Abstract Algebra
let a, b, c, d be integers. Prove the following statements: (a) if a|b and b|c. (b) if a|b and ac|bd. (c) if d|a and d|b then d|(xa+yb) for any x, y EZ
What is an Ordinary Differential Equation (ODE)?
complete assignment with clear solution and explanation
Measuring complexity: Many algorithms have an integer n, or two integers m and n, as input - e.g., addition, multiplication, exponentiation, factorisation and primality testing. When we want to describe or analyse the `easiness' or `hardness' of the a
The focus is on the use of Datalog for defining properties and queries on graphs. (a) Assume that P is some property of graphs definable in the Datalog. Show that P is preserved beneath extensions and homomo
Factorisation by trial division: The essential idea of factorisation by trial division is straightforward. Let n be a positive integer. We know that n is either prime or has a prime divisor less than or equal to √n. Therefore, if we divide n in
Where would we be without stochastic or Ito^ calculus?
(a) Solve the following by: (i) First reducing the system of first order differentiat equations to a second order differential equation. (ii) Decoupling the following linear system of equa
It's a problem set, they are attached. it's related to Sider's book which is "Logic to philosophy" I attached the book too. I need it on feb22 but feb23 still work
integral e^(-t)*e^(tz) t between 0 and infinity for Re(z)<1
Determine into which of the following 3 kinds (A), (B) and (C) the matrices (a) to (e) beneath can be categorized: Type (A): The matrix is in both reduced row-echelon form and row-echelon form. Type (B): The matrix
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