introduction

Introduction

INTRODUCTION

Welcome Students!!

Have you ever asking about influence probability in your life??, this is not a common question however in real life this field of mathematics is mathematical tool widely used. For example when you like use public transport, predict a environmental behaviour or estimate quantity of customer in the bank.

We can observe in the below table some applications of statistics and probability for daily day!!

Objective

The goal of this course is to study the elements that support to student realize the activities used for mathematical and probabilistic modelling, simulating systems applied to real life. The student must know basics mathematics, data structures, computer programming, differential equations, computer science, statistics, linear algebra, probability, discrete mathematics, multi-variable calculus, operations research, analysis and design algorithms.

Process

METHODOLOGY 

  • Professor's master classes.
  • Question and dudes solving by students and teacher.
  • Assignment will be presented in pdf format make it with Latex.
  • R-programming.
  • Home-Exam and Two-person exam.
  • Final Project!

 

PROCESS AND TABLE OF CONTENT



 TOPIC SUPPORT READINGS AND VIDEOS  ASSIGNMENTS 
An brief introduction to simulation and stochastic processes.

[SimulationRoger2015]		  
   A review of Statistics and Probability Theory [TheoryProbabilityRoger2015]
[NormalRoger2015]
 Probability Theory
  • Value Expected
  • An introduction to probability distribution.
[TheoryProbability]
[Bayes' Rule_ExpectedValue] 
An introduction of Stochastic Processes
  • Theory Decision
    • Decision under certainty
    • Decision under risk
    • Decision under uncertainty
    • Bayesian Decision Tree
  • Prediction models
    • Simple Linear Regression
    • Logistic Regression
    • Decision Tree Classification and Regression (C&RT)

       [DecisionTheory]
       [DecisionTheroryII]
       [DecisionTheoryIII]
       [DecisionTheoryIV]
IPython Notebook Prediction Models



First Exam 		    
An introduction of Stochastic Processes


  • Definition Stochastic Processes.
  • Birth-Death Process
  • Renovation theory.
  • Bernoulli Processes.
  • Poisson Processes.
  • Birth and Death Processes


StochasticProcessI
StochasticProcessII




  • Markov Processes.
  • Markov Chain.
  • Transition matrix in Markov chain.
  • Champman Kolmogorov Equation.
  • Absorbing Markov Chain
  • Queue Theory

MarkovChainI
MarkovChainII		  

  • WebSearch Architecture
  • WebCrawling Analysis and PageRank
 [Nayak2013]         [Navak2013PageRank] 
[Page Rank Algorithm]




 Second Exam    
Simulation
  • Introduction and development stages for simulation modelling.
  • Queue Simulation
  • Runge Kutta Simulation
  
Advanced Topics in Stochastic Processes

    
 Final Exam    

Evaluation

GRADES

 

 First Period  Evaluation
AssignmentsQuizzesExam 101010 
Total  30
Second Period   
Assignments QuizzesExam 101010
 Total 30 
 Third Period   
 PaperAssignmentsFinal ProjectExam 551020
 Total      40 / 40