Instructor:	Dr. Michael Oehrtman oehrtman@gmail.com 970-351-2344	Office Hours:	MW: 2:15 pm – 4:15 pm or by appointment in ROSS 2239F
Class Times:	MWF 12:20 pm – 1:10 pm	T 12:30 pm – 1:20 pm
Locations:	MICH L0108	ROSS 2260
Class Website:	http://www.unco.edu/nhs/mathsci/facstaff/oehrtman/math431

Required Text: Understanding Analysis, by Stephen Abbott

Course Description: This course develops the content of calculus through rigorous definition and proof. We will cover Chapters 1-5 in the text, although we may diverge from this occassionally. Learning to read and understand rigorous mathematics and to generate proofs requires significant effort that is different in nature from what was required to succeed in most mathematics classes you have previously taken. Consequently, much of our class time will involve your work in groups and presentations of problems and proofs at the board. I will also expect the class to take responsibility for assessing the integrity of these arguments.

Class Participation and Presentations: I expect everyone in the class to contribute constructively to the class and group discussions. This can take several forms from clearly articulating points of confusion to uncovering problems with previous lines of reasoning to providing key ideas and breakthroughs. If your entire group is stuck and/or confused (there is something wrong if this doesn't happen on a regular basis), you should not give up and wait for me to come around, but you should be resourceful in trying to find new ways to attack the problem or on uncovering what is wrong with your previous attempts. You should also look for ways to draw other students into the conversation, since much of what you need to learn is how to listen and evaluate mathematical reasoning. You are not participating fully if you are at either extreme: either never talking or doing all of the talking. Throughout the semester, you should aim to make 5 presentations to the class about key ideas in definitions, proofs, or examples that I identify.

Homework: You should allot a significant amount of time to spend on the homework for this class well in advance of the due date. Very few students will be able to earn much credit on an assignment worked just a day or two before it is due. You should also seek help in office hours well before the day an assignment is due, since it will take time to solidify and apply the ideas you take away from our discussions. The best way to  make sure that you are developing the appropriate insights and on the right track is to talk to other students about the problems. I encourage you to work together, but each student must write up his/her solutions in his/her own words. All assignments and due-dates will be posted on the homework page of the class website, and you are responsile for keeping track of them. If you forget to bring your homework to class, you may submit it up to 24 hours later with a 20% penalty. No homework will be accepted later than this under any circumstances. Type or write all of your work LEGIBLY on 8½"×11" paper with at least ONE-INCH margins on all sides free of writing except your name, date, and assignment number, and STAPLE all pages together. In general, assigned questions will require significant depth in your responses. In order to earn an A or B for the course, I anticipate that most people will need to spend approximately 10 to 12 hours per week outside of class on homework, reading, and studying.

Reading and Definitions: Reading assignments from the textbook will also be posted on the homework page. In order to understand what is being discussed in class you must have read the assigned material BEFORE coming to class. Reading terse and rigorous mathematical text often requires several passes and an active effort to look up definitions, sketch diagrams, reflect on counterexamples, etc. I view one of the main objectives of this class as helping you to become good at reading and writing rigorous mathematics, but doing so will require time and practice on your part. You should not get discouraged if you experience significant confusion and frustration at times in this process since that is normal, and I will do all I can to help you overcome this. The first and perhaps most important step is for you to learn precise definitions and be able to state them without error and to learn to focus on the definitions of the terms in any statement you are trying to understand, prove, or disprove. Getting a definition "close" (but not exact) or focusing only on intuitive interpretations of terms can lead to completely incorrect reasoning, proofs, and results.

Exams: Five chapter exams will be given in in class, and before each exam, I will provide an overview of what will be covered on the Study Guides page. 

Final:  The final exam will be comprehensive and administered at the officially scheduled time, Tuesday, December 11 from 1:30pm - 4:00pm. Requests to take the final examination at a time other than the published time will not be granted except in cases of conflict with the scheduled exam time for another course, having three or more exams scheduled in one day, personal emergencies, or for reasons of religious practice. In particular, nonrefundable plane tickets, weddings, work schedules, and the like are not acceptable reasons for final examinations. Please keep this policy in mind when making end-of-semester plans.

Graduate Credit: I will create slightly different homework sets and exams for students enrolled in MATH 531 to reflect a heavier emphasis on proof and  thorough development of the logical foundations of calculus over examples and applications.

Collaboration: I assume that you are here to learn. If you talk to each other, you will learn from each other, perhaps more than you will learn from me. I encourage you to form study groups. Try the homework yourself, and then get together with a study group to go over questions, and to study for tests. You will learn a great deal from articulating your questions and explaining material to your peers. Discussion of assigned homework is encouraged, but you should be sure you fully understand the material by writing your solutions on your own. Evidence of any cheating or collaboration on work assigned to be completed individually will result in a 0 for that work, at minimum.

Honor Code: All members of the University of Northern Colorado community are entrusted with the responsibility to uphold and promote five fundamental values: Honesty, Trust, Respect, Fairness, and Responsibility. These core elements foster an atmosphere, inside and outside of the classroom, which serves as a foundation and guides the UNC community's academic, professional, and personal growth. Endorsement of these core elements by students, faculty, staff, administration, and trustees strengthens the integrity and value of our academic climate. UNC's policies and recommendations for academic misconduct will be followed. For additional information, please see the Dean of Student’s website, Student Handbook link http://www.unco.edu/dos/handbook/index.html

Portable Electronic Devices: Please extend courtesy to your instructor and fellow students by turning off your portable electronic devices, and putting them away in your bag, during class. If you know that you may need to accept an emergency phone call during class or if you have children in childcare or school, please let the instructor know. If you need to take a phone call during class, please step out of the classroom while you complete your call.

Students with Disabilities: Students who require special accommodations due to a disability should contact Disabilities Support Services (351-2289) as soon as possible to better ensure that accommodations are implemented in a timely fashion.

Grades will be determined as follows:

				MATH 431			MATH 531
		Points		Grades	Points Earned		Grades	Points Earned
	Homework	300		A	930 - 1000		A	900 - 1000
	Chapter Exams	500		A–	900 - 929		B	800 - 899
	Final Exam	__200__		B+	870 - 899		C	700 - 799
	Total Possible	1000		B	830 - 869		D	600 - 699
				B–	800 - 829		F	0 - 599
				C+	770 - 799
				C	700 - 769
				D	600 - 699
				F	0 - 599

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