Math 236, Section 1, Elementary Abstract Algebra
Professor: George Seelinger
Office: Stevenson 313C (Enter through STV 313)
Office Hours: W 2:00-2:50, R 11:00-11:50, F 12:00-12:50
TEXT:Abstract Algebra, An Introduction, by Thomas W. Hungerford, 2nd Edition, Brooks/Cole, 1997.
COURSE WEB PAGE:http://www.math.ilstu.edu/gfseeli/m236121/
Here you will find links to the current assignments, possible posting of hints, and other resources available on the WEB.
Some Definitions and Theorems (To be updated throughout the semester.)
ABOUT THE COURSE: In this course we will cover most of Chapters 1-6 and Chapter 12 of the text with occassional excursions in the appendices. We will start by examining the familiar set of integers. Our emphasis in looking at the integers is twofold. First, we want to emphasize the algebraic properties of the integers. Second, we want to try to develop the students' ability to understand theoretical mathematical arguments and to be able to write coherent mathematical arguments. Almost all of the mathematical arguments you will be expected to understand and to write take the form of mathematical proofs. Once we gain some experience in the relatively concrete setting of the integers, we will develop some understanding of abstract rings and the functions between them. In this less familiar context, the skills of mathematical argumentation that we developed earlier will become more important to the understanding of these topics. To further our understanding of rings, we then look at the arithmetic of polynomials as an example of a ring that is not the integers. We will then begin the study of quotient fields and the construction of field extensions, the depth of this coverage will depend on the time available at the end of the course.
GRADING: In this course you will be graded on your performance on three one hour in class exams, a comprehensive final exam, and weekly homework assignments. The relative weights of these components will beTest 1 100 pts (Friday, Feb. 17) Test 2 100 pts (Friday, Mar. 23) Test 3 100 pts (Friday, Apr. 27) Homework 150 pts Classwork 50 pts Final Exam 200 pts (Tuesday, May 8, 3:10 - 5:50 pm, STV 229)
Exam I Solutions
Exam II Solutions
Exam III Solutions
Final Exam Review Problems
HOMEWORK: Homework assignments will consist of four or five proofs a week. Assignments will be given in class and will be due each Thursday by the beginning of class. As developing your skills at writing mathematical arguments is one of the central goals in this course, doing as much as you can on each homework assignment is essential for a good grade. NOTE: In general you should not expect to be able to do a good job on a homework assignment if you start the day before it is due. Some problems may require numerous attempts before you will be able to solve them. As well as the formal written assignments given in class, it will be necessary for most students to read and re-read the relevant sections of the text. For your FIRST READING ASSIGNMENT please read ``Appendix A, Logic and Proof'' (pp. 493-503) in the text.
Cognitive Science 236: Thinking, Reasoning, and Decision Making
Kathleen M. Galotti
Instructor office, phone and e-mail: Olin 106/108, x4376, email: kgalotti
Office hours: Wed 2-3:30 pm; Thu 9-10:30 am and by appointment
Home phone 645-4039, ok to call between 7:30 am and 9:30 pm
This course will introduce a variety of issues of interest to cognitive scientists who study people's tutored and untutored reasoning and thinking skills. We will begin by examining skill in well-defined reasoning endeavors, and explore relationships between formal reasoning and everyday reasoning. Later we will turn our attention to decision making, both with laboratory tasks and in the real world. I hope to get you to think carefully about what it means to reason effectively, and to explore your own reasoning strengths and weaknesses. This course counts toward the cognitive science minor and major, and also toward the cognitive component of the psychology major.
Course requirements include two exams, two short papers, very short reports of group discussions, as well as occasional “laboratory assignments” where you will be asked to write about examples of reasoning and decision making from your own experience. The two short papers will consist of descriptions of another person’s reasoning or decision-making. They will each be about 5-7 pages in length. The weights of the assignments are roughly the following: each exam, 22%; each short paper, 22%, group discussion reports, attendance, participation, and completing laboratory work in a timely and thorough way, 12%. Due dates for all assignments are provided on the attached schedule. Take note of them and plan your work accordingly. Late papers and assignments will be penalized 3% per every 24 hours late; exams may not normally be made up.
Readings for the course come from a variety of sources. The required texts are: Halpern, Thought and knowledge (5th ed), and Kahneman, Thinking, fast and slow. You might also want to purchase your own copy of Perkins, The mind's best work, as we will read a good amount of that book in a very short time. Other readings are on Moodle. Note that the reading load varies from week to week, and try to plan ahead. No additional outside reading will be required for the papers, although I assume you will incorporate relevant readings from the syllabus as appropriate.
This course is always an enjoyable one to teach, and I hope you'll find many of the topics enjoyable, too. I'll be announcing office hours shortly, and hope you'll come by to talk about topics related (or even unrelated!) to the course.
Tentative* schedule of topics and assignments
(*we may make changes in the schedule as the term progresses)
Date Topic and Assignment
W 1/3 Introduction and overview; the cases of The Missing Jam and Aunt Sarah
F 1/5 Historical approaches to modeling thinking and problem solving
Read: Halpern, ch. 1, 9
M 1/8 Thinking in the context of other cognitive processes
Read: Halpern, chs. 2
W 1/10 Methods of studying thinking
Read: Ericcson [Moodle]; Perkins (1981,p. 24-40) [main libe reserve; online access through Gould Library site]
F 1/12 Propositional and syllogistic reasoning
Read: Halpern, ch. 4
First paper assigned
M 1/15 Kathie out of town; time to do interviews for your first paper
No class; no reading
W 1/17 Analyzing arguments ; the content effect in reasoning
Read: Halpern, ch. 5
F 1/19 Analogical and other formal inductive reasoning tasks.
Read: Sternberg [Moodle]
M 1/22 Hypothesis formation, testing and evaluation
Read: Halpern, ch. 6 First Paper Due
W 1/24 Creative thinking: The mind's best work?
Read: Halpern, ch. 10; Perkins (1981) 41-161 [rest of book is worth skimming] [ER]
F 1/26 Discussion: Studying everyday thinking
Read: Perkins 1985 [Moodle]; Stanovich, West, & Toplak [Moodle]
M 1/29 Catch up Day
W 1/31 First Midterm
F 2/2 Overview of decision-making
Read: Halpern, chs. 7, 8
M 2/5 Midterm break! You may have the day off. (You are most welcome).
W 2/7 Two systems of thinking
Read: Kahneman, Part 1, p. 3-104
F 2/9 Heuristics and biases in decision making
Read: Kahneman, Part II, p. 109-195
Second paper assigned
M 2/12 Structuring a decision and making a final choice: Expected utility theory
Read: Galotti [Moodle], Galotti, Wiener & Tandler [Moodle]
W 2/14 Overconfidence in decision making
Read: Kahneman, Part III p. 199-265
F 2/16 Discussion: Using our heads, using our hearts
Read: Kleinmuntz [Moodle], Eastwood, Snook, & Luther [Moodle]
M 2/19 Prospect Theory
Read: Kahneman, Part IV, p. 269-374
W 2/21 Narrative-Based Decision Theory
Read: Beach [Moodle]
F 2/23 Two Selves
Read: Kahneman, Part V, p. 377-418
Second Paper Due
M 2/26 Expertise and decision making
Read: Klein [main libe reserve; online access through Gould Library site] ch. 1-4
W 2/28 Making moral and ethical decisions
Read: Haidt [Moodle]
F 3/2 Discussion: Jury decision-making: What we know and what we need to know
Read: Devine, Krouse, Cavanaugh, & Basora [Moodle]
M 3/5 Individual differences in decision-making
Read: Galotti, Tandler & Wiener [Moodle]
W 3/7 Development of decision-making
Read: TBA (to be announced and posted on Moodle)
F 3/9 Catch up day
Self-Scheduled 2nd exam
M 3/12- W 3/14