seed: example course content

COURSE.md

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+---
+id: calculus-it-ale-example
+title: "Basic Calculus for IT — First Year"
+year: 2026
+language: en
+description: "Introductory calculus (limits, derivatives, integrals) with light programming-oriented tasks."
+instructors:
+  - "Instructor Name"
+tags:
+  - calculus
+  - it
+  - first-year
+version: "0.1"
+---
+
+# Basic Calculus for IT — First Year (ALE Example)
+
+This repository is an **ALE example course**.
+
+## How to use this course in ALE
+1) Add this repository URL and a branch in ALE (Instructor role).
+2) Click **Sync Course Content**.
+3) Students will see Activities and can start/continue sessions.
+
+## Authoring notes (quick)
+- Materials live in `materials/` and headings become anchors.
+- Activities live in `activities/`.
+- Every task/question includes `Refs:` in the form `material_id#anchor`.

README.md

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+# Basic Calculus for IT — Example ALE Course
+
+This repository demonstrates the ALE activity content format:
+- `COURSE.md`
+- `materials/` (Markdown with headings)
+- `activities/` (mode-aware tasks with refs)
+  - understanding activity
+  - homework activity
+  - strict test activities
+
+It is intentionally deterministic-friendly for sync and contract fixtures.

activities/01-limits-and-derivatives-understanding.md

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+---
+id: act-01-limits-and-derivatives-understanding
+title: "Unit 01 — Limits and Derivatives"
+mode: understanding
+open_at: "2026-02-01T00:00:00+01:00"
+close_at: "2026-12-31T23:59:59+01:00"
+retakes_enabled: true
+max_attempts: 999
+grade_max: 100
+---
+
+# Unit 01 — Limits and Derivatives
+
+## T1
+Type: essay
+Points: 20
+Prompt: Explain in your own words what a limit means and how it is used to define the derivative.
+Refs:
+- mat-01-limits-continuity#what-is-a-limit
+- mat-02-derivatives#derivative-definition
+Rubric:
+- Clear conceptual explanation (10)
+- Mentions difference quotient and limiting process (10)
+
+## T2
+Type: essay
+Points: 25
+Prompt: Compute the limit of (sin x)/x as x approaches 0 and briefly justify your result.
+Refs:
+- mat-01-limits-continuity#special-limits
+Rubric:
+- Correct limit value (15)
+- Justification is mathematically coherent (10)
+
+## T3
+Type: essay
+Points: 30
+Prompt: Differentiate f(x)=x^3-2x+sin x and simplify the result.
+Refs:
+- mat-02-derivatives#derivative-rules
+- mat-02-derivatives#derivatives-of-common-functions
+Rubric:
+- Applies power rule correctly (15)
+- Differentiates sin x correctly (10)
+- Simplifies correctly (5)
+
+## T4
+Type: file
+Points: 25
+Prompt: Create a small Python script @solutions/numerical_derivative.py that approximates the derivative using a finite difference and prints the approximate derivative of x^3 at x=2 with step h=1e-5.
+Refs:
+- mat-02-derivatives#tangent-line-approximation
+Rubric:
+- Script runs and prints a numeric result (10)
+- Uses finite difference correctly (10)
+- Code is readable (5)

activities/02-integrals-and-applications-homework.md

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+---
+id: act-02-integrals-and-applications-homework
+title: "Unit 02 — Integrals and Applications"
+mode: homework
+open_at: "2026-02-01T00:00:00+01:00"
+close_at: "2026-12-31T23:59:59+01:00"
+retakes_enabled: true
+max_attempts: 999
+grade_max: 100
+---
+
+# Unit 02 — Integrals and Applications
+
+## T1
+Type: essay
+Points: 25
+Prompt: Explain the difference between an antiderivative and a definite integral (interpretation).
+Refs:
+- mat-04-integrals#antiderivative
+- mat-04-integrals#definite-integral
+Rubric:
+- Correct distinction (15)
+- Meaning/interpretation is clear (10)
+
+## T2
+Type: essay
+Points: 25
+Prompt: Compute the definite integral from 0 to 1 of 3x^2 dx.
+Refs:
+- mat-04-integrals#basic-integration-rules
+- mat-04-integrals#definite-integral
+Rubric:
+- Correct antiderivative and evaluation (20)
+- Clear presentation (5)
+
+## T3
+Type: essay
+Points: 25
+Prompt: State the fundamental theorem of calculus in your own words and explain what it connects.
+Refs:
+- mat-04-integrals#fundamental-theorem-of-calculus
+Rubric:
+- Correct statement at a high level (15)
+- Explains connection between differentiation and accumulation (10)
+
+## T4
+Type: essay
+Points: 25
+Prompt: Optimization mini-task: For f(x)=x^2-4x+1, find the x that minimizes f(x) and the minimum value.
+Refs:
+- mat-03-derivative-applications#optimization-workflow
+- mat-02-derivatives#critical-points
+Rubric:
+- Computes derivative and critical point correctly (15)
+- Correct minimum value and interpretation (10)

activities/03-limits-derivatives-test.md

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+---
+id: act-03-limits-derivatives-test
+title: "Test 01 — Limits and Derivatives Quiz"
+mode: test
+open_at: "2026-02-05T00:00:00+01:00"
+close_at: "2026-12-31T23:59:59+01:00"
+retakes_enabled: true
+max_attempts: 5
+grade_max: 100
+time_limit_seconds: 1500
+---
+
+# Test 01 — Limits and Derivatives Quiz
+
+## T1
+Type: mcq
+Points: 25
+Prompt: The derivative of a function at a point is defined as:
+Refs:
+- mat-02-derivatives#derivative-definition
+Choices:
+- [ ] The area under the curve from 0 to x
+- [x] The limit of the difference quotient as the step approaches 0
+- [ ] The average rate of change over an interval
+
+## T2
+Type: short
+Points: 25
+Prompt: Compute d/dx of x^4.
+Refs:
+- mat-02-derivatives#derivative-rules
+Answer: 4x^3
+
+## T3
+Type: mcq
+Points: 25
+Prompt: What is the limit of (sin x)/x as x approaches 0?
+Refs:
+- mat-01-limits-continuity#special-limits
+Choices:
+- [ ] 0
+- [x] 1
+- [ ] Does not exist
+
+## T4
+Type: short
+Points: 25
+Prompt: Differentiate sin x.
+Refs:
+- mat-02-derivatives#derivatives-of-common-functions
+Answer: cos x

activities/04-integrals-test.md

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+---
+id: act-04-integrals-test
+title: "Test 02 — Integrals Quiz"
+mode: test
+open_at: "2026-02-12T00:00:00+01:00"
+close_at: "2026-12-31T23:59:59+01:00"
+retakes_enabled: true
+max_attempts: 5
+grade_max: 100
+time_limit_seconds: 1500
+---
+
+# Test 02 — Integrals Quiz
+
+## T1
+Type: mcq
+Points: 25
+Prompt: A definite integral is best interpreted as:
+Refs:
+- mat-04-integrals#definite-integral
+Choices:
+- [x] Accumulated change / signed area under the curve
+- [ ] The slope of the tangent line
+- [ ] A function that undoes differentiation only in indefinite form
+
+## T2
+Type: short
+Points: 25
+Prompt: Compute the integral from 0 to 1 of 2x dx.
+Refs:
+- mat-04-integrals#basic-integration-rules
+- mat-04-integrals#definite-integral
+Answer: 1
+
+## T3
+Type: mcq
+Points: 25
+Prompt: The fundamental theorem of calculus connects:
+Refs:
+- mat-04-integrals#fundamental-theorem-of-calculus
+Choices:
+- [ ] Limits and continuity
+- [x] Differentiation and integration
+- [ ] Optimization and related rates
+
+## T4
+Type: short
+Points: 25
+Prompt: An antiderivative of 3x^2 is:
+Refs:
+- mat-04-integrals#antiderivative
+- mat-04-integrals#basic-integration-rules
+Answer: x^3

materials/01-limits-and-continuity.md

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+---
+id: mat-01-limits-continuity
+title: "Limits and continuity"
+---
+
+# Limits and continuity
+
+## What is a limit
+A limit describes the value that a function approaches as the input approaches a point.
+
+## Basic limit laws
+If limits exist, they follow linearity, product, quotient, and power laws.
+
+## Special limits
+Two important special limits are:
+- sin x / x as x approaches 0
+- (1 + 1/n)^n as n grows
+
+## Continuity
+A function is continuous at a point if the limit equals the function value.
+
+## One sided and infinite limits
+Sometimes we consider limits from the left or right, or limits that diverge to infinity.

materials/02-derivatives-rules.md

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+---
+id: mat-02-derivatives
+title: "Derivatives: definition and rules"
+---
+
+# Derivatives
+
+## Derivative definition
+The derivative at a point is the limit of the difference quotient.
+
+## Derivative rules
+Key rules include:
+- constant and power rule
+- sum and product rule
+- quotient rule
+- chain rule
+
+## Derivatives of common functions
+Examples:
+- derivative of x^n
+- derivative of sin x and cos x
+- derivative of e^x and ln x
+
+## Tangent line approximation
+A derivative gives the slope of the tangent line and supports local linear approximation.
+
+## Critical points
+Critical points occur where the derivative is zero or undefined (within the domain).

materials/03-derivative-applications.md

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+---
+id: mat-03-derivative-applications
+title: "Applications of derivatives"
+---
+
+# Applications of derivatives
+
+## Increasing decreasing and extrema
+Use the sign of the derivative to determine where a function increases or decreases, and locate maxima or minima.
+
+## Optimization workflow
+Typical steps:
+1) define the objective function
+2) compute derivative
+3) find critical points
+4) test candidates (including endpoints if relevant)
+5) interpret the solution
+
+## Related rates idea
+Differentiate an equation relating variables with respect to time to connect their rates of change.
+
+## Error and sensitivity
+Derivatives quantify sensitivity: how much output changes per unit input.

materials/04-integrals-basics.md

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+---
+id: mat-04-integrals
+title: "Integrals: basics and the fundamental theorem"
+---
+
+# Integrals
+
+## Antiderivative
+An antiderivative is a function whose derivative is the integrand.
+
+## Definite integral
+A definite integral measures accumulated change and is interpreted as signed area under a curve.
+
+## Fundamental theorem of calculus
+The fundamental theorem connects derivatives and integrals:
+- differentiation and accumulation are inverse operations (under suitable conditions)
+
+## Basic integration rules
+Rules include:
+- linearity
+- power rule for integrals (with n not equal to -1)
+- integral of 1/x is ln|x|
+
+## Substitution idea
+Substitution changes variables to simplify the integrand when a composition structure appears.