MAT135 SNHU Milestone 5 Final Project Pascal Triangle

Anonymous
timer Asked: Feb 23rd, 2019
account_balance_wallet $10

Question Description

TOPIC: PASCAL TRIANGLE

PLEASE MAKE THE FOLLOWING CHANGES ON THE PASCAL TRIANGLE MATHEMATICS PART ( PROFESSOR SUGGESTIONS) : I see two mathematical ideas related to Pascal's triangle in your paper: how the triangle is constructed and the application of power's of 2. What is your third idea?

PLEASE MAKE THE FOLLOWING CHANGES ON THE REAL WORLD APPLICATIONS PART ( PROFESSOR SUGGESTIONS): You certainly provided a lot of examples of how Pascal’s triangle is applied in the real world. I might encourage you to slim down the list for the final paper submission and talk a bit more about a smaller subset of applications so we can learn a bit more about those applications. You might limit each paragraph to one particular application instead of putting 3 -5 examples in each paragraph. You have a good problem of probably having a little too much information - be selective and tighten up the section a bit. You have the start of something good. Please make sure your final project is in APA formatting.

PLEASE FIX THE CONCLUSION..

ATTACHED IS THE ESSAY RUBRIC.

MAT 135: Final Project Guidelines and Grading Guide Overview The final project for this course is the creation of a comprehensive final paper that includes the following main components:      Introduction Strand 1: Historical Significance Strand 2: Mathematics Strand 3: Real-World Applications Conclusion The project is divided into five milestones, which will be submitted at various points throughout the course to scaffold learning and ensure quality final submissions. These milestones will be submitted in Modules Two, Three, Four, Five, and Seven. Outcomes To successfully complete this project, you will be expected to apply what you have learned in this course and should include several of the following course outcomes: 1. Communicate and problem solve in mathematics, without the constraints of formal mathematical notation 2. Demonstrate knowledge in fundamental areas of higher mathematics, including number theory, infinity, geometry, topology, fractals, and other topics 3. Experiment with viewing the world from a mathematical perspective Main Elements Students will select and research one of the following topics (students may also propose their own topic) and submit this for instructor approval. MAT 135 Final Project Topic List      Logic Mathematical Puzzles Irrational Numbers Prime Numbers Number Theory               Fibonacci Sequence Numbers in Nature Euclidean Geometry Non-Euclidean Geometry Tessellations Mathematical Patterns Symmetry Infinity Fractals Knot Theory Graph Theory Linear Algebra Chaos Theory Self-Selected Topic NOTE: Instructors will approve topics for which they know sufficient research and information exists for the student to complete the final paper. Students will research three areas of this topic and submit each “strand” for grading and feedback. The strands are as follows: 1. Strand 1: The Historical Significance: Students will research the historical development of the topic from inception through modern-day usages. Students may select the most significant developments and contributors to the topic. 2. Strand 2: Mathematics: Students will research and explain the mathematics of the topic chosen. This may include the most significant discovery, theory, or usage. Students will fully explain the mathematics of the topic. 3. Strand 3: Real-World Applications: Students will research and make connections between the topic and the usages in the real world. Students may make connections to other fields where appropriate. Final Paper: Students will write an introduction to this paper, briefly outlining the topic and explaining the three strands. Students will include all three strands as subsections to the final paper, taking into account specific instructor feedback and suggestions for improvement. Given the nature of specific topics, students may need to consolidate repetitive sections to make a cohesive paper. Students will write a conclusion paragraph, which will be a reflective analysis of what the student gained from researching this topic. The final paper will include a cover sheet and reference page, using proper APA formatting. Total paper length: no less than 10 pages (exclusive of cover page and references). The final paper should be submitted as one document with the following components:        Cover Sheet Introduction Strand 1: Historical Significance Strand 2: Mathematics Strand 3: Real-World Applications Conclusion References Format Milestone One: Topic Selection & Outline In Task 2-2, you will submit your chosen topic to the instructor for approval and an outline of the three strands of the paper, including potential references. The topic may come from the list provided above or it can be self-designed. This milestone will be graded separately using the Final Project Topic Selection and Outline Rubric, and feedback will be provided for revisions to the final paper. Milestone Two: Strand 1—Historical Significance In Task 3-2, you will submit the paper for Strand 1: Historical Significance. This strand should be between 2–3 pages and fully explain the history of the topic. Proper APA citations and references are expected. This milestone will be graded separately using the Strand Paper Rubric, and feedback will be provided for revisions to the final paper. Milestone Three: Strand 2—Mathematics In Task 4-2, you will submit the paper for Strand 2: Mathematics. This strand should be between 2–3 pages and fully explain the mathematics of the topic chosen. This may include the most significant theory, theorem, or finding. Proper APA citations and references are expected. This milestone will be graded separately using the Strand Paper Rubric, and feedback will be provided for revisions to the final paper. Milestone Four: Strand 3—Real-World Applications In Task 5-2, you will submit the paper for Strand 3: Real-World Applications. This strand should be between 2–3 pages and fully explain the real-world applications of the topic chosen. This may include common usages of the topic, applications, and/or connections to other fields. Proper APA citations and references are expected. This milestone will be graded separately using the Strand Paper Rubric, and feedback will be provided for revisions to the final paper. Milestone Five: Final Paper In Task 7-2, you will submit the final paper. Include an introduction outlining the topic and what the reader can expect within each of the three strands. This paper will then consist of the three strands of research that has been conducted over the course of the term. Finally, write a conclusion, which will be a reflective analysis of what you learned from the research you conducted. The final paper should be cohesive and polished and take into consideration feedback provided by the instructor throughout the term. The paper should be no less than 10 pages, excluding the cover sheet and references page. Proper APA citations are expected. This milestone will be graded using the Final Project Rubric. Deliverable Milestones Milestone Deliverables Module Due Grading Paper will be graded (50 points total) with Final Project Topic Selection and Outline Rubric —feedback will be provided Paper will be graded (100 points total) with Strand Paper Rubric—feedback will be provided Paper will be graded (100 points total) with Strand Paper Rubric—feedback will be provided Paper will be graded (100 points total) with Strand Paper Rubric—feedback will be provided Graded separately; Final Project Rubric (200 points total) 1 Topic Approval & Paper Outline Two 2 Strand 1—Historical Significance Three 3 Strand 2—Mathematics Four 4 Strand 3—Real-World Applications Five 5 Final Product: Final Paper Seven Final Project Rubric Requirements of submission: Written components of projects must follow these formatting guidelines when applicable: double spacing, 12-point Times New Roman font, one-inch margins, and discipline-appropriate citations. Final paper should be no less than 10 pages, excluding coversheet and references page; proper APA formatting is expected. Critical Elements Communication Exemplary (100%) Demonstrates comprehensive communication of mathematical issues and ideas using accurate mathematical language and proper terminology Demonstrates knowledge of multiple mathematical issues through extensive collection and in-depth analysis of evidence to make informed conclusions All of the mathematical concepts are correctly applied and integrated with supporting evidence in a real-world context Proficient (85%) Demonstrates moderate communication of mathematical issues and ideas using accurate mathematical language and proper terminology Demonstrates knowledge of some mathematical issues through collection and in-depth analysis of evidence to make informed conclusions Needs Improvement (55%) Demonstrates minimal communication of mathematical issues and ideas using accurate mathematical language and proper terminology Demonstrates minimal knowledge of mathematical issues through collection and analysis of evidence to make informed conclusions Not Evident (0%) Does not demonstrate communication of mathematical issues and ideas using accurate mathematical language and proper terminology Does not demonstrate knowledge of mathematical issues through collection and analysis of evidence and does not make informed conclusions Most of the mathematical concepts are correctly applied and integrated with supporting evidence in a real-world context Some of the mathematical concepts are correctly applied and integrated with supporting evidence in a real-world context Does not correctly apply or integrate mathematical concepts 20 Main Elements Includes almost all of the main elements and requirements and cites multiple examples to illustrate each element Includes most of the main elements and requirements and cites many examples to illustrate each element Includes some of the main elements and requirements Does not include any of the main elements and requirements 25 Writing (Mechanics/Citations) Student meets all requirements for submission. No errors related to organization, grammar and style, and citations Student meets most requirements for submission. Minor errors related to organization, grammar and style, and citations Student meets some requirements for submission. Some errors related to organization, grammar and style, and citations Student does not meet requirements for submission. Major errors related to organization, grammar and style, and citations 15 Knowledge of Fundamental Areas Integration and Application Total Value 20 20 100%

Tutor Answer

nkostas
School: UCLA

Attached.

Running head: PASCAL TRIANGLE

1

Pascal Triangle

Institution Affiliation

Date

PASCAL TRIANGLE

2
Introduction

The topic selected for this project is “Pascal’s Triangle”. Pascal's triangle is a
mathematical and triangular array of coefficients derived binomially. The triangle is arranged
with the 0th row (n=0) at the top. The entries of the triangle are made from the left-hand side. In
the first row (row 0), the entries are nonzero, which is entry 1 (Lee et al., 2016). The rest of the
entries are made by adding the number above to the left and the right as well and the blank
entries as zero. Pascal's triangle has been used widely and intensively across the world as it's
used spans a wide array.
Pascal's triangle has been used since early days in mathematical contexts especially in
combinatorics and binomial numbers. The triangle has eased the work of mathematicians
especially in the expansion of functions. Pascal's triangle wide usage over years and its
significance has led to setting up of Pascal's rule (Majumdar, 2017). Pascal's triangle with higher
dimensional generalizations has led to the development of Pascal's tetrahedron, while the general
format which is simple is known as Pascal's simplices (Lee et al., 2016). Iranians and Chinese
have had their variants of the same with most of their works being undocumented or put on
record.
Years after it first appeared in Persia and China, the triangle came to be known as
Pascal’s Triangle with Blaise Pascal’s completion of Traité du triangle arithmétique in 1654.
Making use of the already known array of binomial coefficients, French mathematician Pascal
developed many of the triangle’s properties and applications within these writings. Although
Pascal is best known for his work with the arithmetic triangle, he made many other contributions
to mathematics during his lifetime. Throughout his thirty-nine years, Pascal also discovered an
important theorem in geometry, worked with cycloids, invented a calculating machine, laid the

PASCAL TRIANGLE

3

foundations of probability, and planted the seeds of calculus (Eves 242-6). Pascal’s
contributions to mathematics, especially of ‘his’ triangle, were unquestionably brought forth
from the mind of a highly intelligent man.
In mathematical contexts, Pascal's triangle is used in binomial expansions. By using the
triangle, it becomes easy to expand functions up to nth terms. Expanding polynomials is
simplified as it is easy to find the coefficients (Majumdar, 2017). The second mathematical usage
of Pascal's triangle is in binomial probability distributions, which is important to model the
number of successes in a wide sample size that is drawn with instances of replacement.
Mathematics, especially those on polynomials and probability has been improved with the input
of Pascal (Lee et al., 2016). Leibniz's rule of differentiation has also been built and borrowed so
much from the works of Pascal.
The most widely used example of Pascal's triangle in the real-world application is in
gambling and insurance companies. In these contexts, it is used to find out the different
combinations an object may have by using the nCr formulae (Lee et al., 2016). Pascal's triangle
has played a significant role in present-day mathematics with most mathematicians basing and
advancing their work from what Pascal did. In the real world, most mathematical figures have
been derived from the product of the triangle.
Pascal's triangle defined as the set of numbers which precisely arranged in a triangle
containing a certain amount of patterns...

flag Report DMCA
Review

Anonymous
Tutor went the extra mile to help me with this essay. Citations were a bit shaky but I appreciated how well he handled APA styles and how ok he was to change them even though I didnt specify. Got a B+ which is believable and acceptable.

Similar Questions
Hot Questions
Related Tags
Study Guides

Brown University





1271 Tutors

California Institute of Technology




2131 Tutors

Carnegie Mellon University




982 Tutors

Columbia University





1256 Tutors

Dartmouth University





2113 Tutors

Emory University





2279 Tutors

Harvard University





599 Tutors

Massachusetts Institute of Technology



2319 Tutors

New York University





1645 Tutors

Notre Dam University





1911 Tutors

Oklahoma University





2122 Tutors

Pennsylvania State University





932 Tutors

Princeton University





1211 Tutors

Stanford University





983 Tutors

University of California





1282 Tutors

Oxford University





123 Tutors

Yale University





2325 Tutors