MATH 3200-105 (13894), Fall 2016

Applied Linear Algebra

Catalog Description:
A course on linear algebra with an emphasis on applications and computations. Solutions to linear systems, matrices and matrix algebra, determinants, n-dimensional real vector spaces and subspaces, bases and dimension, eigenvalues and eigenvectors, diagonalization, norms, inner product spaces, orthogonality and least squares problems.
Desired Learning Outcomes:
MATH 1350 or MATH 2301. No credit for both this course and MATH 3210 (first taken deducted).
Martin J. Mohlenkamp,, (740)593-1259, 315-B Morton Hall.
Office hours: Monday, Wednesday, and Friday 12:55-1:50pm, or by appointment.
Web page:
Class hours/ location:
Monday, Wednesday, Friday 2:00-2:55pm in 122 Morton Hall.
Matrix Methods: Applied linear Algebra. Third edition, by Richard Bronson and Gabriel Costa, Academic Press 2009; ISBN: 978-0-12-374427-2. If you plan to study with one of your classmates, you might want to share a book.
Text Homework/ Practice:
From each section of the book, several homework problems are listed. The problems in the text are not collected or graded, but doing them is the foundation for your learning. Most of the answers are in the back of the book.
Online Homework/ Practice:
We will use WeBWork for online homework, which you access here. Your initial username and password are your PID; change your password the first time you log in. The online homework problems do not cover all topics, so you still need to do the text problems. I recommend you work the online problems out on paper (and save this work) before entering them.
Good Problems:
There are nine Good Problems, which will be collected and graded. These problems are graded half on presentation, with the required presentation skills building through a series of handouts. Your best 8 out of 9 scores count toward your grade.
There will be 4 midterm tests. Your best 3 out of 4 scores count toward your grade. Calculators are not permitted. Bring your student ID to the tests. The tests are cumulative.
Why all these tests?
The purpose of the tests is not to assess your mastery in order to assign you a grade; a final exam would be enough for that. Instead, the purpose is to help you learn through what Psychologists have determined to be effective learning techniques.
Practice Testing:
(Rated "high" utility.) Recalling information and practicing skills in a test environment convinces your brain that they are important and should be saved in your long-term memory.
Distributed Practice:
(Rated "high" utility.) Learning/ studying in smaller amounts distributed over time (rather than cramming every few weeks) also convinces your brain to use your long-term memory.
Interleaved Practice:
(Rated "moderate" utility.) Mixing up the problem types (e.g. by having cumulative tests) makes you learn how to distinguish which technique to use and also convinces your brain to use your long-term memory.
(FYI: Elaborative interrogation and self-explanation were rated "moderate" utility. Summarization, highlighting, keyword mnemonics, imagery use for text learning, and rereading were rated "low" utility.)
Final Exam:
The final exam is Monday, December 5, at 12:20 pm in our regular classroom. Calculators are not permitted.
Your grade is based on the online homework at 6%, your best 8 (out of 9) Good Problems at 3% each, your best 3 (out of 4) tests at 15% each, and the final exam at 25%. An average of 90% guarantees you at least an A-, 80% a B-, 70% a C-, and 60% a D-.
I do not count attendance in your grade, since absences will automatically penalize you through your loss of learning.
Electronic Devices:
Computers, tablets, smartphones, and calculators are permitted in class for learning purposes (consulting an online text, producing graphs, etc.). Other uses, especially any that distract your classmates, are prohibited.
Missed or Late work:
Online Homework:
Individual extensions for the online homework will not be given. (If there are problems with the website, I will delay the due date for everyone.)
Good Problems:
Late Good Problems are penalized 5% for each 24 hour period or part thereof, excluding weekends and holidays.
Only reasons given in advance of a missed test will be considered; otherwise a score of 0 will be given. (Note that only your best 3 out of 4 tests count.)
Academic Misconduct:
Text Homework:
You are strongly encouraged to work together on the homework problems in the text.
Online Homework:
The online homework must be done by you, but you may use any help that you can find. Keep in mind that the purpose of the homework is to develop your ability to do such problems on your own.
Good Problems:
You can help each other on the Good Problems and proof-read each other's work. Simply copying is not permitted. You must acknowledge in writing what help you received and from whom. A minor, first-time violation will receive a warning and discussion and clarification of the rules.
Tests, final exam:
You may not give or receive any assistance during a test or the exam, including but not limited to using notes, phones, calculators, computers, or another student's solutions. (You may ask me questions.) A minor, first-time violation will result in a zero grade on that test.
Serious or second violations will result in failure in the class and be reported to the Office of Community Standards and Student Responsibility, which may impose additional sanctions. You may appeal any sanctions through the grade appeal process.
Special Needs:
If you have specific physical, psychiatric, or learning disabilities and require accommodations, please let me know as soon as possible so that your learning needs may be appropriately met. You should also register with Student Accessibility Services to obtain written documentation and to learn about the resources they have available.
Learning Resources:
  • Your classmates.
  • Your instructor.
Ohio University Resources:
Written Material:
(Use sparingly. Over-reliance on videos will retard the development of your reading comprehension ability.)
  • Matlab is available on campus and there are MATH 3200 exercises.
  • The sage cell lets you do math on the web.
    There are some preloaded cells. There is a "sagemath" app for mobile devices.


Subject to change.

Week Date Section/Topic Text Homework Resources Test/ Good Problem/ WeBWork
Chapter 1: Matrices
Mon Aug 22 Introduction sage tool
1.1 Basic Concepts1,3,5,7,11,13
Wed Aug 24 1.2 Operations1,5,7,9,15,19,23,27,29 sage
1.3 Matrix Multiplication1,3,5,9,11,15,17,20,21,23,25,29,31,33,37 sage
Fri Aug 26 1.4 Special Matrices1,2,3,5,7,9,15,17,23 sage WeBWork 1.3
Mon Aug 29 1.6 Vectors1,3,5,7,11,13 sage
1.7 The Geometry of Vectors1,3,5,11,13,17 sage
Chapter 2: Simultaneous Linear Equations
Wed Aug 31 2.1 Linear Systems1,3,5,9,13 Good Problem 1: 1.4 #17 using Layout
2.2 Solutions by Substitution1,3,5,7sage
Fri Sep 2 2.3 Gaussian Elimination1,5,7,11,13,17,19,21,23,30,32,34,36 sage WeBWork 2.2 (drop deadline)
Mon Sep 5 Labor day holiday, no class
Wed Sep 7 2.5 Linear Independence1,5,9,11,21,23,24,25,32,36 Good Problem 2: 2.1 #13 using Flow (and Layout)
Fri Sep 9 2.6 Rank1,3,5,6,12,17,27 WeBWork 2.5
Mon Sep 12 2.7 Theory of Solutions1,3,5,7,9
Wed Sep 14 Test through Section 2.6 sample questions; test solutions Test
Chapter 3: The Inverse
Fri Sep 16 3.1 Introduction1,3,6,11,13,15,27,29,35,37,51,57 WeBWork 2.7
3.2 Calculating Inverses1,7,10,11,19,22sage
Mon Sep 19 3.3 Simultaneous Equations1,5,7,14
Wed Sep 21 3.4 Properties of the Inverse1,3,5,8,13 Good Problem 3: 3.1 #57 using Logic (and Layout,...)
Fri Sep 23 3.5 LU Decomposition1,5,7,13,18,20 sage WeBWork 3.4
Chapter 5: Determinants
Mon Sep 26 5.1 Introduction1,3,5,10,12,21,23,27
Wed Sep 28 5.2 Expansion by Cofactors1,3,7,19,26 sage Good Problem 4: 3.5 #20 using Intros etc.
Chapter 6: Eigenvalues and Eigenvectors
Fri Sep 30 6.1 Definitions1,2,5,6 WeBWork 5.2
6.2 Eigenvalues 1,3,5,7,9,11,17,19,21,34,35,36 sage
Mon Oct 3 Reading day holiday, no class
Wed Oct 5 Test through Section 5.2 sample questions; test solutions Test
Fri Oct 7 6.3 Eigenvectors1,3,7,9,13,22,24,27 sage WeBWork 6.2
Mon Oct 10 6.4 Properties of Eigenvalues and Eigenvectors1,3,7,9,10-21 WP Mathematical induction WeBWork 6.2
Wed Oct 12 6.5 Linearly Independent Eigenvectors 1,3,5,11,15 Good Problem 5: 6.2 #36 using Symbols etc.
Fri Oct 14 Supplement: Diagonalization WeBWork only sage; WP Matrix similarity, WP Diagonalizable matrix WeBWork 6.5 (notes)
Mon Oct 17 Supplement: Introduction to the Jordan Form see the supplement sage; WP Jordon normal form WeBWork 6.5 (notes)
Chapter 7: Matrix Calculus
Wed Oct 19 7.1 Well-Defined Functions1,3,4,5,7,9,13,16,17 Good Problem 6 is in the supplement
Fri Oct 21 7.2 Cayley-Hamilton Theorem 1,3,5 WeBWork Jordan
Mon Oct 24 7.3 Polynomials of Matrices-Distinct Eigenvalues1,2,7,13,19,21,25
Wed Oct 26 Test through Section 7.2 Jordan Form sample questions; test solutions Test
Fri Oct 28 7.4 Polynomials of Matrices-General Case1,2,3,7,8,9,12 (no WeBWork) (drop deadline with WP/WF)
Mon Oct 31 7.5 Functions of a Matrix1,3,9,13,15
Wed Nov 2 7.6 The Function \(e^{At}\)1,3,7 sage Good Problem 7: 7.4 #13
7.7 Complex Eigenvalues 1,3,7
Fri Nov 4 7.8 Properties of \(e{^A}\)1,3,6,8 WeBWork 7
Mon Nov 7 7.9 Derivatives of a Matrix1,2,6
Chapter 10: Real Inner Products and Least Squares
Wed Nov 9 10.1 Introduction 1,3,7,15,18,24,29-33,35,36,37 Good Problem 8: 7.8 #7
Fri Nov 11 Veterans day holiday, no class
Mon Nov 14 10.2 Orthonormal Vectors 1,3,7,11,13
Wed Nov 16 Test through 10.1 sample questions; test solutions Test
Fri Nov 18 10.3 Projections and QR-Decompositions1,3,7,9,11,15,17,23 sage WeBWork 10.2
Mon Nov 21 10.4 The QR-Algorithm1,2,4,5 sage
Wed Nov 23 Thanksgiving holiday, no class
Fri Nov 25 Thanksgiving holiday, no class
Mon Nov 28 10.5 Least-Squares 1,5,11 sage
Wed Nov 30 Supplement: Norms see the supplement sage; WP Norm, Matrix Norm Good Problem 9: 10.3 #23
Fri Dec 2 Recap/ Review WeBWork 10.5
Mon Dec 5 Final Exam 12:20-2:20 pm in our regular classroom. sample questions; test solutions Final Exam

Martin J. Mohlenkamp
Last modified: Tue Oct 11 17:25:33 EDT 2016