--- title: "Complete Data & Analytics Mathematics Masterclass - Statistics to Machine Learning" description: "The most comprehensive 2-year data science mathematics program. Master statistics, probability, linear algebra for ML, optimization, deep learning mathematics, Bayesian methods, causal inference, and cutting-edge analytics techniques. Build the mathematical foundation for AI and data science." slug: data-analytics-mathematics-masterclass canonical: https://learn.modernagecoders.com/courses/data-analytics-mathematics-masterclass/ category: "Data Science & Analytics Mathematics" keywords: ["data science mathematics", "statistical analysis", "machine learning math", "probability theory", "linear algebra for ML", "optimization theory", "deep learning mathematics", "bayesian statistics", "time series analysis", "causal inference"] --- # Complete Data & Analytics Mathematics Masterclass - Statistics to Machine Learning > The most comprehensive 2-year data science mathematics program. Master statistics, probability, linear algebra for ML, optimization, deep learning mathematics, Bayesian methods, causal inference, and cutting-edge analytics techniques. Build the mathematical foundation for AI and data science. **Level:** Basic Math Knowledge to Advanced Data Science Mathematics **Duration:** 24 months (104 weeks) **Commitment:** 20-25 hours/week recommended **Certification:** Data Science Mathematics Expert Certificate upon completion **Group classes:** ₹1499/month **1-on-1:** ₹4999/month **Lifetime:** ₹89,999 (one-time) ## Complete Data & Analytics Mathematics Masterclass *From Statistical Basics to Advanced AI Mathematics - Master the Math Behind Data Science* This intensive 2-year program provides complete mathematical foundations for data science, machine learning, and AI. Whether you're aspiring to be a data scientist, ML engineer, quantitative analyst, or AI researcher, this masterclass gives you the deep mathematical understanding needed for excellence. You'll master statistical thinking, probability theory, linear algebra for ML, optimization methods, deep learning mathematics, Bayesian inference, causal analysis, and more. Learn not just formulas but the intuition behind algorithms. By completion, you'll understand the mathematics behind every major data science and ML technique. **What Makes This Different:** - Specifically designed for data science applications - Heavy emphasis on practical implementation - Python/R code alongside mathematical concepts - Real datasets and industry case studies - Covers both classical and modern techniques - Deep learning and AI mathematics included - Interview preparation for data science roles - Industry-relevant projects throughout ### Learning Path **Phase 1:** Foundation (Months 1-6): Statistics, Probability, Linear Algebra Essentials **Phase 2:** Core Analytics (Months 7-12): Statistical Inference, Regression, Classification, Clustering **Phase 3:** Advanced ML Math (Months 13-18): Optimization, Deep Learning, Bayesian Methods **Phase 4:** Cutting Edge (Months 19-24): Causal Inference, Time Series, Big Data, Research **Career Outcomes:** - Data Scientist - Machine Learning Engineer - Quantitative Analyst - AI/ML Researcher - Statistical Consultant - Business Intelligence Analyst - Data Engineer (Analytics) - Research Scientist ## PHASE 1: Mathematical Foundations for Data Science (Months 1-6, Weeks 1-26) Build rock-solid foundations in statistics, probability, and linear algebra essential for data science. ### Month 1 2 #### Months 1-2: Descriptive Statistics & Data Fundamentals **Weeks:** Week 1-8 ##### Week 1 2 ###### Introduction to Statistical Thinking **Topics:** - 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:** - Design a data collection strategy - Data quality assessment tool - Sampling simulation study **Practice:** Analyze 20 real-world datasets for quality issues ##### Week 3 4 ###### Measures of Central Tendency and Spread **Topics:** - 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:** - Statistical calculator from scratch - Outlier detection system - Interactive visualization dashboard **Practice:** Calculate statistics for 50 different distributions ##### Week 5 6 ###### Data Visualization and Graphical Analysis **Topics:** - 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:** - Build comprehensive EDA toolkit - Create interactive data dashboard - Visualization best practices guide **Practice:** Create 100 different types of visualizations ##### Week 7 8 ###### Probability Fundamentals **Topics:** - 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:** - Probability simulator - Bayes theorem calculator - Monte Carlo estimation tool **Practice:** Solve 150 probability problems with data applications ### Month 3 4 #### Months 3-4: Probability Distributions & Linear Algebra Basics **Weeks:** Week 9-17 ##### Week 9 10 ###### Discrete Probability Distributions **Topics:** - 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:** - Distribution calculator and visualizer - A/B test simulator - Discrete event simulator **Practice:** Work with 100 discrete distribution problems ##### Week 11 12 ###### Continuous Probability Distributions **Topics:** - 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:** - Distribution fitting tool - Normal distribution simulator - Reliability analysis system **Practice:** Master 100 continuous distribution applications ##### Week 13 14 ###### Linear Algebra for Data Science - Vectors **Topics:** - 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:** - Vector similarity calculator - Distance metric visualizer - Feature space explorer **Practice:** Complete 100 vector operations in data context ##### Week 15 16 ###### Linear Algebra for Data Science - Matrices **Topics:** - 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:** - Matrix operations library - Linear system solver - Sparse matrix handler **Practice:** Solve 100 matrix problems with data applications ##### Week 17 ###### Eigenvalues and PCA Foundations **Topics:** - 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:** - PCA implementation from scratch - Eigenface recognition system - Dimensionality reduction tool **Practice:** Apply PCA to 20 different datasets ### Month 5 6 #### Months 5-6: Statistical Inference & Hypothesis Testing **Weeks:** Week 18-26 ##### Week 18 19 ###### Sampling Distributions and CLT **Topics:** - 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:** - CLT demonstration tool - Sample size calculator - Sampling distribution simulator **Practice:** Explore 50 sampling distribution scenarios ##### Week 20 21 ###### Confidence Intervals **Topics:** - 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:** - Confidence interval calculator - Bootstrap CI implementation - CI visualization tool **Practice:** Calculate 100 different confidence intervals ##### Week 22 23 ###### Hypothesis Testing Fundamentals **Topics:** - 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 **Projects:** - Hypothesis testing framework - Power analysis tool - A/B testing platform **Practice:** Conduct 100 hypothesis tests ##### Week 24 25 ###### ANOVA and Multiple Comparisons **Topics:** - One-way ANOVA principles - F-statistic and ANOVA table - Assumptions of ANOVA - Post-hoc tests: Tukey, Bonferroni, Scheffé - Two-way ANOVA - Interaction effects - Repeated measures ANOVA - MANOVA basics - Kruskal-Wallis test (nonparametric) - Multiple testing problem - False Discovery Rate (FDR) - Benjamini-Hochberg procedure **Projects:** - ANOVA analysis suite - Multiple comparison visualizer - FDR control system **Practice:** Perform 50 ANOVA analyses ##### Week 26 ###### Phase 1 Capstone Project **Topics:** - Complete statistical analysis pipeline - Integration of all Phase 1 concepts - Report writing and presentation - Reproducible research practices - Statistical consulting simulation **Projects:** - MAJOR CAPSTONE: End-to-End Statistical Analysis - Complete EDA and inference on real dataset - Build statistical analysis dashboard - Create statistical consulting report **Assessment:** Phase 1 Comprehensive Exam - Foundations ## PHASE 2: Core Analytics & Machine Learning Mathematics (Months 7-12, Weeks 27-52) Master regression, classification, clustering, and core machine learning mathematics. ### Month 7 8 #### Months 7-8: Regression Analysis **Weeks:** Week 27-35 ##### Week 27 28 ###### Simple Linear Regression **Topics:** - 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:** - Linear regression from scratch - Regression diagnostics tool - Outlier detection system **Practice:** Build 50 linear regression models ##### Week 29 30 ###### Multiple Linear Regression **Topics:** - 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:** - Multiple regression toolkit - Feature selection system - Model comparison framework **Practice:** Develop 50 multiple regression models ##### Week 31 32 ###### Regularized Regression **Topics:** - 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:** - Regularized regression implementation - Lambda tuning system - High-dimensional regression tool **Practice:** Apply regularization to 40 datasets ##### Week 33 34 ###### Generalized Linear Models **Topics:** - Exponential family of distributions - Link functions and canonical links - Logistic regression for binary outcomes - Maximum likelihood estimation for GLMs - Newton-Raphson and IRLS algorithms - Odds ratios and interpretation - Poisson regression for count data - Negative binomial regression - Ordinal logistic regression - Multinomial logistic regression - Deviance and goodness of fit - Quasi-likelihood methods **Projects:** - GLM framework implementation - Logistic regression classifier - Count data modeling tool **Practice:** Build 50 different GLMs ##### Week 35 ###### Nonparametric Regression **Topics:** - Kernel regression - Local polynomial regression (LOESS) - Bandwidth selection - Spline regression - Smoothing splines - Penalized splines - Generalized Additive Models (GAMs) - Regression trees basics - K-nearest neighbors regression - Gaussian Process regression introduction - Quantile regression - Robust regression methods **Projects:** - Nonparametric regression suite - GAM implementation - Smoothing parameter selector **Practice:** Compare 30 parametric vs nonparametric models ### Month 9 10 #### Months 9-10: Classification & Clustering **Weeks:** Week 36-44 ##### Week 36 37 ###### Classification Fundamentals **Topics:** - 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 **Projects:** - Classifier comparison framework - Decision boundary visualizer - Imbalanced data handler **Practice:** Implement 50 classification models ##### Week 38 39 ###### Tree-Based Methods **Topics:** - 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:** - Decision tree from scratch - Random Forest implementation - Boosting algorithm suite **Practice:** Build 40 tree-based models ##### Week 40 41 ###### Support Vector Machines **Topics:** - Maximum margin classifiers - Hard margin SVM - Soft margin SVM and slack variables - Lagrangian formulation - Dual problem and support vectors - Kernel trick and Mercer's theorem - Common kernels: RBF, polynomial, sigmoid - Multi-class SVM strategies - SVM for regression (SVR) - Nu-SVM and One-class SVM - Kernel selection and tuning - SMO algorithm basics **Projects:** - SVM implementation from scratch - Kernel comparison tool - SVM hyperparameter tuner **Practice:** Train 50 SVM models with different kernels ##### Week 42 43 ###### Clustering Algorithms **Topics:** - 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 **Projects:** - Clustering algorithm suite - Cluster validation tools - Optimal K finder **Practice:** Apply clustering to 40 datasets ##### Week 44 ###### Model Evaluation and Selection **Topics:** - Confusion matrix and derived metrics - Precision, recall, F1-score - ROC curves and AUC - Precision-recall curves - Multi-class metrics - Cross-validation strategies - Stratified and time series CV - Nested cross-validation - Bootstrap validation - Learning curves - Validation curves - Grid search and random search **Projects:** - Model evaluation framework - Hyperparameter optimization tool - Model comparison dashboard **Practice:** Evaluate 50 models comprehensively ### Month 11 12 #### Months 11-12: Optimization & Neural Network Mathematics **Weeks:** Week 45-52 ##### Week 45 46 ###### Optimization Theory for ML **Topics:** - 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:** - Optimizer implementations - Convergence visualizer - Learning rate scheduler **Practice:** Implement 20 optimization algorithms ##### Week 47 48 ###### Neural Network Fundamentals **Topics:** - 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 **Projects:** - Neural network from scratch - Backpropagation visualizer - Activation function explorer **Practice:** Build 30 neural network architectures ##### Week 49 50 ###### Convolutional Neural Networks Mathematics **Topics:** - Convolution operation in 1D and 2D - Padding and stride calculations - Pooling operations: max, average - Parameter sharing and translation invariance - Receptive field calculations - Backpropagation through convolutions - Popular architectures: LeNet, AlexNet, VGG - ResNet and skip connections - Inception modules - Depthwise separable convolutions - Transfer learning mathematics - Feature map visualization **Projects:** - CNN implementation from scratch - Convolution visualizer - Architecture comparison tool **Practice:** Implement 20 CNN architectures ##### Week 51 ###### Recurrent Neural Networks Mathematics **Topics:** - Vanilla RNN formulation - Backpropagation through time (BPTT) - Gradient clipping - Long Short-Term Memory (LSTM) - LSTM gates mathematics - Gated Recurrent Units (GRU) - Bidirectional RNNs - Encoder-decoder architectures - Attention mechanism basics - Sequence-to-sequence models - Applications to time series - RNN regularization techniques **Projects:** - RNN/LSTM from scratch - Sequence prediction tool - Attention visualizer **Practice:** Build 20 RNN models ##### Week 52 ###### Phase 2 Capstone Project **Topics:** - End-to-end ML pipeline - Model deployment considerations - A/B testing for ML - Model monitoring - ML system design **Projects:** - MAJOR CAPSTONE: Complete ML System - Build production ML pipeline - Implement model monitoring - Create ML API service **Assessment:** Phase 2 Comprehensive Exam - ML Mathematics ## PHASE 3: Advanced Analytics & Deep Learning (Months 13-18, Weeks 53-78) Master Bayesian methods, deep learning, reinforcement learning, and advanced statistical techniques. ### Month 13 14 #### Months 13-14: Bayesian Statistics & Inference **Weeks:** Week 53-61 ##### Week 53 54 ###### Bayesian Fundamentals **Topics:** - 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:** - Bayesian inference engine - Prior selection tool - Posterior calculator **Practice:** Solve 100 Bayesian inference problems ##### Week 55 56 ###### Markov Chain Monte Carlo **Topics:** - Monte Carlo integration review - Importance sampling - Markov chains for sampling - Metropolis algorithm - Metropolis-Hastings algorithm - Gibbs sampling - Convergence diagnostics - Gelman-Rubin statistic - Effective sample size - Hamiltonian Monte Carlo - NUTS sampler - Variational inference basics **Projects:** - MCMC sampler implementation - Convergence diagnostic suite - HMC from scratch **Practice:** Implement 20 MCMC algorithms ##### Week 57 58 ###### Bayesian Regression and Classification **Topics:** - Bayesian linear regression - Predictive distributions - Bayesian model averaging - Spike and slab priors - Horseshoe prior - Bayesian logistic regression - Probit regression - Gaussian processes for regression - Kernel selection in GPs - Sparse Gaussian processes - Bayesian neural networks - Uncertainty quantification **Projects:** - Bayesian regression toolkit - GP implementation - Uncertainty visualization **Practice:** Build 50 Bayesian models ##### Week 59 60 ###### Hierarchical and Mixture Models **Topics:** - Hierarchical Bayesian models - Random effects models - Mixed effects models - Nested data structures - Shrinkage and pooling - Dirichlet process mixtures - Infinite mixture models - Chinese Restaurant Process - Stick-breaking construction - Latent Dirichlet Allocation - Topic modeling - Hidden Markov Models **Projects:** - Hierarchical model builder - Topic modeling system - HMM implementation **Practice:** Develop 30 hierarchical models ##### Week 61 ###### Bayesian Model Selection **Topics:** - Bayes factors - Model evidence and marginal likelihood - Savage-Dickey density ratio - DIC and WAIC - LOO cross-validation - Posterior predictive checks - Model comparison strategies - Bayesian hypothesis testing - Reversible jump MCMC - Bayesian variable selection - Bayesian model averaging - Ensemble methods in Bayesian context **Projects:** - Model comparison framework - Bayes factor calculator - Model selection tool **Practice:** Compare 40 Bayesian models ### Month 15 16 #### Months 15-16: Deep Learning & Advanced Architectures **Weeks:** Week 62-70 ##### Week 62 63 ###### Advanced Deep Learning Theory **Topics:** - Deep learning optimization landscape - Loss surface geometry - Mode connectivity - Lottery ticket hypothesis - Neural tangent kernels - Double descent phenomenon - Implicit regularization - Neural architecture search - AutoML for deep learning - Meta-learning basics - Few-shot learning - Self-supervised learning **Projects:** - NAS implementation - Meta-learning framework - Self-supervised trainer **Practice:** Explore 30 advanced DL concepts ##### Week 64 65 ###### Transformers and Attention **Topics:** - Self-attention mechanism - Multi-head attention - Positional encoding - Transformer architecture - BERT and GPT architectures - Vision Transformers (ViT) - Cross-attention mechanisms - Efficient attention variants - Linear attention - Sparse transformers - Transformer training dynamics - Large language model mathematics **Projects:** - Transformer from scratch - Attention mechanism visualizer - Mini-BERT implementation **Practice:** Build 20 transformer models ##### Week 66 67 ###### Generative Models **Topics:** - Variational Autoencoders (VAE) - ELBO derivation - Reparameterization trick - Beta-VAE and disentanglement - Generative Adversarial Networks (GANs) - Wasserstein GAN - GAN training dynamics - Mode collapse solutions - Normalizing flows - Diffusion models mathematics - Score matching - Energy-based models **Projects:** - VAE implementation - GAN from scratch - Diffusion model builder **Practice:** Train 30 generative models ##### Week 68 69 ###### Graph Neural Networks **Topics:** - Graph representation learning - Message passing neural networks - Graph Convolutional Networks (GCN) - GraphSAGE algorithm - Graph Attention Networks (GAT) - Spectral graph convolutions - Graph pooling methods - Link prediction - Node classification - Graph classification - Knowledge graph embeddings - Geometric deep learning **Projects:** - GNN implementation suite - Graph embedding visualizer - Knowledge graph builder **Practice:** Apply GNNs to 20 graph datasets ##### Week 70 ###### Reinforcement Learning Mathematics **Topics:** - Markov Decision Processes - Bellman equations - Value iteration - Policy iteration - Q-learning algorithm - Deep Q-Networks (DQN) - Policy gradient methods - REINFORCE algorithm - Actor-Critic methods - Proximal Policy Optimization (PPO) - Soft Actor-Critic (SAC) - Multi-armed bandits **Projects:** - RL environment builder - Q-learning implementation - Policy gradient trainer **Practice:** Solve 20 RL problems ### Month 17 18 #### Months 17-18: Time Series & Causal Inference **Weeks:** Week 71-78 ##### Week 71 72 ###### Time Series Analysis **Topics:** - 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:** - Time series toolkit - ARIMA model builder - Forecast evaluator **Practice:** Analyze 50 time series ##### Week 73 74 ###### Advanced Time Series Methods **Topics:** - Vector Autoregression (VAR) - Cointegration and error correction - GARCH models for volatility - Long memory models (ARFIMA) - Regime switching models - Dynamic Factor Models - Spectral analysis - Wavelet analysis - Deep learning for time series - LSTM for forecasting - Temporal Convolutional Networks - Prophet algorithm **Projects:** - Advanced TS model suite - Volatility forecaster - DL time series framework **Practice:** Implement 30 advanced TS models ##### Week 75 76 ###### Causal Inference **Topics:** - Correlation vs causation - Potential outcomes framework - Average Treatment Effect (ATE) - Randomized experiments - Selection bias and confounding - Propensity score matching - Inverse probability weighting - Doubly robust estimation - Instrumental variables - Regression discontinuity - Difference-in-differences - Synthetic control methods **Projects:** - Causal inference toolkit - Matching algorithm suite - Treatment effect estimator **Practice:** Apply causal methods to 40 datasets ##### Week 77 ###### Structural Equation Modeling **Topics:** - Path analysis - Confirmatory factor analysis - Structural equation models - Latent variable models - Measurement models - Model identification - Maximum likelihood for SEM - Fit indices and model evaluation - Multi-group SEM - Growth curve models - Mediation and moderation - Directed Acyclic Graphs (DAGs) **Projects:** - SEM implementation - DAG builder - Mediation analyzer **Practice:** Build 20 structural models ##### Week 78 ###### Phase 3 Capstone Project **Topics:** - Advanced analytics pipeline - Deep learning deployment - Causal analysis project - Research paper writing - Industry presentation **Projects:** - MAJOR CAPSTONE: Advanced Analytics System - Deploy production DL model - Conduct causal analysis study - Write research-quality paper **Assessment:** Phase 3 Comprehensive Exam - Advanced Analytics ## PHASE 4: Big Data, Production Systems & Research (Months 19-24, Weeks 79-104) Master big data analytics, production ML systems, experimental design, and conduct original research. ### Month 19 20 #### Months 19-20: Big Data & Distributed Analytics **Weeks:** Week 79-87 ##### Week 79 80 ###### Big Data Fundamentals **Topics:** - Big data characteristics: 5 V's - Distributed computing principles - CAP theorem and data consistency - MapReduce paradigm - Hadoop ecosystem overview - HDFS architecture - Apache Spark fundamentals - RDDs and DataFrames - Spark SQL and optimization - Spark MLlib algorithms - Streaming data concepts - Lambda and Kappa architectures **Projects:** - Distributed computing setup - MapReduce implementation - Spark ML pipeline **Practice:** Process 20 big data workloads ##### Week 81 82 ###### Scalable Machine Learning **Topics:** - Distributed gradient descent - Parameter server architecture - Data parallelism vs model parallelism - Federated learning - Online learning algorithms - Stochastic gradient methods at scale - Approximate algorithms for big data - Random sampling techniques - Sketching algorithms - MinHash and LSH - Bloom filters - Count-Min sketch **Projects:** - Distributed ML trainer - Federated learning system - Sketching algorithm suite **Practice:** Implement 30 scalable algorithms ##### Week 83 84 ###### Stream Processing & Real-time Analytics **Topics:** - Stream processing concepts - Apache Kafka architecture - Apache Flink fundamentals - Window functions in streaming - Watermarks and late data - Exactly-once processing - Complex event processing - Real-time aggregations - Streaming ML predictions - Online learning in streams - Anomaly detection in streams - Time series databases **Projects:** - Stream processing pipeline - Real-time dashboard - Anomaly detection system **Practice:** Build 20 streaming applications ##### Week 85 86 ###### NoSQL and NewSQL for Analytics **Topics:** - NoSQL database types - Document stores: MongoDB analytics - Column stores: Cassandra, HBase - Graph databases for analytics - Time series databases: InfluxDB, TimescaleDB - NewSQL systems - Data modeling for NoSQL - CAP theorem implications - Consistency models - Data warehousing concepts - Data lakes vs data warehouses - Apache Iceberg and Delta Lake **Projects:** - Multi-database analytics system - Data lake implementation - NoSQL analytics toolkit **Practice:** Design 20 data architectures ##### Week 87 ###### Cloud Analytics Platforms **Topics:** - Cloud computing for analytics - AWS analytics services - Google Cloud Platform ML tools - Azure Machine Learning - Serverless analytics - Auto-scaling for ML workloads - Cost optimization strategies - Multi-cloud strategies - Data governance in cloud - Security and compliance - MLOps in cloud - Edge analytics **Projects:** - Cloud ML pipeline - Serverless analytics app - Multi-cloud deployment **Practice:** Deploy 20 cloud analytics solutions ### Month 21 22 #### Months 21-22: Experimental Design & A/B Testing **Weeks:** Week 88-96 ##### Week 88 89 ###### Design of Experiments **Topics:** - Principles of experimental design - Randomization, replication, blocking - Completely randomized designs - Randomized block designs - Latin square designs - Factorial designs - 2^k factorial designs - Fractional factorial designs - Response surface methodology - Central composite designs - Optimal design theory - Sample size calculations **Projects:** - Experiment design tool - Power calculator - Optimal design finder **Practice:** Design 50 experiments ##### Week 90 91 ###### A/B Testing at Scale **Topics:** - 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 **Projects:** - A/B testing platform - Bandit algorithm suite - Variance reduction tool **Practice:** Run 40 A/B tests ##### Week 92 93 ###### Quasi-Experimental Methods **Topics:** - Natural experiments - Interrupted time series - Regression discontinuity design - Fuzzy RDD - Difference-in-differences advanced - Triple differences - Synthetic control advanced - Matching methods review - Coarsened exact matching - Genetic matching - Sensitivity analysis - Bounds for causal effects **Projects:** - Quasi-experimental toolkit - RDD analyzer - Sensitivity analysis suite **Practice:** Apply 30 quasi-experimental designs ##### Week 94 95 ###### Survival Analysis **Topics:** - Censoring and truncation - Survival and hazard functions - Kaplan-Meier estimator - Nelson-Aalen estimator - Log-rank test - Cox proportional hazards model - Stratified Cox models - Time-varying covariates - Parametric survival models - Accelerated failure time models - Competing risks - Recurrent events analysis **Projects:** - Survival analysis toolkit - Cox model implementation - Competing risks analyzer **Practice:** Analyze 30 survival datasets ##### Week 96 ###### Longitudinal Data Analysis **Topics:** - Repeated measures data - Mixed effects models review - Generalized Estimating Equations (GEE) - Growth curve models - Latent growth models - Cross-lagged panel models - Dynamic panel data models - Fixed effects vs random effects - Hausman test - Missing data in longitudinal studies - Multiple imputation - Attrition and selection bias **Projects:** - Longitudinal analysis suite - Panel data toolkit - Imputation system **Practice:** Analyze 25 longitudinal studies ### Month 23 #### Month 23: Advanced Topics & Specializations **Weeks:** Week 97-100 ##### Week 97 ###### Spatial Statistics & GIS **Topics:** - Spatial data types - Spatial autocorrelation - Moran's I and Geary's C - Spatial regression models - Kriging and interpolation - Point pattern analysis - Spatial clustering - Geographically weighted regression - Space-time models - Disease mapping - Environmental statistics - GIS integration **Projects:** - Spatial analysis toolkit - Kriging implementation - Disease mapping system **Practice:** Analyze 20 spatial datasets ##### Week 98 ###### Text Analytics & NLP Mathematics **Topics:** - Text preprocessing mathematics - TF-IDF and BM25 - Word embeddings: Word2Vec, GloVe - Document embeddings - Topic modeling: LDA, NMF - Named entity recognition - Part-of-speech tagging - Dependency parsing - Sentiment analysis methods - Text classification algorithms - Sequence labeling with CRFs - Transformer-based NLP **Projects:** - NLP pipeline builder - Topic modeling system - Sentiment analyzer **Practice:** Build 30 NLP applications ##### Week 99 ###### Computer Vision Mathematics **Topics:** - Image processing fundamentals - Convolution and filtering - Edge detection algorithms - Feature extraction: SIFT, SURF, HOG - Image segmentation methods - Object detection: R-CNN family - YOLO architecture - Semantic segmentation - Instance segmentation - Face recognition mathematics - Optical flow - 3D vision basics **Projects:** - CV algorithm suite - Object detector - Segmentation tool **Practice:** Implement 25 CV algorithms ##### Week 100 ###### Recommendation Systems **Topics:** - Collaborative filtering - User-based vs item-based CF - Matrix factorization methods - Singular value decomposition - Non-negative matrix factorization - Alternating least squares - Content-based filtering - Hybrid recommendation systems - Deep learning for recommendations - Sequential recommendations - Multi-stakeholder recommendations - Evaluation metrics for RecSys **Projects:** - Recommendation engine - Matrix factorization suite - Hybrid recommender **Practice:** Build 20 recommendation systems ### Month 24 #### Month 24: MLOps, Ethics & Career Preparation **Weeks:** Week 101-104 ##### Week 101 102 ###### MLOps & Production Systems **Topics:** - ML system design patterns - Feature engineering pipelines - Feature stores - Model versioning - Experiment tracking - Model registry - CI/CD for ML - Model serving architectures - Batch vs online inference - Model monitoring and drift detection - A/B testing for ML models - Rollback strategies - Edge deployment - Model compression techniques - Quantization and pruning **Projects:** - FINAL CAPSTONE: Production ML System - Complete MLOps pipeline - Model monitoring dashboard - Feature store implementation ##### Week 103 ###### Ethics, Fairness & Interpretability **Topics:** - Bias in data and algorithms - Fairness metrics - Demographic parity - Equalized odds - Calibration - Fair ML algorithms - Model interpretability methods - LIME and SHAP - Counterfactual explanations - Privacy-preserving ML - Differential privacy - Federated learning for privacy - AI governance - Regulatory compliance **Deliverables:** - Fairness audit toolkit - Interpretability framework - Privacy-preserving ML system - Ethics guidelines document ##### Week 104 ###### Research & Career Development **Topics:** - Reading research papers effectively - Reproducing research results - Writing technical reports - Creating data science portfolio - Interview preparation for DS roles - Case study methodology - Technical presentation skills - Open source contribution - Kaggle competition strategies - Networking in data science - Continuous learning strategies - Career paths in data science **Deliverables:** - Research paper implementation - Complete portfolio website - Kaggle competition submission - Technical blog posts - Interview preparation materials - Career roadmap document **Assessment:** FINAL COMPREHENSIVE EXAM - Complete Data Science Mathematics ## Additional Learning Resources **Projects Throughout Course:** - Phase 1: Statistical analysis dashboards, EDA tools, Probability simulators, PCA implementations - Phase 2: ML pipelines, Classification systems, Clustering tools, Neural networks from scratch - Phase 3: Bayesian models, Deep learning architectures, Time series forecasters, Causal analysis - Phase 4: Big data systems, A/B testing platforms, Production ML services, Research projects **Total Projects Built:** 200+ data science projects and implementations **Skills Mastered:** - Statistics: Descriptive, Inferential, Bayesian, Frequentist, Nonparametric - Machine Learning: Supervised, Unsupervised, Semi-supervised, Reinforcement Learning - Deep Learning: CNNs, RNNs, Transformers, GANs, VAEs, GNNs - Optimization: Convex, Non-convex, Stochastic, Constrained, Multi-objective - Time Series: ARIMA, State Space, Deep Learning methods, Forecasting - Causal Inference: RCTs, Observational studies, Natural experiments, IV methods - Big Data: Spark, Streaming, Distributed ML, NoSQL analytics - Production: MLOps, Monitoring, A/B testing, Model deployment - Specialized: NLP, Computer Vision, RecSys, Spatial statistics #### Weekly Structure **Theory Lectures:** 8-10 hours **Hands On Coding:** 8-10 hours **Projects:** 3-4 hours **Paper Reading:** 2-3 hours **Practice Problems:** 2-3 hours **Total Per Week:** 20-25 hours #### Support Provided **Mentorship:** 1-on-1 mentoring sessions **Office Hours:** Weekly instructor office hours **Peer Collaboration:** Study groups and peer review **Industry Mentors:** Guest lectures from industry **Career Support:** Resume review, interview prep **Community:** Active Slack/Discord community #### Certification **Phase Certificates:** Certificate after each phase **Final Certificate:** Data Science Mathematics Expert Certificate **Specialization Badges:** Badges for specialized tracks **Portfolio:** Industry-ready portfolio **Linkedin Credentials:** LinkedIn verifiable certificates ## Prerequisites **Mathematics:** High school algebra and basic statistics helpful **Programming:** Basic Python/R knowledge beneficial but not required **Statistics:** No prior statistics knowledge required **Commitment:** Strong dedication to learning **Equipment:** Computer with internet, cloud credits provided **Software:** All software and platforms provided ## Who Is This For **Aspiring Data Scientists:** Those starting a data science career **Analysts:** Business/Data analysts seeking deeper skills **Engineers:** Software engineers moving to ML/AI **Researchers:** Academic researchers in any field **Professionals:** Domain experts adding data skills **Students:** Undergraduate/graduate students **Career Switchers:** Professionals transitioning to data science ## Career Paths After Completion - Data Scientist (Entry to Senior level) - Machine Learning Engineer - Applied Research Scientist - Quantitative Analyst - AI/ML Product Manager - Statistical Consultant - Business Intelligence Lead - MLOps Engineer - Data Science Manager - Chief Data Scientist ## Salary Expectations **Entry Level:** ₹8-15 LPA / $70-100k USD **Mid Level:** ₹15-30 LPA / $100-150k USD **Senior Level:** ₹30-60 LPA / $150-250k USD **Expert Level:** ₹60+ LPA / $250k+ USD **Consulting:** ₹5000-15000/hour **Research:** Varies by institution and grants ## Course Guarantees **Job Readiness:** Industry-ready skills guaranteed **Project Portfolio:** 20+ production-ready projects **Interview Prep:** Mock interviews and prep materials **Lifetime Access:** All content and future updates **Community:** Lifetime community membership **Support:** 6 months post-completion support --- ## Enroll - Book a free demo: https://learn.modernagecoders.com/book-demo - Course page: https://learn.modernagecoders.com/courses/data-analytics-mathematics-masterclass/ - All courses: https://learn.modernagecoders.com/courses *Source: https://learn.modernagecoders.com/courses/data-analytics-mathematics-masterclass/*