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Welcome to Math 3333: Linear Algebra I, this Fall 2020! Today is .

Current presentation (Week 13 presentation)

Possible topics:

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1. Linear dynamical systems (bird population, diagonalizable matrices, dominant eigenvalue, graphical description)

Some examples you can use (choose just some of these or find your own):

• pg 171, Example 3.3.1: Setting up bird population model

• pg 182, Example 3.3.12: Solving the linear dynamical system of the bird population

• (Optional) theorems:
  • diagonalizable matrices: You don’t need to understand the theory of diagonalizable matrices to present this topic, but it can be helpful. Lecture 15c will explain diagonalizable matrices. You can also learn it from the textbook pg 178-181 or any linear algebra resource.
  • dominant eigenvalue: See Theorem 3.3.7 for how to approximate steady state of a dynamical system using a dominant eigenvalue
• pg 187-188 Graphical description of 2x2 linear dynamical system

Exercises from the book Section 3.3 (see solution manual):

• pg 189 Exercise 3.3.2(b),(d) more linear dynamical system
• pg 192 Exercise 3.3.31(b),(d) (about the bird population model from Example 3.3.1)
• pg 192 Exercise 3.3.34 (about the bird population model from Example 3.3.1)

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2. Linear recurrence (Textbook Section 3.4)

Some examples you can use (choose just some of these or find your own):

• pg 192 Example 3.4.1 number of ways to park cars and trucks (aka Fibonacci/Pingala numbers)
• pg 194 Example 3.4.2 Finding a formula for a linear recurrence using eigenvalues and eigenvectors

• pg 194-195 Example 3.4.3 Finding a formula

• (Optional) theorem:
  • diagonalizable matrices: You don’t need to understand the theory of diagonalizable matrices to present this topic, but it can be helpful. Lecture 15c will explain diagonalizable matrices. You can also learn it from the textbook pg 178-181 or any linear algebra resource.

Exercises from the book Section 3.4 (see solution manual):

• pg 196 Exercise 3.4.1(b),(d) Finding a formula for a linear recurrence
• pg 197 Exercise 3.4.5 Counting words
• pg 197 Exercise 3.4.7 Counting ways to stack poker chips

• pg 197 Exercise 3.4.9 Modeling long-term wheat production

• Warning: There are many myths on the role of Fibonacci/Pingala numbers in the sciences. Since it’s not easy to discern which publications on the internet can be trusted, it’s better to stick to just linear algebra examples in your presentation.

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3. Approximation and least squares (Textbook Section 5.6)

(You do not need to include every definition mentioned in the book. Give just enough information to explain your examples)

• pg 312 Example 5.6.1 (best approximation to a solution of a linear system)
• pg 312-313 Example 5.6.2 (best fitting function for average number of goals)
• pg 315 Example 5.6.3 (least squares approximating a line)
• pg 318 Example 5.6.4 (least squares approximating a quadratic polynomial)

Exercises from the book Section 5.6 (see solution manual):

• pg 320 Exercise 5.6.1 (best approximation to a solution of a linear system)
• pg 320 Exercise 5.6.2 (least squares approximating lines)
• pg 320 Exercise 5.6.3 (least squares approximating quadratic functions)
• pg 321 Exercise 5.6.7 (least squares approximating gravity)
• pg 321 Exercise 5.6.9 (best approximation for modeling wheat production)

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4. Correlation and Variance (Textbook Section 5.7)

(You do not need to include every definition mentioned in the book. Give just enough information to explain your examples)

• pg 322-326 textbook reading (example of the data on sick days, doctor visits, and vitamin C)
• pg 327 Exercise 5.7.1 and 5.7.2
• Other examples

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5. Error Correcting Codes (Textbook Section 8.8)

• pg 473 Modular arithmetic (don’t worry about the definition of a field)
• pg 475-476 Example 8.8.1 and 8.8.2 (example of arithmetic mod 2 and mod 17)
• pg 476 Example 8.8.3 (matrix algebra for modular arithmetic)
• pg 477-479 Error correcting codes explanation (you don’t need to explain every definition or theorem, only take what’s needed to understand the examples)
• pg 480 Example 8.8.6 (linear codes)

Exercises from the book Section 8.8 (see solution manual):

• pg 486 Exercise 8.8.1 (b),(d)
• pg 486 Exercise 8.8.3(b) (inverse of 11 mod 19)
• pg 486 Exercise 8.8.7(b) (Gaussian elimination with modular arithmetic)

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6. Another topic not listed above but uses elementary linear algebra concepts

Talk to me first before preparing the presentation.

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Textbook links

• Links: Link to chapter 3 of the textbook, Link to chapter 5 of the textbook

Timeline (Nov 13 - Nov 20)

• Fri (Nov 13) Live Session
  • Study the materials
• Mon Live Session
  • Study the materials, start creating slides
  • Assign who’s presenting what
  • Week13 in-progress due Mon after class (Gradescope) topic, student roles, and link to unfinished visual aids (this will be not be graded yet - it’s OK if the slides just consist of the title page).
• Wed Live Session
  • Continue preparing the presentation materials
  • If you are ready, you can record on Wednesday.
• Fri (Nov 20) Live Session
  • Give the presentation to another group (please record your Q&A session as well). Turn your camera on.
  • Attentively watch the other group give their presentation. Turn your camera on.
  • During or after a group’s presentation, every student (not in the group) should ask questions. If you are giving comments, be specific.
  • Record questions on the chat. Each group’s “Gradescope submitter” should download the chat so that they can later (Sun/Mon) submit these to Gradescope.
  • Make improvement to your visual aids based on comments and questions from your audience
  • If you are OK with how your Q & A session goes, please make it part of your video recording. You are not graded on the correctness of your answers.
• Submit on Gradescope (week13 presentation slides and video): Final version of slides and recording (accepted until Mon, Nov 23 at noon)

Past presentations

Past presentations