Engineering↗
Functors, Natural Transformations and Adjunctions
Handbook guide to functors, natural transformations and adjunctions, covering definitions, key results, methods, verification checks and worked examples.
Content type
Guides
Structured, multi-part guides that take a subject from first principles to applied practice. 2916 pages.
Engineering↗
Fundamental Structure Theorems for Modules
Handbook guide to Fundamental Structure Theorems for Modules, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.
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Fundamental Theorem of Algebra via Winding
Topological proof strategy showing that every non-constant polynomial with complex coefficients has a complex root, using images of circles and winding number.
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Fundamental Theorem of Galois Theory
Handbook guide to Fundamental Theorem of Galois Theory, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.
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Galois Group of a Cubic
Handbook guide to Galois Group of a Cubic, covering core definitions, key results, formulas, reasoning methods and worked examples in graduate abstract algebra.
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Galois Theory and Differential Galois Theory
Galois theory studies equations through symmetry groups of field extensions. The differential analogue replaces algebraic equations by linear differential equations and field au…
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Gear Geometry, Types, Rating and Selection: Gear Terminology
Engineering handbook for gear geometry, types, rating and selection, covering gear terminology: the language you must speak, the two pitch systems: diametral...
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Gear Geometry, Types, Rating and Selection: Making the Pinion Harder Than the Gear
Engineering handbook for gear geometry, types, rating and selection, covering making the pinion harder than the gear, case-hardening steels reference,...
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Gear Geometry, Types, Rating and Selection: The Language of Gears
Engineering handbook for gear geometry, types, rating and selection, covering context and scope, the language of gears: definitions that unlock everything, the...
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Gear Geometry, Types, Rating and Selection: The Pitch Systems
Engineering handbook for gear geometry, types, rating and selection, covering the pitch systems: diametral, circular, and module, how pitch determines...
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Gear Geometry, Types, Rating and Selection: Thrust (Axial) Load
Engineering handbook for gear geometry, types, rating and selection, covering thrust (axial) load, motor selection method (three-phase), worked example — motor...
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Gearboxes and Geared Motors: Selection and Integration: Coupling Selection Decision Tree
Engineering handbook for gearboxes and geared motors: selection and integration, covering coupling selection decision tree, power transmission system overview,...
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Gearboxes and Geared Motors: Selection and Integration: Mechanical Design Reference
Engineering handbook for gearboxes and geared motors: selection and integration, covering mechanical design reference, . coupling types, pin-type flexible...
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Gearboxes and Geared Motors: Selection and Integration: Mistake #4
Engineering handbook for gearboxes and geared motors: selection and integration, covering mistake #4: not checking physical dimensions, mistake #5: using...
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Gearboxes and Geared Motors: Selection and Integration: Single vs. Double Reduction
Engineering handbook for gearboxes and geared motors: selection and integration, covering single vs. double reduction: when one stage isn't enough, boosting...
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Gearboxes and Geared Motors: Selection and Integration: The Full Motor Power Range at a Glance
Engineering handbook for gearboxes and geared motors: selection and integration, covering the full motor power range at a glance, engineering takeaway, your next...
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Gearboxes and Geared Motors: Selection and Integration: Worm Gearbox Operating Parameter Relationships
Engineering handbook for gearboxes and geared motors: selection and integration, covering worm gearbox operating parameter relationships, overhung load...
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Gemba Observation and Work-Study Practice
Engineering handbook for gemba observation and work-study practice, covering context and scope, current-state problem, technical challenge.
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General Relativity: Geometry, Fields and Applications: /20 Summary
Engineering handbook for general relativity: geometry, fields and applications, covering context and scope, /20 summary, from special to general relativity.
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General Relativity: Geometry, Fields and Applications: Distance Measures
Engineering handbook for general relativity: geometry, fields and applications, covering distance measures, the cmb, big bang nucleosynthesis.
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General Tensor Products
Handbook guide to General Tensor Products, covering core definitions, key results, formulas, reasoning methods and worked examples in graduate abstract algebra.
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Generators and Relations
Handbook guide to Generators and Relations, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.
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Generic Quintic Root Functions and Radical Impossibility
Complete source-based proof architecture for the generic degree-five radical impossibility result using a one-parameter polynomial family, branch points, transpositions and non-…
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Geometric and Wave Optics: /20 Summary
Engineering handbook for geometric and wave optics, covering context and scope, /20 summary, geometric optics & the eikonal approximation.
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Geometric and Wave Optics: Final Takeaways
Engineering handbook for geometric and wave optics, covering troubleshooting, cheatsheet, glossary with practical methods, verification checks and source-controlled examples.
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Geometric Sequences and Series
Handbook guide to geometric sequences and series, with formulas, methods, worked examples, checks and engineering-oriented applications.
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Global Dimension and Regular Local Rings
Handbook guide to global dimension and regular local rings, covering definitions, key results, methods, verification checks and worked examples.
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Graded, Tensor and Exterior Algebras
Handbook guide to graded, tensor and exterior algebras, covering definitions, key results, methods, verification checks and worked examples.
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Graphing Linear Equations with Slope and Intercepts
Graph linear equations using slope-intercept form, rise over run, y-intercepts and transformations from standard form.
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Graphing Linear Inequalities in Two Variables
Graph two-variable linear inequalities using boundary lines, solid or dashed styles, test points and shaded solution regions.
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Graphing One-Variable Inequalities on a Number Line
Represent one-variable inequality solution sets with open or closed endpoints, directional rays and interval interpretation.
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Graphing Polynomial Functions
Handbook guide to graphing polynomial functions, with formulas, methods, worked examples, checks and engineering-oriented applications.
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Graphing Systems of Linear Equations and Inequalities
Solve systems graphically by interpreting intersections, coincident lines, parallel lines and overlapping inequality regions.
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Greatest Common Factor and Factoring by Grouping
Handbook guide to greatest common factor and factoring by grouping, with rules, worked examples, verification, common errors and practical engineering.
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Green BIM for Sustainable Design and Performance Analysis: Building Orientation
Engineering handbook for green bim for sustainable design and performance analysis, covering step 3: reduce resource consumption (the most important step),...
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Green BIM for Sustainable Design and Performance Analysis: The Ordinary World
Engineering handbook for green bim for sustainable design and performance analysis, covering the ordinary world — how we got here, the silent crisis nobody...
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Green BIM for Sustainable Design and Performance Analysis: Wind Energy Assessment
Engineering handbook for green bim for sustainable design and performance analysis, covering wind energy assessment, sustainable materials and lifecycle...
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Green Building Design, Materials and Performance: Energy Benchmarks in the supplied reference and System
Engineering handbook for green building design, materials and performance, covering energy benchmarks in the supplied reference and system, primary energy: the...
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Green Building Design, Materials and Performance: Improvement method and result
Engineering handbook for green building design, materials and performance, covering context and scope, current-state problem, improvement method and result.
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Green Building Design, Materials and Performance: Lead Roofing
Engineering handbook for green building design, materials and performance, covering lead roofing: the environmental paradox, thatch and green roofs: the living...
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Green Building Design, Materials and Performance: Renewable Energy
Engineering handbook for green building design, materials and performance, covering renewable energy: a quick-reference decision framework, the wood-burning...
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Green Building Design, Materials and Performance: The Moment of Truth
Engineering handbook for green building design, materials and performance, covering the moment of truth — commissioning and verification, why commissioning...
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Group Actions in Combinatorics
Handbook guide to group actions in combinatorics with core definitions, structural results, reasoning methods and verification checks.
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Group Actions, Orbits and Stabilisers
Handbook guide to group actions, orbits and stabilisers with core definitions, structural results, reasoning methods and verification checks.
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Group Actions, Orbits, Stabilisers and Counting
Handbook guide to group actions, orbits, stabilisers and counting, covering definitions, key results, methods, verification checks and worked examples.
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Group Applications: Coverings, Invariants and Symmetry Classification
Groups organise covering spaces, invariant functions and symmetry-based classification. These applications show how a group can be both an object of study and a tool for structu…
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Group Axioms, Subgroups and Cyclic Structure
Handbook guide to group axioms, subgroups and cyclic structure, covering definitions, key results, methods, verification checks and worked examples.
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Group Homomorphisms and Isomorphism Principles
Handbook guide to group homomorphisms and isomorphism principles, covering definitions, key results, methods, verification checks and worked examples.