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Knot theory
Did you tie your shoe laces the same way today as yesterday?
We are all
familiar with knots from everyday life. But when does a
mathematician
consider two knots to be the same? To capture the
mathematical, rather
than physical, features of a knot, we glue the ends together to
form a circular
loop, and then treat the string as infinitely strong, thin, and
stretchy. The
downside of doing so is that it is not immediately clear how to
distinguish
two knots, as there are infinitely many configurations for the
same knot.
For this project you should find out about how knots are
represented, and
about some of the invariants used to tell them apart. Some
possible areas of
investigation include:
• tricolourability.
• genus.
• the Jones polynomial.
You should include plenty of your own examples to illustrate
your under-
standing.
Prerequisites
No particular background knowledge is needed, but you will
need to be able
to interpret a 2D diagram as a 3D object in space and visualise
it moving
over time.
Literature
• Colin Adams, The Knot Book
• Peter Cromwell, Knots and Links
Additional tips:
The purpose of the final assignment is for you to analyze an
existing policy (at the federal, state, or local level) and discuss
its impact on a social problem. You aren’t proposing a policy,
but analyzing an existing policy of interest to you.
Be sure to take enough time reading about the policy you
selected to thoroughly understand it in an in-depth way and be
able to confidently answer the questions in the assignment.
Please take time to carefully read each question in the
assignment and be sure to answer it. As you proof-read your
paper, take the opportunity to again review the assignment and
double check that you have thoroughly but succinctly provided
the information for each applicable question.
Please make sure you are using APA style in your final paper,
including the title page with name and dates.
The assignment is 8 – 10 pages long because that’s roughly the
length of a comprehensive social policy analysis. Please try to
refrain from adding more words than necessary to stretch the
length.
Proof-reading more than once is a great idea to try to catch
sentences that aren’t sentences and words that are inadvertently
misused. Read it out loud. I understand that the U of MD’s
writing lab is available to help those interested in strengthening
their writing skills – don’t hesitate to take advantage of it!
My expectation is that direct quotes be kept to a minimum in
that graduate-level writing involves synthesizing ideas and then
presenting them in your OWN words. For those quotes you do
use, please be sure to use the correct citation and quotation
marks. Not doing so may be considered plagiarism and will be
responded to accordingly.
Assignment 2: Policy Analysis. DUE: 11/28
For this assignment, you will examine a social policy at the
local, state or federal level by the legislative, executive, or
judicial branch of government. The policy may be addressing a
social issue that directly or indirectly affects the clients served
by your field placement, agency of employment, your
community, or who you plan to work with after graduation.
Drawing from class materials and external sources, write an 8-
10 page policy analysis (double-spaced, 12 point font, with 1”
margins). Your paper should address the following:
Describe the social issue and identify the population-at-risk.
Summarize existing research on this social issue.
What is the historical context of the policy? How did the social
issue come to the attention of policymakers? Who were/are the
key actors who made the issue “legitimate” and mobilized
support for or against the policy? Were there previous policy
attempts to address this issue?
Describe the social policy, answering the following questions:
What kinds of benefits are offered?
What are the bases of social allocation? (who is eligible)
How are the benefits to be delivered?
How are the benefits financed?
What is the purpose/goal of the social policy? What
assumptions about problem causation underlie the policy’s
approach to the identified social issue?
What are the effects of this social policy? Summarize any
existing research or evaluation. Your assessment should include
a discussion of the policy in terms of its actual or potential
(refer to your Reisch textbook for the definitions):
Horizontal and Vertical Adequacy
Individual and Social Equity
Inclusiveness of Coverage
Based on your analysis of this social policy, including existing
research and evidence, what are your recommendations? Do you
recommend it as currently implemented? Would you suggest
modifications, and if so which ones? How would you improve
the policy? If more funding is recommended, be prepared to
identify a source for that funding.
SOWK 600. Policy Analysis Grading Rubric
Student Name:
Content Area
Possible Points
Points Earned
Comments
Policy Process: Description of social problem and population at
risk. Background and history of the social problem, including
how the issue came to the attention of policymakers, how it
became legitimated, and the politics of the issue
16
Policy Product: Description of a specific policy, its goals and
underlying assumptions
15
Benefits offered, basis for social allocation (i.e. eligibility
criteria), how the benefits are delivered, and how they’re
financed
15
Policy Performance: Analysis of the specific policy, including
summary of research evaluating the policy, and an assessment
of the policy in terms of adequacy, equity, and inclusiveness of
coverage.
18
Do you recommend the policy as currently implemented? Would
you suggest modifications, and if so which ones? How would
you improve it?
16
Quality of the writing, including grammar, spelling,
organization of paper, and clarity
12
Appropriate use of APA; quality of external sources (including
citing some scholarly sources)
8
Rubric for Policy Analysis
Exemplary
Proficient
Needs Improvement
Unsatisfactory
CSWE Core Social Work Competencies for Foundation Year
Engage in Policy Practice (Competency 5)
Identify social policy at the local, state, and federal level that
impacts well-being, service delivery, and access to social
services (Practice Behavior 5.1)
Student is able to identify a specific policy that affects the
ability of social work clients or constituents to access social
services and/or agencies to deliver social services. The paper is
well-written and well-organized and is supported by evidence.
Student is able to identify in general terms a policy that affects
the ability of social work clients or constituents to access social
services and/or agencies to deliver social services. The paper is
written clearly and is generally well-organized. It makes some
use of evidence.
Student can identify a broad area of policy that affects the
ability of social work clients or constituents to access social
services and/or agencies to deliver social services. Ideas are
often not presented clearly or supported by evidence.
Student has difficulty identifying a policy that affects the
ability of social work clients or constituents to access social
services and/or agencies to deliver social services. The paper is
poorly written and
organized and makes
little or no use of
evidence.
Assess how social welfare and economic policies impact the
delivery of and/or access to social services (Practice Behavior
5.2)
Student is able to identify in detail how a specific policy affects
the ability of social work clients or constituents to access social
services and/or agencies to deliver social services, and suggests
specific adaptations to improve service access and delivery.
Student is able to identify how a policy affects the ability of
social work clients or constituents to access social services
and/or agencies to deliver social services, but has difficulty
suggesting specific adaptations to improve service access and
delivery.
Student can describe only in general terms how a policy affects
the ability of social work clients or constituents to access social
services and/or agencies to deliver social services, and cannot
suggest ways to improve service access and delivery.
Student is not aware
of the relationship
between policies and
the ability of clients
to access services and/or
agencies’ ability to deliver effective services. Paper is poorly
written and organized.
Knot theoryDid you tie your shoe laces the same way today .docx

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Knot theoryDid you tie your shoe laces the same way today .docx

  • 1. Knot theory Did you tie your shoe laces the same way today as yesterday? We are all familiar with knots from everyday life. But when does a mathematician consider two knots to be the same? To capture the mathematical, rather than physical, features of a knot, we glue the ends together to form a circular loop, and then treat the string as infinitely strong, thin, and stretchy. The downside of doing so is that it is not immediately clear how to distinguish two knots, as there are infinitely many configurations for the same knot. For this project you should find out about how knots are represented, and about some of the invariants used to tell them apart. Some possible areas of investigation include: • tricolourability. • genus. • the Jones polynomial. You should include plenty of your own examples to illustrate your under- standing.
  • 2. Prerequisites No particular background knowledge is needed, but you will need to be able to interpret a 2D diagram as a 3D object in space and visualise it moving over time. Literature • Colin Adams, The Knot Book • Peter Cromwell, Knots and Links Additional tips: The purpose of the final assignment is for you to analyze an existing policy (at the federal, state, or local level) and discuss its impact on a social problem. You aren’t proposing a policy, but analyzing an existing policy of interest to you. Be sure to take enough time reading about the policy you selected to thoroughly understand it in an in-depth way and be able to confidently answer the questions in the assignment. Please take time to carefully read each question in the assignment and be sure to answer it. As you proof-read your paper, take the opportunity to again review the assignment and double check that you have thoroughly but succinctly provided the information for each applicable question. Please make sure you are using APA style in your final paper, including the title page with name and dates.
  • 3. The assignment is 8 – 10 pages long because that’s roughly the length of a comprehensive social policy analysis. Please try to refrain from adding more words than necessary to stretch the length. Proof-reading more than once is a great idea to try to catch sentences that aren’t sentences and words that are inadvertently misused. Read it out loud. I understand that the U of MD’s writing lab is available to help those interested in strengthening their writing skills – don’t hesitate to take advantage of it! My expectation is that direct quotes be kept to a minimum in that graduate-level writing involves synthesizing ideas and then presenting them in your OWN words. For those quotes you do use, please be sure to use the correct citation and quotation marks. Not doing so may be considered plagiarism and will be responded to accordingly. Assignment 2: Policy Analysis. DUE: 11/28 For this assignment, you will examine a social policy at the local, state or federal level by the legislative, executive, or judicial branch of government. The policy may be addressing a social issue that directly or indirectly affects the clients served by your field placement, agency of employment, your community, or who you plan to work with after graduation. Drawing from class materials and external sources, write an 8- 10 page policy analysis (double-spaced, 12 point font, with 1” margins). Your paper should address the following: Describe the social issue and identify the population-at-risk. Summarize existing research on this social issue.
  • 4. What is the historical context of the policy? How did the social issue come to the attention of policymakers? Who were/are the key actors who made the issue “legitimate” and mobilized support for or against the policy? Were there previous policy attempts to address this issue? Describe the social policy, answering the following questions: What kinds of benefits are offered? What are the bases of social allocation? (who is eligible) How are the benefits to be delivered? How are the benefits financed? What is the purpose/goal of the social policy? What assumptions about problem causation underlie the policy’s approach to the identified social issue? What are the effects of this social policy? Summarize any existing research or evaluation. Your assessment should include a discussion of the policy in terms of its actual or potential (refer to your Reisch textbook for the definitions): Horizontal and Vertical Adequacy Individual and Social Equity Inclusiveness of Coverage Based on your analysis of this social policy, including existing research and evidence, what are your recommendations? Do you recommend it as currently implemented? Would you suggest modifications, and if so which ones? How would you improve the policy? If more funding is recommended, be prepared to identify a source for that funding. SOWK 600. Policy Analysis Grading Rubric Student Name: Content Area
  • 5. Possible Points Points Earned Comments Policy Process: Description of social problem and population at risk. Background and history of the social problem, including how the issue came to the attention of policymakers, how it became legitimated, and the politics of the issue 16 Policy Product: Description of a specific policy, its goals and underlying assumptions 15 Benefits offered, basis for social allocation (i.e. eligibility criteria), how the benefits are delivered, and how they’re financed 15 Policy Performance: Analysis of the specific policy, including summary of research evaluating the policy, and an assessment of the policy in terms of adequacy, equity, and inclusiveness of coverage. 18 Do you recommend the policy as currently implemented? Would you suggest modifications, and if so which ones? How would you improve it? 16 Quality of the writing, including grammar, spelling, organization of paper, and clarity
  • 6. 12 Appropriate use of APA; quality of external sources (including citing some scholarly sources) 8 Rubric for Policy Analysis Exemplary Proficient Needs Improvement Unsatisfactory CSWE Core Social Work Competencies for Foundation Year Engage in Policy Practice (Competency 5) Identify social policy at the local, state, and federal level that impacts well-being, service delivery, and access to social services (Practice Behavior 5.1) Student is able to identify a specific policy that affects the ability of social work clients or constituents to access social services and/or agencies to deliver social services. The paper is well-written and well-organized and is supported by evidence. Student is able to identify in general terms a policy that affects the ability of social work clients or constituents to access social services and/or agencies to deliver social services. The paper is written clearly and is generally well-organized. It makes some use of evidence. Student can identify a broad area of policy that affects the ability of social work clients or constituents to access social services and/or agencies to deliver social services. Ideas are often not presented clearly or supported by evidence. Student has difficulty identifying a policy that affects the ability of social work clients or constituents to access social
  • 7. services and/or agencies to deliver social services. The paper is poorly written and organized and makes little or no use of evidence. Assess how social welfare and economic policies impact the delivery of and/or access to social services (Practice Behavior 5.2) Student is able to identify in detail how a specific policy affects the ability of social work clients or constituents to access social services and/or agencies to deliver social services, and suggests specific adaptations to improve service access and delivery. Student is able to identify how a policy affects the ability of social work clients or constituents to access social services and/or agencies to deliver social services, but has difficulty suggesting specific adaptations to improve service access and delivery. Student can describe only in general terms how a policy affects the ability of social work clients or constituents to access social services and/or agencies to deliver social services, and cannot suggest ways to improve service access and delivery. Student is not aware of the relationship between policies and the ability of clients to access services and/or agencies’ ability to deliver effective services. Paper is poorly written and organized.