1st Principles
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Subject

Mathematics

Definitions, structure, and proof habits from numbers through calculus. Each chapter groups concepts you can read in any order once prerequisites are met.

105 sub-topics · use search below on large subjects

Topics

Algebra

Functions, equations, and the structure of expressions.

  • FunctionsMathematics · 22 min

    A rule that assigns exactly one output to each allowed input. Functions are the main way algebra names relationships you can graph, compose, and invert.

Calculus

Limits, rates of change, and accumulation.

No published concepts in this chapter yet.

Geometry and space

Shapes, measurement, and transformations at an introductory level.

No published concepts in this chapter yet.

Numbers and proof

What counts as a proof, and how integers and rationals behave.

No published concepts in this chapter yet.

Probability

Randomness, models, and expectation.

No published concepts in this chapter yet.

Application

Constraints in real jobs (Mathematics)

Constraints in real jobs as it applies to Mathematics.

Cost and benefit (Mathematics)

Cost and benefit as it applies to Mathematics.

Failure modes (Mathematics)

Failure modes as it applies to Mathematics.

Implementation steps (Mathematics)

Implementation steps as it applies to Mathematics.

Maintenance over time (Mathematics)

Maintenance over time as it applies to Mathematics.

Problem framing (Mathematics)

Problem framing as it applies to Mathematics.

Risk (Mathematics)

Risk as it applies to Mathematics.

Scaling up (Mathematics)

Scaling up as it applies to Mathematics.

Stakeholders (Mathematics)

Stakeholders as it applies to Mathematics.

Trade-offs (Mathematics)

Trade-offs as it applies to Mathematics.

Communication

Cross-disciplinary talk (Mathematics)

Cross-disciplinary talk as it applies to Mathematics.

Explaining to beginners (Mathematics)

Explaining to beginners as it applies to Mathematics.

Media coverage (Mathematics)

Media coverage as it applies to Mathematics.

Open questions (Mathematics)

Open questions as it applies to Mathematics.

Policy briefs (Mathematics)

Policy briefs as it applies to Mathematics.

Presentations (Mathematics)

Presentations as it applies to Mathematics.

Public controversy (Mathematics)

Public controversy as it applies to Mathematics.

Teaching others (Mathematics)

Teaching others as it applies to Mathematics.

Visuals that teach (Mathematics)

Visuals that teach as it applies to Mathematics.

Writing clear summaries (Mathematics)

Writing clear summaries as it applies to Mathematics.

Comparison

Analogies from other fields (Mathematics)

Analogies from other fields as it applies to Mathematics.

Common confusions (Mathematics)

Common confusions as it applies to Mathematics.

Competing models (Mathematics)

Competing models as it applies to Mathematics.

Consensus areas (Mathematics)

Consensus areas as it applies to Mathematics.

Debates that matter (Mathematics)

Debates that matter as it applies to Mathematics.

Historical shifts (Mathematics)

Historical shifts as it applies to Mathematics.

Interdisciplinary links (Mathematics)

Interdisciplinary links as it applies to Mathematics.

Regional differences (Mathematics)

Regional differences as it applies to Mathematics.

Schools of thought (Mathematics)

Schools of thought as it applies to Mathematics.

Translation of terms (Mathematics)

Translation of terms as it applies to Mathematics.

Context

Climate and environment (Mathematics)

Climate and environment as it applies to Mathematics.

Demographics (Mathematics)

Demographics as it applies to Mathematics.

Equity and access (Mathematics)

Equity and access as it applies to Mathematics.

Funding (Mathematics)

Funding as it applies to Mathematics.

Future scenarios (Mathematics)

Future scenarios as it applies to Mathematics.

Global trends (Mathematics)

Global trends as it applies to Mathematics.

Institutions (Mathematics)

Institutions as it applies to Mathematics.

Regulation (Mathematics)

Regulation as it applies to Mathematics.

Social impact (Mathematics)

Social impact as it applies to Mathematics.

Technology change (Mathematics)

Technology change as it applies to Mathematics.

Core ideas

Abstraction levels (Mathematics)

Abstraction levels as it applies to Mathematics.

Cause and correlation (Mathematics)

Cause and correlation as it applies to Mathematics.

Central definitions (Mathematics)

Central definitions as it applies to Mathematics.

Equilibrium and change (Mathematics)

Equilibrium and change as it applies to Mathematics.

Feedback loops (Mathematics)

Feedback loops as it applies to Mathematics.

Laws, rules, or patterns (Mathematics)

Laws, rules, or patterns as it applies to Mathematics.

Models and diagrams (Mathematics)

Models and diagrams as it applies to Mathematics.

Scale: micro to macro (Mathematics)

Scale: micro to macro as it applies to Mathematics.

Systems and parts (Mathematics)

Systems and parts as it applies to Mathematics.

Units and measurement (Mathematics)

Units and measurement as it applies to Mathematics.

Deep dives

Advanced preview (Mathematics)

Advanced preview as it applies to Mathematics.

Capstone directions (Mathematics)

Capstone directions as it applies to Mathematics.

Classic papers or texts (Mathematics)

Classic papers or texts as it applies to Mathematics.

Edge cases (Mathematics)

Edge cases as it applies to Mathematics.

Landmark discoveries (Mathematics)

Landmark discoveries as it applies to Mathematics.

Minority reports (Mathematics)

Minority reports as it applies to Mathematics.

Open research fronts (Mathematics)

Open research fronts as it applies to Mathematics.

Paradigm shifts (Mathematics)

Paradigm shifts as it applies to Mathematics.

Synthesis projects (Mathematics)

Synthesis projects as it applies to Mathematics.

Where to go next (Mathematics)

Where to go next as it applies to Mathematics.

Evidence

Anomalies (Mathematics)

Anomalies as it applies to Mathematics.

Bias and blind spots (Mathematics)

Bias and blind spots as it applies to Mathematics.

Case studies (Mathematics)

Case studies as it applies to Mathematics.

Conflicting studies (Mathematics)

Conflicting studies as it applies to Mathematics.

Data tables and charts (Mathematics)

Data tables and charts as it applies to Mathematics.

Primary sources (Mathematics)

Primary sources as it applies to Mathematics.

Secondary summaries (Mathematics)

Secondary summaries as it applies to Mathematics.

Strong versus weak claims (Mathematics)

Strong versus weak claims as it applies to Mathematics.

Triangulation (Mathematics)

Triangulation as it applies to Mathematics.

Uncertainty language (Mathematics)

Uncertainty language as it applies to Mathematics.

Methods

Documentation (Mathematics)

Documentation as it applies to Mathematics.

Estimation and error (Mathematics)

Estimation and error as it applies to Mathematics.

Ethics in method (Mathematics)

Ethics in method as it applies to Mathematics.

Experiments and controls (Mathematics)

Experiments and controls as it applies to Mathematics.

Observation protocols (Mathematics)

Observation protocols as it applies to Mathematics.

Peer review (Mathematics)

Peer review as it applies to Mathematics.

Replication (Mathematics)

Replication as it applies to Mathematics.

Reproducible workflows (Mathematics)

Reproducible workflows as it applies to Mathematics.

Simulation and models (Mathematics)

Simulation and models as it applies to Mathematics.

Surveys and samples (Mathematics)

Surveys and samples as it applies to Mathematics.

Orientation

Careers and roles (Mathematics)

Careers and roles as it applies to Mathematics.

Everyday examples (Mathematics)

Everyday examples as it applies to Mathematics.

History in one glance (Mathematics)

History in one glance as it applies to Mathematics.

How claims get checked (Mathematics)

How claims get checked as it applies to Mathematics.

Jargon worth learning first (Mathematics)

Jargon worth learning first as it applies to Mathematics.

Objects you study (Mathematics)

Objects you study as it applies to Mathematics.

Reading habits that stick (Mathematics)

Reading habits that stick as it applies to Mathematics.

Tools practitioners use (Mathematics)

Tools practitioners use as it applies to Mathematics.

What questions the field asks (Mathematics)

What questions the field asks as it applies to Mathematics.

What the field is not (Mathematics)

What the field is not as it applies to Mathematics.

Skills

Checklists (Mathematics)

Checklists as it applies to Mathematics.

Collaboration norms (Mathematics)

Collaboration norms as it applies to Mathematics.

Debugging mistakes (Mathematics)

Debugging mistakes as it applies to Mathematics.

Hands-on practice (Mathematics)

Hands-on practice as it applies to Mathematics.

Mentorship (Mathematics)

Mentorship as it applies to Mathematics.

Pattern recognition (Mathematics)

Pattern recognition as it applies to Mathematics.

Portfolio pieces (Mathematics)

Portfolio pieces as it applies to Mathematics.

Self-assessment (Mathematics)

Self-assessment as it applies to Mathematics.

Speed versus accuracy (Mathematics)

Speed versus accuracy as it applies to Mathematics.

Tooling basics (Mathematics)

Tooling basics as it applies to Mathematics.