...Mathematical Writing by Donald E. Knuth, Tracy Larrabee, and Paul M. Roberts This report is based on a course of the same name given at Stanford University during autumn quarter, 1987. Here’s the catalog description: CS 209. Mathematical Writing—Issues of technical writing and the effective presentation of mathematics and computer science. Preparation of theses, papers, books, and “literate” computer programs. A term paper on a topic of your choice; this paper may be used for credit in another course. The first three lectures were a “minicourse” that summarized the basics. About two hundred people attended those three sessions, which were devoted primarily to a discussion of the points in §1 of this report. An exercise (§2) and a suggested solution (§3) were also part of the minicourse. The remaining 28 lectures covered these and other issues in depth. We saw many examples of “before” and “after” from manuscripts in progress. We learned how to avoid excessive subscripts and superscripts. We discussed the documentation of algorithms, computer programs, and user manuals. We considered the process of refereeing and editing. We studied how to make effective diagrams and tables, and how to find appropriate quotations to spice up a text. Some of the material duplicated some of what would be discussed in writing classes offered by the English department, but the vast majority of the lectures were devoted to issues that are specific to mathematics and/or computer science. Guest lectures by...
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...Strictly from a mathematical viewpoint: What Equals 100%? What does it mean to give MORE than 100%? Ever wonder about those people who say they are giving more than 100%? We have all been in situations where someone wants you to give over 100%. How about achieving 101%? What equals 100% in life? Here's a little mathematical formula that might help you answer these Questions: If: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Is represented as: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 Then: H-A-R-D-W-O-R- K 8+1+18+4+23+15+18+11 = 98% and K-N-O-W-L-E-D-G-E 11+14+15+23+12+5+4+7+5 = 96% But, A-T-T-I-T-U-D-E 1+20+20+9+20+21+4+5 = 100% AND, look how far the love of God will take you L-O-V-E- O-F -G-O-D 12+15+22+5+15+6+7+15+4 = 101% Therefore, one can conclude with mathematical certainty that: While Hard work and Knowledge will get you close, and Attitude will get you there, it's the Love of God that will put you over the top! It's up to you if you'll share this with your friends & loved ones just the way I did....
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...be astronomical as long as the process is correctly developed. Cellonics is the future. Transmitting data over radio waves and then defragmenting is soon to be a method of the past, Cellonics offers technology with the ability to increase modem speed by up to 1000 times. The breakthrough came from the study of human cells, when stimulated these cells generated waveforms separated by periods of silence. The Cellonics technology has developed a procedure which mimics these signals in a way in which they can be applied to the communications industry. This sophisticated technology accepts slow analog input and distributes rapid pulse waveforms encoding digital information and broadcasting it over communication channels. NDS mathematical formulas are applied to the cells to stimulate responses; this is a non-linear system so the output can exceed normal capacities while the application remains straightforward. Cellonics is set to revolutionize the communication industry. Businesses or corporations which communicate remotely will be able to increase their speed, reliability and decrease their power consumption. All of these factors combine to offer a lower overhead operating cost and in return a higher profit margin. The face of telecommunications is changing, Cellonics is leading the charge. References: Hariharan, S. (2009) Cellonics Technical presentation under supervision of Dr. M. S....
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...DOK Question Stems DOK 1 • Can you recall______? • When did ____ happen? • Who was ____? • How can you recognize____? • What is____? • How can you find the meaning of____? • Can you recall____? • Can you select____? • How would you write___? • What might you include on a list about___? • Who discovered___? • What is the formula for___? • Can you identify___? • How would you describe___? DOK 2 • Can you explain how ____ affected ____? • How would you apply what you learned to develop ____? • How would you compare ____? Contrast_____? • How would you classify____? • How are____alike? Different? • How would you classify the type of____? • What can you say about____? • How would you summarize____? • How would you summarize___? • What steps are needed to edit___? • When would you use an outline to ___? • How would you estimate___? • How could you organize___? • What would you use to classify___? • What do you notice about___? DOK 3 • How is ____ related to ____? • What conclusions can you draw _____? • How would you adapt____to create a different____? • How would you test____? • Can you predict the outcome if____? • What is the best answer? Why? • What conclusion can be drawn from these three texts? • What is your interpretation of this text? Support your rationale. • How would you describe the sequence of____? • What facts would you select to support____? • Can you elaborate on the reason____? • What would happen if___? • Can...
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...Math Investigation of Painted Cubes Introduction I was given a brief to investigate the number of faces on a cube, which measured 20 small cubes by 20 small cubes by 20 small cubes (20 x 20 x 20). To do this, I had to imagine that there was a very large cube, which had had its outer surface painted red. When it was dry, the large cube was cut up into the smaller cubes, all 8000 of them. From there, I had to answer the question, 'How many of the small cubes will have no red faces, one red face, two red faces, and three faces? From this, I hope to find a formula to work out the number of different faces on a cube sized 'n x n x n'. Solving the Problem To solve this problem, I built different sized cubes: 2 x 2 x 2; 3 x 3 x 3; 4 x 4 x 4; 5 x 5 x 5; 6 x 6 x 6; 7 x 7 x 7; 8 x 8 x 8; 9 x 9 x 9, using multi-links. I started by building a cube sized '2 x 2 x 2'. As I looked at the cube, I noticed that all of the corners had three faces. I then went onto a '3 x 3 x 3' cube. As I observed the cube, I saw that the corners all had three faces, the edges had two, and the faces had one. I looked into this matter to see if this was true. As I went further into the investigation, I found this was true. This made it much easier for me to count the cubes, and be more systematic. Now I could carry on building the cubes, and be more confident about not missing any out. Whilst building the cubes, I also drew them and decided to color code the different faces...
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...WEEK 1 TUTORIAL 1.Stock Watcher for Mydin Zamri has created a basic stock watcher worksheet for Mydin that the uses to report on gains or losses from when the company purchased the stock and the last recorded date and price. Since Zamri is busy with other task, he has given you a snapshot of his spreadsheet (see Figure below) that you can use to recreate this spreadsheet for yourself. Here are some basic steps to follow: 1. Create a new workbook 2. Enter all the information provided in figure below. 3. Apply the Currency format to the respective columns 4. The data should be entered as a function. 5. Enter a formula for Gain/Loss (%) column 6. Format the percent in the Gain/Loss (%) column 2. Total ToyStory ToyStory, Inc is a regional pet toy supplier that tracks its businesses sales in a spreadsheet. The owner, Douglass Tatnall, has provided you with a skeleton worksheet, ToyStory_Data.xls (see below), with the totals for each quarter by sales region. Tatnall needs you to total each column and row, and then provide her with a clustered column chart of each region by quarter. Regional Sales Summary | | | | | | | 1st Quarter | 2nd Quarter | 3rd Quarter | 4th Quarter | Northeast | $ 119,900.00 | $ 125,170.00 | $ 133,700.00 | $ 139,550.00 | South | $ 50,000.00 | $ 52,000.00 | $ 49,601.00 | $ 54,500.00 | Midwest | $ 34,800.00 | $ 32,200.00 | $ 47,900.00 | $ 45,900.00 | West | $ 56...
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...Assignment brief – QCF BTECAssignment front sheet | Qualification | Unit number and title | BTEC Level 3 Extended Diploma in Business | Unit 42: Spreadsheet Modelling | Learner name | Assessor name | Martyna Litvinaite | Irene McCourt Francesse Mooney | Date issued | Hand in deadline | Submitted on | 15/09/14 | Task 1 15/10/14 Task 2 12/12/14 Task 3 20/03/15 Task 4 29/05/15 | 15/10/1410/12/14 | | | Assignment title | GamerWorld | In this assessment you will have opportunities to provide evidence against the following criteria. Indicate the page numbers where the evidence can be found. | Criteria reference | To achieve the criteria the evidence must show that the learner is able to: | | Task no. | | Evidence | P1 | * explain how spreadsheets can be used to solve complex problems | | 1 | | Pages1-2 | P2P3M1 | * develop a complex spreadsheet model to meet particular needs * use formulae, features and functions to process information * refine a complex spreadsheet model by changing rules and values | | 2 | | 2 Spreadsheets | P4P5P6P8M2M3 | * use appropriate tools to present data * customise the spreadsheet model to meet a given requirement * use automated features in the spreadsheet model to meet a given requirement * export the contents of the spreadsheet model to an alternative format * analyse and interpret data from a spreadsheet model * compare different automation methods...
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...This assignment covers the following grading criteria (P1, P2, P5, M1, and D1) The assessed tasks in this unit are based on the scenario below Scenario MNK is a local company who publish 10 different magazines/newspapers in a variety of languages specifically for the Bradford area. They have been approached by other cities interested in their work. MNK are therefore looking to expand their operation to at least one more large city. To achieve this they will need to apply for extra funding from their bank. To support the funding application, the company needs to analyse and review the sales data and costs for the last financial year, which is included in Appendix A. This will require the production of a working spreadsheet model which will enable the production of suitable reports and graphs of current and predicted sales and financial data. You have been approached by MNK to create this spreadsheet model. By using the MNK Sales Data provided, your spreadsheet will hopefully show that MNK is a well run business, capable of expansion. You need to carry out the tasks listed below. Successful completion of these tasks may enable you to achieve the following grading criteria: P1 - create a complex spreadsheet that is fit for purpose and check accuracy P2 - use formulae and functions to solve a complex problem P5 – use conversion facilities to export the contents of a spreadsheet to an alternative format M1 - check accuracy of a spreadsheet using a range of...
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...understanding of relationships between numerical, geometric, verbal, and symbolic form and arithmetic sequences in order to extend algebraic reasoning. Students will use words and symbols to describe the relationship between the terms in an arithmetic sequence and their positions in the sequence. After this assessment students should have the understanding of the relationships between numerical, geometric, verbal and arithmetic sequences in to extend algebraic reasoning. Learning Outcomes a. Students will be able to identify appropriate formulas for solving algebraic problems (knowledge). b. Students will use equations to solve problems (application). c. Students will formulate problem situations when given a simple equation and formulate an equation when given a problem situation (synthesis). Assessment Context Students will demonstrate different representations of data and generate formulas or expressions that represent the data. Students will be able to write a statement that represents the relationships of data...
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...EXERCISE C.1 You are a Sales Analyst for an export company called “Bicol Food Corporation.” As part of your work, you are tasked to prepare a Daily Shipment Summary Report based on the sales data faxed to you by the Sales Managers. To start preparing your report, do the following: 1. Type the company name in cell B2 using all caps. 2. Type the report name in cell B3 using all caps again. In this case, the report name should be “Daily Shipment Summary Report – Pili Cake.” Make the report name more obvious by changing the font to bold, font 16. 3. Type the report coverage in cell B4. The report you are preparing is for January 6, 2013. 4. Type the following headers from B7 to I7. Distributor Name Distributor Country Quantity Shipped Unit of Measure Unit Cost (Php) FC Unit Unit Price in FC Exchange Rate 5. Fix the column headers by highlighting/selecting cell B7:I7. Do not deselect cells unless mentioned below. * Under Home > Alignment, select “wrap text” to make all words fit in one box. Change also the cell alignment to “center.” * Change the font to bold. * Under Home > Font, click the border icon. Select the one that shows bottom border to insert a border after the headers. * Deselect the rows. 6. From B9 to B15, encode the following distributors: James Company Pte. Ltd. Lim Enterprises Hodge Wholesale Goods Alison Retail Dealer Tanaka Distributors Fang Lau Company Ah Kong Goods ...
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...references. When copying and pasting a cell with a relative reference, the copied formula changes in relation to the original formula. Changing a cell to an absolute cell reference provides a permanent reference to that cell. If copied and pasted elsewhere, the formula stays exactly the same. A mixed cell reference combines the two, where either the column letter or row number remain the same. I have learned that the use of spreadsheets in business is very broad. I now know that small businesses can track accounts, like a checkbook ledger, can calculate and keep track of payroll and taxes. Learning about the relative, absolute and mixed reference of cells and formulas will provide me with the skills necessary to create some more advanced analytical spreadsheets. Spreadsheets are used in the workplace when a group of information is gathered lot of the information is than sent out on a spreadsheet. So we have to get familiar with how it is used. I hadn't work much with spreadsheets prior to this course so the whole chapter was a learning experience. Being able to understand Excel better will benefit me in the future. I have gained a better understanding of how to use the formula feature which I know will be beneficial to me as an...
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...day. I guess you can say that this is where my love for math started. I am not saying that I never had to study or that I have never struggled with any math in my life, but for the most part, most of the math classes I have taken in my life have come pretty easily to me. I love when you are struggling with something in math and all of a sudden you have that a-ha moment where everything suddenly makes sense. In the past I have taken all the basics in math including Algebra and Geometry. However, these courses were also taken almost 20 years ago, and I have to admit that I am a bit rusty when it comes to all of the formulas and properties. Even though I may not remember all of the formulas, I still consider my previous courses a success. I may not remember the exact formula, but I do remember that the formulas exist and it is just a matter of looking the formula up and plugging in the right numbers to get the correct answer. For example, I remember how I used to love doing proofs in geometry, the longer the better. I probably could not jump right into one of those long proofs now, but I don’t think it would take me long to get back to being able to solve one. This is because math is always the same. It is not like English where the rules are always changing. Two plus two will always be four, and this is...
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...- c(1-t) + m ] = c0 + I + G + X Denoting the RHS (the sum of the autonomous components) with the symbol A, we have Y = 1 / [1 - c (1-t) + m]* A which gives us the equilibrium level of national income, but can also be expressed as changes: ΔY = 1 / [1 - c (1-t) + m]* ΔA The expression { 1 / [1 - c (1-t) + m] } is the multiplier (K). Dividing both sides of the above equation by ΔA ECON 1002 Feb 2013 We have ΔY / ΔA = 1 / [1 - c (1-t) + m] which gives us our first formula for K. What about the second formula? What is z? It is the marginal propensity to spend out of national income, which include the propensity to consume and the propensity to import. As we saw above, consumption spending comes out of disposable income, and therefore, the propensity to consume out of national income is c(1-t). We also assumed that imports represent a leakage from the circular flow, therefore, – m represents the propensity to import. We therefore have z = [c(1-t) – m] Notice that the minus sign in front of z in the multiplier formula will change the sign of its two terms and gives us the exact expression of K we derived above. What is obvious from the multiplier? From this expression we derived for K, we see that when c increases, the multiplier will increase, and when t and m...
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...hours. o Column H: Gross Pay is calculated by adding the regular pay and the overtime pay o Column I: NIS is calculated by multiplying the NIS rate by the Gross Pay. This calculation should be rounded to two decimal positions o Column J: NHT is calculated by multiplying the NHT Tax Rate by the Gross Pay. This calculation should be rounded to two decimal o Column K: Education Tax is calculated by multiplying the Education Tax Rate by the Gross Pay. This calculation should be rounded to two decimal positions o Column L: Net Pay is calculated by subtracting all deductions from Gross Pay The lower left corner of the sheet contains rates. Your formulas must reference the cell, You must also apply absolute cell references in this formula so that it can...
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...miscalculations that were created by the old system of data collection are rectified. The research shows the ineffectiveness of the previous methods of data clustering through a comparative analysis of the new and the old data clustering method. Introduction Clustering of data is important for any process of data reduction. This is because classification of data allows research to have reduced data upon which they can make an analysis. Huge data that is not classified makes it difficult for researchers to handle data within a short period of time. There are various methods and formulas that are used in data reduction. These formulas are meant to correct certain inconsistencies that previous formulas had towards data reduction. In data analysis, it becomes difficult for researchers to analyze data because of unclassified data that increases the time for making calculations. Classification of data through the new formulas will ensure that there are sets of data that are classified on the basis of the level of similarity and difference of a certain chosen data trait. Methodology This section will concentrate on analyzing...
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