What application motivates the mathematics included in the Sulva Sutras? What mathematical subjects studied by Indian mathematicians long ago have no counterpart in the other cultures studied up to this point?

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Applied Mathematics

Complete 15 of the following problems. Include all work and explanation needed to fully answer the question.

References APA format

  1. What application motivates the mathematics included in the Sulva Sutras?
  2. What mathematical subjects studied by Indian mathematicians long ago have no counterpart in the other cultures studied up to this point?
  3. One reflection of Mesopotamian influence in India is the division of the circle into 360 degrees. Does having this system in
  4. Use Aryabhata’s rule to compute the altitude of the sun above the horizon in London (latitude 5132’) at 10:00 AM (local solar time) on the vernal equinox. Assume that the sun rises at 6:00 AM on that day and sets at 6:00PM.
  5. How does the trigonometry used by Aryabhata I differ from what had been developed by Ptolemy four centuries earlier?common indicate that the Hindus received their knowledge of trigonometry from the Greeks?
  6. Besides the sine function, we also use the tangent and secant and their cofunctions. What is the origin of the words tangent and secant (in Latin), and why are they applied to the objects of trigonometry?
  7. Given the Pell equation , which has solutions x = 3, y = 10 and x = 60, y = 199, construct a third solution and use it to get an approximation to .
  8. Solve Bhaskara’s problem of finding the number of positive integers having five nonzero digits whose sum is 13.
  9. How accurate are the rules given by Brahmagupta for computing areas and volumes?
  10. How did Bhaskara II treat division by zero?
  11. How is the Pythagorean theorem treated in the Zhou Bi Suan Jing?
  12. Find all the solutions of the cubic equation without doing any numerical approximation. [Hint: If there is a rational solution r = m/n, then m must divide 243 and n must divide 2.]
  13. Why were the Chinese mathematicians undeterred by the prospect of solving equations of degree 4 and higher?
  14. Compare the use of thin slices of a solid figure for computing areas and volumes, as illustrated by Archimedes’ Method, Bhaskara’s computation of the area of a sphere, and Zu Chongzhi’s computation of the volume of a sphere. What differences among the three do you notice?
  15. What areas of mathematics became specialties in Japan, and what innovations arose there?

 

Write a 3-page paper including a summary of what you learned about identity theft, how identity theft affects accountants, and how to addresses web security and privacy concerns.

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Algebra

Write a 3-page paper including a summary of what you learned about identity theft, how identity theft affects accountants, and how to addresses web security and privacy concerns.

Assignment should follow APA guidelines with respect to use of subheadings, 1” margins and double-spaced. Use the CSU-Global APA Instructions (Links to an external site.).

Page length requirements for the assignment exclude the title page and the reference page. References need to include your textbook plus two additional credible academic references. All sources used, including your textbook, must be referenced; paraphrased and quoted material must have accompanying citations and cited per APA guidelines.

 

How do you think the confidence interval that was presented in the study was calculated? Explain the mathematical concepts could you extract from this article/study.

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Confidence Interval

Read/review the following resources for this activity:

https://openstax.org/details/books/statistics

Textbook: Chapter 8
Lesson
Minimum of 1 scholarly source
In your reference for this assignment, be sure to include both your text/class materials AND your outside reading(s).

Confidence Intervals

In everyday terms, a confidence interval is the range of values around a sample statistic (such as mean or proportion) within which clinicians can expect to get the same results if they repeat the study protocol or intervention, including measuring the same outcomes the same ways. As you ask yourself, “Will I get the same results if I use this research?”, you must address the precision of study findings, which is determined by the Confidence Interval. If the CI around the sample statistic is narrow, you can be confident you will get close to the same results if you implement the same research in your practice.

Consider the following example. Suppose that you did a systematic review of studies on the effect of tai chi exercise on sleep quality, and you found that tai chi affected sleep quality in older people. If, according to your study, you found the lower boundary of the CI to be .49, the study statistic to be 0.87, and the upper boundary to be 1.25, this would mean that each end limit is 0.38 from the sample statistic, which is a relatively narrow CI.

(UB + LB)/2 = Statistic [(1.25 + .49)/2 = .87]

Keep in mind that a mean difference of 0 indicates there is no difference; this CI does not contain 0. Therefore, the sample statistic is statistically significant and unlikely to occur by chance.

Because this was a systematic review, and tai chi exercise has been established from the studies you assessed as helping people sleep, based on the sample statistics and the CI, clinicians could now use your study and confidently include tai chi exercises among possible recommendations for patients who have difficulty sleeping.

Now you can apply your knowledge of CIs to create your own studies and make wise decisions about whether to base your patient care on a particular research finding.

Initial Post Instructions

Find an example of a confidence interval in the news, scholarly source or medical journal. Summarize the article/study. Does the article/study include the sample size and the level of confidence used to create the confidence interval? Explain what the confidence interval means in context of the news article or scholarly source.

Follow-Up Post Instructions

Respond to at least two peers or one peer and the instructor. Further the dialogue by providing more information and clarification.

Here are some suggested responses

How do you think the confidence interval that was presented in the study was calculated?
Explain the mathematical concepts could you extract from this article/study.

Writing Requirements

Minimum of 2 posts (1 initial & 1 follow-up)
APA format for in-text citations and list of references

NOTE
*Credited means stating where the information came from (specific article, text, or lesson). Examples: our text discusses…., The information from our lesson states…, Smith (2010) claimed that…, Mary Manners (personal communication, November 2017)…

**Assigned readings are those listed on the syllabus or assignments page as required reading. This may include text readings, required articles, or required websites.

***Scholarly source – per APA Guidelines, only scholarly sources should be used in assignments. These include peer-reviewed publications, government reports, or sources written by a professional or scholar in the field. Wikipedia, Wikis, .com websites or blogs should not be used as anyone can add information to these sites. For the discussions, reputable internet sources such as websites by government agencies (.gov) and respected organizations (.org) can be counted as scholarly sources. Outside sources do not include assigned required readings.

Come up with a real-life situation in which you might be curious to know if there is a difference between two means (averages). State the null and alternative hypothesis of your real-life situation.

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STAT 280-Week 7

RESPOND

Come up with a real-life situation in which you might be curious to know if there is a difference between two means (averages). State the null and alternative hypothesis of your real-life situation.

Alternatively, you may research other examples of situations where hypothesis testing could be used in decision-making. Describe the study and/or situation, noting the null and alternative hypothesis if the study or situation.

 

Demonstrate a wide range of clustering, estimation, prediction, and classification algorithms to solve a specific program or application. Demonstrate a wide range of clustering, estimation, prediction, and classification algorithms to solve a specific program or application.

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2 Marks

 

Learning Outcome(s):

Demonstrate a wide range of clustering, estimation, prediction, and classification algorithms to solve a specific program or application.

Question One

By using Cosine Similarity Formula, find the similarity between documents: Document 1 (A) and Document 2 (B), with given value of A and B is as follows:

Document 1: [1, 1, 1, 1, 1, 0] let’s refer to this as A

Document 2: [1, 1, 1, 1, 0, 1] let’s refer to this as B

Above we have two vectors (A and B) that are in a 6-dimension vector space

[Given formula Cosine similarity (CS) = (A . B) / (||A|| ||B||)].

3 Marks

 

Learning Outcome(s):

Demonstrate a wide range of clustering, estimation, prediction, and classification algorithms to solve a specific program or application.

Question Two

1000 people (350 less than or equal to 20 years old, and 650 greater than 20 years old) were asked, “Which take-out food do you prefer – junk food or healthy food?

The results were:

  Junk food Healthy food
Ages <= 20 225 125
Ages > 20 350 300

 

Calculate chi-square

Note :

      Expected value   is calculated using the following equation

    =

2.5 Marks

 

Learning Outcome(s):

Demonstrate a wide range of clustering, estimation, prediction, and classification algorithms to solve a specific program or application.

Question Three

What is the Manhattan distance between different points as shown below? Fill the table with appropriate Manhattan distances. As an example, the distance between points A and C is computed in the appropriate table cell.

  A B C D
A        
B        
C 13      
D        

 

0.5 Marks

 

Learning Outcome(s):

Employ data mining and data warehousing techniques to solve real-world problems.

Question Four

Apply the discretization filter in iris dataset. (Note: iris dataset can be directly loaded into WEKA from the “C:\Program Files\Weka-3-8\data” link). After applying the discretization filter, list all the features (attributes

 

Demonstrate what you’ve learned about proper sampling techniques and displaying data using descriptive statistics .

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Stats midterm project

For this project, you will demonstrate what you’ve learned about proper sampling techniques and displaying data using descriptive statistics . Choose one of the project ideas listed in the document below, or come up with one of your own, and write a 3-5 page report that includes an introduction, a body with any statistical measures, charts, and graphs that are appropriate to the study, and a conclusion. Your raw data should be included in an appendix at the end of the report. If you are surveying, be sure to describe your sampling method and target population as well as any biases inherent in your sample. Also be sure to cite any sources you used, including stores for data collection.All graphs must be clearly labeled and information displayed in a logical fashion. All written sections must be clear and concise, and able to be understood by someone with no prior knowledge of the project and limited statistics background.

In CSMA/CD, after the 5th collision, what is the probability that a node chooses K=4? List the serious security flaws of Wired Equivalent Privacy (WEP) for 802.11 wireless networks. How those security flaws are addressed by WiFi Protected Access (WPA)?

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MATHEMATICAL ASSIGNMENT

Assignment#3

1, Define and contrast the following terms: subnet, prefix, and BGP route? (6 points)

2, Consider a datagram network using 16–bit host addresses. Suppose a router uses longest prefix matching and has the following forwarding table:
Prefix Match Interface
1 0
11 1
111 2

Otherwise 3
For each of the following 5 host addresses, give the matched interface # using above forwarding table. (10 points)
11100000 10111111
10110000 10111111
11010000 10111111
01110000 10111111
10000000 10111111

3, How big is the MAC address space? The IPv4 address space? The IPv6 address space?

Note: The size of an address space is the maximum number of different addresses it can have. (3 points)

4, In CSMA/CD, after the 5th collision, what is the probability that a node chooses K=4? The result K=4 corresponds to a delay of how many seconds on a 100 Mbps Ethernet? (5 points)

5, List the serious security flaws of Wired Equivalent Privacy (WEP) for 802.11 wireless networks. How those security flaws are addressed by WiFi Protected Access (WPA)? (6 points)

6, Describe IPsec and how it can be used to create virtual private networks (VPNs). (6 points)

7, What is the difference between a permanent address and a care–of address? Who assigns a care–of address? (4 points)

8, Identify and describe at least three common network vulnerabilities? (6 points)

9, What is an important difference between a symmetric key system and a public key system? (5 points)

10, True or False, explain why? (4 points)
a, Ethernet and 802.11 uses the same frame structure.
b, The addresses in an Ethernet frame header are IP addresses.

11, Complete the Wireshark Lab: SSL. The answers to all the questions in the lab are posted in Canvas. Follow all the steps in the lab and try to answer all the questions. Then check your answers using the solution file provided. There is no need to submit your answers to me for grading. You only need to submit a screenshot to show me that you opened the trace file and did the lab. (6 points)

Note: The files for the Wireshark Lab and the solutions are provided separately.
• Wireshark_SSL_v8.0.pdf
• Wireshark_SSL_SOLUTION_v8.0.pdf

12, Conduct a survey on routing protocols, select one protocol and discuss how it works, identify its advantages and disadvantages. The length of your review should be no more than 2 pages in length.

Use APA (American Psychological Association) style for in–text citations and references.(https://owl.english.purdue.edu/owl/resource/560/01/). (9 points)

A company had cash and marketable securities worth $200,000 accounts payables worth $51,000, inventory of $1,501,500, accounts receivables of $5,288,128, short-term notes payable worth $220,000, other current liabilities of 100,000, and other current assets of $121,800. Calculate the company net working capital and describe how managers manage the firm working capital.

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Assignment Questions:    (Marks: 15)

A company had cash and marketable securities worth $200,000 accounts payables worth $51,000, inventory of $1,501,500, accounts receivables of $5,288,128, short-term notes payable worth $220,000, other current liabilities of 100,000, and other current assets of $121,800. Calculate the company net working capital and describe how managers manage the firm working capital. (2 Marks)

 

  • Your parents have given you $1,500 a year before your graduation so that you can take a trip when you graduate. You wisely decide to invest the money in a bank CD that pays 7% interest. You know that the trip costs $1600 right now and that inflation for the year is predicted to be 3%. Will you have enough money in a year to purchase the trip? Show your calculations. (2 Marks)

 

  • If the following financial information related to XYZ Company. Total Revenues last year $970, depreciation expenses $50, costs of goods sold $450, and interest expenses $55. At the end of the year, current assets were $121 and current liabilities were $107. The company has an average tax rate of 35%. Calculate the net income for XYZ Company by setting up an income statement. (2 Marks)

 

  • Calculate the common-size balance sheet from the following information for the company: (2 Marks)

 

Cash 50,000 Accts/Pay 25,800
Acct/Rec 60,000 Accrued expenses 30,000
Inventories 200,500 Short-term N/P 9,700
  Total Current assets 310,500   Current liabilities 65,500
Net fixed assets 132,000 Long-term debt 150,000
  Total assets 442,500 Total liabilities 215,500
    Owner’s equity 227,000
    Total liabilities and owners’ equity 442,500

 

  • Ten years ago, Amanda Cortez invested $20,000 in an account paying an annual interest rate of 5%. What is the value of the investment today? What is the interest on interest earned on this investment? (2 Marks)

 

  • You have just won a lottery that promises an annual payment of $120000 beginning immediately. You will receive a total of 15 payments. If you can invest the cash flow in an investment that is paying 8% annually, what is the present value of this annuity? (2 Marks)

 

  • XXX company has forecast a rate of return of 20% if the economy booms (30% probability); a rate of return of 19% if the economy in in a growth phase (40% probability); a rate of return of 2.50% if the economy in in decline (20% probability); and a rate of return of -10% if the economy in a depression (10% probability). What is the company standard deviation of returns? (3 Marks)

 

 

Given that we have no documents from the time of Greek mathematics—the earliest manuscripts we have are medieval—how can we be sure that the texts we have are actually what the authors wrote?

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Capital Budgets Discussion

Discuss the long-term implications of capital expenditures

Complete question below. Given that we have no documents from the time of Greek mathematics—the earliest manuscripts we have are medieval—how can we be sure that the texts we have are actually what the authors wrote? Were the copyists who wrote the early medieval manuscripts simply concerned with reproducing the text faithfully, or is it possible that they tried to improve it by revisions they thought of themselves? How could we know if they did?

  1. Given that we have no documents from the time of Greek mathematics—the earliest manuscripts we have are medieval—how can we be sure that the texts we have are actually what the authors wrote? Were the copyists who wrote the early medieval manuscripts simply concerned with reproducing the text faithfully, or is it possible that they tried to improve it by revisions they thought of themselves? How could we know if they did?
  2. What are the main topics investigated in ancient Greek number theory? How much of number theory has a practical application nowadays? (If you don’t know about RSA codes, for example, look them up on-line.)
  3. What mathematical ideas were ascribed to the Pythagoreans by ancient commentators?
  4. For what reason would the ancient Greeks have been investigating figurate numbers, perfect numbers, and the like? Did they have a practical application for these ideas?
  5. Assuming that there are two square integers whose ratio is 5, derive a contradiction using the principle that underlies Knorr’s conjecture. (If the integers are relatively prime, then both must be odd. Use that fact and the fact that the square of any odd number is one unit larger than a multiple of 8 to derive a contradiction.)
  6. How do you resolve the paradoxes of Zeno?
  7. Summarize the progress made on each of the three classical problems during the fourth century BCE.
  8. Why was it important to Menaechmus’ solution of the problem of two mean proportionals that the plane cutting the cone be at right angles to one of its generators?
  9. How would you establish that two triangles with equal altitudes and equal bases are equal (“in area,” as we would say, although Euclid would not)?
  10. Why is the problem of squaring the circle much more difficult than the problem of doubling the cube or trisecting the angle?
  11. It appears that the Greeks overlooked a simple point that might have led them to break out of the confining circle of Euclidean methods. If only they had realized that composite ratios represent multiplication, they would have been freed from the need for dimensional consistency, since their ratios were dimensionless. They could, for example, multiply and number of ratios, whereas interpreting the product of two lines as a rectangle precluded the possibility of any geometric interpretation of product containing more than three factors. Could they have developed analytic geometry if they had made this realization? What else would they have needed?
  12. Granting that if two lines perpendicular to the same transversal line meet on one side of that line, reflection about the midpoint of the interval between the two points where the lines meet the transversal shows that they must also meet on the other side. How do you know that these two points of intersection are not the same point? What other assumption must you introduce in order to establish that they are different?
  13. Was the Elements an exposition of the most advanced mathematics of its time?

14.What advances in geometry, beyond the basic results found in the Elements, are due to Archimedes?

  1. Show from Apollonius’ definition of the foci that the product of the distances from each focus to the ends of the major axis of an ellipse equals the square on half of the minor axis.

 

What resources will you use in order to prepare for the exam? After looking at the objective review, what one concept do you feel you need to develop a bit more before the exam?

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Week 4

What resources will you use in order to prepare for the exam?
After looking at the objective review, what one concept do you feel you need to develop a bit more before the exam?
What day do you plan to take your first attempt? What day do you plan to take your 2nd attempt?