Campus: | Ohio University, Athens Campus |
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Department: | Mathematics |

Academic Year: | 2014 - 2015 |

Term: | Fall Semester |

Course: | MATH 3200 and MATH 5200 |

Title: | Applied Linear Algebra |

Section: | 100 (Class Number 1515 and 1544) |

Instructor: | Mark Barsamian |

Contact Information: | My contact information is posted on my web page. |

Office Hours: | My office hours are posted on my web page. |

**Class Meets:** Monday, Wednesday, Friday 8:35am - 9:30am in Morton 126

**Course 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.

**Prerequisites: **(MATH 163A or 263A or 1350 or 2301) and WARNING: No credit for both this course and the following (always deduct credit for first course taken): MATH 3210

**Paper Syllabus **The syllabus handed out on the first day of class can be obtained at the following link: (syllabus) The information on the paper syllabus is the same as the information on this web page.

Textbook Information | ||
---|---|---|

Title: | Linear Algebra, 2014 Edition |
click to enlarge |

Author: | Jim Hefferon | |

Publisher: | Orthogonal Publishing | |

ISBN-10: | 0989897524 | |

ISBN-13: | 978-0989897525 | |

Price: | roughly $20 for the paperback version at www.Amazon.com | |

Links: | Author's web page for the book: (Link) | |

Free online PDF of the book: (Link) (You still have to buy a paperback copy for our class!) | ||

Free online PDF of the solutions manual: (Link) |

**Online Math Software and Resources: **(Link)

**Grading: **During the semester, you will accumulate points:

Homework Sets (10 Sets, 10 points each): | 100 points possible |

In-Class Exams (best 3 of 4 exams, 200 points each): | 600 points possible |

Comprehensive Final Exam: | 300 points possible |

Total: | 1000 points possible |

At the end of the semester, your Total will be converted to your Course Grade:

Total Score | Percentage | Grade | Interpretation |
---|---|---|---|

900 - 1000 | 90% - 100% | A | You mastered all concepts, with no significant gaps |

850 - 899 | 85% - 89.9% | A- | |

800 - 849 | 80% - 84.9% | B+ | You mastered all essential concepts and many advanced concepts, but have some significant gaps. |

750 - 799 | 75% -79.9% | B | |

700 - 749 | 70% - 74.9% | B- | |

650 - 699 | 65% - 69.9% | C+ | You mastered most essential concepts and some advanced concepts, but have many significant gaps. |

600 - 649 | 60% - 64.9% | C | |

550 - 599 | 55% - 59.9% | C- | |

400 - 439 | 40% - 54.9% | D | You mastered some essential concepts. |

0 - 399 | 0% - 39.9% | F | You did not master essential concepts. |

Note that although this grading scale may look easy compared to the usual 90,80,70,60 scale, it is actually not easier. The reasons are:

- The letter grades in this course mean the same thing as the letter grades in other courses.
- When I grade homework and exams, I give out fewer points. (In this course, you do grade C work on a 20 point exam problem, you will get between 11, 12, or 13 points for the problem. That is in the range 55% - 69.9%. But in somebody else's course that uses the 90,80,70,60 scale, you would have gotten 14 or 15 points for the problem. That is in the range 70% - 79.9%.)
- There is no curve.

**Course Structure: **One learns math primarily by trying to solve problems. This course is designed to provide structure for you as you learn to solve problems, and to test how well you have learned to solve them. This structure is provided in the following ways:

**Textbook Readings:**To succeed in the course, you will need to read the book.**Suggested Exercises:**Farther down this web page, you will find a table of suggested exercises, taken from the textbook. The table is only partially filled-in right now, but it will get filled up as the course proceeds. The goal of the course is for you to be able to solve the exercises on this list. These exercises are not to be turned in and are not graded, but you should do as many of them as possible and keep your solutions in a notebook for study. Note that the solutions to all of the textbook exercises are available free online.**Homework Sets:**Ten homework sets will be collected, graded, and returned to you. The homework sets will be described on cover sheets that will be handed out in class and also posted farther down this web page.**Lectures:**In lecture, I will sometimes highlight textbook material that is particularly important, sometimes present material in a manner different from the presentation in the book, and sometimes solve sample problems. We have 37 lectures, totaling 2035 minutes. It is not possible to cover the entire content of the course in 2035 minutes, and the lectures are not meant to do that. Lectures are meant to be a supplement to your reading the textbook and solving problems.**Exams:**The exams will be made up of problems based on suggested and assigned homework exercises.

**Attendance Policy: **Attendance is required for all lectures and exams, and will be recorded by a sign-in system.

**Missing Class: **If you miss a class for any reason, it is your responsibility to copy someone’s notes and study them. I will not use office hours to teach topics discussed in class to students who were absent.

**Missing an Exam Because of Illness: **If you are too sick to take an exam, then you must

- send me an e-mail before the exam, telling me that you are going to miss it because of illness,
- then go to the Hudson Student Health Center.
- Later, you will need to bring me documentation from Hudson showing that you were treated there.

**Missing Exams Because of a University Activity: **If you have a University Activity that conflicts with one of our exams, you must contact me before the exam to discuss arrangements for a make-up. I will need to see documentation of your activity. If you miss an exam because of a University Activity without notifying me in advance, you will not be given a make-up exam.

**Late Homework Policy: **Homework is due at the start of class on the due date. Late homework is not accepted.

**Suggested Exercises: **The goal of the course is for you to be able to solve all of the problems in this table. These exercises are not to be turned in and are not graded, but you should do as many of them as possible and keep your solutions in a notebook for study. Note that the solutions to all of the textbook exercises are available free online. (The table is only partially filled-in right now, but it will get filled up as the course proceeds.)

Chapter | Section | Subsection | Suggested Exercises | Pages | Supplemental Materials |
---|---|---|---|---|---|

One | I | 1 | 18, 20, 23, 29, 30, 32, 33, 35 | pages 9 - 12 | |

One | I | 2 | 18, 20, 21, 22, 23, 24, 26, 27, 30 | pages 19 - 22 | |

One | I | 3 | 14, 16, 17, 19, 20 | pages 32 - 33 | |

One | II | 1 | 1, 3, 4, 6, 7 | pages 40 - 41 | |

One | II | 2 | 11, 12, 14, 15, 23, 25, 30, 35, 38 | pages 46 - 48 | |

One | III | 1 | 8, 9, 10, 12 | pages 54 - 55 | |

One | III | 2 | 10, 16, 18, 19 | pages 62 - 63 | |

Two | I | 1 | 19, 20, 21, 22, 24, 29, 32, 37 | pages 86 - 90 | |

Two | I | 2 | 20, 21, 22, 25, 26, 27, 28, 30, 31, 39, 43 | pages 97 - 101 | |

Two | II | 1 | 10, 21, 23, 26, 27, 29, 29, 34, 41ac | pages 110 - 114 | |

Two | III | 1 | 18, 19, 20, 21, 22, 23, 26, 27, 29, 33, 35, 36 | pages 118 - 120 | |

Two | III | 2 | 18, 19, 23, 24, 25, 29, 31 | pages 125 - 126 | |

Two | III | 3 | 19, 20, 21, 23, 24, 25, 27, 35, 36, 38 | pages 132 - 134 | |

Three | I | 1 | 13, 15, 16, 18, 21, 22, 27, 30, 31, 35 | pages 172 - 175 | Notes on Images, Preimages, and Inverse Functions |

Three | I | 2 | 10, 15, 17, 20 | pages 181 - 182 | |

Three | II | 1 | 18, 19, 20, 21, 23, 24, 26, 30, 31, 34, 39, 41, 42 | pages 188 - 191 | |

Three | II | 2 | 21, 22, 23, 24, 26, 31, 33, 36 | pages 200-201 | |

Three | III | 1 | 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 28 | pages 210-213 | |

Three | III | 2 | 12, 16, 20, 21, 22, 23, 26 | pages 218-221 | |

Three | IV | 1 | 8, 12, 14, 15, 16 | pages 224 - 226 | |

Three | IV | 2 | 14, 17, 20, 25, 26, 31, 33, 34 | pages 237 - 234 | |

Three | IV | 3 | 24, 26, 29, 31, 32, 33, 36, 37, 41, 42 | pages 241 - 243 | |

Three | IV | 4 | 15, 17, 18, 20, 21, 26, 27, 30 | pages 249 - 251 | |

Three | V | 1 | 8, 11, 12, 15, 18 | pages 255 - 256 | |

Three | V | 2 | 12, 15 | pages 262 - 263 | |

Five | II | 1 | 4, 6, 7, 11, 18 | pages 387 - 388 | |

Five | II | 2 | 7, 8, 9, 10, 11, 14, 15, 17, 18 | pages 392 - 393 | |

Five | II | 3 | 20, 21, 23, 25, 27, 28, 31, 33, 40 | pages 400 - 402 |

**Homework Assignments to Turn In: **These homework sets will be collected, graded, and returned to you. Staple the cover sheet to the front of your work. (The table is only partially filled-in right now, but it will get filled up as the course proceeds.)

Assignment | Due Date | Cover Sheet | Supplemental Materials |
---|---|---|---|

H1 | Fri Aug 29 | H1 Cover Sheet | |

H2 | Mon Sep 8 | H2 Cover Sheet | |

H3 | Mon Sep 22 | H3 Cover Sheet | |

H4 | Mon Sep 29 | H4 Cover Sheet | |

H5 | Wed Oct 15 | H5 Cover Sheet | Notes on Images, Preimages, and Inverse Functions |

H6 | Mon Oct 20 | H6 Cover Sheet | |

H7 | Mon Oct 27 | H7 Cover Sheet | |

H8 | Fri Nov 7 | H8 Cover Sheet | |

H9 | Mon Nov 17 | H9 Cover Sheet | |

H8 | Wed Dec 3 | H10 Cover Sheet |

**Calendar** (The Calendar is only partially filled-in right now, but it will get filled up as the course proceeds.)

Week | Dates | Class topics |
---|---|---|

1 | Mon Aug 25 | One.I.1 Solving Linear Systems: Gauss's Method |

Wed Aug 27 | One.I.2 Solving Linear Systems: Describing the Solution Set | |

Fri Aug 29 | One.I.3 Solving Linear Systems: General = Particular + Homogeneous (H1 Due) | |

2 | Mon Sep 1 | Holiday: No Class |

Wed Sep 3 | One.I.3 Solving Linear Systems: General = Particular + Homogeneous | |

Fri Sep 5 | One.I.3 Singular & Non-Singular Matrices; The Set Generated by a Set of Vectors | |

3 | Mon Sep 8 | One.III.1 Reduced Echelon Form: Gauss-Jordan Reduction (H2 Due) |

Wed Sep 10 | One.III.2 Reduced Echelon Form: The Linear Combination Lemma | |

Fri Sep 12 | In-Class Exam 1 Covering Chapter 1 | |

4 | Mon Sep 15 | Two.I.1: Definition of Vector Space |

Wed Sep 17 | Two.I.2: Subspaces | |

Fri Sep 19 | Two.I.2: Spanning Sets | |

5 | Mon Sep 22 | Two.II.1: Linear Independence (H3 Due) |

Wed Sep 24 | Two.II.1: Linear Independence | |

Fri Sep 26 | Two.III.1: Basis | |

6 | Mon Sep 29 | Two.III.2: Dimension (H4 Due) |

Wed Oct 1 | Two.III.3: Vector Spaces and Linear Systems | |

Fri Oct 3 | Holiday: No Class | |

7 | Mon Oct 6 | In-Class Exam 2 Covering Chapter 2 |

Wed Oct 8 | Three.I.1: Isomorphisms: Definitions and Examples | |

Fri Oct 10 | Three.I.1: Isomorphisms: Definitions and Examples | |

8 | Mon Oct 13 | Three.I.2: Isomorphisms: Dimension Characterizes Isomorphism |

Wed Oct 15 | Three.II.1.Homomorphisms: Definition (H5 Due) | |

Fri Oct 17 | Three.II.1.Homomorphisms: Definition | |

9 | Mon Oct 20 | Three.II.1.Homomorphisms: Definition (H6 Due) |

Wed Oct 22 | Three.II.2.Homomorphisms: Range Space | |

Fri Oct 24 | Three.II.2.Homomorphisms: Null Space | |

10 | Mon Oct 27 | Three.III.1: Computing Linear Maps: Representing Linear Maps with Matrices (H7 Due) |

Wed Oct 29 | Three.III.1: Computing Linear Maps: Representing Linear Maps with Matrices | |

Fri Oct 31 | In-Class Exam 3 Covering Chapter 3 Sections I, II | |

11 | Mon Nov 3 | Three.III.2: Computing Linear Maps: Any Matrix Represents a Linear Map |

Wed Nov 5 | Three.III.2: Computing Linear Maps: Any Matrix Represents a Linear Map | |

Fri Nov 7 | Three.IV.1: Matrix Operations: Sums and Scalar Products (H8 Due) | |

12 | Mon Nov 10 | Three.IV.2: Matrix Operations: Matrix Multiplication |

Wed Nov 12 | Three.IV.3: Matrix Operations: The Mechanics of Matrix Multiplication | |

Fri Nov 14 | Three.IV.4: Matrix Operations: Inverses | |

13 | Mon Nov 17 | Three.V.1: Change of Basis: Changing Representations of Vectors (H9 Due) |

Wed Nov 19 | Three.V.2: Change of Basis: Changing Map Representations | |

Fri Nov 21 | In-Class Exam 4 Covering Chapter 3 Sections III, IV, V | |

14 | Mon Nov 24 | Five.II.1,2: Similarity, Diagonalizability |

Wed Nov 26 | Holiday: No Class | |

Fri Nov 28 | Holiday: No Class | |

15 | Mon Dec 1 | Five.II.3 Eigenvalues and Eigenvectors |

Wed Dec 3 | Five.II.3 Eigenvalues and Eigenvectors (H10 Due) | |

Fri Dec 5 | Five.II.3 Eigenvalues and Eigenvectors | |

14 | Wed Dec 10 | Comprehensive Final Exam 8:00am - 10:00am in Morton 126 |

(page maintained by Mark Barsamian, last updated December 16, 2014)