Math 301

Fall 2011

Prof. Donnay


Course Play by Play




Topics Covered





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.


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   


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 16th by 5pm in box outside office.


Part 1 due Wed 9/21

Part 2 due Fri 9/23   


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


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).



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.


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).


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.


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.


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



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





M 11/20 T 11/21

Subsequences, Bolzano – Weierstrass Thm


HW wk 12

HW wk 12 Answer Key

HW due

Friday Dec 2


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


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



Topics Covered





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


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.


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.


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


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.



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


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.


M 10/26

Unions/Intersections of Open Sets

Continuity: 3 equivalent conditions. f: Rn --> Rm

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 4th and Friday Nov 6th.



Subsequences; Bolzano-Weierstrass Thm

Ch 8





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.






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 11th and Friday Nov 13th.

You should hand in the worksheet as part of the Wed hw.



LUB Exists for a bounded sequence

Ch 8





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





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.



Max-Min and continuous functions.

Ch. 9





Compact Sets

Ch. 8





Proof of Max-Min Theorem

Ch. 9

Wk 10 and 11 Review Sheet.

Quiz wk 10 and 11 (due Monday Nov 30th 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


M 11/30

Cauchy sequences converge in R



Midterm Redo due Mon Dec 7th 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 9th. Extension given till 5pm on Thur.

Midterm Redo due Mon Dec 7th at 5pm. Extension given till class on Wed.


M 12/7

Cantor Set is totally disconnected (intro to Derivatives for 10am)





W 12/9

Prep for Exam. See info on homepage.