MATH 450 Topology
Syllabus for Spring 2011
Mon, Wed, & Fri, 9:00 – 9:50am
Maxwell 379

Prerequisite: MATH210 or any other proof writing background

About This Course:  Topology is the study of spaces shapes when size and angle don’t matter. In the attempt to classify and understand these spaces we will find methods of construction, dissection, and computation of invariants,

Expectations: Students who complete this course with a passing grade are expected to be able to demonstrate the following skills: (i) Mastery of prerequisite material, (ii) Compute knot invariants and prove other properties of knots (iii) Compute the classification of a surface, (iv) Understand and use the algebraic tools required in analyzing topological spaces, (v) and other stuff to be determined as the course unfolds.

Text & Calculator: Topology Now! by Messer and Straffin
No calculators will be allowed on any quiz or exam, but might be required for some homework problems.

Course Website:     http://course1.winona.edu/eerrthum/math450

Instructor: Dr. Eric Errthum                          Office: 124A Gildemeister Hall

Winona Email Username: eerrthum             Office Phone: 474-5775

Office Hours:  See schedule on my home page.

Grading:   Homework (scaled as needed)                                  125 points---- 21.74%
                  Quizzes (5 @ 25 points each, drop lowest)              100 points---- 17.39%
                  Midterms (2 @ 100 points)                                       200 points---- 34.78%
                  Final                                                                          150 points---- 26.09%
                                                                                                    --------------

                                                                                                     575 points total

Grades:  A = 90% (517 pts), B = 80% (460 pts), C = 70% (402 pts), D = 60% (345 pts)

Homework:    All the problems from the sections covered during each week of class are due the following week on Monday (or the first class meeting after the weekend) unless announced differently in class. The problem numbers for each section are given below in the rough schedule. Homework should be readable or it will not be graded. (If you have any desire to learn how to type your homework in LaTeX, I will gladly show you.) Homework Reviews (if we do them) will count toward your Homework portion.

Quizzes:    We will have a short quiz after each chapter (or set of chapters), see schedule below. The lowest quiz score will be dropped.

Exams:     There will be two in-class midterms and one final exam. The final exam will be like a third midterm with a comprehensive take-home portion. Midterms/Final are planned to cover approximately Chapters 1 & 2, Chapters 3&4, and Chapters 5 – 7. However exam dates are tentative until officially announced in class. The final exam is scheduled for Tuesday, May 3rd, 8am – 10am. The take-home portion will be due by noon on Wednesday, May 4th.

Extra Credit: There will be bonus questions on quizzes and exams. If you’d like to do more extra credit, I will give a lecture (outside of regular class time, 8am?) on a section of the book we didn’t cover and assign work from that section.

Resources: You’re more than welcome to stop by during my office hours and ask questions.

Desire2Learn:            Some course materials and approximate grades can be found on D2L.

No Class Days:          There will be no class on Jan 17 (MLK Day), Feb 2 (Personal Day), March 7 thru 11 (Spring Break), and April 22 (Spring Break Day). If for some reason more classes need to be canceled, I will email the class.

Late/Missed Work:   Missed quizzes will result in a score of zero. There are no make-up quizzes. Make-up exams will be given at the discretion of the instructor. If you miss class, it is your responsibility to obtain notes and assignments from fellow students. If you have an unavoidable absence, please inform the instructor beforehand.

Academic Dishonesty:  Any type of academic dishonesty (cheating, copying, etc.) will result in failure and will be reported to school authorities. If you are having trouble with an assignment, please see the instructor first.

Note:   This syllabus is subject to change if deemed necessary by the instructor.

Tentative Schedule of Events – Math 450

(subject to immense change)

 

Week Starting

Monday

Wednesday

Friday

1/10

Introductions

Section 1.1

Section 1.1, cont
HW (pg 4): 2, 5, 9, 10

Section 1.2
HW (pg 11): 5, 11, 16, 19, 20

Section 1.3

Section 1.3, cont.
HW (pg 18): 5, 6abc, 7ab, 9, 10, 12

Section 1.4

1/17

No Class
MLK Day

HW 1.1, 1.2 & 1.3 Due

Section 1.4, cont.
HW (pg 23): 6, 7, 10, 11, 15, Give T-1

Section 1.5

Section 1.5, cont
HW (pg 31): 3, 7, 8bc, 10, 13, 14

1/24

HW 1.4 Due

Section 1.6
Video Demo
HW (pg 37): 3, 4, 5cd, 9, 11, 12
“An Unshellable Triangulation of a Tetrahedron”

Chapter 1 Activity

HW 1.5, 1.6 Due

Chapter 1 Quiz

Solution to #3
(requires Mathematica)

1/31

Section 2.1
HW (pg 46): 3, 5, 7, 9abd, 10

No Class

Sections 2.2 & 2.3

HW (pg 53): 3, 5, 8, read 11, 13, 14(just the middle one).

2/7

HW 2.1 Due

Section 2.3 & Section 2.4

HW (pg 58): 3, 4, 6, 8, 9, 11

HW (pg 64): 2, 6, 7, 8, 10

Section 2.5

HW (pg 75): 1, 3, 5, 7b, 8

Mathematica Determinant

Knot Atlas

Alexander Polys

Chapter 2 Activity

2/14

Extra Lecture: 2.6 & 2.7

Extra Credit:
 HW (pg 81): 4, 7, 9
HW (pg 87): 2, 4, 5b, 6, 9, Show Thm 2.75 works on Reidemeister Moves

---------------------

HW 2.2, 2.3, 2.4 & 2.5 Due

Chapter 2 Quiz

Assessment Day

No Class

Midterm Review

2/21

Midterm I

Extra Credit 2.6 & 2.7 Due

Section 3.1

HW (pg 95): 1, 4, 5, 7, 9

Solutions to 3.1 5b:

·         Wikipedia

·         from “A topological picturebook” by George K. Francis

Science Fair Activity

2/28

Section 3.2 & 3.3

HW (pg 101): 2, 3, 7, 8, 9, 11

Section 3.3, cont.

HW (pg 108): 1, 4, 6, 9, 11

HW 3.1 & 3.2 Due

Exam I Retakes Due by 3pm

Section 3.4

HW (pg 117): 2d, 3, 4bef, 6, 7, 9, 10

3/7

SPRING BREAK

3/14

Chapter 3 Activity

HW 3.3 & 3.4 Due

Section 4.1

HW (pg 129): 2, 4, 7, 8

Chapter 3 Quiz

3/21

Extra Lecture: 3.5

Extra Credit:
 HW (pg 124): 1b, 3, 5, 6, 7

---------------------

Section 4.2

HW (pg 134): 1, 3, 5, 6, 8

Section 4.3

HW (pg 141): 2, 3, 4, 7

HW 4.1 & 4.2 Due

Section 4.3, cont

Chapter 6 Overview

3/28

 Chapter 4 Activity

HW 4.3 Due

Midterm Review

Chapter 4 Quiz

4/4

Extra Credit 3.5

Sections 5.1

HW (pg 155): 5, 7, 9, 10

Midterm II

Section 5.3 & 5.4

HW (pg 160): 10,
(pg 163): 2,
(pg 166): 1, 2

4/11

Extra Lecture: This pdf Document

Extra Credit:
HW (from the pdf): 1, 3, 5, 6, 7

---------------------

Section 7.1

HW 5.1 – 5.4 Due

Section 7.1 cont

Section 7.2

HW (pg 215): 1c, 2c, 6b, 7(part 3), 8, 10

Section 7.2, cont

Section 7.3

HW (pg 221): 3b, 4, 5, 9, 10

4/18

Section 7.3 cont.

Section 7.4

HW (pg 226): 2, 3, 6, 7

HW 7.1 – 7.2 Due

Section 7.4, cont.

Section 7.5

HW (pg 228): 1, 3, 5, 6b, 8
(pg 230): 2, 4, 5

Spring Break Day
No Class

4/25

HW 7.3 – 7.5 Due

Extra Credit pdf Due

Chapter 7 Activity

Chapter 7 Quiz

Review?

 

Final Exam (8 – 10am, May 3rd)

 

 

Welcome to college math!

 

If this is your first math class taken in college, there are some important things you need to know. College math classes are run very differently from high school math classes. On the surface it may seem they are similar as you listen to the lecture and take notes, but there are significant underlying differences. Knowing these ahead of time can help you make the most of this coming semester.

 

#1: College math classes generally stay on the schedule in the syllabus. If there is one day allotted to the topic that is probably all of the class time that will be spent on it, even if “most” of the students “don’t get it.”

 

#2: It is expected that you will read the text and do the problems in order to learn the material, even if no one checks up on you. The instructor might never collect the homework, but that doesn’t mean it doesn’t affect your grade.

 

#3: You will sometimes be responsible for material in the textbook that is not covered in class. If there is a text reading and/or homework problems covering a concept that was not discussed in class, you are still expected to learn it. If you don’t understand it, make an appointment with your instructor for help.

 

#4: Some material is covered only in class, is not in the textbook, and may not have any homework problems on it. If you miss class, you may miss content that you are responsible to know. If you have an unavoidable absence, be sure to get the notes and any announcements from a classmate.

 

#5: There will be test questions that don’t look “just like the homework.” In college, you are expected to focus on learning the concepts, not just memorizing how to do certain types of problems. These concepts can – and will – appear in very different forms on tests and quizzes.

 

#6: At times you will be expected to be able to explain why a problem is done a certain way in addition to being expected to do the problem. As you work on problems in class and on homework, don’t be satisfied with getting the correct answer; ask yourself why that method is logical, and how you could explain that logic to someone else.

 

#7: Most importantly, you are responsible for your own learning. If you attend class faithfully, get the notes and announcements if you have an unavoidable absence, read the text, do the homework and question yourself (as in #6), and still don’t understand something, it is up to you to get the extra help you need. Visit the instructor during office hours or make a special appointment to ask questions, form a study group, etc. There are many resources and people willing and happy to help, but you need to take the initiative and seek out the help you need.

 

Good luck on a happy and successful semester!

 

 

Commitment to Inclusive Excellence:  WSU recognizes that our individual differences can deepen our understanding of one another and the world around us, rather than divide us. In this class, people of all ethnicities, genders, religions, ages, sexual orientations, disabilities, socioeconomic backgrounds, regions, and nationalities are strongly encouraged to share their rich array of perspectives and experiences.  If you feel your differences may in some way isolate you from WSU’s community or if you have a need of any specific accommodations, please speak with the instructor early in the semester about your concerns and what we can do together to help you become an active and engaged member of our class and community. 

 

Campus Resources (Short version):

 

Campus Resources (Long version):

 

The Standard Disclaimer applies.