Ultraproducts and Jonsson's Lemma
Ultraproducts in the algebraic setting, congruence-distributive varieties, Jónsson's lemma and its proof strategy, and the consequences for finitely generated varieties.
Engineering articles and subject areas in the KEVOS knowledge library. 2189 pages.
Ultraproducts in the algebraic setting, congruence-distributive varieties, Jónsson's lemma and its proof strategy, and the consequences for finitely generated varieties.
Ultraproducts as reduced products over an ultrafilter, Łoś's theorem and its proof, ultrapowers and the elementary embedding, and the applications to compactness and non-standar…
The sourcing policy for this collection: what is written here, what is deliberately not transcribed, the reasoning behind the split, and where to obtain current computational re…
Structural overview of universal algebra: what an algebra of arbitrary type is, why congruences rather than substructures carry the quotient theory, how Birkhoff's two theorems …
The universal coefficient theorems for homology and cohomology, the Ext and Tor correction terms, naturality and splitting, and the dual Kunneth formula.
The Yoneda description of Ext^n by n-fold extensions, the equivalence relation, splicing as composition, and the Yoneda product.
Assembly modelling in parametric CAD: standard, mechanical and advanced mates, bottom-up versus top-down approaches, the assembly tree, exploded views, interference and collisio…
The analysis capabilities built on a CAD model: neutral file data exchange, mass property calculation, motion analysis, flow simulation, the finite element method, and interpret…
How CAD models move between systems: native versus neutral formats, STEP IGES and the de facto standards, export and import translators, why translation loses data, healing impo…
The conceptual base of parametric CAD: the four model types, solid model topology and the Euler-Poincare relation, parametric modelling, sketch relations, patterns and Boolean o…
The mathematics of curves in CAD: analytic versus synthetic families, explicit and parametric representation, the tangent vector and why it matters for mass properties and NC pr…
What design intent means in parametric CAD, how it is captured through modelling plans, relations, equations and mates, and how to document it so that models survive change and …
How engineering drawings are generated from CAD models: ASME drafting and dimensioning rules, first and third angle projection, view types, sheets, title blocks, bills of materi…
Tolerancing from first principles: sources of variability, nominal basic and actual size, the four ways to express a tolerance, standard fits, tolerance accumulation, statistica…
The full feature set of a parametric modeller beyond extrude and revolve — sweep, loft, hole wizard, rib, draft, shell and dome — plus design libraries, configurations, design t…
Injection moulding for designers: the machine, the four-stage cycle, mould classification, core and cavity, part design guidelines including wall thickness draft ribs and bosses…
Numerical control machining from a design perspective: machine tool anatomy, motion axes and cutting parameters, turning, drilling, milling and EDM, design for manufacture rule …
How rapid prototyping turns a CAD model into a physical part: the RP process chain, triangulation and STL resolution, build orientation, layer thickness, support structures, the…
How CAD rendering works: scenes and light types, the reflection model, decals, textures, materials versus appearances, transparency, camera sleds and key-frame animation.
Specialised modelling for sheet metal and welded structures: gauge and bend allowance, the K-factor, flange types, flat pattern generation, the four sheet metal creation methods…
The sketching layer of parametric CAD in detail: model and working coordinate systems, sketch planes, the three sketch states, sketch entities, relations, equations and link val…
An engineering-led overview of the SOLIDWORKS Design Approach series: treating CAD as a design system rather than a menu structure, and the eighteen-part pathway from first prin…
How SOLIDWORKS certification works and how to prepare for it: exam structure, the associate and professional levels, discipline-specific certificates, a mapping of exam topics t…
Surface modelling for free-form parts: what a surface is, the available surface types and their inputs, parametric surface representation, curvature visualisation, and the three…
Sustainable design as an engineering discipline: design guidelines, the product life cycle, life cycle assessment, the four core environmental impact factors, ISO framework stan…
How the engineering design process, the CAD process, the manufacturing process and the CAM process nest together, and what each one contributes between an idea and a finished en…
Orientation to the CAD working environment: the three panes and the modes they serve, system options versus document properties, customisation and productivity tools, templates …
Five milestones that removed the distance limit on electricity supply, decided a commercial contest fought partly by public smear, and ended in the two systems being combined ra…
Three milestones that turned living systems into a manufacturing platform, made the instructions programmable, and compressed the development timeline to months.
Between 1899 and 1910 the living body became an object of measurement, controlled energy delivery and remote manipulation. How each of those three problems was actually solved.
Designing bolted joints in tension, shear, gasketed pressure joints and combined loading: stress area, preload stress, assembly torque, bearing on the plate and shank against th…
Two machines that move in opposite directions and solve the same problem: making ground and height usable without disturbing what is already there.
Four milestones in spanning a gap and standing up, using materials strong in compression and nearly useless in tension.
Four milestones in which building height stopped being limited by structure and started being limited by economics.
Industrial ammonia synthesis resolved a direct conflict between thermodynamics and kinetics, and in doing so established catalysis, high pressure, recycle and continuous operati…
Three milestones in which software became the thing keeping a machine stable, and one standard written because that made software a structural safety concern.
Three milestones in which an engine was designed from a thermodynamic argument rather than developed from an existing machine, and immediately outperformed everything else.
Two recent milestones included for their engineering content rather than settled historical weight: computing became a utility, and pattern recognition became a matter of scale.
Setting up a .NET project against the SOLIDWORKS interop assemblies, attaching to a running session, starting one when none exists, casting rules, and COM object lifetime discip…
Producing detail drawings in CAD — absolute, relative and polar coordinate entry; the template and layer standard; dimension styles set to AS 1100; the model-space insertion-sca…
Selecting three phase and single phase squirrel cage motors: frame size, pole count and synchronous speed, slip and design-load speed, part-load efficiency, IP protection and ra…
Three milestones in which electricity moved into railway traction, and in which the alternating-versus-direct argument was fought again under different constraints.
Four milestones in the institutional answer to applied science: if engineering rests on theory, apprenticeship alone can no longer produce an engineer.
Three milestones within two years, none of which invented a device. Each fixed an interface or made a hidden structure explicit, and each generated more value than most inventio…
The guard preamble every SOLIDWORKS tool needs, batch export of every drawing sheet to DXF, save options and error codes, reading document information, and the system-units trap.
The moving line made work flow at a fixed cycle; the control chart made process variation intelligible. Together they define how physical goods have been made ever since.
Three milestones united by fluid mechanics: a machine that generates lift to fly, a rig that generates lift to outrun the wind, and a cycle that moves heat against its gradient.
Nine milestones over a century and a half, at the end of which a complete engineering discipline could be built from results none of whose discoverers were engineers.