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. 

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. 

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 
themes: convdiv; 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 . 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
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 midterm exam
procedure. 




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. Deltaepsilon limit of function. (Sequences in R^{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.



W 10/19 Th 10/20 
Open / closed sets. Boundary
points (Ch. 5) 
Ch 5 

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. 

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) 
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 



11 
M 11/13 T 11/14 
Monotone Convergence Theorem using Cauchy sequences 

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 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 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 








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. 

Friday 9/4 


F 9/4 
If A then B logic; sqrt(2) irrational 
Ch 1 
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 
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 
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 
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 
Start preparing for midterm (see instructions) For Monday, make up one Òtest questionÓ 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). 
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 

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 

Quiz #4 (from material of Wk6) Quiz #5 (from material of Wk7) 
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 
Deltaepsilon equivalent to seq definition of conty 
Ch 6 



F 10/30 
Composition of conts fns, Dynamical Systems Fixed pt theorem. 
Ch 7 

Quiz due Monday at 4pm (available on shelf). HW due on Wed Nov 4^{th} and Friday Nov 6^{th}. 
9 
M 
Subsequences; BolzanoWeierstrass Thm 
Ch 8 



W 
BW Thm; Completeness 
Ch 8 
Worksheet on Continuity via sequences and open sets 
Do for FridayÕs class; we will go over it in class. 


Least Upper Bound; Greatest Lower Bound, Increasing Bounded sequences. 




F 
Thm: Increasing sequences converge 
Ch 8 
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 7pm9 pm, Rm. 338. Please review before then and send any questions you have to Prof Donnay by 5pm Sunday. 
11 
M 
Ch. 9 




W 
Compact Sets 
Ch. 8 



F 
Proof of MaxMin Theorem 
Ch. 9 
Quiz wk 10 and 11 (due Monday Nov 30^{th} at 4pm) 
When you are ready, you may print out the quiz for wk 1011 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 



F 12/4 
Totally Disconnected Sets; Review of Derivative 

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. 














