Mathematik für Informatiker II
Probability Theory
Overview
Foundations of probability and statistical analysis
Learning Objectives
- Understand probability concepts
- Master random variables
- Work with probability distributions
- Apply statistical inference
- Analyze expected values and variance
Learning Resources
Probability and Statistics
MIT's probability course
MIT OCW
Statistics & Probability
Interactive probability lessons
Khan Academy
Probability Theory
Stanford's probability course
Stanford
Statistics 110
Harvard's probability course
Harvard
Visual Probability
Interactive probability visualizations
Seeing Theory
Probability Theory
ETH's probability materials
ETH Zürich
Probability
Interactive probability problems
Brilliant
Probability & Statistics
Free probability textbook
OpenStax
Statistics Fundamentals
Visual statistics explanations
StatQuest
Probability Tools
Probability visualization tools
GeoGebra
Practical Applications
Data Science
Statistical analysis of datasets
Example: Analyzing user behavior patterns
Machine Learning
Probabilistic models
Example: Building recommendation systems
Network Security
Risk assessment
Example: Analyzing security breach probabilities
Practice Problems
- Calculate probability distributions
- Analyze random variables
- Apply Bayes' theorem
- Compute confidence intervals
Numerical Methods
Overview
Computational techniques for mathematical problems
Learning Objectives
- Master numerical integration
- Understand error analysis
- Implement numerical algorithms
- Solve differential equations
- Apply optimization methods
Learning Resources
Numerical Methods
MIT's numerical methods course
MIT OCW
Scientific Computing
Python numerical methods
SciPy
Numerical Analysis
Comprehensive numerical methods
NPTEL
NumPy Documentation
Numerical computing library
NumPy
Scientific Computing
Stanford's numerical methods
Stanford
Computational Tools
Online computational platform
Wolfram Alpha
Numerical Recipes
Classic numerical methods text
Berkeley
Numerical Methods
Visual mathematics explanations
3Blue1Brown
Numerical Problems
Mathematical programming problems
Project Euler
Numerical Analysis
ETH's numerical analysis course
ETH Zürich
Practical Applications
Scientific Computing
Solving complex equations
Example: Simulating physical systems
Financial Analysis
Numerical optimization
Example: Portfolio optimization algorithms
Computer Graphics
Numerical algorithms
Example: 3D rendering calculations
Practice Problems
- Implement numerical integration methods
- Solve systems of linear equations
- Create optimization algorithms
- Develop differential equation solvers
Statistics for Computer Science
Overview
Statistical methods and their applications in computing
Learning Objectives
- Apply statistical testing
- Understand data analysis
- Master regression methods
- Work with sampling techniques
- Implement statistical algorithms
Learning Resources
CS109: Data Science
Harvard's data science course
Harvard
Statistics in Python
Interactive statistics practice
DataCamp
Statistical Learning
Stanford's statistics course
Stanford
Statistics Package
Statistical computing tools
SciPy Stats
Statistics for CS
Applied statistics tutorials
Towards Data Science
Think Stats
Statistics for programmers
Think Stats
Statistics for Applications
MIT's applied statistics
MIT OCW
Statistical Computing
R programming for statistics
R Studio
Statistical Analysis
Real-world statistics practice
Kaggle
Statistics and R
HarvardX statistics course
edX
Practical Applications
Machine Learning
Statistical learning models
Example: Building predictive models
A/B Testing
Statistical hypothesis testing
Example: Website conversion optimization
Data Analysis
Statistical inference
Example: User behavior analysis
Practice Problems
- Implement hypothesis tests
- Create regression models
- Analyze large datasets
- Build sampling algorithms