Engineering↗
Exact Functors and Projective Modules
Handbook guide to exact functors and projective modules with core definitions, structural results, reasoning methods and verification checks.
Content type
Guides
Structured, multi-part guides that take a subject from first principles to applied practice. 2916 pages.
Engineering↗
Exact Sequences and Diagram Chasing
Handbook guide to exact sequences and diagram chasing with core definitions, structural results, reasoning methods and verification checks.
Engineering↗
Experiential Training and Workforce Capability
Engineering handbook for experiential training and workforce capability, covering context and scope, the framework: 5 steps that turn passive audiences into...
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Explicit Solvability Classes, Differential Fields and Extension Towers
Advanced handbook guide to defining explicit solvability by function classes, differential fields, extension towers, elementary functions and quadratures.
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Exponent Laws for Products, Quotients and Powers
Handbook guide to exponent laws for products, quotients and powers, with rules, worked examples, verification, common errors and practical engineering.
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Exponent Rules and Powers
Understand exponent notation and apply product, quotient and power rules accurately when simplifying algebraic expressions.
Engineering↗
Exponential Functions and Graphs
Handbook guide to exponential functions and graphs, with formulas, methods, worked examples, checks and engineering-oriented applications.
Engineering↗
Exponential Growth, Decay and Compound Interest Models
Handbook guide to exponential growth, decay and compound interest models, with formulas, methods, worked examples, checks and engineering-oriented applicat.
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Ext and Tor Calculations
Handbook guide to Ext and Tor Calculations, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.
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Extension and Torsion Functors with Group Cohomology
Handbook guide to extension and torsion functors with group cohomology, covering definitions, key results, methods, verification checks and worked examples.
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Factoring Polynomials
Handbook guide to factoring polynomials, with formulas, methods, worked examples, checks and engineering-oriented applications.
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Factoring Polynomials: GCF, Difference of Squares and Trinomials
Factor polynomials using greatest common factors, difference of two squares and basic trinomial patterns, with multiplication checks.
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Factoring Quadratic Trinomials
Handbook guide to factoring quadratic trinomials, with rules, worked examples, verification, common errors and practical engineering applications.
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Field Extensions
Handbook guide to Field Extensions, covering core definitions, key results, formulas, reasoning methods and worked examples in graduate abstract algebra.
Engineering↗
Field Extensions and Automorphism Correspondence
Handbook guide to field extensions and automorphism correspondence, covering definitions, key results, methods, verification checks and worked examples.
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Field Extensions, Minimal Polynomials and Extension Degree
Field Extensions, Minimal Polynomials and Extension Degree: core definitions, structural results and verification methods in abstract algebra.
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Fields, Polynomials and Polynomial Division
Guide to field axioms, polynomial arithmetic, roots, degree, division with remainder, irreducibility and the algebraic setting required for complex-root theory.
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Fields: Axioms, Subfields, Extensions and Isomorphisms
A field is a set with addition and multiplication satisfying the familiar arithmetic laws, including additive inverses and multiplicative inverses for every nonzero element. Thi…
Engineering↗
Files and Rotary Burs for Precision Metalwork
Engineering handbook for files and rotary burs for precision metalwork, covering the complete guide to files & burs: how to choose, use, and master every type...
Engineering↗
Finite Abelian Groups, Direct Sums and Structure Classification
Handbook guide to finite abelian groups, direct sums, with definitions, key results, methods, verification checks and worked examples.
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Finite Fields
Handbook guide to Finite Fields, covering core definitions, key results, formulas, reasoning methods and worked examples in graduate abstract algebra.
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Finite Fields, Characteristic and Algebraic Closure
Fields can be classified partly through characteristic and finite extensions. The source develops finite fields, adjoining polynomial roots, prime subfields and algebraic closure.
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Finite Group Representations, Characters and Orthogonality
Finite-group representations convert group elements into matrices. Characters compress matrix information into class functions and make irreducible decomposition computable thro…
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Finite Groups, Symmetry and Crystallography
Finite groups arise from permutations, polygon and polyhedron symmetries, lattice symmetries and reflections. Visual geometry makes abstract group operations concrete.
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Fixed Fields and Galois Groups
Handbook guide to Fixed Fields and Galois Groups, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.
Engineering↗
Fixed Fields, Galois Groups and the Galois Correspondence
Fixed Fields, Galois Groups and the Galois Correspondence: core definitions, structural results and verification methods in abstract algebra.
Engineering↗
Flat Modules
Handbook guide to Flat Modules, covering core definitions, key results, formulas, reasoning methods and worked examples in graduate abstract algebra.
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Flat Modules, Direct Limits and Inverse Limits
Handbook guide to flat modules, direct limits and inverse limits with core definitions, structural results, reasoning methods and verification checks.
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Flexible and Indented Geometry in 3D CAD
Engineering handbook for flexible and indented geometry in 3d cad, covering feature constraints & rules, core elements, trim planes.
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Fluid Dynamics: Conservation, Flow and Stability: /20 Summary
Engineering handbook for fluid dynamics: conservation, flow and stability, covering context and scope, /20 summary, foundations of fluid dynamics.
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Fluid Dynamics: Conservation, Flow and Stability: Petschek Reconnection
Engineering handbook for fluid dynamics: conservation, flow and stability, covering petschek reconnection, modern view (plasmoid instability), mhd instabilities.
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Formula-Based Linear Modelling and Unit Relations
Handbook guide to formula-based linear modelling and unit relations, with rules, worked examples, verification, common errors and practical engineering.
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Fraction Multiplication and Division
Handbook guide to fraction multiplication and division, with rules, worked examples, verification, common errors and practical engineering applications.
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Fractional Ideals
Handbook guide to Fractional Ideals, covering core definitions, key results, formulas, reasoning methods and worked examples in graduate abstract algebra.
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Fractional Inch, Decimal Inch and Millimetre Conversion: A Real Conversion Walkthrough
Engineering handbook for fractional inch, decimal inch and millimetre conversion, covering a real conversion walkthrough, the scenario, step-by-step solution.
Engineering↗
Fractional Inch, Decimal Inch and Millimetre Conversion: The Number That Almost Destroyed a Satellite
Engineering handbook for fractional inch, decimal inch and millimetre conversion, covering the number that almost destroyed a satellite: everything you need to...
Engineering↗
Fractions, Decimals and Percentages for Engineering Work: Advanced Concepts
Engineering handbook for fractions, decimals and percentages for engineering work, covering music, advanced concepts — for the curious and the bold, continued...
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Fractions, Decimals and Percentages for Engineering Work: The Grand Conversion Chart
Engineering handbook for fractions, decimals and percentages for engineering work, covering the grand conversion chart, mental math shortcuts for percentages,...
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Fractions, Decimals and Percentages for Engineering Work: THE WORLD OF NUMBERS
Engineering handbook for fractions, decimals and percentages for engineering work, covering context and scope, the world of numbers, what even *is* a number?.
Engineering↗
Free Groups, Presentations and Subgroup Structure
Handbook guide to free groups, presentations and subgroup structure, covering definitions, key results, methods, verification checks and worked examples.
Engineering↗
Free, Projective and Injective Modules
Handbook guide to free, projective and injective modules, covering definitions, key results, methods, verification checks and worked examples.
Engineering↗
Friction Brake Design and Selection
Engineering handbook for friction brake design and selection, covering the complete engineering guide to band brakes, block brakes, and the coefficient of...
Engineering↗
Function Behaviour, Piecewise Models and Extrema
Handbook guide to function behaviour, piecewise models and extrema, with formulas, methods, worked examples, checks and engineering-oriented applications.
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Function Germs, Several Variables and Generalised Quadratures
Advanced guide to algebraic functions of several variables, local germs, thin singular sets, closure operations and multi-variable topological obstructions.
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Function Rings, Direct Products and Boolean Rings
Commutative rings arise naturally from functions, direct products and set operations. These examples reveal why zero divisors and idempotent elements are structurally meaningful…
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Functions and Graphs
Handbook guide to functions and graphs, with formulas, methods, worked examples, checks and engineering-oriented applications.
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Functions Representable by Radicals
Precise handbook definition of radical-representable multi-valued functions and the branch-surface consequences of arithmetic, powers and root extraction.
Engineering↗
Functors and Natural Transformations
Handbook guide to Functors and Natural Transformations, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.