MA110 INTRODUCTION TO LINEAR ALGEBRASYLLABUS - SUMMER 2007Instructor: Patrick Barrow Website: http://math.berkeley.edu/∼borispemail: [email protected]: 937 Evanshours: M 10:00 - class, W 2:00 - 4:00, and by appointmentLectures are MTWTh from 12:10 - 2:00, in 433 Latimer.Textbook is Linear Algebra Done Right by Sheldon Axler, and there also will behandouts.Homework will generally be due at the start of class on Tuesdays and Thursdays,and it will be posted on the website. You also have the daily informal assignmentsof checking the website and reading the relevant sections in the book.Homework will account for 25% of your final raw score. Your lowest two home-work scores will be dropped, and no late homework is accepted, under any circum-stances. Towards the end of the summer, I may offer optional problems that mayreplace earlier scores.Exams are each for the full 110 minutes, on July 12, July 31, and August 16.Respectively, they are worth 15%, 25%, and 35% of your final raw score. If youhave conflicts with any of these dates, then you need to see me immediately tomake arrangements.Grading: I minimally guarantee a “15 point curve,” which means I will computeyour final raw score, and then assign letter grades according to the “85-70- 55-40”cutoff scheme. I will only (possibly) revise this downward, so that any revision canonly help you.I am also generally willing to let students switch to a “full final” grading option,and I arrange these on a case by case basis. If at any p oint in the semester you feelyou have fallen significantly behind, then please do not be embarrassed to approachme for help.Comments: The above cutoffs may seem low. This is because we plan to adoptthe grading philosophy of heavily penalizing incorrect reasoning. Arguments withlogical gaps or false claims get no credit.This is a “proof course.” That means answers are to be composed as if you arecommunicating a fully justified solution to a mathematical colleague. Undoubtedlythis description is vague at the moment, but a general theme of this course willbe learning exactly what it means to communicate rigorous mathematics. (Thehardest part of this endeavor is understanding definitions properly, which is thetopic of the first handout.)12That being said, generous partial credit will be awarded for progress towards afull solution. If you have figured some things out, but are stuck at a specific point,then say so in your answer. Think of your writeup of the problem as a response to aquery. If you cannot fully respond, then you are also expected to acknowledge that.Try to prove a specific case, work out an example, or c onjecture that a particulartheorem may be relevant. Whatever you do, DO NOT write something that isdownright false. (Or if you do, do it with a disclaimer of the form “this is what Ihave, and here is why it is wrong.”) To know when you have a partial solution, andto identify precisely the parts you are missing, are invaluable mathematical skills.No one will solve every part of every problem.You are encouraged to work together to solve homework problems. Of course, theactual written solution must be your own composition. The problems will mostlycome directly from the textbook. In fact, you may consider the table of contentsa conceptual syllabus for the class, with one section roughly corresponding to onelecture. This makes it easier for you, minimizes my errors, and gives us both acommon reference. For e ach e xam I will give specific sections for which you will beresponsible. I also plan to keep a quasi-daily record of what we have covered onthe website.While I intend to mirror the book conceptually, I do not plan on lecturing straightfrom the book. My lectures will aim to serve as a companion to the text. Forexample, we will certainly prove the same theorem s, but I may offer proofs that areaesthetically different, simply because I have the advantages of a blackboard andnarration. I will also provide examples that go beyond those in the text.Finally, every time I make a mistake, assume it is on purpose, be cause I amtesting