Define a partition of to be a finite or infinite multiset of real numbers in the interval (that is, an unordered set of real numbers in , possibly with multiplicity) whose total sum is : . For instance, is a partition of . Such partitions arise naturally when trying to decompose a large...
This had a number of analytic number theory consequences, for instance in obtaining asymptotics for additive patterns in primes in such intervals. However, there were multiple obstructions to lowering much further. Even for the model problem when , that is to say the study of primes in short ...
What are the important types of functions frequently encountered in calculus? Give an example of each type. How to prove an algorithm is optimal? Define subsets and give a relevant example along with it. What advantage(s) can yo...
In math, what does it mean when a square has 3 instead of 2? What do brackets mean in math? What is an internal operation in abstract algebra? What does ^ stand for in math? What does the notation \frac {dy}{dx} mean in calculus? What is meant by the term commutative in algebra...
Discrete Mathematics is the study of discrete structures, which are structures that can be fully decomposed into a finite number of objects. Discrete Mathematics focuses on counting and order. It's an area of mathematics with applications in many other fields such as game theory, computer science...
Each of these is an operation or a problem. A method of solving these is called an algorithm. The addition is the simplest. You line the numbers up (to the right) and add the digits in a column writing the last number of that addition in the result. The 'tens' part of that nu...
What does uniformly mean in real analysis? Real Analysis: The word "real" is usually used in mathematics to describe things that can be seen and touched. A practical example of this would be the length of a rectangle. The length and width of a rectangle can be measured and represented by...
Can a company be fined in a value larger than the global GDP? Why are sequences and series typically taught in Calculus 2 and not Calculus 1? Is it bad to ask for accommodations for disability when PhD supervisor might be in bereavement? Has there ever been a co...
So, finding a explicit form for leads us to finding an explicit form for the -th Fibonacci number (which is possible, but I will not treat this here). Another way is diagonalization: If is diagonalizable, i.e. there is an invertible matrix and a diagonal matrix such that you see that...
In this paper we explore how students construe what it means for an informal argument to be the basis of a proof. We use students’ attention as a proxy for their conceptions and document what they pay attention to when assessing whether a proof is based on an informal argument. The data...