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Mathematics & Statistics Training

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Mathematics & Statistics Training for Data Science

Here you will find a list of our trainings in the field of statistics and mathematical methods, along with suggested table of contents. We can also customize the training to suit your requirements..

Please choose the area in which you would like to make significant improvements.

Do you need training or group tutoring in these areas?

Statistical Fundamentals

The prerequisites here include only an introduction to analysis as well as linear algebra or matrix calculations.

  • Introduction and Basic Concepts
  • Data and Data Types
  • Descriptive Measures
  • Data Visualization
  • Introduction to Probability Theory
  • Combinatorics
  • Conditional Probability
  • Random Variables and Probability Distributions
  • Central Limit Theorem
  • Applications of Probability Theory
  • Introduction to Multivariate Statistics
  • Multivariate Data Analysis
  • Multivariate Normal Distribution
  • Multivariate Linear Regression
  • Multivariate Analysis of Variance
  • Multivariate Analysis of Covariance
  • Cluster Analysis
  • Factor Analysis
  • Discriminant Analysis
  • Canonical Correlation
  • Structural Equation Models
  • Applications of Multivariate Statistics
  • Introduction to Sampling Theory
  • Types of Samples
  • Sampling Distributions
  • Confidence Intervals
  • Hypothesis Testing
  • Nonparametric Tests
  • Outliers and Influential Observations
  • Sample Size and Power Analysis
  • Applications of Sampling Theory
  • Introduction to Statistical Testing Methods
  • Types of Testing Methods: Parametric and Non-parametric Testing Methods
  • Choosing the Right Testing Method
  • Conducting Statistical Tests
  • Validity and Reliability of Statistical Testing Methods
  • Application of Statistical Testing
  • Methods in Research
  • Critical Examination and Interpretation of Statistical Results
  • Introduction to Linear Regression Models
  • Simple Linear Regression
  • Multiple Linear Regression
  • Assessment of Regression Models
  • Diagnosis of Regression Models
  • Applications of Linear Regression Models
Schedule a non-binding and free initial consultation

Advanced Statistical Methods

The prerequisites here encompass the statistical fundamentals.

  • Introduction to Econometrics
  • Linear Regression Models
  • Time Series Analysis
  • Panel Data Analysis
  • Endogenous Regressors and Simultaneous Equations
  • Nonparametric Regression Models
  • Selection and Simultaneous Equation Models
  • Introduction to Generalized Linear Regression Models
  • Maximum Likelihood Estimation
  • Binary Dependent Variable
  • Multinomial Dependent Variable
  • Ordinal Dependent Variable
  • Count Data
  • Continuous Dependent Variable with Non-Normal Distribution
  • Nonlinear Relationships
  • Modeling Interactions
  • Model Validation
  • Applications of Generalized Linear Regression Models
  • Introduction to Time Series Data
  • Descriptive Time Series Analysis
  • Stationarity and Trend Analysis
  • Autoregressive Models (AR)
  • Moving Average Models (MA)
  • Autoregressive Integrated Moving Average Models (ARIMA)
  • Seasonality and Seasonality Models
  • Introduction to Time Series Regression
  • Dynamic Regression Models
  • Modeling Volatility and ARCH Models
  • Univariate Time Series Forecasting
  • Multivariate Time Series Forecasting
  • Time Series in Financial Analysis
  • Applications of Time Series Analysis
  • Fundamentals of Genetics
  • Fundamentals of Epidemiology
  • Genetic Association Studies (SNPs)
  • Family-Based Study Types
  • Copy Number Variations
  • Joint Analysis of Different Data Types
  • Survival Analysis
  • Sequence Data
  • Introduction to Experimental Design
  • Types of Experimental Designs
  • Planning of Completely Randomized Designs
  • Planning of Randomized Block Designs
  • Factorial Designs and Interactions
  • Randomized Incomplete Block Designs
  • Response Surface Methods
  • Robust Experimental Design
  • Applications of Experimental Design
  • Introduction to Statistical Decision Theory
  • Optimal Decision Rules
  • Bayesian Decision Theory
  • Decision Theory for Statistical Tests
  • Applications of Statistical Decision Theory
  • Fundamental Concepts of Probability Theory
  • Measure-Theoretic Foundations
  • Random Variables and Their Distributions
  • Convergence of Random Variables
  • Limit Theorems for Random Variables
  • Epidemiologische Maßzahlen
  • Design epidemiologischer Studien
  • Planung epidemiologischer Studien
  • Durchführung epidemiologischer Studien
  • Auswertung epidemiologischer Studien
  • Räumliche Epidemiologie
  • Introduction to Stochastic Processes
  • Fundamentals of Probability Theory
  • Discrete Stochastic Processes
  • Continuous Stochastic Processes
  • Markov Chains
  • Poisson Processes
  • Martingales
  • Brownian Motion
  • Applications of Stochastic Processes
  • Introduction to Bayesian Statistics
  • Simple Bayesian Models
  • Regression Models
  • Hierarchical Models
  • Markov Chain Monte Carlo Methods
  • Software Package: WinBUGS, RStan, R-INLA, brms
  • Nonparametric Bayesian Models
Schedule a non-binding and complimentary initial consultation

Mathematical Foundations

Here are some essential mathematical foundations that are of great importance for you to successfully master the aforementioned statistical methods and subsequently excel in machine learning models.

  • Foundations of Analysis
  • Linear Algebra
  • Multivariable Analysis
  • Differential Equations
  • Introduction to Linear Algebra
  • Vectors and Vector Spaces
  • Matrices and Matrix Operations
  • Linear Systems of Equations
  • Determinants
  • Eigenvalues and Eigenvectors
  • Diagonalization of Matrices
  • Linear Transformations
  • Orthogonality and Scalar Products
  • Vector Spaces with Scalar Products
  • Norms and Convergence
  • Applications of Linear Algebra
  • Introduction to Differential Calculus
  • Applications of Differential Calculus
  • Higher Derivatives and Taylor Series
  • Derivatives of Special Functions
  • Implicit Differentiation and Logarithmic Differentiation
  • Differential Calculus in Multiple Variables
  • Optimization with Multiple Variables
  • Higher Order Differential Calculus
  • Differentiation of Integrals
  • Introduction to Optimization
  • Linear Optimization
  • Nonlinear Optimization
  • Integer Optimization
  • Dynamic Optimization
  • Metaheuristics
  • Applications of Optimization
  • Introduction to Analysis
  • Functions and Their Properties
  • Differential Calculus
  • Integral Calculus
  • Series and Limits
  • Differential Equations
  • Introduction to Algebra
  • Sets and Relations
  • Basic Operations in Algebra
  • Linear Equations and Inequalities
  • Polynomial Equations
  • Quadratic Equations
  • Exponential and Logarithmic
  • Functions Complex Numbers
  • Linear Algebra
  • Algebraic Structures: Groups, Rings, Fields
  • Introduction to Measure Theory
  • Measures and Outer Measures
  • Measurable Sets and Measurable Functions
  • Lebesgue Measure and Lebesgue Integral
  • Convergence Theorems in Measure Theory
  • L^p Spaces and Hilbert Spaces
  • Product Measures and Fubini-Tonelli Theorem
  • Radon-Nikodym Theorem and Absolute Continuity
  • Introduction to Numerics for Linear Equations
  • Direct Solution Methods
  • Iterative Solution Methods
  • Condition and Stability
  • Eigenvalue Problems
  • Nonlinear Equations
  • Applications of Numerics for Linear Equations
Schedule a non-binding and complimentary initial consultation

Popular Machine Learning Models

The following machine learning models are frequently used in various applications. Here, you have the opportunity to comprehend and apply these individual methods professionally.

  • Introduction to the Naive Bayes Method
  • Bernoulli, Multinomial, and Gaussian Naive Bayes
  • Optimization and Enhancement of Naive Bayes Models
  • Practical Use Cases and Best Practices
  • Introduction to Decision Trees
  • Construction and Structure of Decision Trees
  • Algorithms for Constructing Decision Trees
  • Classification and Regression with Decision Trees
  • Evaluation and Interpretation of Decision Trees
  • Use Cases and Practical Examples
  • Advantages and Disadvantages of Decision Trees
  • Summary and Outlook
  • Introduction to Random Forests
  • Structure and Functionality of Random Forests
  • Ensemble Learning Techniques and Bagging
  • Decision Tree Algorithms for Constructing Random Forests
  • Feature Selection and Variation in Random Forests
  • Classification and Regression with Random Forests
  • Evaluation and Interpretation of Random Forests
  • Use Cases and Practical Examples
  • Advantages and Disadvantages of Random Forests
  • Summary and Outlook
  • Introduction to Gradient Boosting
  • Fundamentals of the Boosting Method
  • Gradient Boosting: Concept and Operation
  • Gradient Boosting Trees: Construction and Optimization
  • Hyperparameter Tuning in Gradient Boosting
  • Gradient Boosting for Classification
  • Gradient Boosting for Regression
  • Evaluation and Interpretation of Gradient Boosting Models
  • Use Cases and Practical Examples
  • Advantages and Disadvantages of Gradient Boosting
  • Summary and Outlook
  • Introduction to Neural Networks
  • Structure and Operation of Neural Networks
  • Activation Functions and Weight Initialization
  • Forward Propagation and Backward Propagation
  • Architectures of Neural Networks: Feedforward, Convolutional, Recurrent
  • Training Methods for Neural Networks
  • Optimization and Regularization of Neural Networks
  • Evaluation and Interpretation of Neural Networks
  • Use Cases and Practical Examples
  • Advantages and Disadvantages of Neural Networks
  • Summary and Outlook
  • Introduction to Logistic Regression
  • Fundamental Principles of Logistic Regression
  • Logit Function and Sigmoid Function
  • Maximum Likelihood Estimation and Model Fitting
  • Interpretation of Coefficients
  • Multivariate Logistic Regression
  • Diagnostics and Evaluation of Logistic Regression Models
  • Categorical Predictors and Interaction Effects
  • Model Improvement and Regularization Techniques
  • Use Cases and Practical Examples
  • Advantages and Disadvantages of Logistic Regression
  • Summary and Outlook
  • Introduction to Discriminant Analysis
  • Linear Discriminant Analysis (LDA)
  • Fundamentals of Linear Discriminant Function
  • Classification with Linear Discriminant Analysis
  • Quadratic Discriminant Analysis (QDA)
  • Fundamentals of Quadratic Discriminant Function
  • Classification with Quadratic Discriminant Analysis
  • Model Comparison and Selection Criteria
  • Diagnostics and Evaluation of Discriminant Analysis
  • Use Cases and Practical Examples
  • Advantages and Disadvantages of Discriminant Analysis
  • Summary and Outlook
  • Introduction to Support Vector Machine (SVM)
  • Fundamental Principles of SVM
  • Optimization of the Separating Hyperplane
  • Linearly Separable Data and Hard-Margin SVM
  • Soft-Margin SVM and C-Parameter
  • Kernel Trick and Nonlinear SVM
  • Selection of the Optimal Kernel
  • Classification with SVM
  • Regression with SVM
  • Parameter Optimization and Model Validation
  • Use Cases and Practical Examples
  • Advantages and Disadvantages of SVM
  • Summary and Outlook
Schedule a non-binding and complimentary initial consultation