Easy Explanations to Confusing Mathematics Concepts : Page - 7

Question 1In this question you will practise working with ideals in rings that are extensions of degree 2 over the integers. It involves a number of concepts from Chapter 17. Let R be the ring Z[ √ −19 ]. (a) Let A be a subset of R defined by A = {s + t √ −19 : s,t ∈ Z, s ≡ t(mod 5)}. Show that A is an ideal in the ring R. [3] (b) The subset B = {u + v √ −19 : u, v ∈ Z, u &equiv...

MethodsTask 1: Write an essay (750-1000 words) entitled. “Computational Mathematical Software as a first-year study aid.” With reference to selected codes (all of which should be included in the appendix of your essay) reflect on what mathematical skills you have explored using software in ER1630 and how its use has improved your mathematical skills and your approach to mathematics in other modules you are studying. You should refe...

Submitting Your Work ElectronicallyTo submit work electronically you will need to scan your written solutions and save as /convert to pdf format (not jpeg). You can then submit the pdf via the Assignments link from the Assessments tab in Blackboard. Click on the Submit Assignment link, attach thefile, and submit. You will get a message of completion that will be your receipt of submission. You are advised to: • Ensure that you have acces...

Substitution MethodFor the following exercises, determine whether the given ordered pair is a solution to the system of equations. 1. For the following exercises, solve each system by substitution. 2. For the following exercises, solve each system by addition. 3. For the following exercises, solve each system by any method. 4. Graphical 5. For the following exercises, graph the system of equations and state whether the system is consistent,...