Math 2240

Dr. Sarah's Math 2240 Tentative Calendar Page - Fall 2012

The best way to contact me outside of class is during office hours or as an ASULearn Message. [Participants / my picture / Send message]

Office Hours this week
Math lab hours M/W 2-5, T/Th 3:30-6:30 in Walker 303A. Students answer questions and answers to the odd problems in the book can be found in the solutions manuals.
Syllabus and Grading Policies
Opening and working with Maple on campus
Class highlights If you miss a class, then check here and make up the work before the next class.

Jump down to tomorrow's homework which is located above the red lines

Date	Work is always due at the BEGINNING of class
12 Dec - Wed	Final Research Sessions 9-11:30am. You must participate in the research project to pass the class. Test 3 corrections due for a possible +4 (if they are complete and correct) - turn in your original test and you may mark corrections directly on there.
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6 Dec - Thur	Prepare to share your final research session topic (get it approved on ASULearn Message. [Participants / my picture / Send message]) with the rest of class. Work on the project components.
4 Dec - Tues	Start thinking about a topic for the final research sessions and begin working on them. If you have a topic, then get your topic approved via a message on ASULearn [Participants / my picture / Send message]
29 Nov - Thur	Test 3 study guide. Note that Dr. Thomley will be with you for the test because I am speaking at a conference in Chicago.
27 Nov - Tues	Read through PS 6 solutions on ASULearn and the study guide under Thursday's date. Study for Test 3 and write down any questions you have to turn in, including the study guide.
20 Nov - Tues	Test 2 revisions due for a possible +4 (if they are complete and correct) - turn in your original test and you may mark corrections directly on there. Problem Set 6 See Problem Set Guidelines and Sample Problem Set Write-Ups Note: You may work with two other people and turn in one per group of three Hints and Commands for Problem Set 6
15 Nov - Thur	Begin working on test corrections and problem set 6 (the first 2 questions) for Tuesday.
13 Nov - Tues	Eigenvector hw
8 Nov - Thur	Test 2 study guide Note: Since ASULearn is down, I linked recent ASULearn solutions for chapter 4 inside the study guide link.
6 Nov - Tues	Read over Problem Set 4 and Select Practice Problems 4.4-4.6 Solutions on ASULearn (Problem Set 5 Sols will go up on Tuesday). Then examine the study guide under Thursday's date and write down (to turn in) questions you have. Note that clicker questions can be found on the class highlights page. If you did not complete the hw for last Thursday, which includes the problem set to turn in and the readings, do so...
1 Nov - Thur	Last Tues at 7am, ASU cancelled classes for Tues Oct 30. Use last Tues' class time to read through 4.6 and to look at Span and Linear Independence comments. Tues hw is now due on Thur (4.5 22 and Maple practice problem) Problem Set 5 can be turned in Thur or next Tues, but if you turn it in next week, you won't get it back before the test Problem Set 5 See Problem Set Guidelines and Sample Problem Set Write-Ups Note: You may work with two other people and turn in one per group. Hints and Commands for PS 5 Problem 1: 4.4 16 and include the definition of span in your explanations Problem 2: 4.5 24 and include the definitions of basis, span and l.i. in your explanations Problem 3: 4.5 48 and include the definitions of basis, span and l.i. in your explanations Problem 4: Cement Mixing Continued (ALL IN MAPLE) This problem is worth more than the others Problem 5: 4.6 24 Problem 6: 4.6 27
30 Oct - Tues	Practice Problems (to turn in) 4.5 22 and Maple practice problem Begin working on Problem Set 5 [all but the 4.6 problems]
25 Oct - Thur	Practice Problems (to turn in) 4.4 11, 53
23 Oct - Tues	Problem Set 4 See Problem Set Guidelines and Sample Problem Set Write-Ups Hints and Commands for Problem Set 4 Problems 1: 4.1 36 Problem 2: 4.1 44 Problem 3: *Cement Mixing (ALL IN MAPLE)* This problem is worth more than the others. Problem 4:* 4.2 22 Problem 5: True or False: The line x+y=0 is a vector space. (ie {(x,y) in R^2 so that x+y=0}, with addition and scalar multiplication of vectors in R^2 as usual) Problem 6: Solutions to the plane 2x-3y+4z=5, ie {(x,y,z) in R^3 so that 2x-3y+4z=5}. Prove that this is not a subspace of R³ using axiom 1 (addition of vectors in R^3 as usual). Problem 7: 4.3 (14 part D - Be sure to leave n as general as in class - do not define it as 2x2 matrix). Prove that this is not a subspace (matrix addition as usual) of the set of nxn matrices.
18 Oct - Thur	Complete and correct test 1 revisions due for a possible +4 - turn in your original test and you may mark corrections directly on there. Work on Problem Set 4
16 Oct - Tues	Take a look at my message to you on ASULearn about your class average [problem set and test average] and qualitative feedback on your participation grade. Practice Problems (to turn in) 4.1 For #35, follow the instructions below: a) First solve this algebraically, by setting up the vectors as columns and reducing the augmented matrix for linear combinations. b) Then, as in Chapter 4, plot the columns of the coefficient matrix using commands like: with(plots): col1:=spacecurve([2t,3t,5t],t=0..1): display(col1, col2, col3) Do the columns of the coefficient matrix lie in the same plane [ie can you turn to a "head on" view where they look like they are on the same line]? Explain. c) If your answer to b) was no then they will generate all of 3-space under linear combinations, so anything will be a linear combination of them, so skip part c). However, if your answer to b) was yes, then add the Matrix([[10],[1],[4]]) vector into the spacecurve plot via col1:=spacecurve([10t,1t,4t],t=0..1): display(col1, col2, col3, col4) to see if it also lies in that plane and describe. d) As in chapter 1, plot the three rows of the augmented matrix for the system using commands like row1:=implicitplot3d({2x+y-2z-10},x=-20..20,y=-20..20,z=-20..20, color=yellow): display(row1,row2,row3) Are the rows lines or planes and how do they intersect [no common intersection, a single point, an entire line, or an entire plane]. Explain. 4.1 #43 4.2 # 21 [Show that axiom 1 is violated, ie find two determinant 0 matrices that sum to a matrix with determinant non-zero] Begin working on test 1 corrections [see Oct 18th]
9 Oct - Tues	Practice Problems (to turn in) 4.1 2, 4, 7 and 52.
4 Oct - Thur	Test 1 on Chapters 1, 2 and 3 study guide
2 Oct - Tues	Read over Problem Set 1, 2, and 3 Solutions on ASULearn. Then examine the study guide under Thursday's date and write down (to turn in) questions you have. Note that clicker questions can be found on the class highlights page.
27 Sep - Thur	Problem Set 3 See Problem Set Guidelines, Sample Problem Set Write-Ups Note: You may work with at most two other people and turn in one per group. Maple Commands and Hints for PS 3 I also encourage you to ask me questions about anything you don't understand in office hours or message me on ASULearn. Your group's explanations must distinguish your work as your own. Problem 1: 2.5 24 Problem 2: Healthy/Sick Workers (all on Maple including text comments) This problem is worth more than the others. Problem 3:* 3.1 47 part a Problem 4: 3.2 32 part c Problem 5: 3.3 (28 by-hand and on Maple) Problem 6: 3.3 (50 parts a & c)
25 Sep - Tues	Review the proof that if a square coefficient matrix A and a homogeneous matrix system Ax =0, has only the trivial solution x=0, then A must be invertible. Work on ps 3: problems 1, 2, 3 and 4.
20 Sep - Thur	Practice Problems (to turn in): First read 2.5 number 10 and then answer the following questions: Part A Set up the stochastic matrix N for the system. The first column of N represents A->A, A->B, and A->Neither [.75, .20, .05 is the first column; .75, .15, .10 is the first row]. Part B Using regularity, we can see that the system will stabilize since the columns add to 1, and the entries are all positive. Find the steady-state vector by setting up and solving (I-N)x=0 for x. Recall that if you add a row of 1s at the bottom, this will solve for the value you want [the entries add to 100%]. Reduce in Maple, but be sure to put in fractions instead of decimals. Begin working on Problem 1 and 2 on Problem Set 3, under next weeks due date.
18 Sep - Tues	Read through problem set 2 solutions on ASULearn. Review the proof that in a linear system with n variables and n equations there may be 0, 1 or infinite solutions: be prepared to answer clicker questions on this.
13 Sep - Thur	Problem Set 2 - See Problem Set Guidelines and Sample Problem Set Write-Ups Note: You may work with at most two other people and turn in one per group. Maple Commands and Hints for PS 2 I also encourage you to ask me questions about anything you don't understand in office hours or message me on ASULearn. Your group's explanations must distinguish your work as your own. Problem 1: 2.1 30 Problem 2: 2.2 34 parts a, b & c Problem 3: Show that the following statements about matrices are false by producing counterexamples and showing work: Statement a) A²=0 implies that A = 0 Statement b) A²=I implies that A=I or A=-I Statement c) A² has entries that are all greater than or equal to 0. Problem 4: 2.3 12 on Maple Problem 5: 2.3 14 by hand and on Maple Problem 6: 2.3 28 part a - write the matrix system as Ax=b and apply the inverse method of solution in Maple via MatrixInverse(A).b Problem 7: 2.3 40 part d
11 Sep - Tues	Practice Problems in 2.1 and 2.2: (to turn in). Do not worry about getting the same answer as the back of the book (although it would be nice!) but do concentrate instead on making sure you understand the methods. Do not worry about explaining your work. 2.1 (by-hand: 9, 32) 2.2 (by-hand: 17, 18), (35 parts b and c) Begin working on Problem Set 2 under Thurday's due date - namely the first three problems
4 Sep - Tues	Read through Sample Problem Set Write-Ups and Practice Solutions on ASULearn. Your 1.2 practice problems are on my door (326). Problem Set 1 - See Problem Set Guidelines, Sample Problem Set Write-Ups, and Problem Set 1 Maple Commands and Hints. I also encourage you to ask me questions about anything you don't understand in office hours or on the bulletin board. Your explanations must distinguish your work as your own. Also give proper acknowledgment to any help. For true/false questions, if a part is false, provide a specific counterexample, if it is true, quote a phrase and page # from the text. Note: You may work with at most two other people and turn in one per group. Follow the directions below. If it does not specify you may use any combination of Maple and by-hand that you like, but no calculators since you must print or show all your work. Problem 1: 1.1 60 part c Problem 2: 1.1 74 using GaussianElimination(N) in Maple and then reason from there Problem 3: 1.2 30 by hand and on Maple using ReducedRowEchelonForm(M) Problem 4: 1.2 32 on Maple using ReducedRowEchelonForm(M) Problem 5: 1.2 44 parts a) through d) - in b) and d) find all the values of k and justify Problem 6: 1.3 24 parts a and b
30 Aug - Thur	Go to ASULearn, click on Profile, click on Edit Profile, and add a picture of yourself so that it is easier to get to know each other. Note: To contact anyone in class, click on Participants, click on their picture, and click on Send message. This is the best way to contact me outside of class. Compare your 1.1 practice problems with solutions on ASULearn. A similar style of explanation is necessary for problem set 1 but not for practice problems. Do these practice problems by-hand since you need to get efficient at the by-hand method: 1.2 25, 27, and (43 - in addition to the directions in the book, find all the values of k and justify why these are all of them). Do not worry about getting the same answer as the back of the book (although it would be nice!) but do concentrate instead on making sure you understand the method of Gaussian Elimination. Continue working on problem set 1 under the due date of Sep 4th.
28 Aug - Tues	Do these by-hand since you need to get efficient at the by-hand method. 1.1 55, (59 parts b and c), and (73 use by-hand Gaussian to obtain 0s below the diagonal, with operations like r3'=-k*r1+r3, and then reason from there using the last row of the Gaussian eliminated matrix). Do not worry about getting the same answer as the back of the book (although it would be nice!) but do concentrate instead on making sure you understand the method of Gaussian Elimination. For true/false questions, if a part is false, provide a specific counterexample, if it is true, quote a phrase and page # from the text. Carefully read through Problem Set Guidelines and write down any questions you have Skim Sample Problem Set Write-Ups and Problem Set 1 Maple Commands and Hints and begin working on problem set 1 under the due date of Sep 4th.
23 Aug - Thur	Read through the online syllabus carefully. Search google for Dr. Sarah, click on my page, and click on the MAT 2240 link and then the Syllabus link. Prepare to share something you read there and write down any questions you have - the university considers this a binding contract between us. Obtain the textbook and i-clicker available for rental at the bookstore. Bring the i-clicker to all classes. Practice Problems to turn in - the answers to odd problems are in the back of the book and there is a student solution manual in mathlab 1.1 7, 15, 19 Don't worry about getting the correct answer - instead concentrate on the ideas and the methods. This will count as participation and will not receive a specific grade, although I will mark whether you attemped the problems. For true/false questions, if a part is false, provide a specific counterexample, if it is true, quote a phrase from the text.