Math 301

Fall 2009

Prof. Donnay

Course Play by Play

Wk	Date	Topics Covered	Section	HW	Due
1	M 8/31	Introduction to Dynamical Systems.		Fill in Student Information sheet. Take course PreAssessment, Read through syllabus. Finish Dynamical systems worksheet.	All due Wed 9/2.
	W 9/2	More dynamical systems; concepts for our Real Analysis course.		Hw #2	Friday 9/4
	F 9/4	If A then B logic; sqrt(2) irrational	Ch 1	Wk 2 Hw	Wed 9/9 and Friday 9/11
2	W 9/9	R^n, distance, infinite intersection, functions	Ch 1	As part of wk 2 HW, do group problem on dynamical systems.
	F 9/11	Countable sets	Ch 2	Quiz 1 Review Sheet Hw Wk 3	Wed 9/16 and Friday 9/18.
3	M 9/14	Cartesian products, uncountable sets,	Ch 2
	W 9/15	Mathematical Induction, Cantor Set	Ch. 13
	F 9/18	Limits of sequences, Target Zone game	Ch. 3	Quiz 2 Review Sheet HW Wk 4	Wed 9/23 and Friday 9/25.
4	M 9/21	Technical definition of limit, limit worksheet	Ch. 3
	W 9/23	Cardinality, equivalence relations, Uniqueness of limit, boundness	Ch. 3	Do not do #13, Ch 3 for this Friday's hw. We have not gotten far enough yet to prepare you for that problem.
	F 9/25	Limit Laws	Ch. 3	Quiz 3 Review Sheet Hw Wk 5 Note: Quiz 3 is due Tuesday at 3pm.	Wed 9/30 and Friday 10/2
5	M 9/28	Rates of Growth, Cauchy Seq	Ch. 3
	W 9/30	Some special limits, limits in R^n, Accumulation points	Ch. 3
	F 10/2	Equivalent statement of accumulation pt; acc pts of Q = R	Ch. 3	Week 5 review sheet Start preparing for midterm (see instructions) For Monday, make up one “test question” with answer key and hand it in.
6	M 10/5	Review for Exam
	W 10/7	Limits and Continuity	Ch. 4
	F 10/9	Limits; How to negate a statement	Ch. 4	Hw 7 due after the break(note: a revised HW sheet was posted on 10.19 at 1pm. Please use this one). Wk 6 Review	Wed 10/21 and Friday 10/23
7	M 10/19	Weird functions and limits. Open and closed sets. Boundary of a set.	Ch. 5	Exam Redo Instruction	Mon 10/26
	W 10/21	Alternative characterization of open set in terms of ball around a point.	Ch. 5
	F 10/23	Review of HW questions		HW 8 Wk 7 Review Quiz #4 (from material of Wk6) Quiz #5 (from material of Wk7) See instructions for these quizzes.	Wed 10/28 and Fri 10 Exam redo extension – now due Wed 10/28 Quizzes due at 4pm on Monday 10/26.
8	M 10/26	Unions/Intersections of Open Sets Continuity: 3 equivalent conditions. f: R^n--> R^m	Ch 5 Ch 6
	W 10/28	Delta-epsilon equivalent to seq definition of conty	Ch 6
	F 10/30	Composition of conts fns, Dynamical Systems Fixed pt theorem.	Ch 7	Wk 8 Review HW 9	Quiz due Monday at 4pm (available on shelf). HW due on Wed Nov 4^th and Friday Nov 6^th.
9	M	Subsequences; Bolzano-Weierstrass Thm	Ch 8
	W	B-W Thm; Completeness	Ch 8	Worksheet on Continuity via sequences and open sets	Do for Friday’s class; we will go over it in class.
		Least Upper Bound; Greatest Lower Bound, Increasing Bounded sequences.
	F	Thm: Increasing sequences converge	Ch 8	Week 9 Review HW 10 Worksheet on Continuity (use this latest version that has corrected all the typos).	Quiz due Monday at 4pm (available on shelf). HW due on Wed Nov 11^th and Friday Nov 13^th. You should hand in the worksheet as part of the Wed hw.
10	M	LUB Exists for a bounded sequence	Ch 8
	W	LUB is a boundary point for set. If set is closed and bounded, the lub is in the set (i.e. the maximum exists)	Ch. 8
	F	Review of Key Concepts for midterm		More detailed list of topics for midterm. Note: Answer key for all the old HW is on Blackboard in documents. If you have not yet finished a hw, do not look at that answer key (Honor Code).	No Quiz or HW for next week due to midterm. Review session Sunday at 7pm-9 pm, Rm. 338. Please review before then and send any questions you have to Prof Donnay by 5pm Sunday.
11	M	Max-Min and continuous functions.	Ch. 9
	W	Compact Sets	Ch. 8
	F	Proof of Max-Min Theorem	Ch. 9	Wk 10 and 11 Review Sheet. Quiz wk 10 and 11 (due Monday Nov 30^th at 4pm) HW wk 10 and 11	When you are ready, you may print out the quiz for wk 10-11 and take it. HW due Wed Dec 2 and Friday Dec 4
12	M 11/30	Cauchy sequences converge in R			Midterm Redo due Mon Dec 7^th at 5pm
	W 12/2	Connected and Disconnected sets and Intermediate Value Thm	Ch. 12	Assumptions of a Theorem. Zeros of a function
	F 12/4	Totally Disconnected Sets; Review of Derivative		Wk 12 Review Sheet Quiz wk 12 (due Monday Dec 7 at 5pm) Handout on Connected Sets.	Hw due Wed Dec 9^th. Extension given till 5pm on Thur. Midterm Redo due Mon Dec 7^th at 5pm. Extension given till class on Wed.
13	M 12/7	Cantor Set is totally disconnected (intro to Derivatives for 10am)
	W 12/9	Prep for Exam. See info on homepage.