Advanced Programme in Computational Data Science

• Probabilistic Description of Events and Data: Probability Axioms, Random Variables, PDF, PMF, Conditional Probabilty, Independence, Expectation, Variance
• Describing Common Events using Probability: Bernoulli, Geometric, Binomial, Poisson, Uniform, Normal, Exponential
• Statistical Learning - A/B Testing, Type I and II errors, Sample Size calculation Mini project in hypothesis testing

Introduction to Calculus and Linear Algebra in Data Science

• Importance of Calculus and Linear Algebra in Data Science
• Basics of Univariate and Multivariate Calculus Vector Operations and Norms

Deep Dive into Calculus for Data Science

• Derivatives and Partial Derivatives
• Composite Functions and the Chain Rule
• Introduction to Automatic Differentiation

Optimizing with Gradient Descent and Backpropagation

• Gradient Descent Fundamentals
• The Mechanics of Backpropagation

Fundamentals of Linear Algebra

• Vector Spaces, Bases, and Dimensions
• Linear Transformations and Matrices Matrix Operations in Data Science

Principal Component Analysis and Matrix Factorization

• Principal Component Analysis (PCA): Theory and Application
• Principal Component Analysis (PCA): Theory and Application Overview of Matrix Factorization Techniques (e.g., SVD, QR decomposition)

Foundations of ML 

• Problem-solving strategy with data science tools, ML, and DL.
• Model selection, feature importance

Regression Models

• Least Squares; Regularization - Elastic Net, Ridge, Lasso; Bias-Variance tradeoff
• Development-testing paradigm

Classification Models

• Classification algorithms
• Evaluation Metrics: MSE, Accuracy, Precision, Recall, F1 Score

Decision Trees and Random Forests

• Decision Tree Algorithms
• Voting Classifiers, Bagging Ensemble models
• Random Forests

Boosting Models

• XGBoost
• Light GBM

Unsupervised Learning

• Clustering (k-means, dbscan), Agglomerative clustering
• Anomaly Detection

Mini-Project: Five Mini Projects in Machine Learning

Introduction to Scalable Computing 

• Overview of scalable computing in AI/ML
• Understanding parallel architectures
• Importance of scalability in data science

Introduction to Parallel Computing 

• Types of parallelism: Data parallelism vs. Task parallelism
• Introduction to Shared Memory (OpenMP) and Distributed Memory (MPI)

Deep Dive into Scalable Computing Technologies

• Deep dive into OpenMP and MPI
• Introduction to GPUs and Nvidia accelerators
• Overview of CUDA programming

Scalable Data Science Tools

• JIT Compiler, Numba, and Dask
• Introduction to TensorFlow distributed computing

Machine Learning at Scale with Parallel ML Libraries

• Introduction to Dask, MLLib, cuDF, cuML, cuPY
• Focused exploration of Horovod, Ray, and Rapids

Deep Neural Networks

• Multi-Layer Perceptrons (MLP), backprop, Regression/Classification with MLP, gradient issues, and activation functions batch normalization, overfitting, drop out, optimizers and learning rate

Convolutional Neural Networks

• Filtering, Convolution, pooling, Various architectures: U-net, Resnet, etc., classification, localization, segmentation (Computer Vision Applications)

Recurrent Neural Networks

• Sequence modeling, memory cell, GRU, LSTM, gradient issues (NLP Applications)

Dimensionality Reduction and Self-supervised Neural Networks

• PCA, Matrix Completion, LDA, CCA Manifold Learning, t-SNE, LLE
• Advanced Auto-encoder type architectures

Fundamentals of NLP, attention mechanism, and transformer models.

Mini-Project in Neural Networks

Introduction to Generative AI

• Understanding Generative AI - Introduction to models like GPT, DALL-E, Midjourney,
• Sora (and others) including their capabilities and limitations.
• Exploring the Potential of Generative AI using APIs of large models (e.g., OpenAI).

Enhancing Applications with Advanced Techniques

• Advanced Interaction with Generative Models - Prompt Engineering Techniques and Fine-Tuning
• Retrieval-Augmented Generation (RAG)

Building and Deploying Business Applications

• Identifying business problems and architecting solutions incorporating generative models.
• Integrating Generative AI into Applications though API integration
• Navigating Ethical Implications - Privacy, bias, and copyright issues

Introduction to Big Data storage systems 

• Relational Databases
• NoSQL Databases: HBase, Graph DB
• Distributed File Systems/HDFS
• Cloud storage

Introduction to Big Data processing platforms

• Data Volume: Hadoop, Spark
• Data Velocity: Storm, Complex Event Processing
• Cloud platforms

Deep dive into Apache Spark

• Resilient Distributed Dataset
• Transformations, Actions
• Designing computational and analytics application using Spark
• Hands-on with PySpark programming

Mini-Project in Data Engineering

Time Series Modeling

• Fundamentals, Stationarity, Measures of dependence
• ARMA modeling

Business Case Studies

• Market Basket Analysis (Association Rule Mining)
• Optimal Financial Portfolio Allocation
• Customer Churn Analysis

Mini-Project in Business Analytics