I have a fondness for Abstract Algebra (but not much ability). It answers the question: "Given the most basic, minimal assumptions about a set and its mathematical operations, what can be proven?". Once that is addressed, it is surprising how many examples and applications it has in all fields...
You might want to look at the requirements for entering into the PhD program at the University and field of your choice. I would be surprised if Real Analysis was not required. Abstract Algebra might be, but I can think of others (like statistics) that are more likely. You might have to pass a...
So it seems as though your hypothesis may be wrong. Perhaps the success of a team tends to depend on having a superstar player whose handicap increases the SD.
By the time one takes complex analysis, he should be comfortable leaving it as ##\sqrt 2##.
Leave the approximation accuracy for the time that it needs to be determined.
Thanks for clarifying. I conclude that I was just confused about RISK. The demand for programmers when RISK began was probably just part of the startup of RISK. I never programmed or even saw RISK programs and thought it must be like low-level array processor programming.
Now that I think about...
I got the (maybe incorrect) impression that RISC programming was harder when there was a great shortage of RISK programmers. Maybe the shortage was due to the initial flood of RISK processors rather than their programming difficulty. I thought that RISK processing was like low-level array...
To be more precise, an assembly language is matched to the architecture that it runs on. Different architecture has a different assembly language.
The higher level languages have standard versions that should run properly on any compliant machine.
How much you will use assembly language depends on what type of work you do. If you get into real-time device handlers, you will see it a lot. In 37 years of programming, I have only been involved with assembly code a few times. Once was regarding device handlers. Once was in trying to speed up...
If you go back far enough, IBM dominated. I "learned" assembly language in a college class that was 75% IBM employees. There was no real variety. The latest IBM development was all that mattered.
(I quoted the "learned" because I was too immature and lazy at that time to really learn it.)
If you really want to learn assembly code, then do it. Even for a high-level, professional programmer there are occasions to insert inline assembly code into general-purpose code. And there will be occasions to modify assembler code for special uses.
But do not think that it will compete with...
No. Neither engineering nor pure math is like that. The first thing to learn in pure math is to use the tools (already proven theorems) to think at a higher, more abstract, level. When a pure mathematician wants to prove something new using an already-proven theorem, he does not rework all the...