanatham

- MATE-3512

MATE-3520 Estadistica Matematica 1

Estimation methods: time for confidence intervals. Methods of moments, least squares, maximum likeliness. Theory of optimality criteria estimate UMVU, the information. Consistent estimators, asymptotic distribution, efficient estimators, non-biased. Confidence intervals and hypothesis tests. Theme of Neyman-Pearson. Likeliness reason. Tests of fitting, contingency tables. Linear models, Gauss-Markov theorem, Testing in linear models.

Credits

3

Distribution

-

MATE-3523 Estadística No Paramétrica y Recuenteo

Credits

3

Distribution

-

MATE-3530 Cálculo Estocástico

Credits

3

Distribution

-

MATE-3533 MATE-3533

Distribution

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MATE-3707 Introduccion a la Optimizacion Convexa

Credits

3

Distribution

-

MATE-3710 Matemáticas Financieras

Credits

3

Distribution

-

MATE-3712 Teoria de Juegos

Credits

3

Distribution

-

MATE-3716 Optimización Combinatoria

Credits

3

Distribution

-

MATE-3717 Introducción A la Teoría de Control

Credits

3

Distribution

-

MATE-3754 Teoría de Colas

Credits

3

Distribution

-

- MATE-3755

MATE-3761 Optimización Lineal

Credits

3

Distribution

-

MATE-3801 Practica Ensenanza 1

Training in teaching methodology. Micro-teaching practice on how to handle questions, the use of the blackboard and diagnostic sessions. Instructions prior to each class, observations on development, creation of exams. Students teach one section of problems relating to a lecture under the guidance of a professor from the Department.

Credits

3

Distribution

-

MATE-3802 Practica Ensenanza 2

Instructions on how to teach a class, reading and discussion of articles in Mathematical Education, creation of exams, observations. Students teach a course under the guidance of a professor from the Department.

Credits

3

Distribution

-

MATE-3902 Proyecto de Grado

Students write a paper in a specific area of mathematics in which they show their capacity as regards research and presenting a topic with all the requirements of clarity, correctness and proper style.

Credits

3

Distribution

-

MATE-3904 Seminario de Proyecto de Grado 1

Students start out in the current events of research in mathematics.

Credits

1

Distribution

-

MATE-3905 Seminario de Proyecto de Grado 2

Students start out in research as an independent activity, as well as the proper oral and written communication of mathematics by reading articles and solving problems. This course requires students to choose a topic for their graduation thesis.

Credits

1

Distribution

-

MATE-3990 Inscripción a Grado

Credits

0

Distribution

-

- MATE-3992

- MATE-3993