In Nocedal and Wright's optimization book, it defines, Observe that the isolated local minimizer is defined as a local minimizer, therefore, if $x^\s...

I was wondering whether the Cancellation Law of Addition is the same as the Addition Property of Equality. The Cancellation law of addition states that a=...

WARNING this is a very long report and is likely going to cause boredom. Be warned!! I've heard of the determinant of small matrices, such as: $$\det...

For a group $G$ there is a natural notion of left action on subsets of $G$ given by $g \triangleright H := gH$. But simultaneously, there is a natural rig...

What are the natural numbers? Is it a valid question at all? My understanding is that a set satisfying Peano axioms is called "the natural numbers" and fr...

I'm in my first proof based class and I'm just having a lot of trouble writing proofs. I mean I know it's not going to come natural and it ...

Is there a way of calculating where the apex of an exponential lies? There's probably a deeper / more mathematical way of explaining what this is exa...

Quoting from Wolfram definition of group action - In general, a group action is when a group acts on a set, permuting its elements , so that the map from ...

Let $A=\{m \in \mathbb{Z} \mid m=4 a+3$ for some integer $a\}$ and let $B=\{n \in \mathbb{Z} \mid n=12 b+7$ for some integer $b\}$. Prove that $B \subset ...

I am trying to find a book to learn measure theory that contains complete solutions manual. Does someone know of any? Also, I would like to know if there ...