3000

MATE-3000 Seminario Electivo

Credits

2

Distribution

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Instructor

Ferri Stefano

MATE-3101 Algebra Abstracta II

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

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MATE-3105 Teoría Algebráica de Números

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3

Distribution

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MATE-3112 Geometria Discreta

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3

Distribution

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MATE-3116 Combinatoria de Determinantes

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3

Distribution

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MATE-3120 Developing the Creative Organization

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

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Instructor

Corredor Londoño Luis

MATE-3121 Capitalism and Entrepreneurship in the Global Economy

Credits

3

Distribution

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MATE-3129 Topología Dócil y Estructuras O-Minimales

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3

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MATE-3131 Sustainable Business Models - Challenges and Future Tendencies

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3

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MATE-3132 MATE-3132

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MATE-3147 MATE-3147

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MATE-3157 Introducción A Las Representaciones de Grupos Finitos

Credits

3

Distribution

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MATE-3158 Geometría Algebraica Computacional

Credits

3

Distribution

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MATE-3162 MATE-3162

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- MATE-3172

MATE-3175 Introduccion a la Geometria Algebraica

Credits

3

Distribution

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MATE-3181 Complejidad Computacional

Credits

3

Distribution

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MATE-3182 La Paradoja de Banach-Tarski

Credits

3

Distribution

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MATE-3205 Teoría Ergodica

Credits

3

Distribution

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MATE-3210 Análisis Complejo

Credits

3

Distribution

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MATE-3302 Ecuaciones de la Física Matemática

Credits

3

Distribution

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MATE-3361 Análisis Asintótico

Credits

3

Distribution

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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

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Instructor

Vargas Dominguez Andres

MATE-3410 Geometría Diferencial 2

Credits

3

Distribution

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MATE-3414 Variedades Toricas I

Credits

3

Distribution

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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

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MATE-3422 MATE-3422

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MATE-3426 Grupos de Lie

Credits

3

Distribution

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MATE-3441 MATE-3441

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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

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Instructor

Arunachalam Viswanatham

MATE-3520 Estadística Matemática I

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

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Instructor

Garrido Lopeña Liliana

MATE-3523 Estadística No Paramétrica y Recuenteo

Credits

3

Distribution

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MATE-3530 Cálculo Estocástico

Credits

3

Distribution

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MATE-3533 MATE-3533

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MATE-3707 MATE-3707

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MATE-3710 Matemáticas Financieras

Credits

3

Distribution

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MATE-3712 Teoría de Juegos

Credits

3

Distribution

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MATE-3716 Optimización Combinatoria

Credits

3

Distribution

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MATE-3717 Introducción A la Teoría de Control

Credits

3

Distribution

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MATE-3754 Teoría de Colas

Credits

3

Distribution

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MATE-3761 Optimización Lineal

Credits

3

Distribution

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MATE-3801 Practica Enseñanza I

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

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Instructor

Paramo Fonseca Aquiles

MATE-3802 Practica Enseñanza II

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

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Instructor

Botero De Meza Maria

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

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Instructor

Ferri Stefano

MATE-3904 Seminario de Proyecto de Grado I

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

Credits

1

Distribution

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Instructor

Ferri Stefano

MATE-3905 Seminario de Proyecto de Grado II

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

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MATE-3990 Inscripción a Grado

Credits

0

Distribution

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