Reference Directory
Reference provides centralized support for definitions, notation, laws, formulas, methods, examples, history, connections, and navigation throughout Malone Math. Resources are grouped below by category.
Categories
6.1 Mathematical Terminology
6.2 Symbols and Notation
- Symbols and Notation Directory
- Arithmetic and Algebraic Symbols
- Logic and Set Notation
- Function and Mapping Notation
- Geometric and Trigonometric Notation
- Calculus and Analysis Notation
- Probability and Statistical Notation
- Vector and Matrix Notation
- Discrete and Computational Notation
- Pronunciation and Spoken Forms
- Context-Dependent Meanings
6.3 Numbers, Constants, and Special Values
6.4 Properties, Laws, and Principles
6.5 Axioms, Postulates, Theorems, and Proofs
6.6 Formula Library
- Formula Library
- Arithmetic and Algebra Formulas
- Geometry and Measurement Formulas
- Trigonometric Identities
- Coordinate and Vector Formulas
- Probability and Statistics Formulas
- Calculus and Differential-Equation Formulas
- Financial and Applied Formulas
- Conditions, Variables, and Units
- Derivations and Applications
6.7 Methods, Algorithms, and Procedures
6.8 Tables and Conversions
- Tables and Conversions Directory
- Unit Conversions
- Fraction, Decimal, and Percentage Tables
- Powers, Roots, and Logarithms
- Trigonometric Values
- Probability Distribution Tables
- Statistical Critical Values
- Mathematical Constants
- Coordinate and Transformation Tables
- Prefixes, Orders of Magnitude, and Numerical Forms
6.9 Visual Reference Library
- Visual Reference Library
- Number-Line Diagrams
- Coordinate and Function Graphs
- Geometric Figures
- Transformation Diagrams
- Unit-Circle and Trigonometric Charts
- Vector and Matrix Diagrams
- Probability Trees and Distributions
- Graphs, Networks, and Flow Diagrams
- Calculus and Field Visualizations
- Infographics and Concept Maps
6.10 Function and Curve Catalog
- Function and Curve Catalog
- Constant, Linear, and Affine Functions
- Polynomial and Power Functions
- Rational and Radical Functions
- Exponential and Logarithmic Functions
- Trigonometric and Inverse Trigonometric Functions
- Piecewise and Step Functions
- Parametric and Polar Curves
- Conic Sections
- Special Functions
- Domains, Ranges, Transformations, and Characteristic Behavior
6.11 Problem-Type Index
- Problem-Type Index
- Equation and Inequality Problems
- Ratio, Proportion, and Percentage Problems
- Motion, Work-Rate, and Mixture Problems
- Geometry and Measurement Problems
- Counting and Arrangement Problems
- Probability and Statistics Problems
- Growth, Decay, and Financial Problems
- Optimization Problems
- Modeling and Approximation Problems
- Method-Selection Diagnostics
6.12 Worked-Example Library
- Worked-Example Library
- Foundational Calculations
- Algebraic Transformations and Solutions
- Geometric Reasoning
- Discrete Counting and Proof
- Probability and Statistical Inference
- Calculus and Analysis
- Matrix and Vector Methods
- Numerical Approximation
- Modeling and Optimization
- Multiple-Solution Comparisons and Verification
6.13 Errors, Misconceptions, and Diagnostic Checks
- Errors and Diagnostics Directory
- Undefined Operations
- Sign and Order-of-Operations Errors
- Invalid Cancellation
- Misused Properties and Identities
- Domain Restrictions
- Extraneous and Missing Solutions
- Diagram and Scale Misinterpretation
- Probability and Statistical Misconceptions
- Numerical and Rounding Errors
- Verification Checklists
6.14 History of Mathematics
- History of Mathematics Directory
- Historical Timelines
- Development of Number and Notation
- Algebraic and Geometric Traditions
- Calculus and Analysis
- Probability and Statistics
- Computation and Modern Mathematics
- Contributions across Civilizations
- Historical Problems and Methods
- Institutions and Mathematical Communities
- Primary and Secondary Sources
6.15 Mathematical Figures
- Mathematical Figures Directory
- Mathematician Biographies
- Major Contributions
- Historical Context
- Collaborators, Teachers, and Students
- Institutions and Schools of Thought
- Publications and Discoveries
- Controversies and Attribution
- Influence on Later Mathematics
- Timelines
- Associated Concepts and Theorems
6.16 Branches and Applications of Mathematics
- Branches and Applications Directory
- Foundations and Logic
- Algebra and Number Theory
- Geometry and Topology
- Discrete Mathematics and Computation
- Probability and Statistics
- Analysis and Calculus
- Applied and Computational Mathematics
- Mathematical Physics
- Economics, Engineering, Biology, and Data Science
- Interbranch Connections
6.17 Technology and Computational Reference
6.18 Cross-References and Concept Maps
- Cross-References and Concept Maps Directory
- Prerequisite Maps
- Related-Concept Networks
- Representation Maps
- Tool-Progression Matrices
- Logic and Proof Progression
- Function-Family Relationships
- Algebra–Geometry Connections
- Discrete–Probability Connections
- Modeling Dependencies
- Introductory Use to Formal Theory