Overview

Math components

• Directory

  algebra/

  • Directorybasic-algebra/

    • elementary-algebra
    • CK-12-algebra-I
    • beginning-and-intermediate-algebra
• Directory

  plane-geometry/

  • ck-12-geometry
  • euclids-elements-redux (contains number theory and logic)
• Directory

  pre-calculus/

  • trigonometry-michael-corral
  • [optional]openstax-algebra-and-trigonometry
  • [optional]active-prelude-to-calculus
  • CK-12-algebra-II-with-trigonometry

• linear-algebra

• single-variable-calculus

• multi-variable-calculus

• ordinary-differential-equations

• partial-differential-equations

Contents

• Pre-algebra:

  • Taking powers, prime factorization, divisibility test (done)

• Algebra:

  • Linear and quadratic equations
  • Identifying properties of lines and vertical parabolas from their equations.
  • determining average rates of change and estimated accumulation
  • Factorization, expansion of polynomials
  • Operations on exponents and roots
  • Systems of equations in multiple variables
  • Operations on 2x2 and 3x3 matrices

• Plane Geometry (require basic algebra): motivate integral

  • Parallel and perpendicular lines
  • Congruent triangles

• Pre-calculus (require basic algebra):

  • Elementary functions (including exponentials, logarithms functions)
  • Trigonometry
  • Analytic Geometry (no need for now)

• Linear Algebra

OS Data structures

Discrete math

• Book of proof:
  • Sets
  • Logic: truth tables, etc
  • Counting
  • Direct proof
  • Math induction
  • Relations
  • Functions
  • Cardinality of sets
• Chapter 1. Foundation: logic and proofs
• Chapter 2: sets, functions, sequences, sums, and MATRICES => Chapter 9: relations => Chapter 10: Graphs => Chapter 11: Trees
• Chapter 3: agorithms complexity

Data structure

• Queues
• Stacks
• Linked lists
• Tree:
  • Binary trees
  • Binary Search Trees (BST)
  • AVL Trees, Red-Black Trees
  • B-Tree