Syllabus

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Data Structures and Algorithms

Definition: Data Structures and Algorithms focuses on organizing data efficiently and designing algorithms for problem-solving with emphasis on time and space complexity.

Module 1: Introduction

• Overview of data structures.
• Algorithm analysis, asymptotic notations.

Module 2: Linear Data Structures

• Arrays, linked lists.
• Stacks, queues, deque.

Module 3: Non-Linear Data Structures

• Trees: binary, BST, AVL.
• Heaps, priority queues.

Module 4: Graphs

• Representations, traversals.
• Shortest paths, MST.

Module 5: Sorting & Searching

• Bubble, insertion, merge, quick, heap sort.
• Hashing techniques.

Module 6: Advanced Topics

• Dynamic programming basics.
• Greedy algorithms.

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Database Systems

Definition: Database Systems introduces data modeling, relational databases, SQL querying, and management principles.

Module 1: Introduction

• Database concepts, architecture.
• Data models, schemas.

Module 2: ER Modeling

• Entities, relationships.
• ER diagrams.

Module 3: Relational Model

• Relational algebra.
• Integrity constraints.

Module 4: SQL

• DDL, DML.
• Queries, joins, subqueries.

Module 5: Normalization

• Functional dependencies.
• Normal forms.

Module 6: Advanced Concepts

• Transactions, concurrency.
• Indexing.

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Mathematics for Data Science

Definition: Mathematics for Data Science provides foundational tools in discrete mathematics, graph theory, algebraic structures, formal languages, and numerical methods.

Unit 1: Counting, Logic and Relations

• Counting Techniques, Permutation & Combination.
• Pigeonhole Principle, Basic Proof Techniques, Induction.
• Propositional Logic, Quantifiers, Equivalences and Normal Forms.
• Sets, Functions and Relations.
• Equivalence Relation, Partial Order Relation, Hasse Diagram, Posets, Concept of Lattice.

Unit 2: Graphs

• Graphs and Relations, Directed Graphs, Undirected Graphs.
• Connectivity, Trees, Tree Traversal.
• Minimum spanning tree, Graph Coloring.
• Hamiltonian and Euler’s Graph, Planar Graph.
• Shortest Path algorithm.

Unit 3: Algebraic Structures

• Generating function.
• Algebraic Structure, Group, Abelian Group, Cyclic Group.
• Permutation group, Cosets, Lagrange’s Theorem.
• Normal Subgroup.

Unit 4: Formal Languages

• Formal definition of a language.
• Discussion on grammar, Terminal, Non-Terminal, Production System.
• Chomsky Hierarchy of Grammar and associated machines.

Unit 5: Numerical Methods

• Solution of polynomial using Bisection, Regula Falsi and Newton Raphson Method.
• Solving definite integrals using Trapezoidal method and Simpson Rule.
• Solving differential equation using Runge-Kutta Method.

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Statistics

Definition: Statistics covers descriptive and inferential methods for data analysis, probability, distributions, and hypothesis testing.

Module 1: Descriptive Statistics

• Measures of central tendency, dispersion.
• Data visualization.

Module 2: Probability

• Basic concepts, rules.
• Conditional probability, Bayes theorem.

Module 3: Distributions

• Discrete: binomial, Poisson.
• Continuous: normal, exponential.

Module 4: Sampling

• Sampling techniques.
• Central limit theorem.

Module 5: Inference

• Estimation, confidence intervals.
• Hypothesis testing.

Module 6: Correlation & Regression

• Correlation coefficients.
• Linear regression.

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Effective Technical Communication

Definition: Effective Technical Communication develops professional skills in writing, speaking, and presenting technical information.

Module 1: Technical Documentation

• Types of technical documents.
• Information design, organization.

Module 2: Writing Skills

• Technical writing process.
• Grammar, editing, style.

Module 3: Self Development

• Self-assessment, goal setting.
• Time management, creativity.

Module 4: Oral Communication

• Public speaking, presentations.
• Group discussions, interviews.

Module 5: Professional Ethics

• Business ethics, etiquettes.
• Engineering ethics.

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