Rational and irrational numbers – Online Assignment Services

MAT 135 Final Paper Outline Template
You may use this template to help organize your thoughts about the final paper. This outline should be submitted to the instructor during Module Two for feedback. See the examples and notes provided below for each section of the paper.
Title: Infinity: The Continuum Hypothesis
The title should be brief but explain to the reader the focus of the paper.
Introduction
This section should summarize the three strands of the paper and what the reader can expect to learn in this paper. This should be 1–2 paragraphs in length and written after the final paper is composed.
Strand 1: The History of [Your Topic]
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Aristotle (actual and potential infinity)
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Georg Cantor
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One-to-one correspondence
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Continuum hypothesis
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Kurt Gödel
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Paul Cohen
This section should focus on the historical evolution of the chosen topic. Bulleted items may include the most significant aspects of the history of the topic. Each of these may be expanded upon in the Strand 1 paper.
The history of the selected topic should be chronological and focus on the most important aspects of the topics development. It does not need include every contribution.
Strand 2: The Mathematics of [Your Topic]
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One-to-one correspondence
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Cardinality of infinite sets
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Subsets
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Proving or disproving the CH
This section should focus on the mathematical aspects of the topic. Bulleted items may include important formulas, interpretations of proofs, and/or consideration of arguments made by mathematicians. Each of these may be expanded upon in the Strand 2 paper.

MAT 135 Milestone 1 Final Project Topic Selection and Outline Guidelines and Rubric
Overview: The final project for this course is the creation of a comprehensive final paper that includes the following main components:
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Introduction
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Strand 1: Historical Significance
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Strand 2: Mathematics
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Strand 3: Real-World Applications
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Conclusion
Prompt: In Module Two, you will submit your chosen topic to the instructor for approval. You will research three areas of this topic and submit an outline for each “strand” for grading and feedback. Your submission should include potential reference sources. Take note that this milestone rubric requires three resources for your outline at this point in time so that you can receive valuable feedback from your instructor. However, additional research and resources are expected as you complete your paper.
The topic may come from the list provided below or it can be self-designed, but it still must be approved prior to writing the outline. The final paper will not be accepted without topic approval.
Final Project Topic List: Choose one
Logic/Proof
Euclidean Geometry
Hilbert’s Hotel
Koch Curve
Pythagorean Theorem
Irrational Numbers
Non-Euclidean Geometry
Power Set Theory
Sierpinski Triangle
Pythagoras Musical Scale
Prime Numbers
Penrose Tiles
Fractals
Linear Algebra
Fibonacci Sequence
Number Theory
Mobius Bands
Mandelbrot Set
Chaos Theory
Infinity
Pascal’s Triangle
Klein Bottles
Knot Theory
Graph Theory
Continuum Hypothesis
Euler’s Königsberg Bridge Problem
Self-Selected Topic*
*NOTE: Instructors will only approve topics for which they know sufficient research and information exists for the student to complete the final paper.
In addition to the points you receive based on the grading rubric on the following page, you will also receive formative feedback from the instructor. Apply this feedback to the strands as you complete them.