Mathematics for Data Science and Analytics
The difference between running models and understanding them is mathematics. This is that mathematics, taught honestly in twelve months.
Syllabus updated August 2026
Recordings are free with a Google sign-in. These recordings show how we teach, not the exact syllabus of this course.
How long this course takes
This course runs 12-14 months (48-56 weeks) at 2 live classes/week + 4-6 hours practice. The range allows for background and pace: a complete beginner uses the full span, and a student with prior knowledge finishes sooner. The syllabus below is planned to the shorter end, with margin kept for revision.
For personalised duration planning, call +91 91233 66161 and we'll map a schedule to your goals.
At a glance
- Who it is for
- School-level maths assumed; built for college students and working professionals. Age: College students and working professionals (18+).
- Prerequisites
- School mathematics (Class 12 or equivalent). Calculus is refreshed where needed; no university maths assumed
- Format
- Live, interactive classes with a real instructor, never pre-recorded videos. Live classes run about one hour.
- Language
- English or Hindi, depending on the batch.
- Duration
- 12-14 months (48-56 weeks)
- Weekly commitment
- 2 live classes/week + 4-6 hours practice
- Class size
- Group batches of 5 to 10 students, mini batches of 3 to 4, or 1-on-1.
- Certificate
- Certificate from Modern Age Coders, awarded on passing the final exam
- Watch first
- Free recordings of real classes for ages 13 and up, free with a Google sign-in. These recordings show how we teach, not the exact syllabus of this course.
- Live demo
- Optional. Enroll directly on this page, or book a free live demo if you would like to meet a mentor first.
How we teach
Deep understanding. Real projects. Expert guidance.
Learn coding, AI and maths through careful explanations, practical demonstrations, and hands-on problem-solving. Our instructors guide you from the foundations to advanced ideas, helping you understand what happens, why it happens, and how to build it yourself.
You will explore concepts step by step, write and improve code, investigate mistakes, ask questions, and apply your knowledge to meaningful projects. Lessons are designed around active participation, thoughtful feedback, and growing independence.
Expert-led live teaching, with practical participation built into every lesson.
- Students explain their thinking.
- Instructors demonstrate, then guide practice.
- Learners code, solve, or build during lessons.
- Questions and misconceptions get attention.
- Assignments receive useful feedback.
- Progress is checked before advancing.
Ready to Master Maths for Data Science: Statistics, Linear Algebra and ML?
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International Students (Outside India)
Billed monthly in US dollars, the same price in every country. Contact us with any questions.
Program Overview
Every data career eventually hits the same wall: the tools are easy, the mathematics behind them is not, and interviews, promotions and real analytical judgment all live on the far side of that wall. This live online course teaches exactly the mathematics data work stands on: statistics that tell the truth, probability that calibrates uncertainty, the linear algebra inside every model, regression and classification understood from first principles, optimization, the mathematics of neural networks, Bayesian methods, time series, and the experimental design behind honest A/B testing.
The course is deliberately practical about rigor: every concept is derived enough to be owned, then immediately exercised on real data questions, the kind analysts and data scientists actually face. Statistical malpractice gets named and corrected throughout: p-hacking, leakage, confounding, the graph that lies. By the end, a student does not just know the formulas; they know which analysis is honest and can defend it in an interview or a meeting.
The pace is real: two live classes a week plus four to six hours of practice fits the syllabus in twelve months, and learners who need longer take up to fourteen, the batch adapts. Assessment is honest too: problem sets after every class, monthly mixed reviews that reach back deliberately, phase exams, and a final exam that decides the certificate, with focused revision and a free retest for those who fall short. Real knowledge, real work, depth over dopamine.
What Makes This Program Different
- Mathematics first, tools second: understanding that transfers across every library and language
- Interview-honest coverage: the statistics, linear algebra and ML mathematics that data interviews actually probe
- Statistical malpractice named and corrected: p-hacking, leakage, confounding and misleading charts, studied on purpose
- Every concept lands on real data: derivations earn their keep in applied exercises the same week
- An honest 12-month arc with 2 months of margin: learners who need more time take up to 14, nobody is rushed
- Real assessment: weekly problem sets, monthly mixed reviews, and a final exam that decides the certificate, with focused revision and a free retest
Your Learning Journey
Career Progression
Detailed Course Curriculum
Explore the complete week-by-week breakdown of what you'll learn in this comprehensive program.
Topics Covered
- What is data science? The role of mathematics
- Types of data: numerical, categorical, ordinal
- Scales of measurement: nominal, ordinal, interval, ratio
- Population vs sample concepts
- Parameters vs statistics
- Data collection methods and sampling techniques
- Simple random sampling
- Stratified and cluster sampling
- Sampling bias and selection bias
- Data quality: missing data, outliers, errors
- Data cleaning principles
- Exploratory Data Analysis (EDA) philosophy
Projects You Build
- Design a data collection strategy
- Data quality assessment tool
- Sampling simulation study
Practice & Assignments
Analyze 20 real-world datasets for quality issues
Topics Covered
- Mean: arithmetic, geometric, harmonic
- Median and quartiles
- Mode and multimodal distributions
- Weighted averages and their applications
- Range and interquartile range
- Variance and standard deviation
- Coefficient of variation
- Mean absolute deviation
- Moments: skewness and kurtosis
- Box plots and five-number summary
- Z-scores and standardization
- Detecting outliers: IQR method, z-score method
Projects You Build
- Statistical calculator from scratch
- Outlier detection system
- Interactive visualization dashboard
Practice & Assignments
Calculate statistics for 50 different distributions
Assessment
Month 1 check: describe a messy real dataset honestly, plus a mixed quiz on everything so far
Topics Covered
- Principles of effective visualization
- Histograms and density plots
- Scatter plots and correlation patterns
- Bar charts and categorical data visualization
- Pie charts: when to use and avoid
- Heat maps and correlation matrices
- Time series plots and trends
- Parallel coordinates for high-dimensional data
- Q-Q plots and probability plots
- Interactive visualizations with Plotly
- Dashboard design principles
- Misleading visualizations and how to spot them
Projects You Build
- Build comprehensive EDA toolkit
- Create interactive data dashboard
- Visualization best practices guide
Practice & Assignments
Create 100 different types of visualizations
Topics Covered
- Sample spaces and events
- Classical, frequentist, and subjective probability
- Probability axioms and properties
- Conditional probability and independence
- Bayes' theorem and applications
- Law of total probability
- Combinatorics for probability
- Permutations and combinations in data
- Birthday paradox and probability paradoxes
- Monte Carlo simulation basics
- Random number generation
- Probability in machine learning context
Projects You Build
- Probability simulator
- Bayes theorem calculator
- Monte Carlo estimation tool
Practice & Assignments
Solve 150 probability problems with data applications
Assessment
Month 2 check: a probability problem set with one deliberately misleading chart to expose
Topics Covered
- Random variables: discrete vs continuous
- Probability mass functions
- Bernoulli and binomial distributions
- Geometric and negative binomial distributions
- Poisson distribution and rare events
- Hypergeometric distribution
- Multinomial distribution
- Expected value and variance calculations
- Moment generating functions
- Joint discrete distributions
- Marginal and conditional distributions
- Applications in A/B testing
Projects You Build
- Distribution calculator and visualizer
- A/B test simulator
- Discrete event simulator
Practice & Assignments
Work with 100 discrete distribution problems
Topics Covered
- Probability density functions
- Uniform distribution
- Normal distribution: properties and importance
- Standard normal and z-tables
- Exponential distribution and memoryless property
- Gamma and beta distributions
- Chi-square distribution
- Student's t-distribution
- F-distribution
- Log-normal distribution
- Weibull distribution for reliability
- Distribution fitting and selection
Projects You Build
- Distribution fitting tool
- Normal distribution simulator
- Reliability analysis system
Practice & Assignments
Master 100 continuous distribution applications
Assessment
Phase 1 exam: distributions and probability in anger, mixed with months 1-2 material
Topics Covered
- Vectors as data points
- Vector operations: addition, scalar multiplication
- Dot product and cosine similarity
- Vector norms: L1, L2, L-infinity
- Distance metrics: Euclidean, Manhattan, Minkowski
- Orthogonality and orthogonal projections
- Vector spaces and subspaces
- Linear independence in feature space
- Basis vectors and coordinate systems
- Change of basis for data transformation
- Gram-Schmidt for orthogonalization
- Applications to feature engineering
Projects You Build
- Vector similarity calculator
- Distance metric visualizer
- Feature space explorer
Practice & Assignments
Complete 100 vector operations in data context
Topics Covered
- Matrices as datasets and transformations
- Matrix multiplication as data transformation
- Special matrices: diagonal, symmetric, orthogonal
- Matrix transpose and properties
- Matrix rank and linear independence of features
- Invertible matrices and their meaning
- Determinants and volume interpretation
- Systems of linear equations in ML
- Gaussian elimination for solving systems
- LU decomposition
- Matrix norms and condition numbers
- Sparse matrices in big data
Projects You Build
- Matrix operations library
- Linear system solver
- Sparse matrix handler
Practice & Assignments
Solve 100 matrix problems with data applications
Assessment
Month 4 check: matrix computations plus a mixed review reaching back to statistics
Topics Covered
- Eigenvalues and eigenvectors intuition
- Characteristic equation
- Geometric interpretation of eigenvectors
- Diagonalization of matrices
- Spectral decomposition
- Positive definite matrices
- Covariance matrices in data
- Principal Component Analysis (PCA) theory
- PCA algorithm step-by-step
- Variance explained and scree plots
- PCA for dimensionality reduction
- Applications in data compression
Projects You Build
- PCA implementation from scratch
- Eigenface recognition system
- Dimensionality reduction tool
Practice & Assignments
Apply PCA to 20 different datasets
Topics Covered
- Sampling distribution concept
- Sampling distribution of the mean
- Standard error and its importance
- Central Limit Theorem (CLT)
- CLT applications and limitations
- Sample size determination
- Finite population correction
- Sampling distribution of proportions
- Sampling distribution of variances
- Chi-square distribution from normal samples
- t-distribution for small samples
- F-distribution for variance ratios
Projects You Build
- CLT demonstration tool
- Sample size calculator
- Sampling distribution simulator
Practice & Assignments
Explore 50 sampling distribution scenarios
Assessment
Month 5 check: run and interpret a PCA, plus sampling-distribution questions
Topics Covered
- Point estimates vs interval estimates
- Confidence level interpretation
- CI for population mean (known variance)
- CI for population mean (unknown variance)
- CI for population proportion
- CI for difference of means
- CI for paired differences
- CI for variance and standard deviation
- CI for ratio of variances
- Bootstrap confidence intervals
- Prediction intervals vs confidence intervals
- Sample size for desired margin of error
Projects You Build
- Confidence interval calculator
- Bootstrap CI implementation
- CI visualization tool
Practice & Assignments
Calculate 100 different confidence intervals
Topics Covered
- Null and alternative hypotheses
- Type I and Type II errors
- Significance level and p-values
- Test statistics and rejection regions
- One-sample t-test
- Two-sample t-test (equal and unequal variances)
- Paired t-test
- Z-test for proportions
- Chi-square test for variance
- F-test for equal variances
- One-tailed vs two-tailed tests
- Power of a test and effect size
- ANOVA in one honest lesson: comparing many groups
- p-hacking and multiple comparisons: how analysis goes wrong on purpose
Projects You Build
- Hypothesis testing framework
- Power analysis tool
- A/B testing platform
Practice & Assignments
Conduct 100 hypothesis tests
Assessment
Phase 2 exam: a full inference paper, hypothesis tests defended in writing, mixed with earlier phases
Topics Covered
- Linear relationship between variables
- Least squares estimation
- Geometric interpretation of least squares
- Normal equations derivation
- Properties of least squares estimators
- Gauss-Markov theorem
- R-squared and adjusted R-squared
- Residual analysis
- Assumptions of linear regression
- Diagnostic plots: Q-Q, residual plots
- Outliers and influential points
- Confidence and prediction intervals for regression
Projects You Build
- Linear regression from scratch
- Regression diagnostics tool
- Outlier detection system
Practice & Assignments
Build 50 linear regression models
Topics Covered
- Multiple regression model
- Matrix formulation of regression
- Partial regression coefficients
- Multicollinearity detection and handling
- Variance Inflation Factor (VIF)
- Feature selection methods
- Forward, backward, stepwise selection
- All subsets regression
- Adjusted R-squared and model selection
- AIC, BIC, Mallows' Cp
- Cross-validation for model selection
- Interaction terms and polynomial regression
Projects You Build
- Multiple regression toolkit
- Feature selection system
- Model comparison framework
Practice & Assignments
Develop 50 multiple regression models
Assessment
Month 7 check: fit, diagnose and defend a regression on real data
Topics Covered
- Overfitting and bias-variance tradeoff
- Ridge regression (L2 regularization)
- Ridge regression geometry
- LASSO regression (L1 regularization)
- LASSO for feature selection
- Elastic Net regression
- Choosing regularization parameters
- Cross-validation for lambda selection
- Bayesian interpretation of regularization
- Group LASSO
- Adaptive LASSO
- Applications in high-dimensional data
Projects You Build
- Regularized regression implementation
- Lambda tuning system
- High-dimensional regression tool
Practice & Assignments
Apply regularization to 40 datasets
Topics Covered
- Classification vs regression
- Bayes classifier and Bayes error
- Linear Discriminant Analysis (LDA)
- Quadratic Discriminant Analysis (QDA)
- Fisher's linear discriminant
- Naive Bayes classifier
- Gaussian Naive Bayes
- Multinomial and Bernoulli Naive Bayes
- K-Nearest Neighbors classification
- Distance metrics for KNN
- Decision boundaries visualization
- Class imbalance problems
- Logistic regression as a generalized linear model
Projects You Build
- Classifier comparison framework
- Decision boundary visualizer
- Imbalanced data handler
Practice & Assignments
Implement 50 classification models
Assessment
Month 8 check: a classification problem end to end, plus mixed regression revision
Topics Covered
- Decision trees for classification
- Entropy and information gain
- Gini impurity
- Tree pruning methods
- Cost complexity pruning
- Random Forests algorithm
- Out-of-bag error estimation
- Feature importance from trees
- Extremely Randomized Trees
- Gradient Boosting Machines (GBM)
- XGBoost mathematics
- LightGBM and CatBoost
Projects You Build
- Decision tree from scratch
- Random Forest implementation
- Boosting algorithm suite
Practice & Assignments
Build 40 tree-based models
Topics Covered
- K-means clustering algorithm
- K-means++ initialization
- Elbow method and silhouette analysis
- Hierarchical clustering
- Agglomerative vs divisive
- Linkage methods: single, complete, average
- Dendrograms and cutting trees
- DBSCAN algorithm
- Mean Shift clustering
- Gaussian Mixture Models (GMM)
- EM algorithm for GMMs
- Spectral clustering
- Model evaluation essentials: cross-validation, metrics and the leakage trap
- Choosing models like an adult: bias, variance and the problem in front of you
Projects You Build
- Clustering algorithm suite
- Cluster validation tools
- Optimal K finder
Practice & Assignments
Apply clustering to 40 datasets
Assessment
Phase 3 exam: build, evaluate and defend two models on one dataset, mixed with earlier phases
Topics Covered
- Convex sets and convex functions
- Convexity in machine learning
- Gradient descent algorithm
- Learning rate selection
- Momentum and Nesterov acceleration
- AdaGrad and RMSprop
- Adam and AdamW optimizers
- Second-order methods: Newton, L-BFGS
- Stochastic gradient descent (SGD)
- Mini-batch gradient descent
- Convergence analysis
- Constrained optimization for ML
Projects You Build
- Optimizer implementations
- Convergence visualizer
- Learning rate scheduler
Practice & Assignments
Implement 20 optimization algorithms
Topics Covered
- Perceptron algorithm
- Multi-layer perceptrons
- Universal approximation theorem
- Activation functions: sigmoid, tanh, ReLU
- Forward propagation mathematics
- Backpropagation derivation
- Chain rule in neural networks
- Gradient vanishing and exploding
- Weight initialization strategies
- Xavier and He initialization
- Batch normalization mathematics
- Dropout as regularization
- Where this leads: transformers and attention, mapped honestly for the AI/ML masterclass
Projects You Build
- Neural network from scratch
- Backpropagation visualizer
- Activation function explorer
Practice & Assignments
Build 30 neural network architectures
Assessment
Month 10 check: gradient descent by hand on a small network, plus mixed review
Topics Covered
- Bayesian vs Frequentist philosophy
- Prior distributions and their selection
- Likelihood functions
- Posterior distributions
- Conjugate priors
- Beta-Binomial model
- Normal-Normal model
- Gamma-Poisson model
- Credible intervals vs confidence intervals
- Bayesian point estimates
- MAP vs MLE estimates
- Empirical Bayes methods
Projects You Build
- Bayesian inference engine
- Prior selection tool
- Posterior calculator
Practice & Assignments
Solve 100 Bayesian inference problems
Topics Covered
- Time series components: trend, seasonality, noise
- Stationarity and unit root tests
- Autocorrelation and partial autocorrelation
- ARIMA models
- Box-Jenkins methodology
- Seasonal ARIMA (SARIMA)
- State space models
- Kalman filtering
- Exponential smoothing methods
- Holt-Winters method
- STL decomposition
- Time series cross-validation
Projects You Build
- Time series toolkit
- ARIMA model builder
- Forecast evaluator
Practice & Assignments
Analyze 50 time series
Assessment
Month 11 check: one Bayesian update argued in plain language, one forecast defended
Topics Covered
- A/B testing fundamentals
- Statistical power in A/B tests
- Multiple testing corrections
- Sequential testing
- Bandits vs A/B tests
- Multi-armed bandits
- Thompson sampling
- Contextual bandits
- Variance reduction techniques
- CUPED method
- Stratification in experiments
- Network effects in testing
- Design of experiments: the checklist before any test ships
- Ethics and interpretability: what a responsible analyst refuses to do
Projects You Build
- A/B testing platform
- Bandit algorithm suite
- Variance reduction tool
Practice & Assignments
Run 40 A/B tests
Topics Covered
- The capstone: one real dataset, one honest question, full analysis
- From exploration to inference to model to recommendation
- Writing the analysis so a skeptic cannot shake it
- Presenting quantitative work to non-quantitative people
- A full-course spiral review, exam technique included
Projects You Build
- The capstone analysis: explored, modeled, tested and written up defensibly, presented to the batch
Practice & Assignments
Daily mixed revision sets through the final fortnight
Assessment
FINAL EXAM: a written paper plus a practical analysis, with questions mixed from every phase. Passing earns the certificate; falling short earns a focused revision plan and a free retest
Projects You'll Build
Build a professional portfolio with 25+ applied analyses, ending with a defensible capstone on real data real-world projects.
Weekly Learning Structure
Certification & Recognition
Technologies & Skills You'll Master
Comprehensive coverage of the entire modern web development stack.
Support & Resources
Career Outcomes & Opportunities
Transform your career with industry-ready skills and job placement support.
Prerequisites
Who Is This Course For?
Career Paths After Completion
Salary & Market Context
The ranges below are general market salary bands for these roles in India and abroad, drawn from public industry data. They are shown for career context only and are not a promise or guarantee of income. Actual pay depends on your skills, experience, location, and the job market.
Course Guarantees
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Straight answers about Maths for Data Science: Statistics, Linear Algebra and ML
- Who should take this course?
- School-level maths assumed; built for college students and working professionals. Age: College students and working professionals (18+). It suits students and professionals aiming at data analyst and data science roles who keep hitting the maths wall; people fluent in excel, sql or pandas who want to finally understand what the numbers are doing; candidates whose next round is statistics, probability and ml fundamentals.
- What will they learn and build?
- Every data career eventually hits the same wall: the tools are easy, the mathematics behind them is not, and interviews, promotions and real analytical judgment all live on the far side of that wall.
- How deeply are topics covered?
- The course runs 12-14 months (48-56 weeks) at 2 live classes/week + 4-6 hours practice, across 4 phases listed week by week in the syllabus below. A structured, well-paced curriculum taught step by step, with classwork in every session and problem sets after every class.
- Who teaches it?
- Modern Age Coders mentors, who teach the live classes themselves. You can watch them at work in the free class recordings before you decide.
- How do practice, feedback and assessment work?
- Monthly mixed reviews and a final exam that decides the certificate: real knowledge, real work. Doubt support between classes over WhatsApp, so you are never left stuck. A certificate you earn by passing the final exam, with a free retest after revision if needed.
- What does it cost?
- Three monthly plans: a group batch, a mini batch and 1-on-1. Prices are shown in your currency in the plans section. Monthly billing, cancel any time.
- When can classes take place?
- Live classes are scheduled around your week. Group batches meet at a fixed weekly slot; 1-on-1 students choose their own. International students are scheduled in their own timezone. Ask on WhatsApp for the current slots.
- Can I watch the teaching before deciding?
- Yes. Full recordings of real 13 and up classes are free to watch, free with a Google sign-in. These recordings show how we teach, not the exact syllabus of this course. Some classes are in English and some in Hindi; everyone follows at their own pace. Watch a class end to end, like you are in it. Sessions are interactive and each moment builds on the last.
- Can I enroll without a live demo?
- Yes. Choose a plan on this page and enroll directly; a booking or a demo is not required. A free live demo is optional, for anyone who wants to meet a mentor first. Outside India, our team confirms the plan and completes payment with you over WhatsApp, so allow a little time for that step.
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