Text: Friedberg, Insel, Spence, Linear Algebra 3rd/4th ed. (Prentice Hall) ...
spaces and the linear maps between them: Linear Algebra. We will find that a
special.
Math 410: Linear Algebra Winter Term 2012, Lawrence University Professor: Scott Corry Office: 408 Briggs Hall, x7287 Office Hours: MTWRF 8:30-9:30, and by appointment E-mail:
[email protected] Webpage: www.lawrence.edu/fast/corrys Text: Friedberg, Insel, Spence, Linear Algebra 3rd/4th ed. (Prentice Hall)
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Overview
Vector spaces are ubiquitous. This fact of life motivates the abstract study of vector spaces and the linear maps between them: Linear Algebra. We will find that a special class of vector spaces (the finite-dimensional ones) have a particularly simple structure. In fact, will we see that any two n-dimensional vector spaces (over a given field F) are isomorphic! This is in stark contrast to the situation for groups, where it is far from true that any two groups of order n are isomorphic (for instance, there are 5 non-isomorphic groups of order 8). But don’t worry: rather than rendering the subject boring, this simplicity of structure makes linear algebra an ideal mathematical training ground. This course will develop your powers of abstraction, and there are some lovely theorems to discover. The simplicity announced above also has a practical consequence. Many problems in mathematics, physics, economics, etc. have natural formulations in terms of linear maps between vector spaces. Presented with such a problem, a judicious choice of isomorphism can reveal hidden structure and allow for an easy solution. When such a choice is made, vectors and linear maps become boxes of numbers (matrices). This is the reason linear algebra is sometimes referred to as “matrix algebra.” In this course we will come to understand the abstract meaning of matrix manipulations, thereby gaining significant computational power. Linear algebra is a delightful subject, where abstraction blends cleanly with computation, and proofs tend to be elegant and unencumbered by technical details. Moreover, linear algebra is fundamental to many other areas of mathematics (both pure and applied), so your efforts in this course will increase your ability to understand and enjoy a broad range of mathematical topics. 1
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Practicalities
2.1
Homework
There will be regular homework assignments, and problems will be carefully graded on the following five point scale: 5 4 3 2 1
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perfect – correct and well-written one minor error one major error or several minor errors several major errors indicative of relevant thought
Remember that the quality and clarity of your writing are important. Take the time to make your solution sets neat and legible, and strive to effectively convey your ideas. Homework will count for 70% of your final grade, and NO LATE WORK WILL BE ACCEPTED (except under extraordinary circumstances).
2.2
Exams
We will have one in-class midterm exam (Monday, February 13) as well as a final exam at the time set by the registrar (Monday, March 12, 11:30 a.m.). The midterm is worth 10% and the final worth 20% of your course grade. Please note that under no circumstances will you be allowed to take the final at a different time due to early travel plans.
2.3
Office Hours and Other Details
Please feel free to come by my office, whether you are having difficulty or just want to chat about mathematics. Of course, I may not be in, or I may be otherwise engaged and unable to talk. To ensure that you have my undivided attention, you should come during my office hours, which are listed above. Of course, if these times are impossible for you, you can always make an appointment with me. In addition to talking with me, I encourage you to speak with each other about the course, and even to work together on the problems if that suits your style of learning. That being said, I expect you to spend some time thinking privately about the problems before collaborating, and each of your writeups should be the result of your own cogitation and exposition. If you like to work together, a good model would be to make a first pass through the problems on your own, then get together with friends to talk about difficulties and share ideas, and finally find a solitary place to write a polished (and unique) solution set. Of course, all of your work for this course is governed by the Lawrence University Honor Code.
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