The Academic Sphere - Formal Knowledge & Disciplines

Structured learning across formal academic domains and research methodologies

Mathematics & Formal Sciences

Pure Mathematics

  • Algebra Foundational
  • Calculus & Analysis Foundational
  • Geometry & Topology Intermediate
  • Number Theory Advanced
  • Mathematical Logic Intermediate

Statistics & Probability

  • Descriptive Statistics Foundational
  • Probability Theory Foundational
  • Inferential Statistics Intermediate
  • Regression Analysis Intermediate
  • Bayesian Statistics Advanced

Computer Science & Technology

Computer Science Fundamentals

  • Data Structures Foundational
  • Algorithms & Complexity Foundational
  • Computer Architecture Intermediate
  • Operating Systems Intermediate
  • Computability Theory Advanced

Software Engineering

  • Software Design Patterns Intermediate
  • System Architecture Intermediate
  • Testing Methodologies Intermediate
  • DevOps & CI/CD Intermediate
  • Formal Methods Advanced

Artificial Intelligence

  • Machine Learning Intermediate
  • Neural Networks Intermediate
  • Natural Language Processing Advanced
  • Computer Vision Advanced
  • Reinforcement Learning Advanced

Natural Sciences

Physics

  • Classical Mechanics Foundational
  • Electromagnetism Foundational
  • Thermodynamics Intermediate
  • Quantum Mechanics Advanced
  • Relativity Advanced

Biology

  • Cell Biology Foundational
  • Genetics Foundational
  • Evolutionary Biology Intermediate
  • Ecology Intermediate
  • Molecular Biology Advanced

Chemistry

  • General Chemistry Foundational
  • Organic Chemistry Intermediate
  • Inorganic Chemistry Intermediate
  • Physical Chemistry Advanced
  • Biochemistry Advanced

Social Sciences

Psychology

  • Cognitive Psychology Foundational
  • Developmental Psychology Foundational
  • Social Psychology Intermediate
  • Clinical Psychology Advanced
  • Neuropsychology Advanced

Economics

  • Microeconomics Foundational
  • Macroeconomics Foundational
  • Behavioral Economics Intermediate
  • Game Theory Intermediate
  • Econometrics Advanced

Political Science

  • Political Theory Foundational
  • Comparative Politics Foundational
  • International Relations Intermediate
  • Public Policy Intermediate
  • Political Economy Advanced

Humanities

Philosophy

  • Ethics Foundational
  • Epistemology Foundational
  • Metaphysics Intermediate
  • Logic Intermediate
  • Philosophy of Mind Advanced

History

  • Ancient History Foundational
  • Medieval History Foundational
  • Modern History Intermediate
  • Historiography Advanced
  • Intellectual History Advanced

Literature

  • Literary Theory Foundational
  • Poetry Analysis Intermediate
  • Narrative Studies Intermediate
  • Comparative Literature Advanced
  • Critical Theory Advanced

Research Methodologies & Academic Skills

Scientific Method

Hypothesis formulation, experimentation, and validation

Qualitative Research

Interviews, ethnography, case studies, and content analysis

Quantitative Research

Surveys, experiments, statistical analysis, and modeling

Academic Writing

Structuring papers, citations, argumentation, and peer review

Critical Analysis

Evaluating sources, identifying biases, and logical reasoning

Literature Review

Systematic searching, synthesizing research, and identifying gaps