Prerequisites for Data Science

Mathematical Foundation Requirements

What you Need to Know
- Statistics and Probability Fundamentals
  - Descriptive statistics (mean, median, mode, standard deviation)
  - Probability distributions and random variables
  - Hypothesis testing and statistical inference
  - Resources:
    - Statistics and Probability - Khan Academy - Complete statistics course
    - Think Stats - Free statistics book with Python examples
    - Statistics Course - Coursera - Stanford University (Free audit)
- Linear Algebra Basics
  - Vectors, matrices, and basic operations
  - Matrix multiplication and transformations
  - Eigenvalues and eigenvectors concepts
  - Resources:
    - Linear Algebra - Khan Academy - Interactive linear algebra course
    - 3Blue1Brown Linear Algebra - Visual linear algebra explanations
    - MIT Linear Algebra - MIT OpenCourseWare
- Calculus and Mathematical Analysis
  - Derivatives and optimization concepts
  - Basic understanding of functions and graphs
  - Mathematical reasoning and proof techniques
  - Resources:
    - Calculus - Khan Academy - Single variable calculus
    - MIT Calculus Course - MIT calculus course
    - Mathematical Thinking - Stanford mathematical reasoning

What you Need to Know
- Python Programming Fundamentals
  - Variables, data types, and control structures
  - Functions, modules, and object-oriented programming
  - Error handling and debugging techniques
  - Resources:
    - Python for Everybody - Coursera - University of Michigan (Free audit)
    - Python.org Official Tutorial - Complete Python language tutorial
    - Automate the Boring Stuff with Python - Practical Python programming
- Data Manipulation Libraries
  - NumPy for numerical computing
  - Pandas for data manipulation and analysis
  - Basic understanding of data structures
  - Resources:
    - NumPy Quickstart - NumPy fundamentals
    - Pandas Getting Started - Pandas tutorial
    - Python Data Science Handbook - Comprehensive data science guide
- Development Environment Setup
  - Jupyter notebooks and interactive development
  - Package management with pip and conda
  - Version control with Git basics
  - Resources:
    - Jupyter Notebook Tutorial - Interactive development environment
    - Conda User Guide - Package and environment management
    - Git Tutorial - Atlassian - Version control basics

What you Need to Know
- Scientific Method and Research Design
  - Hypothesis formulation and testing
  - Experimental design and controls
  - Data collection and sampling methods
  - Resources:
    - Research Methods - Coursera - University of London research methodology
    - Experimental Design - Khan Academy experimental design
    - Scientific Thinking - University of Alberta scientific reasoning
- Critical Thinking and Problem Solving
  - Logical reasoning and argument evaluation
  - Cognitive biases and statistical fallacies
  - Evidence-based decision making
  - Resources:
    - Critical Thinking - Coursera - University of Edinburgh (Free audit)
    - Cognitive Biases - Duke University behavioral economics
    - Statistical Fallacies - Common statistical errors

What you Need to Know
- Business Fundamentals
  - Understanding of basic business operations
  - Key performance indicators (KPIs) and metrics
  - Business problem identification and framing
  - Resources:
    - Business Foundations - Coursera - University of Pennsylvania business fundamentals
    - Business Analytics Basics - Business analytics introduction
    - KPI Development - Key performance indicator design
- Data-Driven Decision Making
  - Translating business questions into data problems
  - Communicating insights to stakeholders
  - Understanding data limitations and assumptions
  - Resources:
    - Data-Driven Decision Making - University of Virginia decision science
    - Business Intelligence Fundamentals - BI concepts and applications
    - Storytelling with Data - Data communication techniques

What you Need to Know
- Data Storytelling and Presentation
  - Creating compelling narratives from data
  - Audience-appropriate communication strategies
  - Visual design principles for data presentation
  - Resources:
    - Data Storytelling - Tableau data storytelling guide
    - Presentation Skills - University of Washington public speaking
    - Visual Design Principles - Design fundamentals
- Technical Writing and Documentation
  - Writing clear technical reports and analysis
  - Documenting methodology and assumptions
  - Creating reproducible research documentation
  - Resources:
    - Technical Writing - Google - Professional technical writing course
    - Scientific Writing - Stanford scientific writing course
    - Data Science Documentation - Project documentation templates

What you Need to Know
- Technical Skills Validation
  - Perform basic statistical analysis on a dataset
  - Create simple data visualizations
  - Write Python scripts for data manipulation
  - Conduct hypothesis testing and interpret results
  - Resources:
    - Kaggle Learn - Free micro-courses with hands-on practice
    - Google Colab - Free cloud-based data science environment
    - UCI ML Repository - Practice datasets
- Analytical and Research Skills
  - Formulate research questions from business problems
  - Design experiments and identify appropriate methodologies
  - Interpret results and communicate findings clearly
  - Evaluate data quality and identify limitations
  - Resources:
    - Data Science Case Studies - Real-world problem solving
    - Research Design - Research methodology courses
    - Statistical Consulting - Penn State statistical consulting

What you Need to Know
- For Mathematics/Statistics Backgrounds
  - Focus on programming and data manipulation (6-8 weeks)
  - Learn business context and domain applications
  - Practice with real-world datasets and projects
  - Resources:
    - Python for Data Analysis - Pandas creator's comprehensive guide
    - Data Science for Business - Business applications of data science
    - Industry Case Studies - Social impact data science
- For Programming Backgrounds
  - Focus on statistics and mathematical foundations (8-12 weeks)
  - Learn domain expertise and business applications
  - Practice statistical analysis and hypothesis testing
  - Resources:
    - Statistical Learning - Introduction to Statistical Learning (free book)
    - Statistics for Programmers - Duke University Bayesian statistics
    - Applied Statistics - Penn State applied statistics
- For Complete Beginners
  - Complete foundational learning in all areas (16-24 weeks)
  - Start with mathematics and programming simultaneously
  - Build projects incrementally while learning theory
  - Resources:
    - Data Science Foundations - Harvard Data Science Certificate
    - Mathematics for Data Science - Complete mathematics curriculum
    - Programming Fundamentals - University of Michigan Python specialization

Ready to Begin? Once you've completed these prerequisites, start with Module 1: Statistics and Mathematics to begin your Data Science journey.