Math 3626: Applied Matrix Theory

Course description: This course introduces fundamental matrices and matrix algorithms used in applied mathematics, and essential theorems and their proofs. It covers matrices used in linear optimization, solving systems of linear differential equations, and modeling of stochastic processes. It also covers implementing matrix algorithms with mathematical software.

Prerequisite: MATH 2711, MATH 2813, and CSAS 1113 or CSAS 1114

Software: We will make use of the DyKnow client software. Please download and install that software. We also need Mathematica, make sure you have that installed on your laptop.

General Information

• Syllabus

Exams and such

• Exam 2 (Take-home Exam)
• Exam 1 Sample Questions
  (with answers)

Resources

• Wolfram Alpha
• Mathematica tutorial
• DyKnow Vision
• Rotational Matrices
• Linear Programming
  • Graphical Approach [1] [2] [3]
  • Simplex Method [1] [2] [3] [4]
  • Simplex program (complete)
• Systems of 1st Order Linear DEs
• Markov Chains
  

Lectures

• 24: Regular Markov chains
• 23: Ergodic Markov chains
• 22: Absorbing Markov chains
• 21: Hands-on with Markov chains
  
• 20: Markov chains (intro)
  
• 16. Solving ODEs
• 15. Systems of DE's (check with MM)
• 14. ODE Intro
  
• 13. Examples of recursive functions
• 12. Complexity of Algorithms
  
• 10. Simplex program (complete)
• 9. Simplex procedure (part 1 & part 2) 
• 8. Lin Prog: using Mathematica
• 7. Lin Prog: The Dual problem
• 6. Linear Programming Intro
• 5. Outline of a rotating 3D cube program and sample quiz
• 3. Notebook outlining 2D animation and the finished notebook  
• 2. MM Notebook on regular polygons
• 1. Rotational Matices and Notebook
• 0. Introduction and
  Intro Notebook

Assignments

• 20: Complete all transition matrices in Intro lecture; create a Mathematica program to raise a matrix to the n-th power
  
• 16. Solving 2x2 ODE Systems
• 15. Systems of ODE's
• 14. Big-O of Simplex; Solving ODE
  
• 9. HW on Linear Programming  
• 5. Outline of a rotating 3D cube program and sample quiz
• 4. Generate amimated star as shown here
• 3. Complete the 2D animation notebook
  
• 2. Loops in Mathematica
• 1. Rot. Matrix problems;
  PAPER: Rotational Matrices