# Writing Assignment 1 (418) Need this done in Word Document, very detailed! InstructionsAssignmentWrite a complete set of proofs for Theorem 4.5

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Writing Assignment 1 (418) Need this done in Word Document, very detailed! Instructions

Assignment

Write a complete set of proofs for Theorem 4.5 in the Croom book.
– State the hypotheses
– State the conclusions
– Clearly and precisely prove the conclusions from the hypotheses
– Results presented earlier in the text may be used and must be clearly documented
A few notes about format: use Microsoft Word; use Equation Editor for all mathematical symbols, e.g. x ∈ X or Cl(A) ⋂ Cl(X-A); and use the fonts Cambria and Cambria Math in size 11 so your typed work is the same font as your equations.

Course and Learning Objectives

This Writing Assignment supports the following Course and Learning objectives:
CO1: Determine whether a collection of subsets of a set is a topology and determine a basis for a topology.
LO3: Understand the definitions for interior, closure, and boundary of a set.

Written communication is a key piece of modern mathematics. The Discussions as well as many of the homework problems ask you to develop an argument and write it clearly. In addition to the Discussions and homework, you are required to write two formal proofs as writing assignments. These assignments are evaluated according to their validity, readability, and fluency. The definitions for those concepts are given here.

Readability – If your written work is not readable it cannot be assessed. Since the ability to communicate Mathematics is a focal point for this class, special attention will be paid to the readability of your work.

Fluency – Mathematics is a concise and precise language, and I wish to enhance your fluency. Therefore, part of every assessment will focus on your ability to incorporate correct, established notation and terminology into your written work.

Evaluation criteria

Scoring

Validity

logical arguments, deductive reasoning, proper conclusions, complete reasoning

43%

organization, presentation, format, clarity, effectiveness

35%

Fluency

proper notation, proper terminology, appropriate definitions, conciseness

22%

Theorem 4.5:

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