Who this is for

This is written for UK job seekers aiming at roles like:

• Data Scientist (product, commercial, marketing, risk, ops)

• Applied Scientist

• Machine Learning Engineer leaning data science

• Experimentation Analyst / Data Scientist

• Forecasting / Time Series Data Scientist

It works for two common profiles:

Route A: Career changers
You can code & you can analyse, but you want the maths that makes your work defensible in interviews.

Route B: Students & grads
You have seen some of this at uni, but you want job-ready fluency plus the ability to explain trade-offs in plain English.

Why this maths matters in data science jobs

Data science is mostly about making good decisions under uncertainty. The maths helps you do three things reliably:

1) Build models that generalise
Understand bias vs variance, regularisation & why training performance is not the goal.

2) Measure impact correctly
A/B tests, observational comparisons, confidence intervals & power decisions.

3) Communicate what is true & what is unknown
Stakeholders want answers. Your value is giving answers that are correct, scoped & actionable.

If you can do that, you are “maths ready” for a very large share of UK data science roles.

The only maths topics you actually need

1) Statistics that actually shows up at work

If you learn one area well, make it statistics. It is the backbone of experimentation, evaluation & credible reporting.

What you actually need

Descriptive statistics

• Mean, median, variance, standard deviation

• Percentiles & why distributions matter

• Outliers, skew, heavy tails

Uncertainty

• Confidence intervals as a range of plausible values

• Standard error intuition

• Practical interpretation: “how sure are we”

Hypothesis tests in plain English

• What a p-value is & what it is not

• Type I error vs Type II error

• Multiple testing awareness

Power & sample size basics

• Why you can fail to detect real effects

• Why tiny effects can become “significant” with large samples

• How to choose a minimum detectable effect that matches the business question

Netflix’s experimentation writing highlights conventional false positive rates (often 5%) & discusses false positives, significance & related decision-making issues in A/B tests. netflixtechblog.com

Where it shows up in UK roles

• Designing & interpreting A/B tests

• Explaining whether a metric change is meaningful

• Building KPI guardrails for releases

• Choosing sensible evaluation windows & avoiding premature conclusions

The interview-level skill

You do not need to recite formulas. You do need to explain:

• the metric

• the effect size

• the uncertainty

• the risk of false positives & false negatives

• what you would do next

2) Probability for real-world data science

Probability is how you reason about noisy data, rare events & uncertain outcomes.

What you actually need

Core probability

• Conditional probability intuition

• Independence vs dependence

• Bayes rule at a conceptual level

Base rates

• Why rare events create lots of false alarms

• Why model precision can collapse when prevalence is low

Distributions you actually use

• Bernoulli & binomial (conversion, churn events)

• Normal (approximation for many aggregated metrics)

• Poisson (counts per time period)

A free structured route to these basics is Khan Academy’s statistics & probability content. khanacademy.org

Where it shows up in UK roles

• Fraud or risk modelling (rare events)

• Churn & retention analysis

• Forecasting demand & incident counts

• Choosing thresholds for classifiers

The interview-level skill

Be able to explain why a model can look great on paper but disappoint in production when the base rate changes.

3) Linear algebra essentials for modelling & embeddings

You do not need full linear algebra theory, but you do need comfort with vectors & matrices because modern ML is built on them.

What you actually need

• Vectors, dot product, norms

• Matrix multiplication & shape reasoning

• Projections & “direction in feature space”

• PCA intuition: variance explained & why scaling matters

• Cosine similarity for embeddings & retrieval tasks

If you want fast intuition, 3Blue1Brown’s Essence of Linear Algebra is a visuals-first route that helps many job seekers. YouTube

Where it shows up in UK roles

• Feature engineering & scaling

• Linear models & regularisation

• PCA for exploratory analysis

• Embeddings for search, recommendations & NLP pipelines

The interview-level skill

Explain what PCA is doing in business terms: “compressing correlated signals into a smaller set of factors” plus what can go wrong if your data has batch effects or leakage.

4) Calculus & gradients for optimisation & deep learning

Most data scientists do not use calculus daily, but you do need enough to understand how training works, what a gradient means & why learning can fail.

What you actually need

• Derivative as rate of change

• Partial derivatives conceptually

• Chain rule idea

• Gradient descent intuition

• Backprop as repeated chain rule in a computational graph

For intuition-first learning, 3Blue1Brown’s Essence of Calculus is a strong starting point. YouTube

StatQuest also has accessible explanations of gradient descent & related ML ideas which many learners use for clarity. StatQuest

Where it shows up in UK roles

• Explaining model training to stakeholders

• Debugging unstable learning curves

• Choosing learning rates & regularisation

• Understanding why some features dominate training

The interview-level skill

Be able to explain what a loss function is & why gradients are used to reduce it.

5) Optimisation & evaluation that actually gets you hired

In interviews, “maths” questions often disguise a deeper question: do you know how to validate a model properly.

What you actually need

• Loss functions & what they optimise (MSE, log loss, cross-entropy)

• Bias vs variance intuition

• Cross-validation conceptually

• Choosing the right metric for the problem

• Threshold tuning & trade-offs (precision vs recall)

scikit-learn’s documentation covers cross-validation workflows & model evaluation metrics in a practical, implementation-friendly way. Scikit-learn

Where it shows up in UK roles

• Building baselines & choosing models

• Handling imbalanced datasets

• Reporting performance honestly without leakage

• Communicating trade-offs to product, risk, ops & compliance

The interview-level skill

Be able to say:

• which metric matters & why

• how you validated

• how you avoided leakage

• what you would monitor after deployment

A 6-week maths plan for UK data science jobs

This plan is designed so you can learn while applying. Aim for 4–5 sessions per week of 45–60 minutes.

Week 1: Descriptive stats & distributions

Goal: get fluent reading real data, not textbook data
Do

• Summaries: mean, median, std, percentiles

• Visuals: histogram, box plot, time series

• Explain skew & outliers in words
  Output

• A notebook that profiles a dataset & explains what “normal” looks like

Week 2: Confidence intervals & effect sizes

Goal: move from “difference” to “difference with uncertainty”
Do

• Build confidence intervals for a mean & a proportion

• Compare two groups with effect sizes

• Write conclusions that are cautious but decisive
  Output

• A short report: “treatment vs control” with uncertainty & recommendation

Week 3: Hypothesis testing & power

Goal: know when to trust a result & when to collect more data
Do

• Hypothesis testing workflow at a practical level

• Type I vs Type II error

• Power intuition & minimum detectable effect
  Netflix’s discussions on false positives & power can help ground this in product experimentation reality. netflixtechblog.com
  Output

• A one-page A/B test decision note with assumptions & next step

Week 4: Linear algebra for modelling workflows

Goal: be comfortable with vectors, matrices & PCA in practice
Do

• Implement cosine similarity

• Run PCA & interpret variance explained

• Explain what scaling does & why
  Use 3Blue1Brown for intuition support. YouTube
  Output

• PCA notebook with a clear interpretation section

Week 5: Model evaluation like a professional

Goal: validate properly & communicate trade-offs
Do

• Train/test split vs cross-validation

• Choose metrics that match the problem

• Threshold tuning & confusion matrix story
  scikit-learn’s cross-validation & metric docs are a reliable reference. Scikit-learn
  Output

• A “model evaluation pack” notebook that includes metric choice reasoning

Week 6: Gradients, optimisation & a mini modelling capstone

Goal: connect calculus intuition to training behaviour
Do

• Plot a loss curve

• Explain gradient descent in plain English

• Build one end-to-end model with clean evaluation
  Use 3Blue1Brown calculus intuition plus StatQuest explanations if needed. YouTube
  Output

• A portfolio repo with README explaining data, model, validation & decisions

Portfolio projects that prove the maths

These projects are designed to translate maths into hiring signals.

Project 1: A/B test results write-up with power thinking

What you build

• A simulated or public dataset A/B test

• Effect size, confidence interval, decision rule

• A paragraph on power & what you would do if inconclusive
  Why it matters
  Experimentation is common in UK product data science roles. Netflix’s posts provide useful framing around error rates & power. netflixtechblog.com

Project 2: Imbalanced classification with threshold tuning

What you build

• Model a rare event

• Report precision, recall, PR AUC

• Pick a threshold based on cost of false positives vs false negatives
  Why it matters
  This is one of the most common interview conversations.

Project 3: PCA + clustering for exploratory insight

What you build

• Standardise data

• PCA to 2–3 components

• Cluster & interpret segments

• Include a “what could mislead us” section
  Why it matters
  Shows linear algebra fluency plus good scientific caution.

Project 4: Forecasting baseline + evaluation

What you build

• A simple forecasting baseline

• Backtesting

• Error metrics & a clear narrative about seasonality
  Why it matters
  Forecasting shows up across retail, logistics, energy & ops in the UK.

How to describe maths skills on your CV

Avoid “strong maths” as a claim. Use proof:

• Built A/B test decision notes using effect sizes, confidence intervals & power-aware recommendations netflixtechblog.com

• Validated models with cross-validation plus metric selection aligned to business trade-offs Scikit-learn

• Delivered imbalanced classification models with threshold tuning plus precision/recall reporting using scikit-learn evaluation workflows Scikit-learn

• Produced PCA-based exploratory analysis with variance explained interpretation & scaling rationale YouTube

Resources section

Statistics & experimentation

• Khan Academy statistics & probability learning path for foundations. khanacademy.org

• Netflix Tech Blog on interpreting A/B test results including false positives, significance & power. netflixtechblog.com

• “Lessons from designing Netflix’s experimentation platform” for high-level experimentation context. research.netflix.com

Linear algebra

• 3Blue1Brown Essence of Linear Algebra playlist. YouTube

Calculus & gradients

• 3Blue1Brown Essence of Calculus playlist. YouTube

• StatQuest video index for gradient descent & ML explanations. StatQuest

Machine learning fundamentals

• Stanford CS229 course site & lecture notes (solid ML maths reference). cs229.stanford.edu

• An Introduction to Statistical Learning (ISLR) official site plus a freely available PDF version used widely for learning. An Introduction to Statistical Learning

Model evaluation & best-practice workflows

• scikit-learn cross-validation guide. Scikit-learn

• scikit-learn metrics & scoring guide. Scikit-learn