A curriculum is a system, not a course catalogue

A list of relevant courses does not become a curriculum until their prerequisites, concepts, assessments, and applications are coordinated.
AI education should be designed as a dependency graph that repeatedly reconnects mathematical foundations to empirical decisions.
The strongest test of curricular coherence is whether students can carry one idea across courses and use it under changed assumptions.

The Catalogue Illusion

A program can advertise mathematics, machine learning, programming, databases, ethics, and a capstone. The list appears complete. Yet students may experience six unrelated courses, each beginning with a new vocabulary and ending before its assumptions matter elsewhere.

Coverage is not coherence.

Let course $i$ contribute a vector of knowledge

corresponding to mathematics, statistics, computation, domain reasoning, and judgment. A catalogue treats program knowledge as an additive sum:

But education depends on connections among those contributions. A more realistic expression is

where $\Gamma(k_i,k_j)$ measures useful integration and $\omega_{ij}$ measures how deliberately the courses are connected.

The second term is the difference between collecting topics and building capability.

Curriculum as a Dependency Graph

Represent the curriculum as a directed graph

Each node $v\in V$ is a concept, capability, or assessment. An edge $(u,v)\in E$ means that competence in $u$ is needed to learn or demonstrate $v$.

For example:

Another path may be

A course catalogue usually displays nodes. Curriculum design must inspect the edges.

Prerequisites Are More Than Course Names

A formal prerequisite such as “linear algebra” says little about the required capability.

Does the next course require students to multiply matrices, interpret a projection, recognize rank deficiency, derive a quadratic form, or reason about an eigenspace? These are different prerequisites.

Table 1. Curriculum components and their system dependencies

Prerequisite label	Procedural evidence	Conceptual evidence	Applied evidence
Linear algebra	Computes matrix products	Explains projection and rank	Diagnoses collinearity or latent dimension
Probability	Evaluates distributions	Conditions on information	Reconstructs selection and uncertainty
Calculus	Differentiates an objective	Interprets local sensitivity	Explains optimization and marginal effects
Programming	Writes functioning code	Understands state and abstraction	Builds a reproducible analytical pipeline
Statistics	Applies an estimator	States assumptions and target	Designs validation for the DGP

If the later course needs applied evidence but the prerequisite assessed only procedure, the edge exists on paper and fails in practice.

The Vertical Spine

A coherent AI curriculum needs a small set of ideas that recur at increasing depth.

One possible spine is:

1. Representation: What objects and relationships define the problem?
2. Generation: How did the observations arise?
3. Estimation: How will unknown structure be learned?
4. Validation: Which claim is being tested under which distribution?
5. Decision: What action follows under costs and constraints?
6. Revision: How does the solution change when assumptions fail?

The same spine can organize an introductory regression, a neural representation, a causal case, and a dissertation.

Repetition is not redundancy when the state space changes. Students first meet a concept in a controlled setting and later meet it with measurement error, dependence, high dimension, or policy feedback.

Constructive Alignment

Curriculum coherence requires alignment among intended outcomes, learning activities, and assessment.

Let:

• $o_r$ be intended outcome $r$;
• $a_{ir}$ measure how strongly course activity $i$ develops it; and
• $t_{jr}$ measure how strongly assessment $j$ tests it.

An alignment gap can be written

If a program claims that graduates can make decisions under uncertainty but teaching focuses on derivations and assessment rewards code execution, the outcome exists only in marketing language.

Alignment does not require one teaching method. Lectures, problem sets, cases, laboratories, and research can serve different functions. They must converge on the declared graduate capability.

Horizontal Integration

Vertical sequencing is not enough. Students must connect ideas learned at the same stage.

A forecasting module might use:

• probability for uncertainty;
• time-series models for dependence;
• programming for data pipelines;
• economics for structural breaks;
• operations for inventory cost; and
• communication for the recommendation.

Horizontal integration can be designed through a shared case. Each course contributes a different object, but faculty agree on data definitions, timing, and the final decision.

Without that agreement, one course may clean away the anomaly another course is meant to explain. One may define the outcome after the decision time. Another may optimize a metric unrelated to the case's cost.

The Curriculum Matrix

A useful design instrument maps courses against capabilities.

Read as a diagnostic rather than a second scorecard, the framework becomes clear: Foundations — Representation: Introduce; DGP and inference: Introduce; Computation: Introduce; Decision: Expose; Communication: Explain results. Core models — Representation: Develop; DGP and inference: Develop; Computation: Develop; Decision: Compare losses; Communication: Defend assumptions. Advanced methods — Representation: Extend; DGP and inference: Stress-test; Computation: Scale; Decision: Optimize under constraints; Communication: Explain uncertainty. Cases — Representation: Integrate; DGP and inference: Diagnose; Computation: Implement; Decision: Recommend; Communication: Write for a decision owner. Dissertation — Representation: Independently formulate; DGP and inference: Defend; Computation: Reproduce; Decision: Bound the claim; Communication: Sustain an argument.

Blank cells are not always defects. A focused course need not do everything. The program, however, should know where each capability is introduced, developed, integrated, and independently demonstrated.

Avoiding the “Methods Parade”

AI curricula easily become chronological or fashionable parades:

Students learn that progress means moving to the next named method. They do not learn why one representation belongs to one problem.

A systems curriculum instead compares methods around recurring questions:

• Which restrictions does the model impose?
• What structure is learned from data?
• How much data and computation are required?
• What type of uncertainty can be reported?
• How does the method behave under shift?
• What decision does the additional flexibility change?

The sequence becomes conceptual rather than promotional.

Designing Backwards from the Dissertation

The final independent project provides a useful backward-design test.

If graduates must produce a dissertation containing a precise question, DGP analysis, defensible method, reproducible evidence, and bounded conclusion, earlier courses must create those capabilities in stages.

Let dissertation performance be

The minimum emphasizes the bottleneck. A student cannot compensate for an unidentified question with a more complex model.

Each course should therefore leave an artifact that later becomes part of independent inquiry: a model memorandum, data audit, validation plan, comparative analysis, or correction report.

Example: From Cobb-Douglas to Model Judgment

Consider the production function

Taking logs gives

In a fragmented curriculum, mathematics teaches logarithms, statistics teaches regression, economics teaches production, and programming estimates coefficients. The student may never connect them.

A coherent sequence asks:

1. What institutional process could justify the multiplicative form?
2. What units and measurements define $K$ and $L$?
3. Under what conditions can coefficients be interpreted as elasticities?
4. What happens if inputs are chosen in response to productivity shocks?
5. Does the target concern prediction or production causality?
6. How should uncertainty and heterogeneity be represented?
7. Which business decision changes if $\alpha+\beta$ differs from one?

One elementary equation becomes a thread across the curriculum.

Managing Cognitive Load

Coherence does not mean exposing every connection at once.

Students need a controlled progression from worked structure to independent reconstruction. A course can temporarily hold some assumptions fixed:

Later courses relax one element at a time:

The curriculum should make the temporary simplification explicit. Otherwise students mistake a teaching condition for a universal property of the method.

Curriculum Version Control

Curriculum change should be traceable.

Suppose a program replaces one statistical modelling course with a generative-AI applications course. The visible credit total remains unchanged, but the dependency graph may lose edges needed by later causal analysis, validation, or dissertation work.

For curriculum version $v$, define an outcome-coverage matrix

where $b_{ir}^{(v)}$ records the level at which course $i$ develops outcome $r$. A proposed revision should show

and identify which later assessments depend on the changed cells.

Version control should preserve:

• the reason for change;
• evidence motivating it;
• prerequisites added or removed;
• assessments affected;
• transition rules for current students; and
• the date of later review.

This prevents curriculum updates from becoming a sequence of isolated reactions to market attention or individual faculty preference.

The SIAI GSB Curriculum Principle

At SIAI GSB, curriculum coherence means that mathematical foundations, computational methods, cases, and the dissertation should share one intellectual language.

Program tracks may differ in depth. An MSc student may derive and extend a model; an MBA student may interpret the same structure and use it in a decision. Neither should treat the method as an unexplained software function.

The institution should therefore review not only what each course contains, but which later claims depend on it and how those dependencies are assessed.

A practical curriculum therefore needs named ownership of the interfaces between courses. The instructor teaching optimization should know which statistical assumptions students have already learned; the case instructor should know which computational constraints can reasonably be imposed; and the dissertation supervisor should know which forms of evidence the earlier modules have required. Without this coordination, students repeatedly restart at an introductory level while the most difficult connections remain nobody’s responsibility. A coherent program documents those interfaces, tests them through shared assignments, and revises the sequence when students repeatedly fail at the same transition. That record should travel with the curriculum when faculty members change, preventing the program’s intellectual sequence from surviving only as personal memory. Coherence becomes measurable when students can use an idea learned in one module to challenge a decision made in another.

Current AI debates make constructive alignment urgent. Redesigning Education Beyond Procedure in the Age of AI argues that courses must shift time from known procedures toward framing and defense. The Economy’s work on teacher AI literacy shows that this change depends on faculty capability, and SIAI’s research on cognitive outsourcing identifies verification as a curriculum-wide responsibility. Adding an AI elective cannot achieve these outcomes if prerequisites, assessment, and feedback still reward disconnected performance.

Conclusion

A curriculum is a system because education is produced through dependencies and transfer.

The course catalogue identifies the parts. The curriculum determines whether the parts form a capable graduate. That requires explicit prerequisites, a recurring conceptual spine, horizontal cases, aligned assessment, and evidence from later independent work.

The design question is not:

Have we offered every important topic?

It is:

Can students carry the right structure from one problem to another, recognize when it no longer applies, and rebuild it?

That is the difference between curricular coverage and an AI education.

References

John Biggs, “Enhancing Teaching through Constructive Alignment”, Higher Education 32 (1996): 347-364.
National Academies of Sciences, Engineering, and Medicine, Data Science for Undergraduates: Opportunities and Options, National Academies Press, 2018.
Association for Computing Machinery and IEEE Computer Society, Computing Curricula 2020, 2020.
The Economy (2025) ‘Redesigning Education Beyond Procedure in the Age of AI’, The Economy Review, 17 September.
The Economy Editorial Board (2026) ‘Teacher AI Literacy Is the Real Test of AI in Education’, The Economy Review, 22 June.
Swiss Institute of Artificial Intelligence (2026) ‘Cognitive Outsourcing in Education: Why AI’s Real Classroom Crisis Is Verification, Not Cheating’, SIAI Working Papers, 24 July.