Math 301

Fall 2011

Prof. Donnay

Course Play by Play

Wk	Date	Topics Covered	Section	HW	Due
1	T 8/30 W 8/31	Introduction to course (problems facing the world) and to Dynamical Systems, team worksheet.		Fill in online Student Information survey. Take course PreAssessment, Read through syllabus.	All due by start of second class.
	Th 9/1 F 9/3	Iteration using Excel. (Sample program). Links of dynamical systems to analysis concepts. (TTh class, MW class). If then statements.		Read the article on mathematical modeling of hurricanes. Do HW Wk 1 assignment. HW Wk1 Answer Key.	Due Thur 9/8 or Friday 9/9.
2	T 9/6 W 9/7	Cardinality. Countable sets	Ch. 2.	Quiz 1. 20 minute, closed book quiz.	Due Thur 9/8 or Friday 9/9.
	Th 9/8 F 9/9	Uncountable sets, cross products A x B.		HW wk 2. HW Wk2 Answer Key.	Part 1 due Wed 9/14 Part 2 due Fri 9/16
3	M 9/12 T 9/13	Set of subsets; Equivalence relation
	W 9/14 Th 9/15	Types of Sequences themes: conv-div; increase/decrease – oscillate, bounded – unbounded. definition of limit.	Ch. 3	Quz 2 20 minute, closed book quiz. (HW wk3 )Ops ignore this version – use instead revised HW wk3 . HW Wk3 Answer Key. Optional reading: Nature Chemistry article on Women in Science and the cover picture.	Due Friday Sept 16^th by 5pm in box outside office. Part 1 due Wed 9/21 Part 2 due Fri 9/23
4	M 9/19 T 9/20	Theorem: limit is unique; if converge then bounded.		Quz 3 20 minute, closed book quiz.	Quiz due in class either on Wed or Thur.
	W 9/21, Th 9/22	Limit laws; proofs using definition of limit		HW wk 4 HW Wk4 Answer Key. To be posted Friday night. Quiz 4 due in class Wed 9/28 or Thur 9/29.	Countability review notes due Mon/Tues in Class Part 1 due Wed 9/28 Part 2 due Fri 9/30
5	M 9/26, T 9/27	Squeeze law, sum of limits law, proof by induction. Outline of mid-term exam procedure.		Information about midterm Theorems whose proof you will need to know.
	W 9/28, Thur 9/29	More proof by induction. Cantor set construction. Uncountable set of measure zero.		Review sheet for countability topics. Tom Lehrer's New Math (base 8 is just like base 10 if you are missing 2 fingers).
6	M 10/2, T 10/3	Accumulation points.
	W 10/4, Th 10/5	Dense sets. Delta-epsilon limit of function. (Sequences in R²).		HW Wk 5 HW Wk5 Answer Key part 1 HW Wk5 Answer Key part 2	Part 1 due Wed 10/19 Part 2 due Fri 10/21. Extension to Wed 10/ 26.
7	M 10/17, T 10/18	Limit of function, continuous function and examples. Ch 4.		Quiz for wks 5 and 6. Due in class on Wed 10/19 or Thur 10/20. Estimated grades for midterm 1.
	W 10/19 Th 10/20	Open / closed sets. Boundary points (Ch. 5)	Ch 5	HW wk 5 hints. Hw wk 7 HW Wk7 Answer Key	Hw wk 7 is due on Fri 10/28 (only one part, all due same day).
8	M 10/24, T 10/25	Review of accumulation points. Negation of statements.
	W 10/26 Th 10/27	Defn of discontinuous = not continuous. Alternative condition for open sets.		HW wk 8 HW Wk8 Answer Key	Part 1 due Wed 11/2 Part 2 due Fri 11/4.
9	M 10/31 T 11/1	Composition of continuous functions	Ch 7	Quiz wk 8 (due Wed/Thur in class).	Please fill in this midterm course survey by Wed 11/2.
	W 11/2 Th 11/3	Alternative conditions for continuity.	Ch 6	HW wk 9 (typo: Ch. 5 # 7 should be Ch. 5 #8) HW wk 9 Answer key.	Part 1 due Wed 11/9 Part 2 due Fri 11/11.
10	M 11/6 T 11/7	Proof of equivalence of continuity conditions. Last material for midterm. Cauchy sequences.		Quiz wk 9 (due Wed/Thur in class).
	W 11/8 Th 11/9	Review for midterm		Exam2 Review
11	M 11/13 T 11/14	Monotone Convergence Theorem using Cauchy sequences		Instructions for Midterm Hint for Fractal Problem from open book portion.
	W 11/15 Th11/16	Sup = lub; Inf = glb
12	M 11/20 T 11/21	Subsequences, Bolzano – Weierstrass Thm		HW wk 12 HW wk 12 Answer Key	HW due Friday Dec 2
13	M 11/28 T 11/29	Continuous function on closed bounded set attains max.
	W 11/30 Th 12/1	Compact sets, Max Min Theorem, Intermediate Value theorem.		HW wk 13 HW wk 13 Answer Key	HW due Thur Dec 8
14	M 12/5 T 12/6	Dynamical Systems Applications
	W 12/7 Th 12/8	Connected Sets, I.V. Thm		Concept Map Creation
				Exam Instructions, Midterm 2 Redo Questions Hint: Final Exam #5

Math 301; Fall 2009

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	Rⁿ, 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 Rⁿ, 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: Rⁿ--> 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.