Getting Started: How to Prepare for the First Day of Class

Welcome to Math 2B: Introduction to Applied Linear Algebra at Foothill College with Jeff Anderson. For more about Math 2B at Foothill College, please see Foothill's Math Department website. In the space below, I provide you with electronic copies of our course resources for my Math 2B courses in spring 2022.

Resources for Math 2B.01 on Tues/Thurs 10am - 12:15pm in room 5611 for winter quarter 2024

Course Syllabus:       Winter 2024, Math2B.01 Course Syllabus

Meeting Schedule:   Winter 2024, Math 2B.01, T/Th 10AM, Portfolio Meeting Schedule
Winter 2024, Math 2B.01, T/Th 10AM, Example Meeting Schedule

Math Discord: Winter 2024, Math2B.01 Discord Channel

Flipped Learning:         Winter 2024, Math 2B Flipped Classroom Activity List (updated 1/11/2024)

Content Calendar:        Math 2B, Winter 2024 Beginner Calendar (.pdf)
Math 2B, Winter 2024 Intermediate Calendar, Eigenvalue Project (.pdf)
Math 2B, Winter 2024 Intermediate Calendar, LANA Project (.pdf)
Math 2B, Winter 2024 Advanced Calendar (.pdf)

Welcome Emails: Jeff’s First Welcome Email (Sent on 01/01/2024)
Jeff’s Second Welcome Email (Sent on 09/25/2023)
Jeff absent from class Thurs 10/12/2023 (Sent 10/12/23)
Jeff’s Add Code Email (Sent on 09/25/2023)

General Resources

Course Webpage FAQs: Jeff’s Course Website FAQs
Attendance FAQs: Jeff’s Attendance FAQs
Flipped Learning FAQs: Jeff’s Flipped Learning FAQs
Grading FAQs:       Jeff’s Grading FAQs
Team Learning FAQs: Jeff’s Team Learning FAQs
Add Code Policy: Jeff’s Add Code Policy

Applied Project Choices: LANA Project Choices
Conquering College: Lab 1 Prompt
Lab 2 Prompt
Lab 3 Prompt
Lab 4 Prompt

Learning Reflections: Mid-Term Learning Self Evaluation Activity (.docx) or ( .pdf ) - due at start of class 11
Final Learning Self Evaluation Activity ( .docx ) or ( .pdf ) - due at the start of class 23

Final Course Eval: Winter 2024, Math 2B, Final Course Evaluation (Google Forms Survey)
A. Once you complete this survey, please take a snapshot of the confirmation page.
B. Show your snapshot of this page to Jeff to confirm you’ve finished this work.

Copyright Information for Jeff’s Math 2B Lesson Resources

Please note that I maintain the copyright to the work I provide below. This work has taken me well over 1,000 hours to create and I am still actively drafting and editing this material. My Math 2B notes are one part of my multi-decade-long, major professional goal to redesign my introductory linear algebra classroom to be student-centered, experiential, and mastery-based. I yearn to provide each of my readers with numerous opportunities to cultivate valuable, applied modeling skills as part of her introduction to linear algebra. I provide these notes free-of-charge because I believe very deeply in the values of community, democracy, and open access to information.

I ask that you respect my work and the intellectual effort I put into creating these resources

  • You are welcome to use these notes at any time. I plan to sponsor and update this website for as long as I live. In other words, if you want access to these notes, all you need to do is visit this website, find the link you are most interested in, and enjoy!

  • I ask you kindly: Please do not upload this work onto any other website (like Chegg, Scribd, or any other online repository). I do NOT want these notes to be uploaded onto any other website. In fact, I expect that this webpage is the only place these documents can be accessed. Thank you, in advance, for your attention to this matter.

Stay Focused on Exam Content

Many previous students have asked me what I plan to test on. To answer this question, I have a drafted list of all topics that might be covered on in-class quizzes. I plan to ask you to demonstrate deep conceptual understanding of the ideas we study. For more about the exact content I want you to study and master, please watch our course videos. To access a master list of the videos we use in this course, please click on the link below:

Anderson’s Master List of Applied Linear Algebra Videos (.pdf) or (.docx)

To access more information on the type of questions I want you to be able to answer in each individual lesson, click on the link below:

Math 2B Lesson-by-Lesson Content-Specific Learning Objectives

This list should give you a very good idea of the ideas you might want to focus on in each lesson of this class while you are writing your lesson notes. Also, as you prepare for your in-class exams, you can use this list to focus your attention on the most relevant topics that we study in this class. 

Math 2B, Lesson Resources

In Math 2B, we will study the 6 fundamental problems of applied linear algebra. Below I include links to all of my lesson notes that I have written for this course. May you have as much fun reading as I do when I write.

MATH 2B: INTRODUCTION TO APPLIED LINEAR ALGEBRA
LESSON TITLE LESSON PLAYLIST
LESSON 0: MAJOR PROBLEMS IN APPLIED LINEAR ALGEBRA

  1. Lesson 0: Jeff's Notes (.pdf)
  2. Lesson 0 Quiz: Blank Copy (.pdf)
  3. Lesson 0 Quiz: Partial Answers (.pdf)

LESSON 0 PLAYLIST
LESSON 0 EXTRAS PLAYLIST
LESSON 1: INTRODUCTION TO SET THEORY

  1. Lesson 1: Jeff's Notes (.pdf)
  2. Lesson 1 Quiz: Blank Copy (.pdf)
  3. Lesson 1 Quiz: Answers (.pdf)

LESSON 1 PLAYLIST
LESSON 2: RELATIONS AND FUNCTIONS

  1. Lesson 2: Jeff's Notes (.pdf)
  2. Lesson 2 Quiz: Blank Copy (.pdf)
  3. Lesson 2 Quiz: Answers (.pdf)

LESSON 2 PLAYLIST
LESSON 3: VECTORS AND MODELING

  1. Lesson 3: Jeff's Notes (.pdf)
  2. Lesson 3 Quiz: Blank Copy (.pdf)
  3. Lesson 3 Quiz: Answers (.pdf)

LESSON 3 PLAYLIST
LESSON 4: VECTOR ARITHMETIC

  1. Lesson 4: Jeff's Notes (.pdf)
  2. Lesson 4 Quiz: Blank Copy (.pdf)
  3. Lesson 4 Quiz: Answers (.pdf)

LESSON 4 PLAYLIST
LESSON 5: INNER PRODUCTS AND VECTOR NORMS

  1. Lesson 5: Jeff's Notes (.pdf)
  2. Lesson 5 Quiz: Blank Copy (.pdf)
  3. Lesson 5 Quiz: Answers (.pdf)

LESSON 5 PLAYLIST
LESSON 6: LINEAR COMBINATIONS, SPAN, AND LINEAR INDEPEDENCE

  1. Lesson 6: Jeff's Notes (.pdf)
  2. Lesson 6 Quiz: Blank Copy (.pdf)
  3. Lesson 6 Quiz: Answers (.pdf)

LESSON 6 PLAYLIST
LESSON 7: MATRICES AND MODELING

  1. Lesson 7: Jeff's Notes (.pdf)
  2. Lesson 7 Quiz: Blank Copy (.pdf)
  3. Lesson 7 Quiz: Partial Answers (.pdf)

LESSON 7 PLAYLIST
LESSON 8: ANATOMY OF MATRICES

  1. Lesson 8: Jeff's Notes (.pdf)

LESSON 8 PLAYLIST
LESSON 9: OUTER PRODUCTS AND MATRIX ARITHMETIC

  1. Lesson 9: Jeff's Notes (.pdf)
  2. Lesson 9 Quiz: Blank Copy (.pdf)
  3. Lesson 9 Quiz: Partial Answers (.pdf)

LESSON 9 PLAYLIST
LESSON 10: MATRIX-VECTOR MULTIPLICATION

  1. Lesson 10: The matrix-vector multiplication problem (.pdf)
  2. Lesson 10 Quiz: Blank Copy (.pdf)
  3. Lesson 10 Quiz: Partial Answers (.pdf)

LESSON 10 PLAYLIST
LESSON 11: MATRIX-MATRIX MULTIPLICATION

  1. Lesson 11A: The matrix-matrix multiplication problem (.pdf)
  2. Lesson 11B: Properties of elementary operations (.pdf)
  3. Lesson 11C: Properties of orthogonal transformations (.pdf)
  4. Lesson 11D: Matrix-matrix multiplication in action (.pdf)
  5. Lesson 11 Quiz: Blank Copy (.pdf)
  6. Lesson 11 Quiz: Answers (.pdf)

LESSON 11A PLAYLIST
LESSON 11D PLAYLIST
LESSON 12: THE NONSINGULAR LINEAR SYSTEMS PROBLEM (NLSP)

  1. Lesson 12: Jeff's Notes (.pdf)
  2. Lesson 12 Quiz: Blank Copy (.pdf)
  3. Lesson 12 Quiz: Answers (.pdf)

LESSON 12 PLAYLIST
LESSON 13: MATRIX INVERSES

  1. Lesson 13: Jeff's Notes (.pdf)
  2. Lesson 13 Quiz: Blank Copy (.pdf)
  3. Lesson 13 Quiz: Answers (.pdf)

LESSON 13 PLAYLIST
LESSON 14: THE INVERTIBLE MATRIX THEOREM (IMT)

  1. Lesson 14: Jeff's Notes (.pdf)
  2. Lesson 14 Quiz: Blank Copy (.pdf)
  3. Lesson 14 Quiz: Answers (.pdf)

LESSON 14 PLAYLIST
LESSON 15: LU FACTORIZATION

  1. Lesson 15: Jeff's Notes (.pdf)
  2. Lesson 15 Quiz: Blank Copy (.pdf)
  3. Lesson 15 Quiz: Answers (.pdf)

LESSON 15 PLAYLIST
LESSON 16: DETERMINANTS

  1. Lesson 16: Introduction to Permutations (.pdf)
  2. Lesson 16: Blank Permutations Worksheet (.pdf)
  3. Lesson 16: Jeff's Notes (.pdf)
  4. Lesson 16 Quiz: Blank Copy (.pdf)
  5. Lesson 16 Quiz: Answers (.pdf)

LESSON 16 PLAYLIST
LESSON 17: THE GENERAL LINEAR SYSTEMS PROBLEM (GLSP)

  1. Lesson 17: Jeff's Notes (.pdf)
  2. Lesson 17 Quiz: Blank Copy (.pdf)
  3. Lesson 17 Quiz: Answers (.pdf)

LESSON 17 PLAYLIST
LESSON 18: SOLUTIONS TO THE GLSP

  1. Lesson 18: Jeff's Notes (.pdf)
  2. Lesson 18 Quiz: Blank Copy (.pdf)
  3. Lesson 18 Quiz: Answers (.pdf)

LESSON 18 PLAYLIST
ELECTRIFY LINEAR-SYSTEMS PROJECT (ELSP)

  1. Project Website: Electrify Linear-Systems Problem

  2. How to get Math 2B Final Project Materials (.pdf)

  3. LANA Example 3 Circuit (.pdf)

  4. LANA Example 3 Circuit: W21 Student Measurements

  5. P-Block Information Sheet: Draft 3 (.pdf)

  6. Math 2B: What do I turn in (draft1)? (.pdf)


ELSP PART 1 PLAYLIST
ELSP PART 2 PLAYLIST
ELSP PART 3 PLAYLIST
ELSP PART 4 PLAYLIST
LESSON 19: VECTOR SPACES

  1. Lesson 19: Draft of Jeff's Notes (.pdf)

LESSON 20: NULL AND COLUMN SPACES

  1. Lesson 20: Jeff's Notes (.pdf)

LESSON 20 PLAYLIST
LESSON 21: DIMENSION AND RANK

  1. Lesson 21: Jeff's Notes (.pdf)

LESSON 22: THE FULL-RANK LEAST SQUARES PROBLEM (FRLSP)

  1. Lesson 22: Draft of Jeff's Notes (.pdf)

LESSON 23: ORTHOGONAL SETS

  1. Lesson 23: Jeff's Notes (.pdf)

LESSON 24: OTHOGONAL PROJECTIONS

  1. Lesson 24: Jeff's Notes (.pdf)

LESSON 25: THE CLASSICAL GRAM-SCHMIDT ALGORITHM

  1. Lesson 25: Jeff's Handwritten Notes (.pdf)

LESSON 26: MODIFIED GRAM-SCHMIDT QR FACTORIZATION

  1. Lesson 26: Jeff's Handwritten Notes (.pdf)

LESSON 27: THE STANDARD EIGENVALUE PROBLEM (SEP)

  1. Lesson 27, Part 1: Derivation of Coupled Pendulum ODEs

  2. Lesson 27, Part 2: Eigenvalues and McCusker's apparatus

  3. Project Website: Make Eigenvalues Resonate

LESSON 27 PLAYLIST
EIGENVALUE EXTRAS PLAYLIST
LESSON 28: INTRODUCTION TO EIGENVALUE THEORY

  1. Lesson 28: Jeff's Handwritten Notes (.pdf)

LESSON 28 PLAYLIST
LESSON 29: DIAGONALIZAATION

  1. Lesson 29: Jeff's Handwritten Notes (.pdf)

Math 2B: Learning Portfolios

Please click the button below to download and read my first draft description for our Math 2B Learning Portfolio Practice.

LEARNING PORTFOLIO: SAMPLES OF STUDENT WORK
EXAMPLE TITLE PLAYLIST
CONCEPT IMAGE CAPTURE FOR GRADING PURPOSES

  1. A - Level: Example 1, Math 1C, Exam 2, V6, Part 1
    1. Problem: Derive limit def of directional derivative
    2. Problem: Interpret steepest descent

  2. A - Level: Example 2, Math 1C Exam 2, V9A

  3. B+ - Level: Example 3, Math 1D Exam 2, V1

GRADING PLAYLIST
EXAMPLES OF LEARNING PORTFOLIOS

  1. Steve Silva's Learning Portfolio Post

  2. Jeremy Kun's Math and Programming Blog

  3. Terry Tao's Blog

PORTFOLIO PLAYLIST
LaTeX PORTFOLIO RESOURCES

  1. Get LaTeX from the LaTeX project

  2. How to get LaTeX working on your home computer?

  3. Latex distributions: What are their main differences?

  4. What's a good editor for LaTeX programming?

  5. LaTeX Textbook Template

  6. LaTeX Exam Template

PORTFOLIO PLAYLIST

Math 2B: Exam Resources

Timed exams don't reveal anything meaningful about learning. Instead, timed exams measure a students ability to successfully leverage test-taking strategies, manage anxiety, and solve problems under pressure. I also find that timed exams are good predictors of racial and socio-economic factors instead of genuine learning. None of this is necessarily directly correlated to a students actual learning in my class.

At this point in my teaching career, I am focused on building a much more meaningful mechanism to measure student learning. For interested readers, I provide a much more thorough discussion of how I think about learning in the Math 2B course syllabus. In that document, I highlight some of the major aspects of learning that I plan to measure as I collect evidence that I’ll use to assign a final grade.

I am currently focused on helping my students document their learning via a learning portfolio. To assess and guide each student, I plan to look at a sample of that work. I will use my experiences evaluating that sample as part of the evidence I collect in assigning final grades in this class. Please stay tuned : I plan to show great examples of student portfolios from this class in the future. The principles of my

With all this said, I spend many years using student performance on in-class timed exams as a proxy measurement for authentic learning. Below are some of the artifacts of that practice. Contained in these exams are some interesting problems. My hope is this will help my current and future students decide on some problems to study more deeply as they put together their learning portfolios.

MATH 2B, EXAM RESOURCES
IN-CLASS EXAM 1

  1. Math 2B: Sample Exam 1, V1A, Blank (.pdf)
  2. Math 2B: Sample Exam 1, V1A Answers (.pdf)

  3. Math 2B: Sample Exam 1, V2A, Blank (.pdf)
  4. Math 2B: Sample Exam 1, V2A Answers (.pdf)

  5. Math 2B: Exam 1, V1A, Blank (.pdf)
  6. Math 2B: Exam 1, V1A Answers (.pdf)

  7. Math 2B: Exam 1, V2A, Blank (.pdf)
  8. Math 2B: Exam 1, V2A Answers (.pdf)

  9. Math 2B: Exam 1, V3A, Blank (.pdf)
  10. Math 2B: Exam 1, V3A Answers (.pdf)

  11. Math 2B: Exam 1, V4A, Blank (.pdf)
  12. Math 2B: Exam 1, V4A Partial Solutions (.pdf)

  13. Math 2B: Exam 1, V4B, Blank (.pdf)
  14. Math 2B: Exam 1, V4B Partial Solutions (.pdf)

IN-CLASS EXAM 2

  1. Math 2B: Sample Exam 2, V1A Blank (.pdf)
  2. Math 2B: Sample Exam 2, V1A Answers (.pdf)

  3. Math 2B: Sample Exam 2, V2A Blank (.pdf)
  4. Math 2B: Sample Exam 2, V2A Answers (.pdf)

  5. Math 2B: Exam 2, V1A Blank (.pdf)
  6. Math 2B: Exam 2, V1A Answers (.pdf)

  7. Math 2B: Exam 2, V2A Blank (.pdf)
  8. Math 2B: Exam 2, V2A Solutions (.pdf)

  9. Math 2B: Exam 2, V3A Blank (.pdf)
  10. Math 2B: Exam 2, V3A Solutions (.pdf)

  11. Math 2B: Exam 2, V4A Blank (.pdf)
  12. Math 2B: Exam 2, V4A Solutions (.pdf)

  13. Math 2B: Exam 2, V4B Blank (.pdf)
  14. Math 2B: Exam 2, V4B Solutions (.pdf)

  15. Math 2B: Exam 2, V5 Blank (.pdf)
  16. Math 2B: Exam 2, V5 Solutions (.pdf)

IN-CLASS FINAL EXAM