All Graded Assignments - Mathematics Applied to Modern World | MATH 123, Assignments of Mathematics

Download All Graded Assignments - Mathematics Applied to Modern World | MATH 123 and more Assignments Mathematics in PDF only on Docsity! Graded assignment 1: due Friday 8/29 Chapter 1 Mindscapes 3, 6, 9, 12 . (begins p. 28) Write out the solution, including your reasoning, in complete sentences or even a paragraph. You may want to use tables or lists to present your information in some of the cases. Model the way you present your solutions after the solutions in section 1.4. Graded assignment 2: due Monday 9/8 Chapter 2.1 Mindscapes II.8, 14 (pages 46 and 47) Chapter 2.2 Mindscapes II.9, 11, 15 (page 59); for #15, find two people outside of math 123, show them the trick, and record their reactions. Use pencil or type (whatever is easiest for you). Use complete sentences and acknowledge anyone you work with. Graded assignment 3: due Friday 9/19 Chapter 2.3, Mindscapes I.5, II.6, 17, 20 (“bonus” part required ), 21. (begins p. 77) Graded assignment 4: due Wednesday 10/8/2008 Chapter 2.5, Mindscapes II.6, 7, 8, 13, III.17 (Hint: Go over the solution to #16 carefully. That will help you with #17.) (HW begins p. 107) Expectations: • A list of numbers or final results is not a sufficient answer. You must show calculations or give an explanation in words (using complete sentences, referring to theorems, and the like, as necessary) to justify your answers. Take note that each of these questions is partly or completely computational. An answer such as “1 mod 15” with no supporting work or explanation will not receive any credit. Look at the next page to see some samples of work that would receive credit. (I do not expect you to type equations.) Sample results that would receive credit: 26 mod 7 = 1 mod 7. Since 7 is a prime number and 6 is one less than 7, Fermat’s little theorem says that the remainder is 1. OR 26 7 21 5 7 5 7 15625 7 7 2322 1 7 1 7 For general educational purposes, note how handy it is to move from the second solution to the first one. It may take a few trials with some numbers to see the connection. • The work must be shown clearly be written in order. That is, you should work out the whole problem in one place. Parts of it should not appear in an obscure location with arrows drawn to it. Don’t mix single- and double- column work. That is a very good way for part of your answer not to be seen. The work should be clearly laid out with a format that is all single- column (for problem sets with a lot of writing or for people with large handwriting) or double-column (more computational and people with small writing). • All parts of the question must be answered. • The answer should be readable, in pencil, on paper without ragged or “fringed” edges, and stapled if there is more than one page. • Please fold papers in half lengthwise and write your name on the outside. • If you are not sure, come to my office hours! I am happy to look over work ahead of time, help you fix errors, and help you communicate what you know about the problem. Ultimately, your goal is to communicate your knowledge of the problems to me. And of course, we all love to see high grades. ☺ surface of a sphere, so that I make these curved “faces,” will V – E+F always come out to the same number? If so, what number will it be? Number of wedges Number of Vertices (V) Number of Edges (E) Number of Faces (F) V – E+F 6 2 6 10 10 Hints and recommendations: You will find physical models helpful for the mindscapes. I also recommend that you copy out the table we completed in class. (This is the table shows the number of vertices and so on.) To show your work for #11, you may show the table and add a column showing the result of the calculation for each polyhedron, or write out each of the five (5) calculations. Be sure to draw a conclusion. For number 12, make a list. The list corresponds to a line in our table for the Platonic solids, but it is for a soccer ball. Find a soccer ball, or truncate an icosahedron yourself. This one is a “two-for” deal. You now have the 5th line of the table for exercise 21. Again, making some models will help. Get together with a friend and count. ☺ For the orange problem, you may find some fruit helpful. Note: we will do some examples related to the homework in class on Monday, will go over the art galleries and coloring the triangles, and will review some tiling information. There will be a quiz over this material on Friday 11/14. Graded assignment 9: Due Friday 12/5/08. Note: our last two graded assignments will be homework turned in on the next two Fridays. Section 5.1 Mindscapes 7, 8 (be sure to list the steps you take and/or sketch pictures), 9 (one option for the explanation is to list the distortions that show how they are or are not equivalent), 11 (explain as in question 9), 12 (give a list of steps to explain why or why not). (Exercises begin p. 339). Graded assignment 10: Due Friday 12/12/08 Section 5.3 Mindscapes 8, 10, 11, 13, 15, 22. Hints: #8, #10: Write out the information for these like we did with the examples in class today, particularly Mindscapes 5 and 7. #11: Look at the table we made in class with V, E, and F. See what the numbers do in this week’s favorite formula. #13: Do #15 first, and check the solution for Mindscape 12 (not assigned – see back of book). Our favorite formula still works, but you will have only one number. That gives you a relationship between the other two numbers. Also see the section beginning “The Pattern Revealed” on p. 362 of the text. The authors throw around some numbers for your benefit. #22: Get out your old notes or HW with the features of the truncated polyhedra.