Planned topics

Programming

• More data structures and algorithms topics
  • Fundamentals and General Topics
    • Complexity, Big O, and Other Performance Topics
      • Also talk about complexity classes, NP completeness, and P=NP.
    • Binary Representation and Arithmetic
      • Bit shifting
      • IEEE 754 floating point, including special values, and cover quantization error and other important implications
      • overcoming overflow/underflow
      • ASCII, Unicode, and possibly other character encodings
      • Modular arithmetic (especially useful for competitive programming)
    • Dynamic Arrays
    • Array Search, Selection, and Partitioning Algorithms
      • Include Quickselect
    • Sorting Algorithms
    • Linked Lists
    • Binary Search Trees (BSTs)
    • Tries
    • Hash Tables
  • Divide-and-Conquer Algorithms
    • Introduction
      • What is it?
      • What is the master theorem?
    • Karatsuba Multiplication
    • Fast Fourier Transform (FFT)
  • Randomized Algorithms
  • Mathematical Computing
    • TODO: There should be a better name for this chapter since the scope is a little wider than the name suggests. Some of this stuff should maybe be moved to the intro chapter though.
    • How to compute square root? Linear search vs. binary search vs. Newton’s method? What about fast inverse square root?
    • Machine epsilon
    • How to manage overflow and underflow?
  • Appendices
    • Introduction to Fourier Analysis, for Computer Science Students