Class Note for MATH 291 with Professor Lerner at KU
Class Note for MATH 291 with Professor Lerner at KU
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This 3 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Kansas taught by a professor in Fall. Since its upload, it has received 17 views.
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Date Created: 02/06/15
Math 291 Linear Algebra Fall 2008 Instructor David Lerner General information Last year the Honors 291 class with some help from the instructor worked up a set of lecture notes for this course There are about 20 lectures each corresponding pretty closely to what I would say to the class if I were actually lecturing There are exercises not enough and some illustrations also not enough the text of the notes seems to be reasonably complete and understandable to me at least They cover all the material of the Math 290291 syllabus plus a bit more They7ll be posted on the web for you lecture by lecture at the appropriate times You do not need to buy a text If you have bought one then take it back for a refund You can rest assured that you7ll learn everything the Math 290 students do and you7ll know it better And you7ll save money The way the course will work is simple Before every class you download the lecture that7s going to be discussed and you read it and work all the exercises This is your homework The notes are rather terse and they need to be read carefully each lecture is between 5 and 10 pages long The exercises are embedded in the text and must be worked when you get to them not later If you cant do an exercise there7s something you dont understand and you need to take care of it The most common problem is not learning the de nitions properly and therefore not understanding what the question means With practice you7ll get quite pro cient but it may be dif cult at rst Learning how to read the notes is worth doing this is the way mathematicians and scientists write just the bare essentials In class we7ll spend time working out any exercises that give you trouble going over any dif cult points in the text and doing more examples I wont be lecturing except on a few dif cult topics Grading There will be two in class exams the rst after Lecture 8 and the second after Lecture 16 with exact dates to be determined and a nal exam counts the same as 2 hour exams Homework wont be collected So you7ll be able to fake it up until the rst exam7 but I dont advise it To get an A in this course you7ll need at least a B average on the exams7 plus 10 additional points from the list of class projects below Projects A number of things need to be done to enhance the course materials Some are listed below other ideas may occur during the semester The primary goal here is to make the notes more readable and useful they7re intended for students just like yourselves7 so you7re the best judge of whats needed 0 The non trivial exercises those marked in the text by one or two asterisks need to be worked out in detail l7ll put links in the lectures to the solutions7 when we7ve got them In general7 these are proofs7 and they need to be written correctly and concisely7 with no ambiguity about whats meant 1 3 pts7 depending on the dif culty 0 As we go over the material7 questions will arise7 and these will lead to new exercises which need to be worked out 2 pts 0 You may feel that more routine77 computational exercises should be added at some points variable credit 0 Most of our work here will be with small eg7 2 gtlt 2 matrics That7s for instructional purposes7 so you understand how to do the computations But computational linear algebra these days is done on computers7 which can handle large say 1000 gtlt 1000 matrices Computing the determinant of such a matrix could take you weeks7 even if you didnt make any algebraic errors unlikelyl The best software platform for linear algebra computations is called MatLab for Matrix Laboratory7 Those of you with access to the Engineering computer lab may already be familiar with MatLab We need to write a brief7 useful introduction to the use of MatLab which will include 1 An introduction explaining how MatLab works7 how to do simple arithmetic7 graph functions7 etc I will do this 2 2 Eigenvalues7 eigenvectors7 and determinants How to diagonalize a square matrix 3 Solution of linear systems of algebraic equations7 especially when the solution is not unique 4 Things to beware of when doing math on a computer how the computer stores numbers and does arithmetic7 machine precision and round off errors7 ill conditioned matrices7 etc This is probably a group project for 3 4 people Item 3 shouldnt be attempted before the lecture on least squares solutions after the 2nd exam 0 At a more pedestrian level7 most matrix computations can be done as long as the matrices are not too big on a decent graphing calculator We need a short appendix explaining how to do this on the Tl calculators well also need a few exercises that the students can do to make sure they understand how to use the calculator This is also a group project7 which can probably be done soon after the rst exam 0 There are several places in the text where a well drawn gure would improve matters l7ve been using the program X g shareware nd it with Google to draw gures You can use another tool as long as the resullt can be imported into a LaTex document variable credit 0 Last7 but certainly not least7 there will be some many places in the text where you think the exposition is unclear or wrong7 and cant be understood without help These portions of the text obviously need to be rewritten variable credit Guidelines Check with me whenever you want to do one of these7 or something that7s not on the list Email lernerkuedu is ne7 or you can talk to me before or after class We want to avoid duplication of effort points will only be given to one person or group for any given item If there are no volunteers for a particular item7 then l7ll pick someone
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