Introduction To Topology Pure And Applied Solutions

Introduction To Topology Pure And Applied Colin Adams Robert Franzosa Pearson Prentice Hall 2009pdf Addeddate 2020-02-29 22:42:46 Identifier.
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Topology Pdf
Introduction To Topology Pure And Applied Solutions Pdf

File Type PDF Introduction To Topology Pure Applied Solution Manual informatics, and industry. By facilitating communication between communities and building rigorous bridges between disparate worlds, applied category theory has the potential to be a major organizing force. This book offers a self-contained tour of applied category theory.

Introduction to Pure and Applied Topology

Instructor: Prof. Ilya Kapovich

Fall 2013 ; MATH 490 Section ITT

MWF 9-9:50am Altgeld Hall 343

https://math.uiuc.edu/~kapovich/490-13/490-13.html

The final exam has been graded and the results have been posted in ScoreReports. The course grades have also been assigned and posted in ScoreReports. One low h/wk score was dropped for each students.
The course components (midterms 18% each, the final 27% and h/wks 19%) have been weighed and rescaled to the course total maximum of 400 points total. The course grade cut-off levels were as follows:
A+: 382 to 400
A: 365
A-: 347
B+: 331
B: 316
B-: 300
C+: 277
C: 254
C-: 230
D+: 210
D: 190
D-: 170

The final exam is available here. The exam is due by 11am on Wednesday, Dec 18. You can either submit the exam to me by e-mail orput it in my mailbox in the math department mailroom, Altgeld Hall room 250. My mailbox is located inside AH room 250, and my mailbox has my name on it. If you are writing your solutions on a print-out of the exam, please use a ONE-SIDED print-out.
The final exam will be cumulative for the course and will cover the following material:
Ch 1.1-1.4, 2.1-2.3, 3.1-3.4, 4.1-4.2, 5.1, 5.3, 6.1-6.4, 7.1-7.3, 9.1-9.2, 9.4-9.6 in the book.
The exam will most likely consist of 10 problems.

The third midterm has been graded and the results have been posted in ScoreReports. Also, solutions to the third midterm exam are available here.

I do not assign formal letter grades for the midterms, but you can approximately interpret your third midterm scores as follows:

A range (includes A+/A/A-): 52-60
B range (includes B+/B/B-): 41-51
C range (includes C+/C/C-): 30-40

The third midterm will cover the following material:Ch 5.1, 5.3, 6.1-6.4, 7.1-7.3 in the book.

The second midterm is available here. This is a take-home exam: it is due in class on Friday, Nov 1. There will be no h/wk due on Fri, Nov 1. The exam covers the following material: Ch 2.3-2.4, 3.1-3.4, 4.1-4.2 from the book.

The second midterm has been graded and the results have been posted in ScoreReports. Also, solutions are available here.
I do not assign formal letter grades for the midterms, but you can approximately interpret your scores as follows:

A range (includes A+/A/A-): 53-60
B range (includes B+/B/B-): 41-53
C range (includes C+/C/C-): 30-40

The first midterm exam has been graded and the results have been posted in ScoreReports. Also, solutions to the first midterm are available here.I do not assign formal letter-grades for the midterms, but you can approximately interpret your scores as follows:

A range (includes A+/A/A-): 70-80
B range (includes B+/B/B-): 56-69
C range (includes C+/C/C-): 40-55

The first midterm exam will take place on Tuesday, Oct 1. This will be a 'take home' exam. It will be posted online on Tuesday afternoon and it will be due in class on Wednesday, Oct 2. The exam will consist of six problems and will cover the following material: Ch 1.1-1.4, 2.1-2.2 from the book. In the week of Sept 30-Oct 4, I will not have office hours on Tuesday, Oct 1 and instead will have office hours on Mon, Sep 30, 2pm-3pm.

About this course:

Topology, which literally means 'the study of position or location', is the study of 'rubber-sheet' properties of shapes, spaces and configurations, that is, properties that are preserved by deformations such as stretching, pulling or compressing objects without crushing or tearing them. Thus topology is mainly concerned with qualitative questions about shapes and configurations, such as: Is it possible to escape from a given (2-dimensional or 3-dimensional) labirinth? Can one ``comb' a round porcupine so that all the quills lie flat against the surface and there are no bald spots? Is it possible, given two specific configurations of several robots, allowed to move along a rail netwoork on the construction floor of a factory, to transform the first configuration to the second without the robots colliding? And so on.

This course has two main goals: to rigorously cover the basic mathematical ingredients of topology, and to demonstrate the utility and significance of topology in science and engineering and in other areas of math. Thus the course will be taught with an emphasis on real-world examples and applications. This course should be of interest to both engineering and math students. No prior background in topology is required.

Anonymous on-linefeedback form is available

University instructions on what to do in case of emergency

SCOREREPORTS -Math Department gradebook program where you can look up your quiz, h/work and exam grades. (You will be prompted for your NetId and password).

My (preliminary) office hours are Tuesdays 1pm-2:30pm and Thursdays 2pm-3pm (and at other times by appointment). You DO NOT need to tell me in advance if you want to see me during the office hours. If you want to come at a different time, you need to schedule an appointment. My office is located in Altgeld Hall, room 365.

Main Text: Introduction to topology, pure and applied, by Colin Adams and Robert Franzosa

Telephone: 265-0633

e-mail: kapovich@math.uiuc.edu. (Preferred method of reaching me!)

Office location: Altgeld Hall, room 365

Office hours (preliminary): Tuesdays 1pm-2:30pm and Thursdays 2pm-3pm

Grader:we won't have one

Due Friday, Sept 6: Ch 1.1, problems 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8,1.9
Due Friday, Sep 13: Ch 1.2, problems 1.10, 1.11, 1.12, 1.14, 1.15, 1.16, 1.18, 1.19
Due Friday, Sep 20: Ch 1.3 problems no. 1.25, 1.27, 1.28, 1.29, 1.31, 1.33, 1.35, 1.37; Ch 1.4 no 1.40
Due Friday, Sept 27: Ch 2.1 problems no. 2.1, 2.2, 2.3, 2.7; Ch. 2.2 problems no. 2.13, 2.14 [disregard part (d) of problem 2.14], 2.16, 2.19, 2.22
Due Friday, Oct 4: Ch 2.4 problem 2.30; Ch 3.1 problems 3.2, 3.3, 3.5, 3.7
Due Fri, Oct 11: Ch. 3.2 problems 3.14, 3.15, 3.16, 3.18; Ch 3.3 problems 3.23, 3.26, 3.27, 3.33
Due Fri, Oct 18: Ch 4.1 problems 4.1, 4.3, 4.4, 4.5, 4.6, 4.8, 4.11, 4.12
Due Fri, Oct 25: Ch. 4.2 no. 4.23, 4.25, 4.29, 4.31; 5.2, 5.3, 5.9, 5.10
Fri, Nov 1: no h/work due.
Due Fri, Nov 8: no. 5.25, 5.27, 5.28, 6.1, 6.4, 6.6, 6.8, 6.9
Due Fri, Nov 15: no. 6.33, 6.34, 6.35, 7.1, 7.2, 7.4, 7.6, 7.10
Due Fri, Nov 22: no. 7.15, 7.16, 7.18, 7.20, 7.22, 7.23, 7.24, 7.26
Due Wed, Dec 4: no. 9.1, 9.2, 9.3, 9.9, 9.10, 9.11
NOT dueWed, Dec 11: no. 9.16, 9.17, 9.19, 9.20, 9.21 (this h/wk will not be collected and will not be graded, although I recommend that you still try to solve these problems)

Pre-class reading assignments:

Introduction to topology pure and applied solutions class

For Wed, Aug 28: Ch 1.1 in the book (open sets and topological spaces)
For Fri, Aug 30: Ch 1.1 in the book (open sets and topological spaces); also take a look at this worsheet
For Wed, Sep 4: Ch 1.1 in the book (the notion of a neighborhood, and of one topology being finer/coarser than the other); Ch 1.2 (definition of a basis for a topology pp. 29-30)
For Mon, Sep 9: pp. 31-36 in the book and the handout on bases of topologies
For Wed, Sep 11: pp. 38-43 (closed sets and Hausdorff spaces)
For Fri, Sep 13: Ch 1.4 (examples of topologies in applications), pp 44-49.
For Mon, Sept 23: Ch 2.3 (boundary of a set)
For Wed, Sept 25: Ch 2.4 (application to geographic information systems)
For Fri, Sep 27: Ch 3.1 (subspace topology)
For Fri, Oct 4: Ch 3.3-3.4 (quotient topology)
For Mon, Oct 7: Ch 3.4 (examples of quotient topology)
For Wed, Oct 9, Ch 4.1 (continuity)
For Fri, Oct 11: Ch 4.2 (homeomorphisms)
For Mon, Oct 14: Ch 4.2 (homeomorphisms)
For Wed, Oct 16: Ch 4.2 (homeomorphisms)
For Fri, Oct 18: Ch 5.1 (metric spaces)
For Mon, Oct 21: Ch 5.1-5.2 (metric spaces; metrics and information)
For Fri, Nov 1: Ch 6.3 (intermediate value theorem)
For Mon, Nov 4: Ch 7.1 (compactness)
For Wed, Nov 13: Ch 7.2 (compact metric spaces)
For Fri, Nov 15: Ch 9.1 (homotopy)

1. Topological spaces; open and closed sets; basis for a toppology; examples of topologies in applications (digital topology for digital displays, phenotype spaces in biology and neural networks, etc).

2. Interior, closure and boundary of a set; applications to geographic information systems.

3. Creating new topological spaces: subspace topology, product topology, quotient topology. Applications to configuration spaces, robotics and phase spaces.

4. Continuous functions and homemorphisms; applications to motion planning in robotics.

5. Metric spaces and metrizability of topological spaces; separation axioms.

6. Connectedness and path connectedness; application to automated guided vehicles.

Topology Pdf

7. Compactness of topological and metric spaces; local compactness and one-point compactification.

8. Selected topics in algebraic topology: homology, homotopy and degree; application to a heartbeat model;
fixed point theorems and their applications; application to the
existence of economic equilibria;

9. Additional topics, time permitting.

Before every class you will receive a reading assignment for that class; they will be posted about a day before every class online. You'll be expected to do some reading ahead of the material to be covered during each upcoming class.
I will also assign weekly homework from the book. The homework will be collected in class on Fridays and graded. The h/wk will be worth 19% of your course grade.
There will be three midterm exams during the semester. Each of them will be worth 18% of your course grade. Most likely, two of these mid-terms will be take-home exams, and one will be an in-class exam.
The 1-st midterm is currently scheduled for Monday, Sep 30. The 2-nd Midterm is currently scheduled for Monday, Oct28. The 3-d Midterm is currently scheduled for Wed, Dec4.
The final exam will take place 8:00-11:00 AM, Wednesday, December 18. The final exam will be an in-class 'open notes' exam. The final exam will be cumulative for the entire course. The final exam counts as 27% of the course grade.
A modest number of 'extra credit' problems may be assigned, upon request.

Overview

For juniors and seniors of various majors, taking a first course in topology.

This book introduces topology as an important and fascinating mathematics discipline. Students learn first the basics of point-set topology, which is enhanced by the real-world application of these concepts to science, economics, and engineering as well as other areas of mathematics. The second half of the book focuses on topics like knots, robotics, and graphs. The text is written in an accessible way for a range of undergraduates to understand the usefulness and importance of the application of topology to other fields.