Collection
Tables, keys, joins, groups and subqueries you can touch: how a database really reads.
Apps
The practice database prodat as a pot full of tables: relation, attribute and tuple on the table tools, a relation as a subset of name × tag after Codd, keys as joints (products.tool → tools.id, NULL), plus 100 million rows: a full scan against a B-tree index and an SQL sentence next to a loop.
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Every row of tools is a flat, id its key: unique and never empty, otherwise UNIQUE or NOT NULL constraint failed. products.tool points into the other table as a foreign key, key 2 opens the door to beta for round. When the workshop deletes tool 2, two references point into nothing like a dead link; with a declared foreign key the database refuses: FOREIGN KEY constraint failed.
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WHERE as a sieve: the tools table from the lecture is checked row by row, matches move into the result, the rest drops out. The quote trap tag = A shows 'no such column: A', plus price/weight calculated row by row, as and order by … desc with rows visibly changing places.
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Written SELECT … ORDER BY, executed FROM → WHERE → GROUP BY → HAVING → SELECT → ORDER BY: the clauses jump into execution order and the tools table runs station by station along the line (rows, groups, group values, alias). Plus the typical mistakes alias in WHERE and group condition in WHERE.
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Aggregate the tools table with avg, sum, min, max and count, sort rows into bins with GROUP BY, filter rows with WHERE and whole groups with HAVING, step by step in execution order.
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Joins and groups on the practice database prodat: tools join products first forms all 9 combinations, on boils them down to 3 (with ambiguous column name and comma + where). customers × orders gives 23 · 184 = 4232 rows, 184 after on. group by order_id turns them into 80 baskets, sum(quantity) counts the items, having keeps 45. Plus: an order as a line or as a basket, monster table versus separate tables, deletion and foreign keys.
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Five flashlights on the practice database prodat: 17 of 46 deliveries without a value, sum(days)/count(*) = 12 versus avg(days) = 20.55; table aliases c and o that vanish after the statement, and the same statement with join and on; union as the set union {1, 2, 3} ∪ {1, 3, 5} and on X and Y (7 values, union all 10); the customers from Hamburg as a subquery in where (2 customer IDs, 4 order lines, equal to the join) and a subquery in from named T.
Computer scienceTry itCollections
Planning and steering projects: the iron triangle, stakeholders, network diagrams, earned value, schedule risk, team size, Kanban and waterfall against Scrum.
8 appsOpen collection
From sequences to loans: arithmetic and geometric growth, savings plans, annuities, compounding within the year and perpetuities.
11 appsOpen collection
Reading the traces: burial mounds in section, radiocarbon dating, settlements in the landscape and the tomb of Tutankhamun.
5 appsOpen collection
Why robot arms are heavy, how six axes guide a hand and how control holds the load.
4 appsOpen collection
Generative AI in strong images: what it can do, how it writes, why it convinces, how to use it well and where to take care.
7 appsOpen collection
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9 appsOpen collection
Heat in the city centre: heat islands, shade, trees and unsealing, using the old town of Reutlingen as an example.
5 appsOpen collection
Reading the small print, spotting subscription traps, placing risk figures and making texts understandable.
4 appsOpen collection
From equation to curve: initial values, linear equations, substitution and the worlds in which they apply.
7 appsOpen collection
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9 appsOpen collection
From coordinates to the inverse: vectors, dot and cross products, linear equations and matrices in pictures.
12 appsOpen collection
Production principles, waste, one-piece flow, value streams, bills of materials and routing: how a factory is organised.
6 appsOpen collection
What the CRA requires of manufacturers: checking whether it applies, meeting reporting deadlines, keeping software bills of materials.
5 appsOpen collection
Reducing, common denominators, multiplying, dividing and mixed numbers: fractions step by step.
7 appsOpen collection
Proofs of special beauty to touch: Zagier's windmills, the museum guards and Buffon's needle.
3 appsOpen collection
How oscillations break down: coefficients, symmetry, phasor chains, the Gibbs phenomenon and the plucked string.
7 appsOpen collection
What happens inside the machine: objects, methods, operators, slicing and sorting in Python, visible step by step.
9 appsOpen collection
From the Patent Motor Car to the Z3: famous machines and experiments cut open in 3D.
11 appsOpen collection
Keyboard, intervals, scales, chords, the circle of fifths and groove: music theory you hear and play.
9 appsOpen collection
How sound is made and shaped: synthesizers and samplers, envelopes and overtones, waveforms and timbre, voice and orchestra, room acoustics and sound scenography — all audible in your browser.
16 appsOpen collection
Staging space, sight, light, sound and paths: visitor flows, showcase lighting, room acoustics, sound islands, projection mapping and the pavilions of world expos to try out.
15 appsOpen collection
Mathematical questions open for decades, for which an AI model proposed solutions in 2026, as interactive apps: understand the problem, experience the result.
32 appsOpen collection
From neurons and gradients to transformers, RLHF and agents: machine learning you can touch.
44 appsOpen collection
DNA, replication, transcription, translation and cell division as explorable 3D models.
24 appsOpen collection
Perspective, ornament, structure and space: how art and architecture work with mathematics.
21 appsOpen collection
Hyperloop, autonomous vehicles, warehouses and conveyors: logistics as interactive simulation.
17 appsOpen collection
Heart, eye, voice, skeleton and nerves: the human body in 3D, layer by layer.
10 appsOpen collection
Monty Hall, Simpson, Berkson and base rates: where intuition fails us with numbers.
14 appsOpen collection
Planets, stars, black holes and space probes: the cosmos to explore.
10 appsOpen collection
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8 appsOpen collection
Planted participants, smoke in the room, one dollar for a lie and experimenters who are themselves the subjects: famous social psychology experiments to try yourself.
5 appsOpen collection
Relations, classes, orders, bijections, different infinities and topology: mathematics as the science of structure, hands-on.
11 appsOpen collection
Riemann, P vs NP, Poincaré and other great questions of mathematics, made tangible.
16 appsOpen collection
Counting, arithmetic and shapes: maths for beginners, playful and clear.
6 appsOpen collectionWant to use these apps in your courses? Let’s find out what works for you.
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