Math 270: Managerial Mathematics
Spring 2006, 4 credits, MWRF 8:00-8:50 [1/16-2/3: MRC 316; 2/6-5/5: MRC 444]
Instructor: Richard J. Maresh, Assoc. Prof. and Chair, Dept. of Mathematics
Office: MC 521 Hours: MWF 10-11, R 12-1, or by appointment
Phone: 796-3655 (office), 526-4988 (home) Email: rjmaresh@viterbo.edu
Final Exam: Tuesday, 9 May 2006, 7:40 – 9:40 a.m.
Catalog Course Description: Several topics applicable to the study of business are covered. In particular, the course considers systems of linear equations and linear programming, the mathematics of finance, and an introduction to the elementary calculus topics. Emphasis in the course is on applications. This is a General Education course: G9.
Prerequisite: acceptable score on placement exam or a grade of C or higher in Math 110.
Text: College Mathematics For the Managerial, Life, and Social Sciences, by S.T. Tan, Thompson Brooks/Cole Press, 2005.
General Education Core Skill Objectives
1. Thinking Skills: Students engage in the process of inquiry and problem solving, which involves both critical and creative thinking.
(a) The student understands the primary “big problems” this course addresses: paying off loans in a fixed number of equal payments (amortization), optimizing cost or profit functions subject to a set of linear constraints (linear programming), and finding rates of change and solving maximum/minimum problems (calculus).
(b) The student demonstrates the ability to read a problem, set up an appropriate equation, and use appropriate methods to solve the problem. This course is very explicitly about thinking skills.
2. Communication Skills: Students communicate effectively orally and in writing in an appropriate manner both personally and professionally.
(a) The student does group work (labs and practice exams) throughout the course, involving both written and oral communication.
(b) The student uses technology - graphing calculators and DERIVE and Excel in the computer labs - to solve problems and to be able to communicate solutions and explore options.
(c) The student will improve his or her ability to write logically valid and precise mathematical solutions.
3. Life Values: Students analyze, evaluate, and respond to ethical issues from informed personal, professional, and social value systems.
(a) The student develops an appreciation for the intellectual honesty of mathematical reasoning.
(b) The student understands the need to do one’s own work, to honestly challenge oneself to master the material.
4. Cultural Skills: Students understand their own and other cultural traditions and demonstrate a respect for the diversity of the human experience.
(a) The student develops an appreciation of the history of linear programming and calculus and the role played by mathematics in business problems.
(b) The student learns to use the language of mathematics - symbolic notation - correctly and appropriately.
Specific Course Goals:
1. Students will participate in a formal assessment of their algebra skills and do appropriate work to improve their skill level to what this course requires.
2. Students will learn mathematical concepts that apply to business (as determined by the business school).
3. Students will learn how to apply mathematics to various types of business-related problems.
4. Students will improve their problem solving skills.
5. Students will learn to use technology, specifically graphing calculators and computer software, to solve a variety of problems.
6. Students will improve their mathematical reasoning skills.
7. Students will improve their ability to communicate, primarily in writing, mathematical ideas.
Course Details
ALEKS:
This course will consist of two distinct parts: (1) a detailed assessment of your algebraic readiness (“How well have you mastered and remembered the content of the prerequisite college algebra course?”) and an improvement of your skills in the specific areas where you have shortcomings; and (2) the traditional content of Managerial Mathematics, Linear Programming, Financial Mathematics, and an introduction to Calculus.
We have always started this course with some review of algebra, but this semester we will be using a web-based package called “ALEKS” (Assessment and LEarning in Knowledge Spaces) to accomplish the review. We have had the people at ALEKS create a special collection of topics that cover the material we need from MATH 110 to successfully learn the material in this course. The best thing about ALEKS is that it treats each one of you as an individual, finding out what you already know and what you do not yet know and focusing on exactly those things you need to learn.
Here are a few details. You will start the process by typing www.highed.aleks.com in the URL line of your browser. ALEKS will lead you through the process of creating an account. The two numbers you need is the course code: “MATH 270 Algebra Review” is identified by the code JPDUY – EFWM9. You will also need your student license number that you purchased from the bookstore. Once your account is created you will have a user ID and a password and can then log onto your account anywhere in the world-wide-web!
ALEKS will begin your work by doing an initial assessment. It will start with some pretty basic concepts and keep asking you questions until you have made it clear where your limits are. When it starts covering topics it keeps track of what you have accomplished and keeps working on what you need yet to do. These assessments will be done on occasion so that you can convince ALEKS that you have actually learned and retained the material. Once in a while you will make some errors and ALEKS will ask you to back up and re-do a few topics. You want to make sure you take these assessments seriously and perform as well as you can.
Because this is only an algebra review and not the entire course I have asked you to buy a 6-week license. In fact I will formally spend only 3 weeks focusing entirely on ALEKS and will then begin covering the regular course material. Some of you, however, might need to do more algebra learning than others and might end up needing to continue working on the ALEKS material through the month of February.
You grade for this part of the course will consist of three main things:
(1) Three ALEKS-generated quizzes: Quiz 1 covers basic algebra review, is worth 40 points, and must be taken by 1/30/06; Quiz 2 covers the “Functions and Graphs” module, is worth 30 points, and must be taken by 2/10/06; and Quiz 3 covers the “Polynomials and Rational Functions” and “Exponential and Logarithmic Functions” modules, is worth 40 points, and must be taken by 2/20/06. Each of these quizzes may be taken twice – after you take a quiz ALEKS will tell you your score and offer explanations of problems you missed. They may be taken prior to the indicated date, but not after that date, so you want to watch the dates.
(2) Content and effort: there are approximately 80 individual topics included in this review. Some of you may zip right through them because you have already mastered the MATH 110 material and others may need to do quite a bit of work to demonstrate mastery of the content. I have attempted to come up with a system that is fair and reasonable – we shall see how well it works. There will be 80 points possible – if you master all the topics (as shown in an ALEKS assessment) you get all the points, but if you end up short of 80 topics I will add points based on your attendance and on the number of hours you put in (ALEKS conveniently reports the total number of hours you have worked over the semester). There will be 12 class periods dedicated to ALEKS alone and I think a total of 40 hours over the 3-6 weeks is reasonable (“2 hours outside of class for each hour in class” is the rule of thumb). Thus these 80 points will be assigned according to the formula: P = 80 if all topics are completed, and P = (no. topics) + (classes attended + hours worked)/52 * (80 - no. topics). For example, if you only end up completing, say, 60 topics, but attended all classes and put in 30 hours then you will end up with 60 + (42/52)*(20) = 76 points, but if you only came to 8 classes and only put in 20 hours, you would end up with 60 + (28/52)*(20) = 71 points. If you attend all classes and put in 40 or more hours on ALEKS, you will earn all 80 points, regardless of the number of topics you successfully finish.
(3) Half of the first course exam will be dedicated to the algebra review material. This portion of that exam will be taken on Feb 23.
In all, then the ALEKS portion of the course will be worth a total of 240 points. That’s 110 for the 3 on-line quizzes, 80 for the material mastered, and 50 for the algebra paper-and-pencil test.
Labs:
On occasion you will do a group “lab”, worth typically 20 points. These will be problem sets covering material currently being covered. They will be collected at the end of the hour, as if they were a quiz, but you will work on them in a group. My thinking here is that it is extremely important for you to practice, and also that it can be very helpful to occasionally work with others, discussing the material, exploring issues, teaching and learning from one another. It is also important to learn to do the problems alone, but some group work can be very helpful. I have six of these labs scheduled.
Attendance:
Very few students seem able to learn mathematical material independently, and it is therefore important to attend class and participate actively in these class meetings.
Quizzes:
It is extremely important to stay on top of the class work; learning mathematics is something like learning to play the piano – you simply have to practice. To help insure that you do this I will have a little 5-point quiz, based on the homework assignment from the previous class, on most days. This also amounts to a way of taking attendance and checking to see that you are doing the homework. I am trying to create a system that places value on class attendance and homework assignments.
Grading System:
ALEKS 240 points (as explained above)
Daily quizzes 125 points
Exams 300 points
Final exam 150 points
Labs 120 points
Total: 935 points
The grades will then be assigned on the scale: A = 90%, B = 80%, C = 70%, D = 60%.
Disability Statement:
If you are a person with a disability and require any auxiliary aids, services or other accommodations for this class, please see me and/or Wayne Wojciechowski, the campus ADA coordinator (MC 320, 796-3085), within ten days to discuss your needs. I want to include taking exams in the learning center under this category; you will need a written request from Wayne Wojciechowski before I will allow you to take exams there.
MATH 270 Schedule: Spring 2006
Date Material Covered Suggested Minimal Assignment
16 Jan ALEKS (1): Initial Assessment
18 Jan ALEKS (2)
19 Jan ALEKS (3)
20 Jan ALEKS (4)
23 Jan ALEKS (5)
25 Jan ALEKS (6)
26 Jan ALEKS (7)
27 Jan ALEKS (8)
30 Jan ALEKS (9)
1 Feb ALEKS (10)
2 Feb ALEKS (11)
3 Feb ALEKS (12)
6 Feb <1.3> Linear Functions p 37 # 5-21 odd, 29, 31
8 Feb <1.4> Intersection of Straight Lines p 51 # 3-13 odd; p 53 # 3-9 odd
9 Feb <2.1> Systems of Linear Equations (1) p 79 # 1-11 odd, 17-23 odd
10 Feb <2.2> Systems of Linear Equations (2) p 92 # 3-13 odd, 21, 27, 29, 35-43 odd, 55, 57
13 Feb <2.3> Systems of Linear Equations (3) p 105 # 13-25 odd, 33, 37
15 Feb <2.4> Matrices p 117 # 19-23 odd, 37
16 Feb <2.5> Matrix Multiplication p 132 # 7-11 odd, 27, 31, 35, 43
17 Feb <2.6> Inverse of Square Matrices p 149 # 3-11 odd, 17, 19, 25, 37
20 Feb Lab #1
22 Feb Review …
23 Feb Exam #1 – Part A: Algebra Review [50 points]
24 Feb Exam #1 – Part B: Chapters 1-2 [50 points]
27 Feb <3.1> Linear Inequalities p 176 # 5-13 odd, 19-27 odd
1 Mar <3.2> Linear Programming Problems p 186 # 1-11 odd
2 Mar <3.3> Linear Programming: Graphical Solutions p 196 # 1-7 odd, 11-15 odd, 31, 33, 35
3 Mar Lab #2
4 Mar – 12 Mar SPRING BREAK
13 Mar <4.1> Simplex Method (1) p 223 # 1-19 odd, 29, 33
15 Mar <4.2> Simplex Method (2) p 243 # 1-13 odd, 21, 23
16 Mar Lab #3
17 Mar <5.1> Compound Interest p 261 # 3-33 odd
20 Mar <5.2> Annuities p 275 # 3-27 odd
22 Mar <5.3> Amortization, Sinking Funds p 288 # 3-27 odd
23 Mar Lab #4
24 Mar Group Practice Exam #2 [25 points]
27 Mar Exam #2 – Chapters 3-5 [75 points]
29 Mar <10.1> Functions and Graphs p 537 # 1-27 odd, 35-57 odd, 61, 65
30 Mar <10.2> The Algebra of Functions p 554 # 1-11 odd, 25-45 odd, 53, 59
31 Mar <10.3> Functions and Mathematical Models p 566 # 7-25 odd, 41, 45, 51
3 Apr <10.4> Limits p 590 # 1-13 odd, 17-37 odd, 49-67 odd
5 Apr <10.5> Continuity p 606 # 1-37 odd, 43-61 odd
6 Apr Lab #5
7 Apr <10.6> The Derivative p 627 # 1-5 odd, 11, 13, 17-25 odd
10 Apr <11.1> Differentiation: Basic Rules p 647 # 1-37 odd, 41-49 odd, 53, 57, 63
12 Apr <11.2> Differentiation: Product and Quotient Rules p 661 # 1-45 odd, 51
13 Apr – 17 Apr EASTER BREAK
19 Apr <11.3> Differentiation: Chain Rule p 674 # 1-45 odd, 49-57 odd, 61, 65, 69, 79
20 Apr <11.4> Marginal Analysis p 691 # 1, 3, 5, 9-17 odd
21 Apr Lab #6
24 Apr <12.1> Applications of the First Derivative p 740 # 1-21 odd, 37-59 odd, 79, 81, 85
26 Apr <12.2> Applications of the Second Derivative p 758 # 1-39 odd, 45-51 odd, 57-75 odd, 79, 85
27 Apr <12.4> Optimization (1) p 789 # 1-29 odd, 39, 41, 45, 47, 49
28 Apr <12.5> Optimization (2) p 803 # 1-9 odd, 13, 15, 17
1 May Group Practice Exam #3 – Chapters 10-12 [25 points]
3 May Exam #3 – Chapters 10-12 [75 points]
4 May Review…
5 May Group Practice Final Exam [25 points]
9 May Final Exam: 7:40 – 9:40 a.m. [125 points]