Hello, I am soon to be a graduate student in mathematics. I currently have a chalkboard (well, a whiteboard covered with chalkboard paint) and I very much like it. I think chalk is fun, and I am particularly fond of how long chalk will last. The problem is that I have a laptop, on which I have...
Hello. I'm a senior mathematics major at the liberal arts honors college of Florida Atlantic University. I have ~3.96 GPA, and was hoping to apply to math departments with either a string algebra program or strong logic program (more of the latter). Unfortunately, my standardized test taking...
Well, here are more details on my current situation. I am taking a directed independent study in Category Theory. My professor (he is one of the few calling it outdated) wants me to use the book Category Theory: An Introduction by Herrlich and Strecker. I am aware that these authors have another...
Hello. I am about to start learning category theory. I keep hearing mixed opinions on the book Categories for the Working Mathematician, by Sanders MacLane (I am aware he is one of the founders of the theory). Some say it's a "must read", and others have called it "outdated." What would seem...
This is actually a fantastic thing do do with really any subject; read multiple books, even side by side. It's good to see a subject treated a little differently, and for newer students, its good to see how an easier book can be "translated" into more rigorous and terse forms this way. Also even...
Cool, I think I can also borrow Aluffi's text. Does Aluffi cover as much as Lang? Might have forgotten to specify, by I wanted a book that could (to the best of its ability) cover as much as possible.
I just want a complete treatment of abstract algebra, to make the transition to grad school easier as I graduate in a year (I'm becoming a senior in the fall). I had two courses in undergraduate algebra, though I have no problem with tough levels of rigor and terseness from my self study habits...
Hello, I have access to both Algebra (the graduate one) by Lang, and the series of Algebra Chapters 1-7 by the Bourbaki group. I am okay with Lang's style and all, and I am aware that he was in the Bourbaki group, but I was wondering what is considered the better of the two. Thanks in advance.
Thanks for your response, I was going to look into category theory anyways, but now I have even more motivation to do so! I was wondering if recursion theory also fit the bill, or maybe I should just stick with category theory. Thanks again for the help.
Hello everyone. I'm having some trouble deciding on what field I should pursue in graduate school. I really like any branch of math, but I'd have to say that both mathematical logic (and meta-mathematics in general) and abstract algebra might have to be my favorites. I am also interested in...
Hi, I am trying to find a completely rigorous book on combinatorics. For example, one that states the sum and product counting principles in terms of set theory and proves them, treats permutations as a bijection from a set onto itself, etc. Many don't even explain the reasoning behind those...
Every math major eventually learns logic and standard proof techniques. For example, to show that a rigorous statement P implies statement Q, we suppose the statement P is true and use that to show Q is true. This, along with the other general proof techniques are very broad. A math major would...