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Class Times 9:30 - 10:45 TT Rm 231W Mad
Office Hours: 2-3 MWF, 8:30-9:30 TT Rm 209 Mad
(Other times by appointment) Office Phone: 4493
email: psmith@saintmarys.edu Home Phone: 289-2126
Group Roles and Criteria
Knowledge Map for Math 345
Class Activities
Classification of
Learning Skills
Math Department Honesty Policy
Intro to Probability
Answers to Even Problems
Project Assignment
Texts:
This course concerns the study of probability in order to better understand statistical inference. Probability and statistics are branches of applied mathematics which deal with stochastic as opposed to deterministic processes. Stochastic processes involve chance occurrences whereas deterministic processes (such as the ones studied in mathematical programming) do not.
To apply probability and statistical methods to real situations requires that we first gather scientific data (called a sample) and then apply the analytical tools from inferential statistics to better understand the systems that generate the data and to draw conclusions about these systems. Samples are collected from populations which are collections of all individual items of a particular type. (E.g. If we want to study the checkout system at a grocery store, we may observe the number of customers waiting to be served and the length of time they spend in line and at the checkout counter at various times during the day. Here the population would be all the store's customers and the sample would be the ones we observe. We use the recorded behavior of the customers in the sample to draw conclusions about the waiting times of all the store's customers.) We can measure the validity of the conclusions by computing the probability that sample data like we observed could occur in the population given the hypothesized conclusion. We often use measures like the sample mean, variance, and range to test the conclusions. In all cases we must build a mathematical model representing the real system. We apply statistical analysis to the model to measure the validity of the conclusions concerning the real system.
Other important course goals are to increase awareness of and to develop your learning and problem solving skills, and to become efficient working in cooperative groups. By the end of the course, you should be able to learn faster than you do now. You will be conscious of and able to assess your level of the learning skills for life (see the link in the on-line syllabus for a list of learning skills for life). We will use cooperative group learning, discovery learning, applied critical thinking, problem solving, and self assessment in each class. You will also be expected to keep a learning assessment journal to help you assess your progress.
Research has shown that there are four main learning styles. Some people learn best by sounding out their ideas with others as they develop them. For these learners, small group learning is very effective. Others like to absorb ideas, think about them, and then communicate their responses. Lectures are a preferred learning mode for these students. Still others learn best by solving problems. They find that doing homework is essential to their learning. Finally, there are those who want to put their knowledge to use by working on realistic projects. They need this type of challenge to motivate them. For them, "just in time" learning is best (i.e., they want to learn what they need to know to effectively solve real problems when the knowledge is needed and not before). We will try to engage you in all these learning styles during this course so that you can learn to appreciate the learning styles of others.
There will be regular reading assignments to be completed before each class, and regular (individual) written homework assignments due each Thursday. In addition, you will be assigned a project. This will be graded on how well it is written as well as on its technical content. You must hand in a rough draft of your project three classes before the project is due. Failure to hand in the rough draft will result in loss of 5 points on the project grade. Failure to hand in the project on time will result in loss of all credit. Late homework will be corrected but you will receive no points for it.
The primary theme of this course is the improvement of the learning process by practicing learning skills in the mastery of probability concepts and methods. During each class you will work with your team on the following tasks: (1) quiz/problem solving session using information from the reading assignment, (2) minilecture or problem solution presentation, (3) a learning activity (involving concept models to manipulate, critical thinking questions about the models, and skill development exercises to apply the concept to new situations), (4) consulting session (you ask me questions), and (5) assessment of how well you worked as a team to learn the concepts and solve the problems. There will be very little "lecturing." Thus, it is essential that you do the reading for every class.
The reason why we emphasize collaborative learning as described in the preceding paragraph is that employers seek individuals who excel as:(1)
Attendance: A student is expected to attend every class. If you miss a class, it is your responsibility to make up the work and turn in any missed assignments. If you miss an exam or a homework or project deadline, you receive a grade of zero unless you have an official excuse from Mrs. Marcy's office or have made previous arrangements with me. A student who misses more than five classes without valid excuses will be required to withdraw from the class. The reason for this policy is that you have a responsibility to contribute to your team's efforts. If you aren't there your team is severely handicapped since each team member has a specific role to play.
Teams: I will select the team participants. We will probably change team membership right after break. If someone just does not work out on a team for any number of reasons, the two teams can arrange a trade. The two people to be traded must agree and at least one other member of each team must also agree before a trade can take place.
Honesty Policy: See the statement in the student handbook and the attached sheet on academic honesty. In this course, dishonesty will result in a grade of zero for the work involved. Continued infractions will be referred to the Office of Academic Affairs for disciplinary action. You are encouraged to compare ideas with other students but you should write up your own homework without using notes made during joint sessions until you get stuck. Copying someone else's work or using their computer files or programs is never allowed. Failure to adhere to this policy will cause loss of all credit for the work in question. Homework is to be completed on your own. Since most of the course work is in groups, this may be hard to remember.
The general grade letter equivalents: A 92-100; A- 88-91; B+ 84-87; B 80-83; B- 76-79; C+ 72-75; C 68-71; C- 64-67; D+ 60-63; D 56-62; F below 56. To figure final grade break points, multiply the above break points by ___ (to be determined by the class)
Base Concept Mastery Quiz 10 percent of your grade
Two tests (Feb. 12, Mar. 26) 100 points each
Homework * points
Daily Quiz/Problem solution 10 points each
Daily Class Assessment 10 points each
Project (due 4/30) * points
Journal * points
Final Exam (10:30 Mon. 5/3) 100 points
* To be determined by the class
Week Topic
1 Learning Process Models and Base Concepts
2 Counting Processes
3 Probability Concepts
4 Random Variables
5 Review and Test
6 Joint Probability
7 Mathematical Expectation
8,9 Discrete Probability Distributions
10 Review and Test
11 Normal Distribution
12 Other Continuous Distributions
13 Transformations of Random Variables
14 Moment Generating Functions
15 Review
Reading assignments and the learning activity for each class will be given during the preceding class. When you read mathematics you must keep your critical thinking skills honed. Always ask why a particular step is valid and how a new concept relates to those previously learned. It helps to memorize definitions and to be familiar with examples that illustrate each definition and theorem.
Each student must keep a learning journal (composed of the quizzes and activity critical thinking and skill development questions as well as three significant concepts learned, one important process practiced and one learning skill used in our class each day it meets) as well as a class journal (see below) and bring them to every class. I will collect the reflector's journals on the Thursday following the week in which she is the reflector, beginning February 4. Vary the learning skills (see the link above for a list of learning skills for life) you practice. From time to time, I will assign a topic and ask you to write a page about it. In the class journal, you should complete a self assessment form for each class. In addition, the reflector should complete a weekly reflector's report, the recorder should complete a weekly recorder's report, and the captain and spokesperson should each select one activity during the week and complete an activity assessment form. I will grade the journal 60% on completeness; 40% on quality. These journals will help determine whether you have satisfied your Sophomore Advanced Writing requirement.
1. 1 D. K. Apple, S. W. Beyerlein, M. A. Schlesinger, Learning Through Problem Solving, Pacific Crest Software, Corvallis, OR (1992), p. vii.
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