Mathematics is 98% Linear Algebra Jeff Fox, Ph.D., University of Colorado
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1 Mathematics is 98% Linear Algebra Jeff Fox, Ph.D., University of Colorado Spring, 2004 Monday, Wednesday, Thursday, & Friday 11:00-11:50 a.m. Buttrick 215 Dr. Alan Koch Office: Buttrick 329 Homepage: Phone: Office Hours: Mondays, Wednesdays, and Thursdays 2 p.m. 3 p.m. (except for Thursday, March 4). If your schedule does not permit you to come at these times, we can set up an appointment. Text. Elementary Linear Algebra, Applications Version, 8 th edition, by Anton and Rorres. Course Content. We will cover chapters 1-8 as well as selected sections from 9 and 11. Topics include matrices, systems of linear equations, determinants, vectors, vector spaces, higherdimensional geometry, linear transformations, inner product spaces, eigenvalues and eigenvectors, diagonalization, and applications. What is Linear Algebra? It is exactly what the name suggests. Simply put, it is the algebra of systems of linear equations. While you could solve a system of, say, five linear equations and five unknowns, it might not take a finite amount of time. With linear algebra we develop techniques to solve m linear equations and n unknowns, or show when no solution exists. We can even talk about situations where an infinite number of solutions exist, and describe them geometrically. Big deal, you say? You d be surprised. As the quote at the top of this syllabus explains, much of mathematics uses linear algebra, either directly or indirectly. For example, each of the following mathematics topics use linear algebra to some degree: Abstract Algebra Algebra (the regular kind) Analytic Geometry Calculus Chaos Theory Cryptography Differential Equations Fractal Geometry Game Theory Graph Theory Linear Programming Operations Research
2 In addition, we also get to do some cool things, like do geometry in 4, 5, or even 31-dimensional space! Aside from being useful to mathematicians, there are plenty of applications of linear algebra to other fields, for example Anatomy Chemistry Computer Science Electrical Engineering Economics Forest Management Genetics Physics Population Dynamics Hey, those forests don t manage themselves Course Goals. By the end of the semester, you should: Perform linear algebra calculations. Develop an understanding of the philosophy behind higher dimensional mathematics. Have a working familiarity with and an appreciation of Maple. Attendance. You are expected to attend every class. Missing class days does not have a direct impact on your grade, however it will have an indirect impact on your grade. Trust me. Also, you will not be penalized directly for tardiness, however you are expected to arrive to each class on time, and assignments are due in class at the start of the class. Also, you will be graded on participation, and you need to be in class in order to be participating (see below). Blackboard. As you ve already discovered, this class has a site on Blackboard. At this site you will find all the handouts for the course. Many of the handouts will be in will be.pdf files, so make sure the computer you re using has Adobe Acrobat Reader installed.. Seven days this semester are designated. On these days, we will have time for you to both ask and answer questions. We will take as many questions as possible, and sometimes people will have the opportunity to answer the questions at the board.
3 Here s how you ll be graded Homework. Each night, there will be homework problems assigned from the sections covered during the lecture. They will consist (primarily) of odd problems from the book, so you can check your answers in the back. This homework will not be collected, but it is assumed that it will be completed by the start of the next class. You are encouraged to work with other people in the class to solve problems. You won t be graded on this, but it seemed like a good place to put this info. Assignments. There will, however, be three assignments that will be turned in. These assignments are designed to help you keep up with the material. As a word of warning, the assignments do not fully cover the scope of the class, and you should not use them as a substitute for daily homework assignments. Assignments are due in class by the start of class on the day indicated at the top of the problem set. Late assignments will not be accepted. You are encouraged to discuss these assignments with the others in the class, but your write-up must be your own. If you have any questions about this policy, please let me know. Projects. In addition, there will be three projects that use the computer algebra package Maple. Maple is a piece of software (installed on all of the school s public computers) that does a lot of the more tedious matrix calculations. We will have a day in the computer lab (tentatively February 4) to give you a bit of practice with Maple before doing any of these projects. The purpose of these projects is to shift the focus from calculation to analysis. We will use Maple to do some nice applications of linear algebra. For the projects, you are encouraged to work with another person. You may turn in one combined assignment. Teams of three or more are not allowed. You will not have class time to do the projects. Tests. You will have three take-home tests. They will (tentatively) be handed out on Friday, February 13; Friday, March 26; and Wednesday, April 14. They are all timed tests that you will take at a time convenient to you. They are due at the start of the next class. You are forbidden from using your textbook or your notes or any other sources (including people, of course). Again, all tests must be pledged. The tests will cover material from the text, along with material presented in class. You will not be allowed to make-up any test without a doctor s note.
4 Participation. You will be graded on participation for this course. Factors that will be used in computation of participation include both the asking and answering of questions in class. Final Exam. The final exam is cumulative, although there will be more of the material since Exam #3 for obvious reasons. It will be self-scheduled, like most of the exams at Agnes Scott College. The same rules apply as to the take-home exam: you can use your calculator, pencil, exam, and the hand you use to write. Honor Code. All students are expected to follow the honor code throughout the semester. Any graded work, be it an assignment, test, or project, must be pledged (and signed) in order for it to be graded. Please consult the student handbook for more details. Grade Distribution Tests 35% Projects 20% Assignments 20% Final 20% Participation 5% Point Scale A A- B+ B B- C+ C C- D+ D D- F You should not expect a curve to be applied to the point scale, unless you happen to love being disappointed.
5 Note: Intervals represent odd problems unless otherwise specified. Date Section Homework / Comments Thu Jan p. 6: 1-7, 11, 13 Fri Jan p. 19: 1-7, 8, 9, 13-17, 21 Mon Jan p. 33: 1-5, 11-15, 19 Wed Jan p. 47: 1-13, 21, 29, 31 Thu Jan p. 56: 1-9, 15 Fri Jan Read 1.7; p. 64: 1-9, 13, 17, 21, 23 Mon Feb p. 563: 1-5 Wed Feb 4 Computer Day Thu Feb 5 Fri Feb p. 87: 1-11, Mon Feb p. 94: 1-9, 17 Wed Feb p. 102: 1-7, 15, 20 Thu Feb p. 112: 1-13, 17, 21 Fri Feb 13 Receive Test #1 Due Feb. 16 Mon Feb p. 125: 1-9, 13, 17 Wed Feb p. 129: 1, 3, 7, 9 Thu Feb p. 136: 1-5, 9-13 Fri Feb p. 147: 1, 3, 7, 11, 15, 29, 37 Mon Feb 23 Wed Feb p. 170: 1-11, 15, 17, 23 Thu Feb p. 185: 1-13, 17, 21 Fri Feb p. 198: 1-9, 13, 15, 19 Mon Mar p. 434: 1-19 Wed Mar 3 Thu Mar p. 674: 1, 3, 7-11 Fri Mar 5 Mon Mar Wed Mar , 5.2 p. 208: 1-15, 21, 23, 29 Thu Mar , 5.3 p. 219: 1-13, 21, 22, 25 Fri Mar p. 229: 1-5, 9, 11, 15, 17, 20 Mon Mar p. 243: 1-19, 23, 31, 35 Wed Mar p. 257: 1-5, 6, 7-13 Thu Mar p. 269: 2, 3, 4, 5, 7, 11, 15, 19 Fri Mar 26 Receive Test #2 Due Mar. 29 Mon Mar 29 Wed Mar p. 284: 3-17, 23,27 Thu Apr p. 294: 1-9, 13, 15, 19, 21, 31 Fri Apr p. 308: 5-11, 15-19, 29, 31
6 Mon Apr 5 Wed Apr p. 702: 1-9 Thu Apr p. 344: 1-10 all, 13, 17, 21, 25 Fri Apr 9 Easter Break No Classes Mon Apr p. 354: 1, 2, 3-15, 19 Wed Apr 14 Receive Test #3 Due Apr. 15 Thu Apr p. 714: 3, 5, 7 Fri Apr p. 373: 1-25, 29, 31 Mon Apr p. 380: 1-7, 11, 15-21, 24, 25, 29 Wed Apr 21 Student Achievement Day No Classes Thu Apr p. 388: 1-19, 20 Fri Apr 23 Mon Apr p. 399: 1-13, 18, 19 Wed Apr p. 411: 1-15, 19 Thu Apr 29 Fri Apr p. 453: 1-7, 11, 13 Mon May 3 Wed May 5 Reading Day Read Fri, May 7- Wed May 12 Final Exams Have Fun. Score High. * * In the interest of plagiarism issues, let it be known that I got that phrase off an old Yahtzee! box.
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