Computer science theory | Computing | Khan Academy

Computer Science Theory Curriculum

• Algorithms: Covers fundamental sorting and search techniques, including Binary search, Selection sort, Insertion sort, Merge sort, and Quick sort.
• Recursion: Explores recursive algorithms, the factorial function, palindromes, computing powers, the Sierpinski gasket, and methods for improving recursive efficiency.
• Graph Theory: Introduction to graph representation and Breadth-first search (BFS).
• Ancient Cryptography: Historical encryption methods including the Caesar cipher, Polyalphabetic ciphers, the one-time pad, and the Enigma machine.
• Modern Cryptography: Advanced security concepts such as Public key cryptography, the discrete logarithm problem, Diffie-Hellman key exchange, and RSA encryption.
• Modular Arithmetic: Mathematical foundations including the modulo operator, congruence relations, the quotient remainder theorem, modular exponentiation, and modular inverses.
• Number Theory & Primality: Study of the fundamental theorem of arithmetic, Euler's totient function, the Euclidean algorithm, and various primality tests (e.g., Sieve of Eratosthenes, trial division).
• Computational Efficiency: Analysis of algorithmic efficiency, time complexity, and time-space tradeoffs.
• Computer Fundamentals: Basic overview of computer memory.