<p>Could anyone give me a description of a more theory based linear algebra course? Useful? Difficult? Fun?</p>
<p>In case I'm not clear, I'm a math major and I am guessing this is around the same level as undergrad real analysis.</p>
<p>Thanks,
Eddie</p>
<p>At some schools, there may be multiple linear algebra courses:</p>
<ul>
<li>Lower division introductory linear algebra course emphasizing computational methods, taken by math, statistics, computer science, economics, physics, and engineering majors.</li>
<li>Honors lower division course with more theory and proofs and more difficult problems.</li>
<li>Upper division linear algebra course for math majors emphasizing theory and proofs.</li>
<li>Honors upper division course with even more theory and proofs and more advanced topics.</li>
</ul>
<p>At some math departments, they recommend that the upper division linear algebra be among the first upper division math courses that a math major takes, and warn that many students find real analysis particularly difficult.</p>
<p>Here is a free on-line text book for an honors lower division linear algebra course:
[Linear</a> Algebra Done Wrong](<a href=“http://www.math.brown.edu/~treil/papers/LADW/LADW.html]Linear”>Linear Algebra Done Wrong)</p>
<p>Here is a free on-line text book for a real analysis course:
[Basic</a> Analysis: Introduction to Real Analysis](<a href=“http://www.jirka.org/ra/]Basic”>Basic Analysis: Introduction to Real Analysis)</p>
<p>Thanks, I was looking for a good review on linear algebra. I also sold my real analysis book (the one book I regret selling!)</p>
<p>However I think this course is either more of option 3/4. </p>
<p>The only description I’m given is “an abstract treatment of finite dimensional vector spaces. Linear transformations and their invariants.” The linear algebra that is taken after Calc II is the only prerequisite (ARGH … Why can’t they give these things different names???)</p>
<p>Also, since I think your the one who answers my comp sci questions, do you have any advice for taking Networks and Operating Systems? Should I take one before the other?</p>
<p>Thanks,
Eddie</p>
<p>Operating systems might be slightly useful before networks since networking code that you may be studying as examples or used in programming assignments may be in the operating system, but it should not be a big deal unless the CS department makes it an explicit prerequisite.</p>
<p>There seem to be lots of free on-line linear algebra textbooks, but most appear to be intended for a lower division course.</p>
<p>But this book about abstract algebra and linear algebra may be intended more for an upper division course: [Elements</a> of Abstract and Linear Algebra by Edwin H. Connell](<a href=“http://www.math.miami.edu/~ec/book/]Elements”>Elements of Abstract and Linear Algebra by Edwin H. Connell)</p>
<p>I really appreciate you finding all these books for me xD</p>
<p>My guess is that you’re going to be learning about vector spaces in the same fashion you would learn about groups or rings in an abstract algebra course. That is, you typically won’t be concerned with a particular basis, but with the algebraic structure of the vector space. Some things you might learn about that weren’t in an intro linear algebra class (at least, these things were in my upper division linear algebra class):</p>
<p>Free vector spaces (I am still not sure I understand these)
isomporphism theorems
dual spaces
Jordan form
bilinear forms
tensor products
exterior algebras
Hilbert spaces
isometries</p>
<p>Of course, it’s also possible that the course in question is somewhere inbetween the level of an intro class and the class I’m describing.</p>
<p>Thanks!</p>
<p>The only experience I have with “upper level” math is two semesters of real (eh … sort of) and fourier analysis, so I guess I’ll wait until after abstract algebra to decide if I want to take linear or not.</p>
<p>Also, what do you cover in a second semester of real analysis (I’m assuming you have already taken it)? At our school, we have Advanced Calculus I/II instead of Real Analysis I/II and I think the differences might have become more apparent in the second semester from what other schools might teach (e.g. we spent very little time on metric spaces). </p>
<p>Also, sorry this thread isn’t related to the OP anymore!</p>