The proof clearly falls apart when it is stated let Set ##A## be a set of ##k+1## numbers. These number can either be all the same, or different. Hence the proof is invalid from that point on.
I have Advanced Calculus: A Course in Mathematical Analysis by Fitzpatrick [1st edition] but I'm not able to find the errata anywhere. I've found it for the second edition but the first edition is much different from the second. If anyone knows where I can find it thanks.
id basically do this. You need to learn how to write proofs first and the best way to do that is get a book that does just that.. Id recommend the one by Peter J Eccles. It's a very nice introduction to proofs. From there learning linear algebra and number theory can readily be done. I'd say...
I think 2-4 hours for one page is time consuming and normal . I assume you are having to spend a lot of time with analysis II and topology. For topology i'd recommend this book "Introduction to Topology: Pure and Applied" by Colin Adams and for analysis II analysis on manifolds by munkres. I...
This is a typical question that a lot of people have when trying to self study mathematics. To begin with mathematics is an amazing subject and very beautiful and there is no magical answer to becoming good at mathematics. For all of us trying to become the best takes hard work and struggling...
I myself was cheated by the misleading claims homeopaths tell you. I had a skin condition so I fell for their claim (I was desperate) that they could cure it in a no time( three months). What I hoped for three months turned into many months. I did not notice any improvement in fact my condition...
That is quite a time consuming way. What I do is skim the section first to get a good highlight of the section. Then I will reread the section this time but much more in depth. What really helps is stopping at every definition and theorem and to try proving it on your own (try to fiddle around...
I've read through parts of this text. I personally did not like it. It's wordy and lacks examples in some areas but its much better than David's lay book. Though Strang does have his own video series online for linear algebra which are actually pretty good.
It's a very nice textbook. Offers a good introduction with linear algebra. It is rigorous but just enough where it is not overwhelming. It explains the concepts very clearly and the problems range from easy to intermediate level questions. It gives a good mix of computational problems and...
Before you tackle Rudin's book i'd suggest get a book that is a step lower or more so a bridge between Calculus and advance calculus. Rudin's book is a bit too advanced for you right now. I'd recommend Elementary analysis by Kenneth Ross, there is another one by Lay, Spivak's Calculus ( I'd...
Woah yes you need to move out and do it fast. That is not normal for a parent to act like the way your mom does. Sorry I don't want to sound rude. Your 24 and you got a lot going for you. As it is your mom should definitely be proud of you since you do have exceptional marks. With that GPA you...
Depending on how far you would want to go you still need quite a bit of math. A good understanding of Calculus 1-3, linear algebra, and differential equations is a must. Then from there a good understanding of differential geometry, manifolds, and knot theory is necessary as well as a flavor of...