Applied AICollège Unica
2.1Basic KnowledgeSession 2 · Data Engineering & Machine Learning

Mathematics applied to computing II

25classes75htotalTH3 · PR2 · PNW1weighting per class

Class-by-class breakdown

25 classes

TH = theory · PR = practical · PNW = personal work. These are ministry weighting codes (not hours) used to split each class's minutes. Class length = course hours ÷ class count; the three time-boxes below always sum to that length.

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Quiz progress

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First 2 classes free with a referral 24 more with enrollment180 min per classTheory 90mPractical 60mPersonal Work 30m
1

From 1.1 to Calculus — Why Change Matters for AI

FreeTH3PR2PNW1

A Data/Business Analyst who understands rates of change can explain why a metric is improving or stalling instead of just reporting the number.

Theory90m
  • Recap of functions and graphs from 1.1
  • The big idea of calculus: measuring how things change
  • Where calculus shows up in AI (learning curves, optimization)
Practical60m
  • Plot a sample metric over time in a spreadsheet and eyeball where it changes fastest
  • Mark the steepest rising and flattest points on the graph
Personal Work30m
  • Write one paragraph on a business metric you'd want to track the rate of change for
  • Micro-task: submit your paragraph
2

Limits — The Foundation of Calculus

LockedTH3PR2PNW1

Locked class preview

An AI Integration Manager hears 'as it approaches' in model docs — limits are the precise version of that idea

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3

Derivatives — Measuring the Rate of Change

LockedTH3PR2PNW1

Locked class preview

A Digital Marketing Strategist tracking campaign momentum is really reading a derivative — the slope tells you if you're accelerating or fading

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4

Derivative Rules — Power, Sum and Constant Rules

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Locked class preview

A Data/Business Analyst who can take a basic derivative can model marginal cost and marginal revenue — core business math

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5

Higher-Order Derivatives — Acceleration and Curvature

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Locked class preview

A Project Manager who grasps the second derivative can tell 'getting better' from 'getting better faster' — a real planning distinction

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6

Optimization — Finding the Best Value

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Locked class preview

Every E-commerce Director optimizes something — profit, conversion, cost — and calculus finds the exact peak or valley

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7

Gradient Descent — How Models (and LLMs) Actually Learn

LockedTH3PR2PNW1

Locked class preview

An AI Integration Manager who can explain gradient descent demystifies 'training' — including how foundation models and fine-tunes actually update — it's just walking downhill

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8

Partial Derivatives and Gradients — Many Variables at Once

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Locked class preview

A Data/Business Analyst knows real models have many inputs — partial derivatives explain how each feature nudges the output, and underpin embeddings and attention in LLMs

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9

Integrals — Adding Up Continuous Change

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Locked class preview

A Sales and Marketing Manager computing total revenue from a rate uses integration — it's the continuous version of summation

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10

The Chain Rule — Derivatives of Composed Functions

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Locked class preview

An AI Integration Manager meets the chain rule in every neural network — it's how error flows backward through layers

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11

Probability Refresher — From 1.1 to LLM Token Predictions

LockedTH3PR2PNW1

Locked class preview

A Data/Business Analyst who reads model outputs as probabilities makes better calls — and that's exactly how an LLM picks its next token

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12

Conditional Probability and Bayes' Theorem

LockedTH3PR2PNW1

Locked class preview

An AI Integration Manager evaluating a classifier needs Bayes' thinking — it explains why a 'positive' result isn't always a true positive

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13

Distributions — Normal, Uniform and Skewed

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Locked class preview

A Digital Marketing Strategist reading audience data must spot a normal vs skewed distribution — it changes which summary stats to trust

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14

Mean, Variance and Standard Deviation — Describing Spread

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Locked class preview

A Data/Business Analyst who reports variance alongside the mean tells the full story — averages alone can mislead

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15

Correlation and Covariance — How Variables Move Together

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Locked class preview

An E-commerce Director who confuses correlation with causation makes expensive mistakes — this class draws the line

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16

Sampling and the Central Limit Theorem

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Locked class preview

A Project Manager who understands sampling knows when a small test group can represent the whole — and when it can't

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17

Confidence Intervals — How Sure Are We?

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Locked class preview

A Data/Business Analyst who reports a range instead of a single number sets honest expectations — confidence intervals quantify uncertainty

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18

Hypothesis Testing — Making Decisions from Data

LockedTH3PR2PNW1

Locked class preview

A Digital Marketing Strategist running A/B tests lives in hypothesis testing — it's how you know a result is real, not noise

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19

Evaluating Models — Accuracy, Precision and Recall

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Locked class preview

An AI Integration Manager must pick the right metric — accuracy alone hides problems that precision and recall expose

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20

Overfitting and Underfitting — Why Models Fail

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Locked class preview

A Data/Business Analyst who spots overfitting saves a project from a model that looks perfect but breaks in production

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21

Cross-Validation — Trusting Your Evaluation

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Locked class preview

A Project Manager who demands cross-validation gets honest model scores before approving a build

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22

Loss Functions — What Models (and LLMs) Minimize

LockedTH3PR2PNW1

Locked class preview

An AI Integration Manager who knows the loss function understands what the model is actually optimizing — cross-entropy loss is literally what trains an LLM's next-token prediction

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23

Optimization in Practice — Learning Rates and Convergence

LockedTH3PR2PNW1

Locked class preview

A Data/Business Analyst who watches a training curve can tell when a model has converged or is stuck — a real diagnostic skill

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24

Putting It Together — Math Behind a Real Model

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Locked class preview

A future AI Integration Manager who can trace one real model from data to prediction proves the math is job-ready, not abstract

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25

Present and Reflect — Your Math Toolkit for AI

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Locked class preview

A Data/Business Analyst who can present their math reasoning earns trust — this class rehearses the explain-it-to-stakeholders skill

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1.5 · Setting up an AI ecosystem

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2.2 · Advanced computer French

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