Applied AICollège Unica
1.1Basic KnowledgeSession 1 · Foundations of AI & Data Science

Mathematics applied to computing I

25classes75htotalTH3 · PR2 · PNW3weighting 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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Business Studio · B01 — Enrollment Workspace Pilot

This course runs an applied studio layer: you role-play qualifying a fictional prospect inquiring about the A.E.C. Each class adds a lead-to-booking task grounded in that class's math, with two AI Tutor modes — Learn (prediction-first hints) and Check (independent, won't solve it for you) — and an auto-graded independent check tied to G01 (business diagnosis) and G02 (market reasoning).

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First 2 classes free with a referral 24 more with enrollment180 min per classTheory 68mPractical 45mPersonal Work 67m
1

Why Math Powers AI — A Tour of the Math Behind GenAI and Agents

FreeTH3PR2PNW3

A Data/Business Analyst who can see where math lives inside a model trusts it more and explains it better to stakeholders.

Theory68m
  • Tour where math hides in GenAI: vectors in embeddings, probability in next-token predictions, matrices in model weights
  • See how an LLM's 'smart' guess is really a calculated probability over tokens
  • Set personal math goals for the course
Practical45m
  • Sketch a map of one real GenAI product (e.g. a RAG search assistant) and label the math it likely uses
  • Spot the math step in a simple embedding-similarity diagram
Personal Work67m
  • Write a short note: which math topic you most want to understand and why
  • Micro-task: submit your goal note as a one-page PDF
2

Numbers, Sets and Notation — The Shared Language of Data Science

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Every Project Manager scoping a data project starts by agreeing on what the numbers and sets mean — clear notation prevents costly misunderstandings

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3

Logic and Boolean Algebra — The Backbone of Code and Filters

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Digital Marketing Strategists build audience filters every day — every filter is Boolean logic in disguise

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4

Propositional Logic and Reasoning an Analyst Can Verify

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An AI Integration Manager must sanity-check a model's claims — propositional logic is the toolkit for asking 'does this conclusion actually follow?'

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5

Functions and Relations — Mapping Inputs to Outputs

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A Data/Business Analyst thinks in functions constantly: inputs go in, a number comes out — that's every KPI and every forecast

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6

Sequences and Series — The Patterns Behind Data Trends

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Project Managers track trends over time — sequences are the math behind every 'is this going up or down?' question

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7

Summation and the Σ Operator — How Models Add Up Data

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Every AI model sums something — a Data/Business Analyst who reads Σ fluently can decode model formulas instead of guessing

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8

Exponents, Logarithms and Scales — Growth, Decay and Compression

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Sales and Marketing Managers live with exponential growth and log-scaled charts — misreading them turns a win into a panic

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9

Vectors — The Data Structure Behind Every Embedding and GenAI Model

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An AI Integration Manager should know that text, images and user profiles all become vectors (embeddings) under the hood — it's how models 'see' them and how RAG finds matches

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10

Vector Operations — Dot Products, Similarity and How RAG Finds Answers

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RAG systems rank retrieved documents by vector similarity — a Data/Business Analyst who gets this understands why an agent 'finds' the right passage

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11

Matrices — The Tables That Run Neural Networks

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AI Integration Managers don't need to build a neural net by hand, but knowing matrices are the 'engine' makes model talk far less intimidating

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12

Matrix Operations — Addition, Scaling and Multiplication

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A Data/Business Analyst who can picture matrix multiplication can explain how data flows through a model layer without panicking at the math

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13

Linear Transformations — Rotating and Scaling Data Spaces

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Understanding that matrices 'move' data helps a Project Manager grasp why engineers talk about 'projecting' or 'rotating' features

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14

Systems of Linear Equations — Solving and Interpreting

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Data/Business Analysts often juggle several constraints at once — solving systems is the math of 'what satisfies everything?'

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15

Coordinate Systems and the Cartesian Plane — Plotting Data

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Every chart a Digital Marketing Strategist reads lives on a coordinate plane — fluency here means reading trends correctly

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16

Lines, Slopes and Linear Equations — The Simplest Predictive Model

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Linear regression is a Data/Business Analyst's first forecasting tool — and it starts with a line and a slope

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17

Descriptive Statistics — Mean, Median, Mode and What Each Tells You

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An E-commerce Director deciding on pricing needs the right 'average' — picking mean vs median changes the whole story

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18

Variance and Standard Deviation — Measuring Spread and Risk

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Project Managers frame risk as variability — standard deviation is the number that says 'how predictable is this?'

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19

Percentiles, Quartiles and the Box Plot — Spotting Outliers

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A Data/Business Analyst uses quartiles to flag anomalies — an outlier in sales can be a bug or a breakthrough worth chasing

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20

Data Visualization Basics — Reading Histograms and Scatter Plots

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Digital Marketing Strategists and analysts live by charts — reading them correctly is the difference between insight and noise

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21

Probability Fundamentals — Chance, Events and How LLMs Pick the Next Token

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Every LLM output is a probability distribution over tokens — an AI Integration Manager who speaks probability can interpret a model's confidence honestly

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22

Conditional Probability — How New Information Updates Beliefs

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A Digital Marketing Strategist constantly updates 'how likely is this customer to buy?' as new data arrives — that's conditional probability

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23

Combinatorics Basics — Counting Outcomes for Scenarios

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Sales and Marketing Managers count combinations of offers and segments — counting correctly keeps forecasts realistic

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24

Distributions — The Normal Curve and Why It's Everywhere

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A Data/Business Analyst who recognizes the normal curve can sanity-check whether a metric 'looks normal' or needs a closer look

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25

Math in Action — A Mini GenAI Data Exploration Tying It Together

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This is the rehearsal a Data/Business Analyst needs — combining vectors, stats and a line into one small story (like scoring RAG retrieval quality) proves the math clicked

Enroll to unlock every class in this course — the full agenda, the AI tutor, and the quiz.

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