PANTOMATH

Fundamentals of Computer Science

1. Programming Languages

Programming languages are the foundation of computer science, used to write and execute software programs.

• C: Fundamental language for system-level programming, focusing on memory management and performance.
• C++: Extension of C with object-oriented features like classes, inheritance, and polymorphism.
• Java: Platform-independent, widely used for enterprise applications and Android development.
• Python: High-level, easy-to-learn language with applications in web development, AI, and data science.
• JavaScript: Core technology for web development, enabling interactivity on websites.
• Other Languages: Ruby, Go, Rust, PHP, and R (used in statistical computing).

2. Data Structures

Data structures are methods to organize and store data for efficient access and modification.

• Linear Data Structures:
  • Arrays: Fixed-size collections of elements.
  • Linked Lists: Dynamic-size collections with nodes pointing to the next element.
  • Stacks: LIFO (Last In, First Out) structure.
  • Queues: FIFO (First In, First Out) structure.
• Non-linear Data Structures:
  • Trees: Hierarchical data structures (e.g., Binary Trees, AVL Trees, Binary Search Trees).
  • Graphs: Networks with nodes and edges (e.g., Directed, Undirected, Weighted Graphs).
  • Hash Tables: Data stored using key-value pairs for fast lookup.

3. Algorithms

Algorithms define a step-by-step procedure to solve problems efficiently.

• Sorting Algorithms: Bubble Sort, Quick Sort, Merge Sort, Heap Sort.
• Searching Algorithms: Linear Search, Binary Search.
• Graph Algorithms: Dijkstra’s Algorithm, Prim’s Algorithm, Kruskal’s Algorithm, BFS, DFS.
• Dynamic Programming: Optimal Substructure and Overlapping Subproblems (e.g., Fibonacci, Knapsack).
• Greedy Algorithms: Finding solutions step-by-step by choosing the best local option (e.g., Activity Selection).

4. Mathematics for Computer Science

Mathematics plays a crucial role in algorithms, machine learning, and cryptography.

• Discrete Mathematics:
  • Set Theory: Basics of sets, unions, intersections.
  • Logic: Propositional logic, truth tables, Boolean algebra.
  • Combinatorics: Permutations and combinations.
  • Graph Theory: Understanding nodes, edges, paths, and circuits.
• Probability and Statistics:
  • Random variables, probability distributions, Bayes’ theorem.
  • Statistical inference, hypothesis testing.
• Linear Algebra:
  • Vectors, matrices, eigenvalues, eigenvectors.
  • Essential for graphics, machine learning, and data analysis.
• Calculus:
  • Differentiation and integration.
  • Applications in optimization, gradient descent, and signal processing.