Final Exam: Introduction to Math

WHAT YOU WILL LEARN

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  Perform union and intersection operations on sets
  

  recognize the differences between discrete and continuous data and outline topics in discrete mathematics
  

  create and work with sets in python, perform checks for subsets and supersets
  

  create and work with sets in python
  

  model entities and relationships in the real-world using graphs
  

  recognize the different types of graphs, their characteristics, and use cases
  

  associate attributes with the graph, individual nodes, and individual edges
  

  compute the shortest path and a minimum spanning tree for a graph
  

  compute the minimum spanning tree and the shortest path for a graph
  

  perform topological sorting in a directed acyclic graph
  

  create directed graphs using networkx
  

  recall the assumptions and benefits of integer optimization models
  

  model problems using objectives, decision variables, and constraints
  

  solve the linear programming problem graphically
  

  determine the optimal solution from feasible solutions
  

  list the steps in the simplex method to solve linear programming problems
  

  solve minimization problems using the scipy library
  

  solve linear programming problems using the pulp library
  

  recognize the assumptions and benefits of integer optimization models
  

  use lp relaxation to find a starting point for the integer programming solution
  

  formulate the integer programming model for becca luxury goods
  

  solve the manufacturing and distribution problem using pulp
  

  formulate the integer programming model for a capital budgeting problem
  

  gain a basic understanding of calculus and describe differentiation and derivatives
  

  describe differentiation and derivatives
  

  use built-in functions to compute derivatives
  

  outline how to compute the slope at a point by exploring the geometric definition of derivatives
  

  use derivatives in real-world scenarios
  

  outline how partial derivatives work
  

  compute derivatives of linearly changing functions using built-in functions
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  outline derivatives and slope
  

  create partial derivatives with multiple independent variables
  

  compute the velocity of a moving particle
  

  define the integral as the limit of a sum and as the area under a curve
  

  differentiate between definite and indefinite integrals
  

  compute integrals of quadratic and polynomial functions
  

  compute integrals from first principles
  

  frame integration as inverse operations
  

  create a matrix and perform matrix operations
  

  compute determinants and transpose matrices
  

  perform matrix addition
  

  perform matrix multiplication
  

  recognize properties of matrices
  

  identify and work with diagonal and zero matrices
  

  compute the inverse of an invertible matrix
  

  create matrices using scipy
  

  mathematically define matrix decomposition
  

  recognize several types of matrix operations
  

  perform lu decomposition
  

  mathematically define qr and cholesky decomposition
  

  perform qr decomposition
  

  install libraries in python
  

  mathematically define eigenvectors and eigen values
  

  explore properties of eigenvalues and eigenvectors
  

  compute eigenvalues and eigenvectors of a matrix
  

  derive the characteristic equation
  

  differentiate between eigen decomposition and singular value decomposition (svd)
  

  import an image to perform svd
  

  perform singular value decomposition (svd) on a matrix
  

  simplify an image with svd