Campus: | Ohio University, Athens Campus |
---|---|

Department: | Mathematics |

Academic Year: | 2014 - 2015 |

Term: | Spring Semester |

Course: | MATH 3210 and MATH 5210 |

Title: | Linear Algebra |

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. |

**This Course is Cross-Listed**

- MATH 3210 Linear Algebra Section 100 (Class Number 6070)
- MATH 5210 Linear Algebra Section 100 (Class Number 6089)

**Class Meets:** Monday, Wednesday, Friday 10:45am - 11:40am in Morton 215

**Course Description: **A course in linear algebra for students majoring or minoring in the mathematical sciences. The course will introduce both the practical and theoretical aspects of linear algebra and students will be expected to complete both computational and proof-oriented exercises. Topic covered will include:

- Solving Linear Systems, Gauss’s Method, Echelon Forms
- Vector Spaces, Subspaces, Linear Independence, Basis, Dimension
- Homomorphisms, Isomorphisms, Range Space, Null Space
- Matrix Representation of Linear Map, Matrix Operations & Inverses
- Determinants
- Similarity, Diagonalizability, Eigenvalues and Eigenvectors

**Prerequisites: **2302 Calculus II and (3050 Discrete Math or CS 3000) WARNING: No credit for both this course and MATH 3200/5200 (always deduct credit for first course taken)

**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 (4 exams, 150 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 goal of the course is for you to be able to solve the 233 exercises on that list. Those 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.

**Collaborating on Homework:** You are encouraged to work together on the homework. If you work in a productive way with other students, you will probably learn the math better. You will certainly learn valuable communication skills. But collaborating does not mean copying. You may figure out problems and arrive at solutions together, but the words you write and turn in should be your own. If two or three or five students work together, the result should be a higher quality of work, with fewer errors. When I grade homework, if I find identical wording, identical math, and identical mistakes in different students’ papers, I will deduct points. If this happens, it is not meant to be a punitive measure, and I do not mean for you to think that I am accusing you of cheating. But I do mean for it to be feedback that tells you that you are not really collaborating and that you are not doing good work. Collaborating is a skill that requires practice.

**Cheating on Exams:** If cheat on an exam, you will receive a zero on that exam and I will submit a report to the Office of Community Standards and Student Responsibility (OCSSR). If you cheat on another exam, you will receive a grade of F in the course and I will again submit a report to the OCSSR.

**Special Needs:** If you have a physical, psychiatric, or learning disability that requires accommodation, please let me know as soon as possible so that your needs may be appropriately met.

**Suggested Exercises: **The goal of the course is for you to be able to solve the 233 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.

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

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 | 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, 35, 36, 37, 38 | pages 86 - 90 |

Two | I | 2 | 20, 21, 22, 26, 27, 28, 29, 31, 32, 40, 44 | pages 97 - 101 |

Two | II | 1 | 20, 21, 24, 27, 28, 29, 30, 35, 42ac | pages 110 - 114 |

Two | III | 1 | 18, 19, 20, 22, 23, 24, 28, 29, 31, 35, 37, 38 | pages 118 - 120 |

Two | III | 2 | 19, 20, 25, 26, 27, 31, 33 | pages 125 - 126 |

Two | III | 3 | 19, 20, 21, 25, 26, 27, 29, 37, 38, 40 | pages 132 - 134 |

Three | Chapter 3 problems and page numbers shown are from the new edition of the book. The problem numbers and page numbers in (parentheses) are from the old edition of the book | |||

Three | I | 1 | 13, 17(15), 18(16), 20(18), 23(21), 24(22), 29(27), 32(30), 33(31), 37(35) | pages 172 - 175 |

Three | I | 2 | 10, 15, 17, 20 | pages 179-180 (181–182) |

Three | II | 1 | 18, 19, 20, 21, 24(23), 25(24), 27(26), (31)30, 32(31), 35(34), 40(39), 42(41), 42(42) | pages 186-189 (188-191) |

Three | II | 2 | 21, 22, 25(23), 26(24), 28(26), 33(31), 35(33), 38(36) | pages 198-201 (200-202) |

Three | III | 1 | 12, 13, 14, 15, 16, 18(17), 19(18), 20(19), 21(20), 22(21), 24(23), 29(28) | pages 209-212 (210-213) |

Three | III | 2 | 12, 16, 22(20), 23(21), 24(22), 25(23), 28(26) | pages 218-220 (218-221) |

Three | IV | 1 | 8, 12, 14, 15, 16 | pages 223-224 (224-226) |

Three | IV | 2 | 14, 17, 21(20), 26(25), 27(26), 32(31), 34(33), 35(34) | pages 230-233 (231-234) |

Three | IV | 3 | 24, 26, 29, 31(NA), 32(37), 33(NA), 34(31), 35(32), 36(33), 39(36), 43(41), 44(42) | pages 240-243 (241-243) |

Three | IV | 4 | 15, 17, 18, 20, 21, 26, 27, 30 | pages 249-250 (249-251) |

Three | V | 1 | 8, 11, 12, 15, 18 | pages 254-256 (255-256) |

Three | V | 2 | 12, 14(NA), 17(15) | pages 261-263 (262-263) |

Four | I | 1 | 3, 5, 6, 8, 9 (a ≠ 0 and ae-bd ≠ 0), 16, 17 | pages 319 – 321 |

Four | I | 2 | 9, 12, 13, 14, 15, 16, 19 | pages 324 – 326 |

Four | I | 3 | 17, 20, 21, 26, 28, 33 | pages 333 – 335 |

Four | III | 1 | 11, 12, 14, 15, 18, 21, 23, 24 | pages 355 - 356 |

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.

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

H1 | Fri Jan 16 | H1 Cover Sheet | H1 Solutions | |

H2 | Wed Jan 28 | H2 Cover Sheet | H2 Solutions | |

H3 | Mon Feb 9 | H3 Cover Sheet | H3 Solutions | |

H4 | Mon Feb 16 | H4 Cover Sheet | H4 Solutions | |

H5 | Mon Mar 9 | H5 Cover Sheet | H5 Solutions | Notes on Images, Preimages, and Inverse Functions |

H6 | Wed Mar 11 | H6 Cover Sheet | H6 Solutions | |

H7 | Wed Mar 18 | H7 Cover Sheet | H7 Solutions | |

H8 | Wed Apr 1 | H8 Cover Sheet | H8 Solutions | |

H9 | Fri Apr 10 | H9 Cover Sheet | H9 Solutions | |

H8 | Wed Apr 22 | H10 Cover Sheet | H10 Solutions |

**Remark on Errors in the Homework Solutions:** The homework solutions that I write are bound to contain mistakes. If you find a mistake in one of the printed homework solutions and you report it to me in an e-mail before anybody else reports it to me (and before I find it myself), you will earn 1 point. I will reply to your e-mail with an e-mail telling you whether or not you earned a point. The points you earn this way will be added to your course score at the end of the semester, and I will send you an e-mail telling you the total number of points that you earned.

**Calendar**

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

1 | Mon Jan 12 | One.I.1 Solving Linear Systems: Gauss's Method |

Wed Jan 14 | One.I.1 Solving Linear Systems: Gauss's Method (Group Work) | |

Fri Jan 16 | One.I.2 Solving Linear Systems: Describing the Solution Set
(H1 Due) | |

2 | Mon Jan 19 | Holiday: No Class |

Wed Jan 21 | One.I.3 Solving Linear Systems: General = Particular + Homogeneous | |

Fri Jan 23 | One.I.3 Singular & Non-Singular Matrices; The Set Generated by a Set of Vectors | |

3 | Mon Jan 26 | One.III.1 Reduced Echelon Form: Gauss-Jordan Reduction (Group Work) |

Wed Jan 28 | One.III.2 Reduced Echelon Form: The Linear Combination Lemma
(H2 Due) | |

Fri Jan 30 | In-Class Exam 1 Covering Chapter 1 | |

4 | Mon Feb 2 | Two.I.1: Definition of Vector Space |

Wed Feb 4 | Two.I.1: Definition of Vector Space | |

Fri Feb 6 | Two.I.2: Subspaces | |

5 | Mon Feb 9 | Two.I.2: Spanning Sets
(H3 Due) |

Wed Feb 11 | Two.II.1: Linear Independence | |

Fri Feb 13 | Two.III.1: Basis | |

6 | Mon Feb 16 | Two.III.1: Basis (Lecture Notes)
(H4 Due) |

Wed Feb 18 | Two.III.2: Dimension (Lecture Notes) | |

Fri Feb 20 | Two.III.3: Vector Spaces and Linear Systems (Lecture Notes) | |

7 | Mon Feb 23 | In-Class Exam 2 Covering Chapter 2 |

Wed Feb 25 | Three.I.1: Isomorphisms: Definitions and Examples (Lecture Notes) | |

Fri Feb 27 | Three.I.1: Isomorphisms: Definitions and Examples (Lecture Notes) | |

8 | Mon Mar 2 | Spring Break |

Wed Mar 4 | ||

Fri Mar 6 | ||

9 | Mon Mar 9 | Three.I.2: Isomorphisms: Dimension Characterizes Isomorphism (Lecture Notes) (H5 Due) |

Wed Mar 11 | TThree.II.1.Homomorphisms: Definition (Lecture Notes)
| |

Fri Mar 13 | Three.II Homomorphisms (Lecture Notes) (H6 Due) | |

10 | Mon Mar 16 | Three.II.2.Homomorphisms: Range Space (Lecture Notes) |

Wed Mar 18 | Three.II.2.Homomorphisms: Null Space (Lecture Notes)
(H7 Due) | |

Fri Mar 20 | Chapter 3 Sections I, II Leftovers and Review (Lecture Notes) | |

11 | Mon Mar 23 | In-Class Exam 3 Covering Chapter 3 Sections I, II |

Wed Mar 25 | Three.III.1: Computing Linear Maps: Representing Linear Maps with Matrices (Lecture Notes) | |

Fri Mar 27 | Three.III.1: Computing Linear Maps: Representing Linear Maps with Matrices (Lecture Notes) | |

12 | Mon Mar 30 | Three.III.2: Computing Linear Maps: Any Matrix Represents a Linear Map (Lecture Notes) |

Wed Apr 1 | Three.IV.1: Matrix Operations: Sums and Scalar Products; The Trace (Lecture Notes)
(H8 Due) | |

Fri Apr 3 | Three.IV.1: Matrix Operations: The Transpose (Lecture Notes) | |

13 | Mon Apr 6 | Three.IV.2: Matrix Operations: Matrix Multiplication (Lecture Notes) |

Wed Apr 8 | Three.IV.2: Matrix Operations: Matrix Multiplication (Lecture Notes) | |

Fri Apr 10 | Three.IV.3 The Mechanics of Matrix Multiplication
(Lecture Notes)
(H9 Due) | |

14 | Mon Apr 13 | Three.IV.4: Inverses (Lecture Notes) |

Wed Apr 15 | In-Class Exam 4 | |

Fri Apr 17 | Three.IV.4: Gauss's Method for computing Matrix Inverses (Lecture Notes) | |

15 | Mon Apr 20 | Five.II.1,2: Similarity, Diagonalizability (Lecture Notes) |

Wed Apr 22 | Five.II.2,3 Diagonalizability, Eigenvalues and Eigenvectors (Lecture Notes) | |

Fri Apr 24 | Five.II.3 Eigenvalues and Eigenvectors (Lecture Notes)(H10 Due) | |

16 | Mon Apr 27 | Comprehensive Final Exam 10:10am - 12:10pm in Morton 215 (Exam Information) |

(page maintained by Mark Barsamian, last updated Aug 17, 2015)